PROGRAMME HYDROLOGIQUE INTERNATIONAL

Séminaire international annuel du Groupe AMHY de FRIEND (Istanbul, Turquie, octobre 1998)

RAPPORT ANNUEL No6 (1997-1998)

Compte-rendu Résumé des communications

l

Thèmes programmés

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i Groupe AMHY (Alpine and Mediterranean Hydrolog y) de FRIEND: Algérie, Bulgarie, Espagne, France, Grèce, Hongrie, Italie, Pologne,

P Roumanie, Slovaquie, Slovénie, Suisse, Turquie, Yougoslavie

PHI-V Projet l-l

PHI-V 1 Documents Techniques en Hydrologie 1 No. 29 UNESCO, Paris / UR HHLY Cemagref, Lyon 2000

The designations employed and the presentation of material throughout the publication do not imply the expression of any opinion

whatsoever on the part of UNESCO concerning the legal status of any country, territory, city or of its authorities, or

concerning the delimitation of its frontiers or boundaries.

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Edition prepared by the Pane1 of Authors and Chapter Editors, and finalized by Guy OBERLIN, Report Editor, and

H. ASKOY, A. BULU, P. RAMEZ, A. EICHOLZ

Page

1. Seminars and sessions programmes (realized oral communications) 5

2. Plenary session

World water ressources and greater anatolian project (GAR) in Turkey by Z. Sen

Rainfall, river flow and global circulation downscaling, in mediterranean climate conditions

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by M. Vajadis, J. Ganoulis and J. Patrikas Catchement hydrological and biogeochemical processes in changing enviromnent

by P. Miklanek

17 29

3. Seminar on Low Flows (topic AMFIY-II)

Atmospheric process leading to droughty periods in Romania by M. J Adler, A. Busioc, M. Ghioca and S. Stefan

Recession curve of the hydrogmph by H. Aksoy and S. Dakova

Experiences in regionalising Q95 in Switzerland by H. Aschwanden

Regional Analysis of low flows in Gediz and B.Menderes River basins by M. Bayazit, B .Onoz and B. Oguz

Frequency analysis techniques in low flow hydrology by A. Bulu

The minimum mean monthly flow of Maritza River by S. Dakova and N. Neykov

Long range forecasting of hydrological aspect of droughts by V Ungureanu and M. J. Adler

Domains of applicability of theoretical probability distribution hmctions in low flow frequency analysis

by V Vukmirovic and D. Pavlovic

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43

55

65

73

85

97

109

4. Seminar on Erosion and Solid Transport (topic AMHY VII) Introduction, by Philippe Ramez

* Session : Approches déterministes et description des r>hénomènes Ampleur de l’envasement dans les barrages Algériens

By A. Tidjani et alter Transport des sédiments charriés par les rivières

by V Vukmirovic Sediment deposits in a reservoir : possible methods of estimation and choice

by M. Bessenasse & alter *Session : Approches statistiques et stochastiques

Stochastic modelling of monthly sediment discharges by A. Bulu & alter

Application of renewal processes to characterize the riverbed sediment load by V Vukmirovic & alter

Quantification de l’érosion au droit d’un barrage, à partir de stations hydrométriques, en zones semi-arides

by B. Touatbia et alter *Session : Analyse du risque et optimisation

Risque calculé, associé à l’érosion by A. Bekkouche et alter

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129

137

145

1.53

161

171

5. Annexes.

a) Summary of the content for the topics IV (Rare Floods) and VI (Eleavy Rains) 181 (Independant difusion)

b) List of the communications presented by AMHY participants at the joint session with IDNDR and PIARC “Floods and Road9

c) Participants’ directory

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183

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1. PROGRAMME REALISE

October 13, 1998 Tuesdav Arriva1

October Id,1998 Wednesdav

lO:OO-10:30

10:30-12:00

12:00-14:oo

14:00-18:OO

Registration

Opening Ceremony (Conference Room) by D. Ornon, A. Bulu, G. Oberlin, Z. Sen

Lunch break

Plenary session (Conference room) Chairman : V. A. Stanescu

Considering flows in Mediterranean climate region using global circulation downscaling by M. Vafiadis, .I Ganoulis, J. Patrikas

The project 5 inside the NEF Group dealing with process hydrology by P. Miklanek

Opportunities for an European project dealing with hydrological regimes and future water management

by G. Oberlin The assessment of the climate change impact on the qater flow regime. Application for a river basin in Romania

by V. A. Stanescu, hi Simota, C. Corbus, V Ungureanu Stochastic characteristics of long series

b-v Z. Radie, J. Petrovic A general formulation of discharge-duration-frequency curves

by P. Javelle The stability of hydrological regime of Hungarian rivers

by N. Beda, S. Miklos

October 15, Thursdav

09:00-12:00 Joint meeting with the Natural Disaster Reduction for Roads in Mediterranean Countries (Macka Hotel)

Among the communications, the following are assummed by AMHY colleagues 1, Methods developped inside AMHY group for flood estimation

by P. Versace 2. Hydraulic effects of road structures on flood propagation

by A. Paquier 3. The contribution of historical informations for heavy flood estimations

byM. Lang

12:00-14:00 Lunch break

*14:00-18:OO Specialized seminar (Low Flow, Parallel Session) (Avazaga room) Chairman : A. Bulu

Recurrent estimation and spatial presentation of flow rates by Z. Radie & al.

Domains of applicability of theoretical probability distribution functions in low flow frequency analysis

by K Vukmirovic, D. Pavlovic Power transformation of the Gumbel probability distribution

by V Vukmirovic, J. Malisic Coincidence of low flows at neighbouring catchments

b.v J. Petrovic

-..-. __-- .--. -

Regional analysis of low flows in Gediz and B. Menderes River Basins by (M Bayazit)

Some recent evolutions on synthesis modelizations for low flow characteristics by G. Galea, R. UC, M. Kobold G. Oberlin

The minimum mean monthly flow of Maritza River by S. Dakova

Recession curve of the hydrograph by H. Aa, S. Dakova

Experience in regionalising Qg5 in Switzerland b-y H. Aschwanden

Long range forecasting of hydrological aspects of droughts by 1: Ungureanu, M J ildler

*14:00-18:OO Specialized seminar (Erosion and Solid Transport, Parallel Session) (Taskisla Room) Chairman : A. Paquier (in the absence of B. Touaibia)

Modeling of sediment discharges by A. Bulu, T. Akar

Sediments deposits in a reservoir : Possible methods of estimation and choice by M Bessenasse, A. Paquier, P. Ramez

Sediments dynamical investigations in shallow lakes and reservoirs by L. Rakocky

Ampleur de l’envasement dans les barrages algériens b.v Tidjani, D. lébdri, .4. Cherif

Erosion et étude du comportement physique des différents sédiments rencontrés en nature bUy Cher$ D. Yeb,dri, A. Tidjanr

Etude comparative entre les modèles d’écoulements transitoire à surface libre avec transport solide

by K. Ahmed Etude d’érosion et du ruissellement sur bassins versants expérimentaux dans les monts de Beni- Chaougrane, Algérie

b-v M. Mohamed3 A. Morsli Risque “calculé” associé à l’érosion

by.4. Bekkouche, A. B. K. Djeddid Dynamique sédimentaire dans les zones de rejet en mer

b.y H. Mohamed Approche d’homogénéisation des données de transport solide dans les stations hydrométriques. Cas du bassin versant de la Mina

by B. Touaïbia

Meeting Diner

Octoher 16, 1998 Fridav

09:00-12:00 Specialized seminar (Heavy rains and flash floods) Chairman : P. Versace C. Llasat

Part Z : Methodologic contribution session : Analysis of Precipitations

Joint estimation of IDF curves by maximum likelihood method by F. Frances and I. Vaskova

A multifractal explanation for Rainfall Intensity-Duration-Frequency Curves by P. Hubert, H. Bendjoudi, D. Schertzer and S. Lovejoy

Application of PWM method in the regional estimation of parameters for the SQRT-ET max distribution function

by J. Ferrer session : Statistical prohlems for floods

Use of historical information for flood frequency studies: the example of river Guiers by M. Lang, D. Couer, C. Lallement and R. Naulet

Modelling of design hyetograph as a input to hydrologie models by E. Kupczyk and R. Suligowshy

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Application of the rainfall-runoff models to design flood computation by U. Soczynska, B. Nowicka and U. Somorowska

General formulation of QdF mode1 by P. Javelle

Stochastic characteristics of long series by Z. Radie andJ Petrovic

Part ZZ : Case studies Recent flood disasters at north western Black Sea region of Turkev

bv I. Gurer Flash-floods in the Northwest of the Mediterranean Area : the 27th -28th September 1992 event

by h% C. Llasat, C. Ramis and L. Lanza Heavy rainfall intensities in small basins: the flood of Crotone (October 1996. Italy)

by E. Ferrari and P. Versace Flood flows in the Kolubara catchment during June 1996

by A. Vukmirovic, B. Kapor and V. Vukmirovic Flood behaviour on a small Mediterranean basin in French Cevennes

by C. Cosandey

12:00-14:oo Lunch break

11:00-16:00 FRIEND-AMHY Steering Committee Meeting

2. SEANCE PLENIERE

WORLD WATER RESSOURCES AND GREATER ANATOLIAN PROJECT (GAP) IN TURKEY

Zekai Sen Istanbul Technical University, Meteorology Depar-tment, Maslak 80626, Istanbul, Turkey

ABSTRACT Water is becoming more precious commodity than ever due to many social, economic,

industrial and antropogenic reasons a11 over the world. Unprecedented population increase, environmental pollution, and global warming are among the main reasons that cause depletion in the water ressources as a whole and consequently there is an impression that there may be conflicts or at least economic sanctions against many nations in the future. Many nations in the world are trying to hide the real water ressources capabilities within their dominante and presently there are artificial tensions or debates over the water rights internationally. In this paper, total water ressources account in the world is reviewed in general and Greater Anatolian Project is discussed in addition to the water ressources in Turkey. The main conclusions are that although Turkey is self sufficient in water demand but becoming poorer by time in a high rate. Regulation of rivers Tigris and Euphrates within Turkish boundary especially for hydroelectric power generation by high dams is among the water rights of Turkey and presently 500m3/sec of discharge is released to southern neighbors irrespective of wet or dry seasons. However, it is necessary to reconsider this amount under the light of hydrological and especially meteorological drought variations in the region.

INTRODUCTION

Water and its courses on the earth’s surface in the forms of creeks, streams and rivers are still life veins for the prosperity of human existence. Even in the very past historical times a11 the major cities or settlement areas are adjacent to the river or in general to any water toast. Hence, water played a distinctive rôle not only in meeting domestic, agricultural, food and irrigation requirements but also through navigation in the first cripples of the communication. This is the reason why early civilizations were a11 concentrated along the rivers Nile, Euphrates, Tigris, Indus, Ganges, Amazons and the Brahmaputra in different parts of the world. These civilizations were distinct from each other but by invention of navigation their cultural activities started to intermix with each other which led to a better civilization by time. Throughout the human history water ressources have been the key point in fights, battles and wars as well as in the peace durations led to quarrels among the neighbors due to different reasons. Social, economic and environmental integration of a society cannot be obtained without the fresh water ressources. Especially, in the twenty first Century water is expected to be for sure necessary commodity for running industries, providing energy and growing food. In orlden days, aqueducts are build to transport water from far distances, in fact from the spring to exploitation area especially during the Roman reign. Today modern pipelines are used to support water poor areas from water rich locations by transporting water under closed conduits and high pressures.

WORLD WATER BALANCE As the 2 1 st century draws near we should review our water resources for harnessing

water that have been inadequate or mismanaged for many years because rivers, lakes and groundwater resources are becoming increasingly contaminated with the industrial activities. On the other hand, due to this contamination millions of people die every year Çom water- related diseases such as ma.laria, typhoid and choiera. Expected changes in the climate Will alter future water supply, demand and quality.

For hurnan beings the renewable water resources are important for the continuation of many activities and the renovation happens through the hydrological cycle especially by the evaporation depending on the solar radiation. Although the annual evaporation rate is equal to the precipitation rate all over the world more water evaporates fkom the oceans than returns to them directly fkom the atmosphere and this means that water is transferred over the continents and it later returns to the oceans in the form of surface runoff. It is this amount of water that sustains the natural ecosystems and societies and recharge to the aquifers. Annually 47 000 km3 are returned to the oceans as river and ground water runoff.

Water in the atmosphere is renewed every 8 days and in the rivers every 16 days but the renewal period of other resources such as the oceans, ice caps and groundwater resources might continue for thousands of years. If slowly renewable resources such as the groundwater resources are exploited rather rapidly then their natural cycle Will be disturbed in an undesirable manner.

Ahhough more that two-thirds of the earth surface is covered by surface water only 3 percent is potable fresh water, the remaining amount being saline. This 3 percent constitutes only 35~10~ km3 which would make about 70 cm water depth if it were spread uniformly a11 over the world. On the other hand, mean annual global precipitation is about 1040 mm (Chow et al. 1988). Figure 1 shows the armual global cycle of water in the earth- atmosphere system where ail quantities of water are expressed as percentages of the mean annual global precipitation.

INFILTRdTiOid

Figure 1. Schematic diagram of hydrologie cycle

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The hydrologie cycle does not provide main link between the earth, ocean and atmosphere but equally qualitative restoration as well. An enormous amount of water about 505 000 km3 which is equivalent to 1400 mm thick of water layer globally evaporates annually hem the oceans and open water surfaces. About 90% of this amount retums in the form of direct precipitation to the ocean and remaining 10 % falls to dry land. World wide water balance of the continents and dry lands as a whole on the basis of precipitation, evaporation and runoff are presented in Table 1.

The total global runoff averages 44 500 km3 per year. However, almost 9.5% of this amount returns back to oceans directly and leaving about 1000 km3 only for interior hydrologically-closed regions. Table 2 indicates annual runoff distribution in various land masses and it is obvious that the distribution is extremely uneven and more than half the global runoff occurs in Asia and South America. Furthermore, more than 80% of the annual runoff appears in the northem and the equatorial regions where low population concentrations exist leading highly populated sub-tropical zones with very less surface water amounts.

Table 1. Continental water balance (Gleick, 1993)

Continent Runoff 1 Oan

Europe 507 (5 320) ” (2 970) Asia 740 (32 200) 416 (18 100) 324 (14 100) Afiica 740 (22 300) 587 (17 700) 153 (4 600) North America 756 (18 300) 418 (10 100) 339 (8 180) South America 1 600 (28 400) 910 (16 200) 685 (12 200) Australia and Oceania 791 (7 080) 511 (4 570) 280 (2 510) Antarctica 165 (2310) 0 (0) 165 (2 310) Lands as a whole 800 (119 000) 485 (72 000) 315 (47 000) Areas of extreme nmoff 924 (110 000) 529 (63 000) 395 (47 000) Areas of interna1 nmoff 300 (9 000) 300 (9 000) 34 (1 000)

Table 2. River runoff resources.

Annual river runoff

Territory (mm) oUn w Ares( 1 03kmz) Specific Discharge (It/shm*)

Europe 306 3 210 7 10 500 9.7 Asia 332 14 410 31 43 475 10.5 Afiica 151 4 570 10 30 120 4.8 North America 339 8 200 17 24 200 10.7 South America 661 11 760 25 17 800 21.0 Australia 45 348 1 7 683 1.44 Antarctica 160 2 230 5 13 977 5.1 Total land area 314 46 770 100 149 000 10.0

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This may indicate that in future water crisis Will start in sub-tropical or close areas. Furthermore, most of this water is captured in the form of ice layers about both poles and the remaining usable f+esh water is about 100 000 m3 and this is equivalent to 0.03 percent only.

Provided that the world population is estirnated currently as 6 billion, with this amount of water each person should receive more than 8000 m3 per year. Hence, the countries of the world that have more than this level Will be referred to as water rich countries. Otherwise, they are countries with insufficient water of varying degrees. This figure might be subdivided into three ranges, namely, 0 - 3500 m3, 3500 - 6000 m3 and 6000 - 8000 m3, respectively as water poor, moderate and sufficient countries.

The major problem arises from uneven distribution of 8000 m3 per year water ah over the world. It is well known that rainfah and runoff are irregularly distributed and we often get water when we do not need in enormous quantities and in the case of severe need the water availability is scarce. This unbalanced situation occurs not only on time but more signifïcantly on the location basis. As Gleick (1993) states some places receive enormous quantities whereas others receive almost none. For instance, Atacama Desert in South America is one of the world’s driest areas and the raingage in Chili routinely records zero annual precipitation. On the other hand, Mount Waialeale, on the island of Kauai, Hawaii records more than 11.5 m of rainfaI1 in a single year.

WATER RESOURCES IN THE WORLD World potable water resources cari be divided into three major groups SO far as their

connection with the present day hydrological cycle is concemed. These are, namely, buried fossil waters (deep groundwater aquifers), ice locked waters (pale regions, Antarctica and Greenland) and fiesh waters (lakes, rivers and shallow groundwaters aquifers). Apart from these fresh water resources, oceans and seas are full of saline waters that cannot be used prior to some purification process. At the turn of the 20th Century stocks, flows and conditions of the global water resources are not known with certainty and they are distressingly imperfect. About 97 % percent of ail water resources is salt water without direct use. The total volume of f?esh water resources is 35 million km3. Unfortunately, this amount of water is not spread uniformly over the world and consequently, their availability is spatially uneven and therefore, some areas of the world experience water scarcity. Easily exploitable water resources are available at about 100,000 km3 in lakes, rivers and shallow groundwater aquifers. This is only % 0.3 percent of ail the water resources.

Preservation, management and distribution problems of the world fresh water resources Will expose various scientific, social and political problems in the 21st century. These problems are becoming increasingly national, inter-regional, and world wide day by day. On the other hand, environmental and atmospheric pollution due to fossil fuel combustion and industriahzation as well as transportation become potential treats to water resources. Hence, problems arise because majority of the water demands are met by the surface and groundwater resources which are prone to pollution.. In order to make critical and reliable assessment of water resources ail over the world, it is necessary to know approximately the physical states that the water is available and their relationships to the hydrological cycle as well as the human activities. World water stock shares are presented in Table 3.

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According to this table a large fraction of the fresh water is in the for-m of ice and permanent snow caver in the two pole regions. The total volume of f?esh water stocks is 35~10~ km3 just 2.5% of the total stock of water in the world. Human water consumption resources are the lakes and rivers and they contain on the average about 90 000 km3 of water or just 0.26 percent of total global fresh water reserves.

On the other hand, the global runoff is distributed extremely unevenly and almost 50 percent of the global runoff occurs in Asia and South America. Most of the runoff is concentrated in the polar and equatorial zones with dry belt in between where the Middle East lies.

Table 3. Earth water reserves.

Area (m2) Volume (m3) Percentage

World ocean 361 300 1 338 000 Groundwater 134 800 23 400

Freshwater 10 530 30.1 Soi1 moisture 16.5 0.05

Glacier, snow caver 16 227 24 064 68.7 Antarctic 13 980 21 600 61.7 Greenland 1 802 2 340 6.68 Arctic islands 226 83.5 0.24 Mountain regions 224 40.6 0.12

Ground ice 21 000 300 0.86 Water in lakes 2 059 176

Fresh 1236 91 0.26 Saline 822 85

Swamp water 2 682 12 0.03 River flow 148 800 2.12 0.006 Biological water 510 000 1.12 0.003 Atmospheric water 510 000 13 0.04 Total water reserve 510 000 1385 984 Total fresh water 148 800 35 029 100

CATCHMENTS IN TURKEY AND MAJOR RIVERS There are 26 drainage basins in Turkey as shown in Figure 2 where some of these

catchments are international and shared between some neighboring countries. Among these drainage basins Euphrates and Tigris rivers are very important historically, currently and more significantly in the twenty first century. The characteristic features of these drainage basins are shown in Table 4.

Yearly about 500 billion m3 of min water falls over the whole Turkey and after the deduction of losses as around 40 percent 186 billion m3 of water appears as surface flow in Turkish catchments. In addition to this, there are 11 million cubic meter of groundwater due to infiltration. For the time being, about 100 billion cubic meter of the surface flow is

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exploitable in Turkey. Once this amount is divided to the population of Turkey then annual per capita water amount becomes circa 1600 m3.

BULGARIA ‘I r

MEDITERRANEAN

Figure 2. Drainage areas in Turkey

Table 4. Water potential of each drainage basin in Turkey

Drainage basin Ave name l-9

e runoff Potential oim &ar) percentage

Annual average Runoff yield (Vs-km*) coefficient

1. Meriç-Ergene 1.33 0.7 3.6 0.16 2. Mamxua Sea 8.33 4.5 11.0 0.41 3. susurhlk 5.43 2.9 7.2 0.33 4. Northem Aegean 2.09 1.1 7.4 0.30 5. Gediz 1.95 1.1 3.6 0.16 6. K. Menderes 1.19 0.6 2.9 0.13 7. B. Menderes 3.03 1.6 3.9 0.18 8. Western Mediterranean 8.93 4.8 12.4 0.43 9. Antalya 11.06 5.9 24.2 0.63 10. Lake Burdur 0.50 0.3 1.8 0.11 ll.Akarçay 0.49 0.3 1.9 0.13 12. Sakarya 6.40 3.4 3.6 0.19 13. Western Black Sea 9.93 5.3 10.6 0.42 14. Ye@nnak 5.80 3.1 5.1 0.28 15. Klzlhrmak 6.48 3.5 2.6 0.18 16. Konya (closed) 4.52 2.4 2.5 0.14 17. Eastem Mediterraneanll.70 6.0 15.6 0.83 18. Seyhan 8.01 4.3 12.3 0.55 19. Asi 1.17 0.6 3.4 0.18 20. Ceyhan 7.18 3.9 10.7 0.43 21. Fuxt 31.61 17.0 8.3 0.43 22. Eastem Black Sea 14.90 8.0 19.5 0.43 23. Çoruh 6.30 3.4 10.1 0.61 24. Aras 4.63 2.5 5.3 0.44 25. Lake Van (closed) 2.39 1.3 5.0 0.26 26. Dicle 21.33 11.5 13.1 0.54

Total 186.05 100

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Compared to the world standard of 10000 m3 this amount shows that presently Turkey is not water rich country and in fact, after several years Turkey may become poorer in water resources due to population increase and pollution effects. The Greater Anatolian Project (GAP) area is located in the southeastem part of Turkey with 10% areal coverage of all the country surface and the same percentage applies for the population share in total population. There are 9 provinces, namely, Adryaman, Batman, Diyarbakrr, Gaziantep, Kilis, Mardin, Siirt, &nlmrfa and Snnak. The area includes the Upper Mesopotamian plains with lower Tigris and Euphrates rivers. The total surface area is 75 000 km2 of which 42 % is min-fed cultivated, 33 % pastures and 25% is forest and bushy area. The average population density is approximately 60 persons per km2, Annuel population growth as 3.7%

Euphrates river covers about 16% of Turkey’s surface area but ahnost 90% of its waters originate from Turkish territory. However, only 35% of this amount is impounded within Turkey. In other words, 65% of the Turkish territory waters are allowed to enter the neighbor countries f?om Euphrates river only. This amount is shared by Syria and Iraq with golden share in Iraq. On the other hand, 50 % of T&ris river waters originate frorn Turkey but 15 % of this water is used within the country with remaining being discharged to Iraq. This is tantamount to saying that the golden share from Euphrates and Tigris rivers is with Iraq and Syria

CONCLUSIONS Water is a precious commodity that has already become to have economic value more than ever day by day. Not only the population increase but environmental pollution, global warming and climate change, greenhouse effect and ozone layer hole ail add jointly to the depletion of world fiesh water resources. In the 21st century there might arise conflicts between different nations on water rights. For future water resources of Turkey Greater Anatolian Project (GAP) plays very important role. Turkey presently releases 500 m3/sec of surface water to her southem neighbors irrespective of wet or dry seasons. However, this release amount should be calculated on the basis of the hydrological and meteorological features of the re$on. Since during dry years the discharge in the rivers of the region may fall down to 80 m /sec.

REFERENCES

Chow, V.T., Maidmont, D.R., and Mays, L.W., 1988. Applied Hydrology, McGraw-Hill, New York.

Gleick, P.H., 1993. Water in crisis. A Guide to the World’s Fresh Water Resources. Oxford University Press, 473 pp.

Seri,, Z., 1995. Applied Hydrogeology for Engineers and Earth Scientists. CRC Lewis Publishers, 476 pp.

15

RAINFALL, RIVER FLOW, AND GLOBAL CIRCULATION DOWNSCALING IN MEDITERRANEAN CLIMATE CONDITIONS

M. Valïadis, J.Ganoulis and J. Patrikas

DIVISION OF HYDRAULICS AND ENVIRONMENTAL ENGINEERING, ARISTOTLE UNIVERSITY OF THESSALONIKI - GR-54006 THESSALONIKI, GREECE

ABSTRACT

In the Mediterranean countries, most of the small rivers are seasonal or ephemeral rivet-s, directly depending on the rainfall-surface runoff. Big rivers, are also highly dependant on the rainfall-surface runoff. For these reasons it is important to study the precipitation regime and the precipitation-runoff relation for the hydrologie basins of the rivers of interest. The daily precipitation could be estimated as correlated to the global atmospheric circulation (downscaling). The lïrst results from the research done over the headwater basin of Achelloos river, the Mesochora basin, in Greece are presented in this paper.

INTRODUCTION

In Greece, as a11 around the Mediterranean coastal area, most of the small rivers are seasonal or ephemeral rivers, directly depending on the rainfall-surface runoff. Big rivers, are also highly dependant on the rainfall-surface runoff, as their drainage areas are small, comparatively to the main European rivers as the Rhine, the Danube etc., and the water from snow melt and Springs represents a limited percentage of their flow. It is therefore important to study the precipitation regimes and the precipitation-runoff relation, in order to provide a better description and mode1 for river flow.

The effects of a possible climatic change on the river flow is the subject of many research projects. One of those projects is the EU funded project: “Impacts of climatic change on river basin hydrology under different climatic conditions (CC-HYDRO)“. The participating countries are Germany, Austria, Italy and Greece. The main purposes of the project are:

The study of differences of precipitation regime and flow regime in the Central European and the Mediterranean countries.

The study of the variation of river flow under climatic change, that is a change of CO2 content in the atmosphere and the resulting change in global circulation.

The connection between atmospheric circulation, expressed as circulation types (CPS) or weather types (WTs) and precipitation, has been under study for many decades (Mamassis et al. 1996). The main problems in these studies were:

The definition of weather types. In most cases the weather types and the relative CP types are objectively defïned by meteorologists, based on their experience. The characteristics and the number of WTs vary from area to area and they are not directly comparable. For example the classification of Hess and Brezovzky for Central Europe counts 30 WT and the Mahera’s classification for Greece only 16.

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The classification day by day was generally done “by ha&‘, based on the experience and general knowledge of each scientist.

The amount of data for just one day is important, covering a geographic area from 30” East to 50” West and 10” North to 60” North.

A modern automatic classification procedure has been proposed by A.Bardossy et al. (1995) based on tùzzy arithmetic. This method proved to perform satisfactorily with the Hess and Brezowzky classification, but it is a little heavy on computer implementation and it is also dependant on the objective definition of standard CP types, that are used for the classification.

A new fast classification procedure, based on the determination of the centers of pressure anomalies, has been developed in the division of Hydraulics and Environmental Engineering, Aristotle University of Thessaloniki. The first results, comparisons among other classification methodologies, have been presented in Espoo, Finland, (Ganoulis et al., 1998). The next step is the optimization of the correlation between WT and amounts of precipitation and the even further trim of this correlation, based on other climatic factors, as winds and temperatures, aiming an improved precision in daily precipitation depth determination.

The possibility to estimate local daily precipitation amounts from the global circulation (downscaling) is very important in many aspects:

Control and extension of precipitation and river flow data archives. Short term forecasts. Flood and Drought Prevision. Long term previsions Water resources estimation.

CLASSIFICATION OF PRESSURE DISTRIBUTION FIELDS

Daily atmospheric circulation may be defined by geopotential height surfaces of several air pressure levels. These large-scale free-surface circulation patterns may be considered as main causes for enhancing local hydrometeorological characteristics, such as precipitation and temperature.

The basic idea is to find quantitative relations between occurrences of precipitation and temperature on a given basin and characteristic atmospheric pressure patterns. Space-time variability of local hydrometeorological variables may be derived from circulation patterns (CPS) by means of a stochastic approach.

Th.is may be done by two different ways:

1. downscaling conditional to a given classification of the CPS. 2. statistical regression.

The first approach was used in this study and is mainly semi-empirical. It heavily depends on the particular geographic location and local climatic conditions of the river basin.

The Greek area, (Mesochora basin) is located on the SE European corner between 20-28 degrees East and 35-42 degrees North ( Fig. 1). Characteristic CPS in this area are quite different from those of central European ones. For example, pressure systems affecting the

18

Greek area and also location of anticyclonic or cyclonic systems producing precipitation are different from those affecting the central and west Europe. Therefore, use in Mesochora basin of CP types previously defïned for areas in Germany or Austria may induce erroneous downscaling results.

A different classification scheme has been developed for Mesochora basin, after concertation with Greek meteorologists and climatologists. The final list of characteristic CPS has been derived from the one previously introduced by P. Maheras (1989) and shown in Table 1. Location of centers of usual antcyclonic circulations and main trajectories of cyclonic movements over Mediterranean and Southern Europe are shown in Fig. 1.

Table 1 Weather types in Greece (after Maheras, 1989)

Main Category Abbreviation Description

Al Location of tenter in western Europe or northern Atlantic

Continental Anticyclones A2 Location of tenter in Russian or Siberian region

A3 Location of tenter in Balkan

A4 Location of tenter in eastern Mediterranean

Maritimes Anticyclones A5 Location of tenter in western Mediterranean and Africa

Cyclones with zona1

orbit

Wl

w2

Cyclone passes from the Balkans over 45” latitude

Cyclone passes through Greece below 45” latitude

Cyclones with

meridional orbit

Mixed types

Nwl

NW2

SWl

sw2

MT1

MT2

Cyclone from W. Mediterranean through Greece

Cyclone from Scandinavia to Black Sea

Cyclone from W. Malta-Macedonia-Ukraine

Cyclone from E. Malta-Macedonia-Ukraine

Characteristic types

(special mostly dry

period types)

DES

DOR

Special combination between low pressure in south

Very weak pressure gradient over Greece

Pressure of cold air mass at 500 hPa above Greece

19

(4

\ CO

0

Fig. 1 Types of anticyclonic circulation (a) and main trajectories of cyclonic movements (b) (afier Maheras, 1989).

20

Until today, classification of weather types for the Greek area has been made manually using historical data and checking maps of pressure Iïelds day by day.

If the goal is the investigation of the influence of possible climate change on river basin hydrology, circulation types not only based on historical data but also on 2CO2 simulation should be analysed. It is obvious that this classification cari be achieved only by use of a computerized algorithm. For that purpose, a simplified catalogue of characteristic CPS for the Greek area has been defïned (Tab. 2). This is a simplification of CPs defined previously.

In this classification scheme there are 5 anticyclonic and 5 cyclonic systems influencing the weather type in Greece. The usual location of anticyclonic centers and typical trajectories of cyclonic movements are shown in Fig. 2.

Table 2 Circulation types in Greece used in this study.

Main Category

Anticyclones

Abbreviation Description

1 Location of tenter in west or north-west of our area

2 Location of tenter in north or north-east of our area

3 Location of tenter over the Balkans

4 Location of tenter in east or south-east of our area

5 Location of tenter in south or south-west of our area

6 Cyclone passes from the Balkans over 45” latitude

Cyclones

Cyclone passes from northwest to southeast

Cyclone passes from the Balkans under 42” latitude

9 Cyclone passes from southwest to northeast

10 Al1 the other occasions

21

..-,,,-. z ~.- W.T 1

/ i W.T 5 +A_\ W.T4

/’ ---_ - --w-m, 30 ,: _~~~ -... ‘-w ;-1 .~~ ~~ ~-----

-io -5 0 5 10 15 20 25 30 35

(4

4

W.T 9 W.T 9

: ‘-,, :/ ‘--l----.\~M/ W T 7 30.00L’-p---

d

-10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.0

tb)

Fig. 2 Types of anticyclonic circulation (a) and main trajectories of cyclonic movements (b) as defined in the present research project.

22

COMPUTER IMPLEMENTATION

For the period 1950-1990, a classification of weather types for the Greek area has been made by P. Maheras. This classification of historical data was possible by checking maps of air pressure on a daily basis. Our aim was to develop a similar classification by use of computer in order to analyse future CP historical data as well as simulation data for the 2CO2 case.

Steps for nu tonzatic clussifrcation

a) Reading from the CD pressure data at sea surface level over the area of interest, i.e. 15west- 40east and 30north - 55north. Air pressure values on a grid of 2.5 degrees resolution are taken at 0 a.m. and 12 p.m. every day, for the period 1950-90. A binary file has been constructed in form of table containing a11 pressure values over the area at a given time (e.g. time 0).

b) Development of a computer programme for locating the tenter of a characteristic air pressure system which affects the Greek area. In order to define the air pressure tenter the following steps have been defïned

First, the average pressure over Greece was calculated. If this pressure value is above a given pressure threshold the system is considered as anticyclonic and the high pressure tenter is located. In the opposite case we are searching to locate a low pressure system.

The location of the tenter is done as follows: when an anticyclonic system is expected, first we locate the point with the. highest pressure. Then, we search for local pressure centers and we accept the one which is located nearest to the tenter of the Greek area (22,5East, 37.5North).

Tab. 3 Definition of air pressure thresholds over Greece.

February I 1018 I I March I 1018 I

April 1016

Ma y 1014

June I 1011 I t

I

July I 1011

August

September

1011

1014 I I

October 1017

November 1018

December 1018

23

Pressure threshold

This is the critical pressure over Greece defking a CP system as cyclonic or anticyclonic. According to Prof. Maheras classification, the value of this critical pressure may be calculated as the average daily pressure over Greece corresponding to a given CP type for every month. For example in January we have found that statistically the pressure threshold is 1018 mbars: this means that a day with average pressure over Greece greater than 1018 mbars should be of anticyclonic type; in the opposite case it should be of cyclonic one. These pressure thresholds for every month appear in Tab. GR 3.

Based on this fïrst procedure a classification for every day in cyclonic and anticyclonic types has been made. 7746 anticyclonic type days and 7202 cyclonic type days have been found over the period 1950-1990. There are 7599 anticyclonic and 7276 cyclonic type days for the same period according to Prof P. .Maheras classification (Fig. 3).

Weather Type Frequency Weather Type Frequency (Anticyclonic case) (Cyclonic case)

7000

6000

5000

4000

3000

2000

1000

new WT Maheras WT

new WT Maheras WT

Total Precipitation in Anticyclonic case Total Precipitation in Cyclonic case

(Katafyto 1954-1990) (Katafyto 1954-1990)

45000

40000

35000

30000

25000

20000 ~~

15000

40000

35000

30000

25000 -

20000

new W T M aheras W 1 new W T M aheras W T

Fig. 3 Comparison between computer CP classification and that of Prof Maheras for total cyclonic and anticyclonic cases in Mesochora basin (1954-1990)

Statistical characteristics of CPS

Absolute and relative frequencies of historical weather types (WT) or CPS in Greece (Mesochora basin) are given in Tabs 4 and 5 for different seasons and over the total time period (1950-1990).

24

Tab. 4 Absolute frequencies of historical weather types (WT) or CPS in Greece (Mesochora basin)

Weather Type Frequency for period 1950-1990

W.T winter spring summer autumn Year I I , l l I I

1 445 317 812 656 2230 I I 1 I

I 2 1 348 1 207 ( 297 1 478 1 1330 1

1 3 1 282 1 230 1 247 1 294 1 1053 1 I I I I I

1 4 1 231 1 213 ) 146 1 162 1 752 1

I 5 1 270 1 421 1 1199 1 491 1 2381 1 I I I I I I I

I 6 ( 42 1 51 i 68 i 58 1 219 i I I I I !

I 7 1 773 1 766 ) 229 1 419 1 2187 1

I 8 1 516 1 448 1 500 1 514 i 1978 1

I 9 1 604 1 887 1 233 1 549 1 2273 1

I 10 1 183 1 219 1 39 1 104 1 545 1 4 I I 1 I I I

Tab. 5 Relative frequencies of historical weather types (WT) or CPS in Greece (Mesochora basin)

These results are graphically shown in Fig. 4. We cari see that cyclonic systems are dominant in Spring, Autumn and Winter. Anticyclonic CPS are mainly observed mainly in Summer time.

25

W .T Relative Frequency (1950.1990)

3 5%

3 0%

2 5%

2 : 2 0 %

FG E

15% LL

10%

5%

0 %

1

gj w 1” le r

n SPr'"g

gsummer

gautumn

. A II Period

2 3 4 5 6 7 8 9 10

WT

Fig 4 Comparison between different historical relative frequencies of weather types or CPS in Greece (1950- 1990, Mesochora basin)

CONCLUSIONS

Using an appropriate classification of CP types over the Greek area, a computer program has been developed for statistical analysis of local hydro-meteorological characteristics (temperature, rainfall) conditional to particular CP types. Results indicate a strong correlation between precipitation and depression systems located over the Greek area (Fig.5). These results cari be used in hydrologie modeling of rainfall-runoff processes and streamflow simulation. Further refinement of this precipitation downscaling methodology is under way, aiming to optimize the cor-relation between circulation types and rainfall amount, in order to be used for forecast purposes and long term climatic change research on the stream flows.

Precipitation (Al1 period) Mesohora 1962-1990

16000

14000

12000

10000

E 8000 E

6000

4000

2 3 4 5 6 7

W.T

8

0 10

Fig. 5 Total precipitation for different CPS at Mesochora station (1962-1990)

26

REFERENCES

Bardossy, A., Duckstein, A. and Bogardi, 1. (1995), Fuzzy Rule-Based Classification Atmospheric Circulation Patterns, International Journal of Climatology, Vol. 15, 1087-I 097

Ganoulis, J., Vafiadis,M. and Patrikas, J., (1998), Influence of atmospheric circulation classification schemes on local precipitation under climate change, Proceedings of “The Second International Conference on Climate and Water, Espoo, Finland, 17-20 August 1998”, Vol 1, 56-65

Maheras, P. (1989), Delimitation of the Summer-Dry Period in Greece According to the Frequency of Weather Types, Theor. Appl. Climatol. 39, 171-l 76

Mamassis N., and D. Koutsoyannis, (1996), Influence of atmospheric circulation types on space-time distribution of intense rainfall, Journal of Geophysical Research, Vol. 10, 101, No. D2 1,26267-26276

27

CATCHMENT HYDROLOGICAL AND BIOGEOCHEMICAL PROCESSES IN CHANGING ENVIRONMENT

Pavol MIKLANEK, Institute of Hydrology Slovak Academy of Sciences, Bratislava, Slovakia

The study of the hydrological processes in research and experimental basins within the Northern and Western Europe FRIEND Group was included in the Subproject 5 “Physical Processes of Runoff Formation on a Small Catchment Scale” in the last phase. Results of the working group were compiled in FRIEND Report 3 that was distributed during the Postojna FRIEND conference. Pertti Seuna from Finland had retired from the coordinatorship of the subproject during the conference. The conference and a working group meeting itself were a good opportunity to discuss this topic during the informa1 meetings of the people interested in the project.

An intensive discussion about continuation of the project had started at the Prague meeting in 1996. Generally, it was felt desirable to attract new research groups and new activities into the group, e.g. in the tïelds of biogeochemical and environmental studies. Many group members emphasised to have more orientation into water quality aspects. It was discussed and agreed that studies and work should be more impact oriented. At the moment, there was not yet clear agreement of the major common fields of impact studies. Land use changes and deposition were considered important affecting factors in forested environments. At the moment, there was no support for climate change impacts. Catchments were regarded important working tools also in the future.

AAer discussion and change of ideas, the following formulation of the group members was accepted as the working title during the next phase of FRIEND:

CATCHMENT HYDROLOGICAL AND BIOGEOCHEMICAL PROCESSES IN CHANGING ENVIRONMENT

It was regarded to be important to circulate the proposa1 as much as possible, to get comments and ideas, and a view of preliminary interests to participate.

There existed close and fruitful links between ERB (European Reference Basins project) and FRIEND Project 5 in the past which Will hopefùlly continue in the future mainly under the auspices of project’s programme of work, i.e “Catchment hydrological and biogeochemical processes in changing environment”.

Since Pertti Seuna had definitely retired from project’s coordinatorship author of this information agreed to become a coordinator of Project 5 for,a limited period of time in order to guarantee continuity. The last meeting of the working group was held in Prague on 25 September 1998 and the new coordinator of the group was elected Dr. Ladislav HOLKO from Slovakia who is the group member since several years.

The meeting had also finally accepted the enclosed working plan of the group for the recent phase prepared by Ahti Lepisto and Pertti Seuna (Finland), Lotta Andersson (Sweden), and Pavol Miklanek (Slovakia). Do not hesitate to contact us if you are dealing with similar topics and interested in our work.

29

Project 5 : CATCHMENT HYDROLOGICAL AND BIOGEOCHEMICAL PROCESSES IN CHANGING ENVIRONMENT

Co-ordinator : Dr. L. Holko, Institute of Hydrology SAS, Bratislava, Slovakia

Objectives :

(5) to build a greater understanding and synthesis of the processes and mechanisms responsible for streamflow generation, of variation in flow components and cycling of the main nutrients in different physiographic and climatic conditions, Combined effects of e.g. land use changes and atmospheric inputs on nutrient cycles are regarded important.

(5) hydrological processes and material transport Will change with changing climate and land use, emphasising the need of better knowledge of streamflow generation. A distributed mode1 that has a realistic description of hydrological processes in saturated and unsaturated parts of the soil, would make it possible also to identify key processes of material fluxes in different parts of a catchment

(5) the focus of the project is to bring together specialists, techniques and methods from a wide range of catchment studies in countries across Europe, and to combine more efficiently detailed experimental data and mathematical modelling techniques

Programme of work :

(5) A flexible data base Will be established and each participant Will make available short- time (hourly q, P, T) resolution data from their catchments. Small catchments of different land use types (forested, cultivated, peaty) Will be considered.

(2) In order to study streamflow generation and biogeochemical processes, intensified observations including environmental or artificial tracer techniques, interna1 variables (saturated areas, soi1 moisture, groundwater) Will be needed from the catchments, together with meteorological and hydrological observations. The participants Will be encouraged to detect links between hydrology and biogeochemical cycles.

(3) Streamside wetlands, floodplains or riparian zones are the focal point in non-point source loading of nutrients to streams. Effort should be given to study processes in these environments.

(4) Increase of the use of physically based catchment models Will be stimulated. Interna1 variables data Will provide a source of validation for the modelling efforts, Modelling should consider land use change and atmospheric deposition effects.

(5) Expert meetings, researcher exchange and visits in other institutes Will be arranged in order to co-ordinate the project and change experiences and ideas. Closer links between ERE3 and FRIEND project 5 Will be established, e.g. arranging joint meetings and workshops.

30

3. THEME II : ETIAGES

ATMOSPHERIC PROCESS LEADING TO DROUGHTY PERIODS IN ROMANIA

Mary-Jeanne Adler, Aristita Busuioc, Monica Ghioca, National Institute of Meteorology and Hydrology

Sabina Stefan, University of Bucharest, Faculty of Physics

Abstract.

The study of climate variability is important to better understanding the hydrological

and atmospheric processes that lead to droughty periods in Romania. The variability of the

seasonal and annual precipitation for Romanian rain gauge stations are examined for

characterizes the drouhty periods in the atmospheric processes. The discharge series were

statistical analyzed to complete the image of the water ressources behavior in Romania. The

changes, identifïed in the time series of data by means of statistical methods, were proved to

be in connection with the large atmospheric circulation, using Canonical Correlation Analysis.

INTRODUCTION

The drought phenomenon on the Balkan part of Europe is a specific feature for the

geographical conditions.

This phenomenon, although without a strict cyclicity, shows a repeatability at 15-25

year intervals with a persistency of about 12-15 years with short term interruptions of about l-

3 years with rainfalls above the normal values (Adler and all, 1996). These interruptions do

not modify the general features of the droughty periods. From the standpoint of the frequency

of the droughty and excessively droughty periods, three long intervals cari be mentioned when

this occurred during the last Century in a very severe way : 1984-1905, 1942-1953, 1981-1995

(Adler & all, 1998). Taking into account these first results, winter and summer water

ressources characteristics were studied trying to identify the large-scale conditions inducting

this variability. It is well known that atmospheric circulation and climate are linked. But the

regional climate is generated by the simultaneous action of the various processes on local,

31

regional and global scales. The knowledge on the relative contribution of these processes is

important for explaining the regional climate variability. In this paper, the relationship

between seasonal precipitation in Romania and large-scale atmospheric circulation

simultaneous variability is empirically examined by the canonical correlation analysis (CCA)

(von Storch, 1995; Busuioc and von Storch, 1996). The conclusions are related of the

discharge series of data trying to explain the characteristics in the variability of water

ressources in the Carpathian Region.

These results are presented mainly for the winter and summer seasons for which the

climate signals of water ressources series (precipitation and discharge) are signifïcant.

DATA AND METHODS

Data used in this paper are the time series of the annual, monthly and winter

precipiation amount at the 14 meteorological stations, the seasonal mean sea level pressure in

the 1901-1996 interval and discharges at 40 gauging stations in 192 1-1996 interval. The large

scale circulation is represented by the sea level pressure (SLP) field for the area between 30”

N-55” N and 5” E-55” E. The monthly SLP data have been taken from the National Centre

for the Atmospheric Research (USA) with a resolution of 5’~~.

The most affected periods (season and the most representative months in seasons) of

water deficits or of high flow were identifïed. An excessive droughty period was defined as

less than half of normal water ressources were produced. Using monthly data, both the

excessive droughty periods and the synoptically conditions which induced them in Romania,

were identified.

TO see if any changes in water ressources “regimes” was produced, the concept of

“change points” was applied. TO determine these change points - jumps in the mean series of

data, Pettitt - test (Pettitt, 1979), was used.

The Canonical Coi-relation Analysis (CCA) has been used to identifïed the regional

characteristics of the spatial pattems of the sea level pressure (SLP) and of the precipitation in

Romania. Prior to the CCA, the original data are projected onto their empirical orthogonal

functions (EOFs) and only a limited number of them are retained, explaining most of the total

variante.

32

GENERAL ASPECTS OF DATA ON WATER RESOURCES

The annual precipitation trend observed at the meteorological stations in area of

interest did not emphasised always an decreasing tendency, although large areas are

affected by such a phenomenon (Figure la). The analysis of water resources was

extended at the river discharges. The tendency of the mean annual discharges was

extracted. A concordance with the annual precipitation registered in each basin cari be

observed (Figure lb).

The tendency of the annuel precipitation

Figure 1. Water resources tendency regionalization in Romania

The analyse of the time series of data shows that only in few cases the trends are

statistically significant, as the level of signifïcance adopted for the Mann test (Mann,

1945) has been 5% (in central part of the Carpathian arc). Nevertheless, a slight tendency

towards a decrease was detected within all the time series from the gauge stations

located in the southem and south-eastem side of the Carpathian Region, due to the very

low arnounts of precipitation during the last 16 years. During the interval 1982-1996 the

annual precipitation amounts were by more than 50-70% below the monthly annual

normal values (Adler & ah, 1998).

The most of the annual series of precipitation and discharges in the area of

interest emphasised in general a decreasing trend and this trend does not characterised

the repartition of water resources during a11 the seasons. The most affected by deficits

33

was the wintertime (Figures 2, 3) with the great deficits after 1970 and especially during

the last years sub-series 198 1-1995 interval.

I The tendency of the winter precipitation The regionalization of the tendency of the winter discharges

Figure 2. Winter water resources tendency regionalization in Romania

1 The tendency of the summer precipitation The regionalization of the tendency of the swnmer discharges

Figure 3. Summer water resources tendency regionalization in Romania

Pettitt’s statistics derived tiom all data of precipitation downward change points

at about 1969/1970 for several stations (Figure 4aj. The shifts is in the order of -9 to -

66 mm in 1969/1970-1994 interval. It could be observed that if a new splitting of the

precipitation time series is done in 1970, another downward change point is found in

198 1. This shows the fact that after 1970 the precipitation is continuously decreasing,

but more evidently alter 198 1, inducing an important decreasing in water resources.

34

The influence of the physico-geographical conditions of each basin were reflected

in the starting point of droughty period (the downward point), which cari vary with some

years, depending on the inertia of the basin at the deficits in precipitation (figure 4b).

Although in the most cases the downward change point in precipitation was registered in

1969-1970, only in few cases, of the discharge time series, in high mountains (Fagaras),

the downward point was simultaneous. In the other areas, the inertia of the hydrological

basins was important as a result of the water table resources mainly, which entertain the

surface runoff through the base flow. In all cases water resources are diminishing alter

1981 (downward change points) most significant in South and in the middle of the

Carpathian. Some discrepancy in the simultaneity of the change points in winter series of

data of precipitation and discharges is due to the snowmelt phenomenon.

The deficits during summer periods were registered round 1940-1941,when a

very droughty period was registered for the Eastern part of Romania. For the Western

part, the 9* decade of the Century was the driest (1981 is the most significant downward

change point- Figure 5).

SYNOPTICAL CONDITIONS WHICH INDUCED DROUGHTY PERIODS IN

ROMANIA

Four main synoptical conditions were identified which leads to droughty periods in Romania (Donciu, 1963). The first is: anticyclone in the Central Europe, covering Romania too and Island depression extended in the.Eastem Europe. The second shows a

35

Figure 5. Downward change points within the summer water resources (precipitation and discharges)

synoptical situation with anticyclones in the Eastem Europe, Northeast or Sud-East

(covering our country, too) and the low pressure from the Northem Atlantic Ocean to the

Western European part, and to the Mediterranean Sea. The third synoptical situation

contains an anticyclonic ridge covering the area from the North Atlantic to the Central

Europe (and Romania, too) and low pressure in the extreme north-eastem and sud-eastem

of the continent. The fourth synoptical situation contains situations with high pressure in

the Central Europe and our regions induced by Euroasiatic and Azoric Anticyclones and

the low pressure in the North Frozen Ocean and in South of Europe Figure 6.

Figure 6. Specifk synoptical situ I I

ation for droughty periods of Romania

36

The first synoptical situation is specific for the cold period (September-March)

with an exception in May 1947. The frequency of a11 cases is 21.3%. The second takes

place from September to May inter-val, with great frequency during autumn (65% of a11

cases) and in winter (20%) with 21.5% frequency of a11 cases. The third synoptical

situation is producing during summer and springtime, the maximum frequency being

during July (51%) but with a low total cases fi-equency, of only 12.4%. The fourth type

has a maximum frequency of 43.8%. This situation was produced mainly during autumn,

August-September (30% of the total cases - 159) but the possible period is from August

to May - Figures 6a-6d.

CONNECTION BETWEEN SEXSONAL WATER RESOURCES AND THE

LARGX-SCALE CIRCULATION

TO put into evidence the regional seasonal synoptical characteristics the CCA analysis was

applied.

For the winter semon the first CCA pair exhibits a correlation between the

precipitation and SLP coefficient time series of 0.84. The pattems for both variables

represent a link that is very reasonable from the physical point of view: low pressure over

Europe and Mediterranean basin guides maritime air and precipitating weather systems

into Romania, such that above normal precipitation is recorded (figure 7). The time

coefficients associated to these pattems have an upward change-point at about 1933

(Figure 8). The link is strong and therefore we cari assert that changes in the Romanian

winter precipitation are due to changes in the large-scale circulation. For more details see

Busuioc and von Storch (1996). The pattems of the second CCA pair associates the

north-westerly flow over Romania to positive precipitation anomalies in the intra-

Carpathian region the highest being in the Northwest (figure8b).

37

Figure 7(a). Figure 7(b).

Figure 7. The patterns of the first (a) and the second (b) canonical pair of the winter mean sea level pressure (Mb) and total winter precipitation (mm). Continuous lines mark positive values and dashed lines negative values

3

VI 2

E

po L

i

(a)

.j

[ c

-3 1 , / 1880 1900 1920 1940 1960 1980 200

WWWà) 3 1

\ :: : :

1880 19M) 1920 1940 1960 1980 2ool

t(yearsl

Figure 8. The first (a) and the second (b) canonical correlation time coefftcients analysis patterns of the see level pressure anomalies (continuous line) and precipitation anomalies (dashed line) for winter times

38

During summer season the first CCA pair associates (with a maximum correlation

of 0.70) the anticyclone structure with the centre over the Black Sea to the below normal

precipitation in Romania (Figure 9). The time coefficients corresponding to these

pattems have a simultaneous downward change point at about 1941 that is consistent

with same change points in the centre of the country and the Black Sea littoral. The

second CCA pair associates the zona1 circulation over Romania to below normal

precipitation in the intra-Carpathian region and above normal precipitation in the extra-

Carpathian region. The eastern zona1 circulation became more frequent afier 1961 that

could explain the upward change points at about 1968 in the north-eastern part of the

country (Figure 10). Also, some short-lived convective weather systems could be

responsible for the positive precipitation anomalies from the extra-Carpathian region.

Figure 9(a). Figure 9(b).

Figure 9. The patterns of the first (a) and the second (b) canonical pair of the summer mean sea level pressure (Mb) and total summer precipitation (mm). Continuous lines mark positive values and dashed lines negative values for summer times

39

3 , (b)

Figure 10. The first (a) and the second (b) canonical correlation time coeffkients analysis patterns of the see level pressure anomalies (continuous line) and precipitation anomalies (dashed line) for summer times

CONCLUSIONS

Two main periods of defïcits were identified in Romania, after 1940-1942, mainly

in the summer season, 1941-1953 and 198 1- 1995 with comparable intensities and

affected areas.

The decreasing in water resources in the eastern part of Europe was evidently

alter 1981 as a result of the climatological conditions.

The analysis of the areas affected by drought during the last decades shows that,

if at the beginning of this period the most affected areas were in the western part of the

Danubian Plain, presently the area affected by the water deficit extended to the entire

Romanian Plain.

A decreasing in water resources was recorded, mainly during the winter, in

connection with the decreasing of frequency of the Mediterranean south-westerly

circulation, since 1969- 1970

The inter-relation between winter precipitation and winter resources of water of

the river is not always evident, the restitution of the snow layer in water rivers taking

place during the spring as well as in the winter time, affecting the seasonal precipitation-

discharges balance.

40

. . . . _ . __~ - - ^ . “ - . . ^ . . , “ , , ~ . ^ - - - . “ . - - . ^ . .~ . . - _, - . -

The river discharges were affected mainly afier 198 1, the inertia of the

hydrological basins at the dryness of the precipitation having a great role thanks to the

groundwater during droughts.

References

Adler MJ. A.Bulu. M.Vatïadis, ZRadiç, V.Vukmiroviç (1998). Regionalization of droughts in the

Eastem European part of the Ah4HY Area. Proceedings qf the Low Flows AMHY F~EMI

.LIeeting, Belgrad. pp. 3-15

Busuioc, A. and H. von Storch, 1995: The connection between summer precipitation anomalies

in

Romania and large-scale atmospheric circulation. Proceedings ‘Atmospheric Pbysics

and

Dynamics in the Analysis and Prognosis of Precipitation Fields”, Rome 1994, pp. 369-

373.

Busuioc. A., Hans Von Storch (1996) Changes in the winter precipitation in Romania and its

relation to the large scale circulation Tellus 47: pp.538-552

Donciu C. (1985) Studiul secetol in Romania @roughty study in Remania), Meteorologia, Hidrologia

si Gospodarirea Apelor, pp. 170-176

Pettitt, A. N. (1979) A non-parametric approach to the change-point problem App.Statist.28,

NO.~. pp. 126-135

Von Storch, H., 1995a: “Spatial Pattems: EOFs and CCA”. in: H. von Storch and A. Navara

(eds). :Analysis of Climate Variability. Application of Statistical Techniques, Springer

Verlag

41

THE MONTHLY AND ANNUAL FREQUENCY OF EXCESSIVE DROUGHTY CASES IN ROMANIA

TOTAL421 ( 131 27 1 75 ( 9 ---- - -- --

5 9 -i--

I

5.1 9

1 1 1 51 31 261 15.6 31 I l I ( 241 14.5

121 121 -91 61 91 811 ,48.8 751121 9(7917817661700

RECESSION CURVE OF THE HYDROGRAPH

Hafzullah AKSOY Istanbul Technical Univers@ Civil Engineering Faculty Hydraulics Division 80626 Ayazaga, Istanbul-TURKEY

Snejanka DAKOVA

Bulgarian Academy of Sciences, National Institute qf A4eteorology and Hydrology Tzarigradsko Chausse Soja-B ULGA RIA

ABSTRACT

Recession curve. the deterministic part of the hydrograph. is a very useful tool in planning and management of ivater resources to determine low flow values which are important in irrigation. water supply. hydre power plant and water quality applications. The recession curve is also used for graphical separation of flow into its components, surface flow, subsurface flow, and base flow. In this study. a review of literature on the exponential decay fimction which is widely used in recession curve analysis is given. Later it is explained how the master recession curve of a basin cari be developed. Additionally graphical flow separation techniques are summarized and base flow index is explained.

INTRODUCTION

A typical hydrograph has three components, ascension curve, peak point, and recession curve (Fig 1). Along the ascension curve, there is an inflow of water to the basin. Therefore flow increases along that curve. Peak point shows the time that the maximum flow occurs. The recession curve corresponds to the outflow of water from the basin after the inflow (rainfall) to the basin ceased. Shape of the recession curve does not depend on the inflow while shape of the ascension curve depends.

Being a useful tool in hydrology, recession curve of the hydrograph was analysed by many researchers by means of various techniques for different purposes. The recession curve contains valuable information concerning hydrological basin’s storage properties and aquifer characteristics. It is widely used in planning and management of water resources to determine low flow values which are very important in irrigation, water supply, hydro power plant, and water quality applications (Tallaksen, 1995).

Another important use of the recession curve is graphical separation of flow into its three components, surface flow, subsurface flow, and base flow. Of these base flow is that part of the runoff in a river which is not the direct consequence of a rainfall event. It cari be considered as the outflow of ground water reservoir feeding the rivers during rainless period (Frohlich et al., 1994) and be defined as the net flow from ground water storage to a stream under the effect of diverse geological, climatological, and morphological factors, resulting in considerable variations both in time and space (Singh, 1968). A better understanding of baseflow cari help in controlling irrigation withdrawals during low flow periods, making water supply estimates and forecasts, and determining storage requirements for maintenance of adequate flow for waste dilution (Singh, 1969).

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Figure 1. A typical hydrograph and its components

Application of Base Flow Index (BFI), calculated as the ratio of baseflow volume to the total streamflow volume and derived from a simple separation of the daily hydrograph as a sustainable component of streamflow, would be very considerable and convenient. Coming from a definition of base flow and comparing it with this one of low flow, base flow usually occurs in times of sustained and regionally extensive periods of low precipitation and snowmelt, when streamflow is fed from groundwater flow. It is then logical to accept the values of base flow during low flow period to coincide with the values of low flow (Dakova, 1998).

This study attempts to give a general information on recession curve of the hydrograph with a wide literature review. Graphical and analytical techniques developed for separation of flow into two or three are given. Later base flow is investigated.

RECESSION EQUATION

Outflow from the basin alter a rain storm, is widely characterised by an exponential equation. This process cari be thought as a linear reservoir, its outflow is directly proportional to the volume stored in it. Hall (1968) and Tallaksen (1991, 1995) report that mathematical background of such kind of an investigation goes back to the work by Barnes (1939) and originates from Boussinesq’s nonlinear differential equation given for aquifers. Barnes (1939) found that flow values scattered as a straight line in a semi-logarithmic paper from which the well known and the most used exponential recession equation was obtained as

Q, = Qoema (1)

where, a is the recession coefficient, t is time, Qt is flow t days afier the peak, and Qo is the peak flow value. Denoting e-” as K, Eq. (1) cari be rewritten as

44

where, K is always smaller than 1. K is not constant along the recession curve. K at the beginning of the curve is smaller than K at the end of the curve. SO, slope of the line obtained from the plot of flow values on the recession curve on a semi-logarithmic paper is not constant. It varies gradually through the curve due to inflows originating from various storage systems. The recession constant varies seasonally, too (Tallaksen, 1989). It cari be represented by a probability distribution fùnction (Koc and Ozen, 1998). An alternative to the recession constant (K) is the half-life (to.5) which is the time taken by the streamflow to fa11 to half value (Demuth, 1989; Demuth and Schreiber, 1994). The half-life has an advantage of having the dimension of time and hence physical meaning.

Along the recession curve it is assumed that there is no inflow to the basin. The total volume discharged from the basin at the time interval dt is equal to the difference between the basin’s storage volumes at the beginning and at the end of that time interval. Integrating Eq. (2) results in

Qt 4 =-= (3)

where St is water stored in the basin at time t. This is called linear reservoir theory.

At the beginning of the recession the main source of the inflow is surface flow. It reaches to the gauging point fastly. The second source of the inflow is subsurface flow and the last one is ground water flow which arrives to the gauging point in a time of months or years.

The recession curve cari be modelled by different techniques, summarised by Tallaksen (1995) as basic flow equations, linear reservoir models, autoregressive processes, and empirical relations.

James and Thompson (1970) and Singh and Stall (1971) used basic flow equations to define the recession curve of the hydrograph. Kelman (1977, 1980) used the linear reservoir mode1 in his study on modeling of daily intermittent hydrological processes. Kelman (1977, 1980) used two reservoirs instead of one which each corresponds to different flow sources. Another example of this approach is the Tank Mode1 (Sugawara, 1995a,b; Mizumura, 1995) which is based on the linear reservoir theory and includes four serial tanks.

Eq. (2) cari be rewritten as

Q, = W-1 + &t (4)

where E is a normal distributed independent random variable with mean zero and a constant variante. In that case Eq. (4) is a first order autoregressive mode1 (Vogel and Kroll, 1996). The work done by Spolia and Chander (1974) is another example of such kind of an investigation in which relationships between recession curve parameters and parameters of the ARMA mode1 were used.

Empirical relations are the most commonly used way. For example, Radczuk and Szarka (1989) and Clausen (1992) used the exponential recession equation in the form of

Q, = (Q~ -~&-a[ +Qb

45

(5)

__~ ._- cL_---._---. _ _ --

for data from Poland and Denmark, respectively. Also Kupczyk and Kasprzyk (1997) used this approach. Here Qb is the minimum flow of the river. In most cases the minimum flow takes different values for each year (WMO, 1994). Kupczyk et al. (1998) used Eq. (1) in the double exponential form of

Q, = Q, exp(-mt”) (6)

where Qo is the discharge at startiag point of base flow, t is time and m and n are constants.

Sargent (1979) gave an approach splitting the recession curve into two stages. The Upper and lower recessions are respectively assumed to take forms of

Qt = QC (7)

Q, = Qieb+ct’ (8)

where t is time from the start of the Upper recession, t* is the time from the start of the lower recession, Qo is the preceeding peak flow, Qo* is the initial flow in the exponential portion of the recession (lower recession), a, b and c are recession parameters. An arbitrary procedure is adopted. The ratio QJQti is calculated for pairs of succesive days. While this ratio is less than 0.9 surface runoff occurs and the Upper recession form is used, else the lower recession form is used. An approach splitting the recession curve as in the work by Sargent (1979) into two stages was given by Aksoy (1998a,b,c). Observed monthly mean flow is used for splitting the curve into the Upper and lower parts. Both parts are calculated by the exponential recession (Eq. 1) with different coefficients determined from observed recession curves for each month. Kavvas and Delleur (1984) stated that the recession curve parameters depend both on flow and time. In that case the number of parameters to define the recession curve increases dramatically.

Streamflow recessions are greatly affected by transpiration. Elimination of transpiration changed the rate of recession from a rapid decline to the slow recession. Rapid recession occurs when transpiration removes soi1 water that would otherwise drain and become streamflow (Federer, 1973).

Instead of the linear reservoir theory, the non-linear reservoir theory cari also be used. Some examples were given by Wittenberg (1994, 1997, 1998) Wittenberg and Rhode (1997) Gottschalk et al. (1997) and Wittenberg and Sivapalan (1998). In the case of non-linear reservoir theory Eq. (3) takes the form of

The coefficients of d and e are estimated by a non-linear regression or an iterative curve fïtting method which is resulted for most of the applications in e=0.4.

In order to computerise the recession curve analysis some softwares were developed. For instance, Schwarze et al. (1989) developed the DIFGA and Strzalkowski and Sztechman (1996) developed the RCA. The exponential recession equation was used in both softwares.

46

MASTER RECESSION CURVE

Given a number of hydrographs cari be combined to give a master recession curve. A master recession curve cari be obtained by simply averaging many of recession curves. Different techniques are used to obtain the master recession curve of the basin.

The cor-relation method is based on the plotted logarithms of flow values [log Qt] against [log Qt+N] some fixed time N later. The slope of the straight line indicated by data corresponds to the recession constant of the basin. The matching strip method is based on the simple exponential mode1 (Eq. 1). The plots of logarithms of the flows against time result in a straight line. The slope of the line gives the recession constant. Observed individual recession curves are plotted on the same graph, the recessions are then superimposed and adjusted horizontally. A mean line through the set of individual lines represents the master recession curve (Nathan and McMahon, 1990). A composite recession curve cari be similarly developed by piecing together sections of individual recessions. Demuth (1989) and Gustard et al. (1989) gave a modified method for development of the master recession curve of the basin.

Data used for development of a master recession curve should be carefully selected, else the points Will scatter widely and Will be diffkult to construct a master recession curve (Linsley et al., 1949). Since development of master recession curve of the basin is of significant subjectivity it should be caret3 in the development of the curve. Nathan and McMahon (1990) concluded that the cor-relation method was less subjective than the matching strip method.

BASE FLOW SEPARATION TECHNIQUES

Separation of Flow into Two Components

Separation of flow into direct flow and base flow is enough in most of the engineering practices. Direct flow is known as the total of surface flow and subsurface flow. Graphical separation techniques are extensively used. In Figure 2, adapted from Chow et al. (1988), some techniques used in separating flow into direct flow and baseflow, are given.

’ FLOW I

TIME Figure 2. Graphical flow separation techniques

47

In the straight line method (line 1 in Fig. 2), a horizontal line is drawn from the beginning of the ascension curve of the hydrograph to the intersection with the recession limb. This is applicable to ephemeral streams.

In the fixed base method (line 2 in Fig. 2), the surface runoff cari be assumed to end a fïxed time N after the hydrograph peak. A line is obtained by projecting the base flow before the beginning of surface runoff ahead to the time of the peak. This line is connected to the point on the recession limb at the time Iv afier the peak.

Another method is variable slope method (line 3 in Fig. 3). A line is obtained by extrapolating the base flow curve of the previous hydrograph forward to the time of the peak discharge. A second line is obtained by extrapolating the base flow of the current hydrograph backward to the inflection point on the recession curve. By connecting the end points of the lines direct flow and base flow are separated. Another simple separation technique is to connect the beginning of the ascension curve of the hydrograph to the point on the recession curve at time N afier the peak (line 4 in Fig. 2).

Also analytical methods were developed to separate base flow from the total flow hydrograph. For instance, Nathan and McMahon (1990) compared two automated methods (the smoothed minima and recursive digital filter) to separate base flow. Use of the digital filter with the parameter set to 0.925 was found to be a fast and objective method of continuous base flow separation. Another attempt which is based on the exponential recession equation was made by Owoade and Bako (1989). A series of recession constants are calculated by regressing the logarithms of flow on time by succesively deleting the flow nearest the peak of hydrograph. Progressively higher values of recession constant are obtained as the number of time units deleted increases, and the constant stabilizes thereafter. The day on which the constant stabilizes is taken as the beginning of base flow. Szilagyi and Parlange (1998) gave a base flow separation technique based on analytical solutions of Boussinesq’s equation. The technique reduces some of subjectivities associated with base flow separation processes.

Separation of Flow into Three Components

The procedure adapted from Bayazit et al. (1997) and illustrated in Fig. 3 where the hydrograph was plotted on a semi-logarithmic paper is used to separate the flow into three components, surface flow, subsurface flow and base flow. The base flow recession is approximated by a straight line and is extended backward. The difference between the total flow value and the value on the extended line represents the combined surface and subsurface flow. The combined flow is plotted on the semilogarithmic paper and a straight line extended backward is fitted to the subsurface flow recession.

48

10000

1000

-TOTAL FLOW

i--~/ 4 ---.-SUBSLRFACEFLOW

-Sl!BFACEFXOW

Figure 3. Separation of Flow into Three Components

Separation of a Complex Hydrograph

It is easy to separate the flow into direct flow and base flow in a simple hydrograph. In most cases the hydrograph is not of a simple case. It becomes a complex hydrograph with two or more peaks. It is ver-y diffrcult to separate the flow into its components in that case. However, in literature some graphical separation techniques were developed (Linsley et ai., 1949).

BASE FLOW INDEX

A number of studies have highlighted the importance of the base flow index (BFI) when the automatically calculation have been able. A procedure for calculating the BF1 is described in details in Gustard et al. (1989). The BF1 was originally related to the geology of cathcment area and was applied for soi1 classification and geological regionalisation.

Having in mind the definitions mentioned above, the BF1 over some period of time At=tz-ti cari be presented as a proportion of the volume of Base Flow and the total observed volume of flow with the following expression:

BFI = t’t2

J- Q(t) d 11

(10)

where At could be n consequence days (5, 10, 30, 150,... ,365), month, some season, year or more.

49

The monthly annual BF1 could be calculated by two alternative methods. The first is to compute BF1 for each year and then to average for a11 the period. The second is to work with a11 the period. For the territories with a moisture defïcit the first is preferred because of possibility to analyse the BF1 variability. The choice of period depends on the aim of the further investigations and on the character of low flow. The scope and potentialities of utilisation of the BF1 depend on the physicogeographical peculiarities of the region determining the river flow regime. When At is a year or more, the BF1 could be used as a criterion for the wetness of the year in the regions with the enough humidity.

In the Northern Europe countries, the relationship between annual BF1 and annual runoff was obtained through linear regression. The results suggest that the years of extreme drought may produce higher than average BFI. The utilisation of BF1 as a such criterion in the countries of the region with insufficient humidity (like Bulgaria and Turkey, for instance) is impossible because of the different conditions of genesis of the runoff here. The river streamflow is generated from the floods and snowmelt in the framework of the year cycle, which is between 60 and 80% from the annual flow. SO, the value of BF1 is under 0.5 in natural conditions of genesis of flow for a long time period. If BF1 is over 0.5 this manifests an additional subsurface supply of the river, caused from carst or in the majority cases from human activities. As an example, the river Iskar, at the gauging station situated closely under the reservoir Iskar has a BFI=0.726, at the downstream of the gauging station Kounino, has a BFI=O.620 and at the outfall near to the village Oriachovo, has a BFI=0.638. The increase value on the last site is a result both of the infiltration from the irrigation field placed between the last two stations and of the growing of the banks storage in the lower reach of Iskar river. When At is month or season ie. in the framework of the year cycle, BF1 varies on a large scale from a negligible values for the humid months to BFI=l for the summer months in the dry years. At that time the base flow and the low flow have the same value and the surface river supply is tut off practically. The row constituted from BF1 values of the summer months or the summer season could be treated as a random fùnction which is characterised in a defïnite cross-sections.

Although the BF1 is a dimensionless value, it couldn’t be suitable for regionalisation and regional estimation at least over the territories with insufficient humidity and it is influenced from human activities, because it is related to the surface flow. What it is concern the quantitative assessments with practical direction like these ones in Dakova (1998) the more confidential results gives the utilisation directly base flow values. In this case the generalisations would be performed on the reaches or on a small part from the river catchment area with similar conditions.

CONCLUSIONS

As stated in the main body of the paper recession curve analyses plays an important role in hydrological applications. Therefore it is a widely interested area of investigation which goes back to Boussinesq’s work more than one hundred years ago. Through this study the followings were found important to be pointed out:

The investigation of recession curve was extensively done by the classical exponential recession equation which is based on the linear reservoir theory although in fact the structure of the recession is non-linear. Therefore the non-linear investigation approaches, recently

50

observed in literature should be developed. The recession curve cari be investigated as a time series process and the AR, MA or ARMA type models cari be developed. The recession curve cari also be analyzed in a statistical manner. Its seasonal variation cari be determined. A possible probability distribution fùnction cari be Iïtted to the recession coefficients although the recession curve is deterministic rather than to be probabilistic.

It was found that computer softwares using the exponential decay fùnction were recently started to be used for investigation of the recession curve of the basin. Master recession curve for which various techniques were developed is still of significant subjectivity. Also base flow separation from the total flow hydrograph is still of subjectivity although some automated attempts were recently observed. The graphical separation techniques are still more preferable than the recently developed analytical ones.

REFERENCES

Aksoy, H. (1998a) Determination of Recession Curve Parameters. In Proceedings of Low Flows Expert Meeting, ed. by V. Vukmirovic, Z. Radie, A. Buly The University of Belgrade, 10-12 June 1998, Belgrade, Yugoslavia, 8 l-88.

Aksoy, H. (1998b) Modeling of Daily Flows of Intermittent Streams. Ph.D. Thesis, Istanbul Technical University, Institute of Science and Technology, Istanbul (in Turkish with English summaty).

Aksoy, H. (1998c) Relation Between Recession Coefficient and Flow. International Scientific Conference on Stochastic Models of Hydrological Processes and their Applications to Problems of Environmental Preservation (SM&EP), 23-27 November 1998, Moscow, Russia (accepted).

Barnes, B.S. (1939) The Structure of Discharge-Recession Curves. Trans. Am. Geophys. Union, 20, 721-725.

Bayazit, M., Avci, L, Sen, Z. (1997) Manual ofHydrology. Fourth Edition, Istanbul Technical University Press Office, Istanbul (in Turkish).

Chow, V.T., Maidment, D.R, Mays, L.W. (1988) Applied Hydrology. McGraw-Hi11 Book Company, New York.

Clausen, B. (1992) Modelling Streamllow Recession in Two Danish Streams. Nordic Hydrology, 23,73-88.

Dakova, S. (1998) Some Considemtions of Base Flow. Low Flows Expert Meeting, The University of Belgrade, 10-12 June 1998, Belgrade, Yugoslavia.

Demuth, S. (1989) The Application of The West German IHP Recommendations for The Analysis of Data From Small Research Basins. In FRIENDS in Hydrologv, ed. by L. Roald, K. Nordseth, K.A. Hassel, IAHS Publication No. 187, pp. 47-60.

Demuth, S., Schreiber, P. (1994) Studying Storage Behaviour Using an Operational Recession Method. In FRIEND: Flow Regimes from International Experimental and Network Data, ed. by P. Seuna A. Gustard, N. W. Ame11 and G.A. Cole, IAHS Publication No. 221, 5 l-59.

Federer, C.A. (1973) Forest Transpiration Greatly Speeds Streamflow Recession. Water Resour. Res., 9(6), 1599-1604.

Frohlich, K., Frtihlich, W., Wittenherg, H. (1994) Determination of Groundwater Recharge by Baseflow Separation: Regional Analysis in Northeast China. In FRIEND: Flow Regimes from International Ehperimental and Network Data, ed. by P. Seuna, A. Gustard, N.W. Ame11 and G.A. Cole, IAHS Publication No. 221,69-75.

Gottschalk, L., Tallaksen, L.M., Penyna, G. (1997) Derivation of Low Flow Distribution Functions Using Recession Curves. J. Hydrol., 194, 239-262.Gustard, A., Roald, L.A., Demuth, S., Lumadjeng, H.S., Gross, R. (1989) Flow Regimes from Experimental and Network Data (FRIEND), Volume 1, Hydrological Studies,

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Institute of Hydrology, Wallingford. Hall, F.R. (1968) Base Flow Recessions-A Review. Water Resour. Res.. 4(5), 973-983.

James, L.D., Thompson, W.O. (1970) Least Squares Estimation of Constants in a Linear Recession Model. Water Resour. Res., 6(4), 1062-1069.

Kawas, M.L., Delleur, J.W. (1984) A Statistical Analysis of the Daily Streamflow Hydrograph. J. Hydrol., 71, 253-275.

Kelman, J. (1977) Stochastic Modeling of Hydrologie, Intermittent Daily Processes. Hydrology Paper, 89, Colorado State Univers@, Fort Collins, Colorado.

Kelman, J. (1980) A Stochastic Mode1 for Daily Streamflow. J. Hydrol., 47, 235-249.

Koc, GC., Ozen, B. (1998) Determination of the River Feeding Characteristics with Statistical Analysis of the Recession Curve Parameters, Upper Ceyhan Basin Example. In Proceedings of Second National Hydrology Congress, Istanbul Technical University, 22-24 June 1998, Istanbul, 150-154 (in Turkish with an English abstract).

Kupczyk, E., Kaspnyk, A. (1997) Research Catchments Sensitivity to Athmospheric Drought. In LOC Proceedings of Poster Presentations, FRIEND ‘97, 3 ‘rd International Conference on FRIEND, Regional Hydrology: Concepts and Models for Sustainable Water Resources Management, ed. by M. Brilly and A. Gustard l-4 October 1997, Postojna, Slovenia, 41-46.

Kupczyk, E., Kasprzyk, A., Sztechman, J., Stnalkowski, K. (1998) Application of Spline Function Method to Streamflow Recession Curve Analysis. In Proceedings of Low Flows Expert Meeting, ed. by V. Vukmirovic, Z. Radie, A. Bulu, The University of Belgrade, 10-12 June 1998, Belgrade, Yugoslavia, 71-80.

Linsley, RK., Kohler, M.A., Paulhus, J.L.H. (1949) Applied Hydrologv. McGraw-Hi11 Book Company, Inc., New York.

Mizumura, K. (1995) Runoff Prediction by Simple Tank Mode1 Using Recession Curves. J Hydraulic Engineering, ASCE, 121(11), 812-818.

Nathan, RJ., McMahon, T.A. (1990) Evaluation of Automated Techniques for Base Flow and Recession Analyses. Water Resour. Rex, 26(7), 1465-1473.

Owoade, A., Bako, MD. (1989) Riverflow Prediction During Baseflow Recession on Some British Hard Rock Catchments. In FRIENDS in Hydrology, ed. by L. Roald, K. Nordseth, K.A. Hassel, IAHS Publication No. 187. pp. 61-65.

Radczuk, L., Szarska, 0. (1989) Use of the Flow Recession Curve for the Estimation of Conditions of River Supply by Underground Water. In FRIENDS in Hydrology, ed. by L. Roald, K. Nordseth, K.A. Hassel, IAHS Publication No. 187, pp. 67-74.

Sargent, DM (1979) A Simplified Mode1 for the Generation of Daily Streamflows. Hydrological Sciences Bulletin, 24(4), 509-527.

Schwarze, R, Grünewald, U., Becker, A., Friihlich, W. (1989) Computer-Aided Analyses of Flow Recessions and Coupled Basin Water Balance Investigations. In FRZENDS in Hydrology, ed. by L. Roald, K. Nordseth, K.A. Hassel, IAHS Publication No. 187, pp. 75-83.

Singh, K.P. (1968) Some Factors A@ecting Baseflow. Water Resour. Res., 4(5), 985-999.

Singh, K.P. (1969) Theoretical Baseflow Curves. J. Hydraulics Division, ASCE, 95(HY6), 2029-2048.

Singh, K.P., Stall, J.P. (1971) Derivation of Base Flow Recession Curves and Parameters. Water Resour. Rex, 7(2), 292-303.

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Spolia, S.K., Chander, S. (1974) Modelling of Surface Runoff Systems by an ARMA Model. J. Nydrol., 22, 3 17-332.

Strzalkowski, K., Sztechman, J. (1996) Recession Curve Analyses in Sections, The RCS Program-User’s Guide. Technical University in Kielce, Poland.

Sugawara, M. (1995a) Tank Model. Chapter 6 in Computer Models of Watershed Hydrology. ed. by V.P. Sir@. Water Resources Publications, Littleton, Colorado.

Sugawara, M. (1995b) The Development of A Hydrological Model-Tank. C%apter 7 in Time and the River, ed. by G. W. Kite, Water Resources Publications, Colorado.

Szilagyi, J., Par-lange, M.B. (1998) Baseflow Separation Based on Analytical Solutions of the Boussinesq Equation. J Hydrology. 204, 251-260.

Tallaksen, L. (1989) Analysis of Time Variability in Recessions. In FRIENDS in Hydrologv. ed. by L. Roald. K. Nordseth, K.A. Hassel, IAHS Publication No. 187, pp. 85-96.

Tallaksen, L.M. (1991) Recession Rate and Variability with Special Emphasis upon the Influence of Evapotranspiration. Thesis submitted to tbe Department of Geography in Partial Fultïllment of the Requirements for the Degree Doctor Scientiarum, University of Oslo, Oslo, Norway.Tallaksen, L.M. (1995) A Review of Baseflow Recession Analysis. J. Hydrol., 165, 349-370.

Vogel, RM., Kroll, C.N. (1996) Estimation of Baseflow Recession Constant. Water Resources Management, 10, 303-320.

Wittenberg, H. (1994) Nonlinear Analysis of Flow Recession Curves. In FRIEND: Flow Regimesfrom International Experimental and Network Data, ed. by P. Seuna, A. Gustard, N.W. Ame11 and G.A. Cole, IAHS Publication No. 221, pp. 61-67.

Wittenberg, H. (1997) Regionalization of Nonlinear Storage. Discharge and Recharge of Groundwater. Landschaftsokologie und Umwelrforschung, Heft 25. 343-346.

Wittenberg, H. (1998) Baseflow Recession and Recharge as Nonlinear Storage Processes. Hydrological Processes, (accepted for publication).

Wittenberg, H., Rhode, C. (1997) Impact of Groundwater Abstractions on Storage and Baseflow in the Ilmenau Basin, Lueneburg Heatb, Germany. Landschaftsokologie und Umweltforschung, Heft 25, 347-350.

Wittenberg, H., Sivapalan, M. (1998) Watershed Groundwater Balance Estimation Using Streamtlow Recession Analysis and Baseflow Separation, Submitted to J. Hydrology.

WORLD METEOROLOGICAL ORGANIZATION (1994) Guide to Hydrofogical Practices, Fifth Edition, WMO-No. 168.

53

EXPERIENCES IN REGIONALISING Q95 IN SWITZERLAND

Hugo Aschwanden Swiss National I+drological and Geological Survey (SNHGS) CH-3003 Berne

ABSTRACT In recent years the interest for low flows analysis and regionalisation in Switzerland has grown up due to the urgent need for the longterm 95%-percentile of daily discharges (Q95) in connection with the Water Protection Law. The esperience SO far concems thi discharge value derived from the longterm duration curve. The investigations show that a regionalisation is feasible as long as the approach is general and at an overvieu, scale. As soon as going into details conceming time and space the low flow processes must be taken into account. The mentioning of Q95 in the above mentioned law as a basis for the determination of residual flows had the negative effect that for a very long time low flow studies were focussed on this discharge value. Nevertheless the studies carried out bave clearly shown that on the one hand there is still a lack in the comprehension of lou flou processes and that on the other hand the data base for further research in this field is too small. Therefore the Swiss National Hydrological and Geological Survey (SNHGS) will invest into further projects on low flows. The fïrst aims at a systematical and extense low flow statistics, the second at the elaboration of a methodologp to assess and quant@ the human impacts on river systems. The status of knowledge and an outlook to this newer projects is given.

INTRODUCTION

In alpine areas floods are - apart from other natural disasters - a matter of great concern for the population. It may therefore not be surprising that hydrological research in Switzerland has a long-standing tradition in dealing with components of the water balance and questions of flood processes and -protection in particular. At present, however, the situation is different. Both the growing population and increasing energy consumption are compelling for an optimal use of the water resources, a fact that is opposed by those who demand an ecologically justifiable harnessing of the water supply. Impending fear of a possible climate change put the emphasis of research to the topic low flow aRer all, even in an alpine country such as Switzerland. Up till now only one fïeld was predominant: the optimisation of procedures to estimate the 95%-percentile of daily discharges (Q95) at sites without direct measurement.

REGIONALISATION OF THE LONGTERM 95%-PERCENTILE OF DAYLY DISCHARGES (Q95)

Background

As provided for by the Water Protection Law a minimal residual flow below water intakes has to be guaranteed. Determination of this residua! flow is dependent on the discharge Q95 defined in the law as follows: The rate of.flow which, averaged over ten years, is reached or exceeded OH an average of 347 days per year and which is HO~ substantially affected by damming, withdrawal or supply of water. This definition implies that discharge Q95 has to be derived from measurements and calculated from the longterm duration curve. However dense

55

measuring networks may be, daily practice has often proved inaccurate knowledge of flow conditions for sites where hydraulic structures are planned or for river sections where residual flow has to be determined. The law bears this point equally in mind: In cczs~s where data.for any body of water are insufficient, the rate Q95 shall be evaluated by other methods such as hydrological observations or mathematical models. By legislation it is the Swiss National Hydrological and Geological Survey (SNHGS) that is not only responsible for the measurements, but also for the publishing of respective guidelines. The SNHGS acts as an advisory service for different bodies within the federal and the cantonal administrations, the public, the research and private companies as well. In the framework of these tasks the SNHGS has gained a certain experience in regionalisation of low flows during the last years.

Regionalisation

There are different aspects of regionalisation. In the following a definition is given how the SNHGS understands and uses the term ,,regionalisation“. It means the transjër of hydrological data or the application of models in areas, where they could not be calibrated due to the lack of data. This transfer is mostly done by means of the physiographic characteristics of the catchments.

Hydrological aspects

Spatial variability: Discharge processes are controlled by climatic and physiographic characteristics. According to the regional variety of a country the discharge development has to be considered in a differentiated way in SO far as both extent and duration of low flows are absolutely different for alpine and midland areas, the Jura or lower regions south of the Alps. This is due to different processes of discharge: In the alpine region winter precipitation is stored by surface retention as ice and snow. Minor discharge occurs during this period. Extent and duration of the low flow period are controlled by radiation and temperature as climatic factors, and by slope, exposition and altitude as physiographic basin characteristics. Subsoil storage marks low flows in the midland area and the Jura. Depending on the water supply (precipitation or snowmelt) the reservoirs are in the main filled up in winter and spring. Low flows occur when the reservoirs empty, a process that is only interrupted by occasional precipitation events. The difference between the midland area and the Jura is mainly due to complexity of the hydrogeological conditions.

Figure 1: Distribution of the longterm average monthly low flows (lefï. alpine region with glacial regimes. right: midlands with pluvial regime types).

56

In Fig. 1 the extremes are shown: in alpine regions the low flows are concentrated to very few months (decembre to march) whereas in the lower parts of Switzerland low flows cari occur during the whole year with a higher frequency in summertime. The low flow processes depend more or less on the altitude because the storage of water (ice - snow - rocks - groundwater bodies) is different at different elevation levels. Between the alps and the midlands there is a continous transition. The local situation is relevant too. The combination of serveral types of water storage mechanisms and their portion in a catchment make a regionalisation difficult.

Temporal variability: For reason of dry, or wet or cold periods, discharge Q95 is subject to natural fluctuation. The long-term discharge behaviour of an alpine catchment is revealed in Fig. 2. Wet and dry periods occurring regularly are particularly pronounced in the moving averages represented as progression curves. Within the alpine region the relation between maximum and minimum yearly Q95 over a longer observation period attains a maximum value of 4. Corresponding value of 10 for the midland area is significantly higher.

The range of fluctuation in discharge Q95 is neither limited to a certain type of regime nor to a regional unit and is, with reservations, partly explainable by basin characteristics. Generally pronounced is only altitude dependency and this by the fact that the higher a catchment is situated the more moderate the fluctuations are. No relation between glaciation or catchment surface could be distinguished. An interesting fact, however, is the dependency on mean water flow which is in function of an enveloping curve: the more substantial the mean annual discharge the more moderate the fluctuations, yet not vice versa. Small annual discharge and small fluctuations in low flow is typical of another specific kind of catchment

3.6

3.4

3.2

3.0

2.8

2.6

2.4

22

20

1.8

1.6

1.4

1.2

1.0

0.8

0.6

04

02

00

l 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995

Figure 2: Natural fluctuations of low flows: yearly discharge Q95 and moving averages (Lütschine-Gsteig, alpine region)

57

--.. -.

The average fluctuation of discharge Q95 could be defïned as a threshold mark, a term that cari most readily be related to standard deviation (sx). For purposes of’comparison, however, the variation coefficient (c,) defining standard deviation of the mean value: c, = sx CZ 100 / is more suitable. Up to now there isn’t any systematic investigation on the spatial variability of the variation coefficient available. Within the alpine region the variation coefficient tends to range between 10-20 %, in the midland area between 20-40 %

Figure 3: Low pass filtering of yearly Q95 in alpine catchments (left) and the number of days per year with a discharge !ower than the longterm average 095 (right)

Comparing the yearly Q95 of a longer observation period from a set of catc.hments in a strongly generalised form e.g. as low pass filtered values, it cari be easily recognised that common tendencies and variations are observed in wide areas. But looking at details - in Fig. 3 the number of days per year with a discharge lower than the average QS5 - it is remarkable that the corresponding yearly patterns are different from catchment to catchment. This means that a regionalisation in respect to low flows is promising if it restricts to the general and the longterm behavior

Determination of Q95

A few years ago, Swiss National Hydrological and Geological Survey has published guidelines for the estimation of Q95 in alpine regions (Aschwanden, 1992). As input into the statistical approach some simple basin characteristics (mean elevation, relief factor) and climatic parameters (mean annual precipitation and temperature) were used. In spite of this restriction the elaboration of these space related input data was at this time connected to quite an effort. ln the meantime not only the geographic information systems (GIS) developped, but also a range of digital datasets were made available (cf. Tab. 1) Most of them caver the who!e area of Switzerland. Therefore the door was open to restart the projest ,,Regionalisation of Q95“.

Table 1: Nationwide spatial digital datasets for Switzerland (GEOSTAT, 1992).

Climate

Landuse

Geology / Soi1

Digital elevation mode1 Background data

Dataset GWN GWN25 BASIS-98 HUG-CH SEEN RR-JAHR, RR_KORR N-0140 NJA-7292

EVA-7292 TJA 7292 BONU72 BN85 VZ90PT GT-CH BODEN DHM25 TOPOPT PK25...PK50C VECTOR200

Content River network 1:200’000 River network 1:25’000 Small catchments [Swiss Hydrological Atlas] (1:200’000) Representative basins (1:25’000) Lakes1:25’000) Uncorrected mean anmral precipitation 195 l-80 (1000 x 1000 m) Corrected mean annual precipitation 195 l-80 (1000 x 1000 m) Mean annual precipitation 190 l-40 (1000 x 1000 m) Mean animal, summer and winter precipitation 1972-92 (1000 x 1000 m) Mean annual evapotranspiration 1972-92 (1000 x 1000 m) Mean annual temperature 1972-92 (1000 x 1000 m) Landuse statistics 1972 (100 x 100 m) Landuse statistics 1979/85 (100 x 100 m) Residents 1990 (100 x 100 m) Geotechnical map of Switzerland (1:200’000) Soi1 suitability map of Switzerland (1:200‘000) Digital elevation mode1 (25 s 25 m) Digital elevation mode1 (100 x 100’m ) Pixel maps1:25’000 - 1:500’000 Vector map 1:200’000

Owner BWW/L+T BWW/L+T LHG LHG L+T

SMA/LHG SMAIWSL ETHZ

ETHZ ETHZ BFS BFS BFS LHG FAL L+T BFS L+T L+T

Abbreviations: BFS Federal Statistics Office BWW Federal Office for Water Management ETHZ Federal Technical University Zurich FAL Federal Office of Agriculture LHG Swiss National Hydrological and Geological Survey L+T Federal Office for National Survey SMA Swiss Meterological Institute

Most of these datasets were not established with respect to hydrological problems. It was therefore necessary to elaborate first a methodology how to extract hydrologically relevant information from these datasets. A feasibility study characterising the representative basins of the SNHGS was carried out (Aschwanden, 1996). The subsequent study using this methodology (Aschwanden & Kan, 1998a) made then clear that the above mentioned guidelines for the determination of Q95 had to be revised and amended. Today a full range of procedures depending on data and situation of impacts are known, however different in accuracy of evidence. In spite of remarkable improvements in both the modelisation of discharge and the capture of more precise data the modelling of hydrological extreme values remains problematic. Neither mode1 nor estimation method meets the accuracy of correctly performed measurements. Methods based directly on measured values are therefore superior to those transferring measured values from downstream or adjacent gauging stations, or to those transferring estimations based on climatic and physiographic basin characteristics. The SNHGS has - in coordination with the Federal Office for Environment, Forest and Landscape - thus realised new guidelines for the determination of discharge Q95 and for an evaluation of the different procedures, indicating the following order (Aschwanden & Kart, 1998b):

1. Evaluation of measurement series over a sufficient period (greater thanl0 years) 2. Evaluation of measurement series of limited duration and their extrapolation into a longer

time-period 3 Implementation of estimations and subsequent check based on short-term measurements

59

._-

(a) Implementation of measurement campains (b) Use of measured values of downstream stations (c) Definition of regional mean values (d) Statistical procedures: estimations based on climatic and physiographic basin

characteristics.

The order of the procedures shows that the emphasis is on the use of measured data, longterm or shortterm observations or even measurement campains. Despite improved methods and the use of GIS technologies the general impression of statistical approaches remains ambivalent. Even though the results are of acceptable accuracy on average, maximum deviation is still very large. The new estimation method is due to calculate discharge Q95 by means of climatic and physiographic characteristics based on statistical correlation between flow rate and the catchment features. The resulting regionalisation is presented in Fig. 4. Yet the interpretation of the regions has to be done caretùlly. What cornes out as regions or zones are not areas with a homogenous hydrological behaviour in respect to low flows, but areas where the same set of parameters and variables are used to estimate Q95. The regions were built with a stepwise procedure for optimising the regression tünctions over the whole country

The amounts of discharge Q95 emanating from estimation methods have to be considered critically and checked carefùlly. Plausibility of the estimates, for example, cari be compared with outcomes from catchments of the similar regime type. Because statistical approaches are based on water balance aspects, the local features (hydrogeology, geology) have to be given particular attention. The calculated estimate must equally meet the check with short-term measurements from at least 3 years.

- Figure 4: Regionalisation of Switzerland with respect to low flows: regions with the same set of parameters and variables to estimate Q95.

60

- - . - - - I I _ , . - . .l..“l-.ll--llll.l . . . “ - - . - - _.

The map ,,Basic elements for the estimation of Q95“

Although statistical approaches to determine discharge Q95 worked out over recent years permit estimation for any location in Switzerland questions on accuracy and practicability are still ignited. Problems, for instance, are faced within the fïelds of the spatial compatibility of estimation formulas, the delimitation of low flow regions, the availability of input data for immediate use. The estimation methods mentioned before are founded on climatic and physiographic basin characteristics. Although these data caver a11 Switzerland, their supply for a specific catchment is not manageable without Geographical Information Systems (GIS). It’s for this reason that the Swiss National Hydrological and Geological Survey in coordination with the Federal Office for the Environment, Forestry and the Landscape decided on a synthetic map usable for practice to present the current status of knowledge on discharge Q95. TO resume the results by way of a map means an advantage in many ways: Not only does it fit an accuracy actually obtainable but helps to combine results of different study and is suitable for integration of measuring data from hydrometric networks.

i

X-COORD = Y-COORD = SURFACE MEAN-ALTITUDE 1 MIN-ALTITUDE = MAX-ALTITUDE = RELIEF-FACTOR = PLAINS = NORTH-EXP = STEEP-SLOPE = MEAN-Y-TEMP = WI-SEASJEMP = TEMP-STAT TEMP-STAT-NO 1 TEMP-STAT-ALT = TEMP-STAT-DIST = MEAN-PRECIP = SUMMER-PRECIP = WINT-PRECIP = QUO-SUM-WIN = A-GLACIER = A-INT-AGRIC = AALP-AGRIC = A-SETTLEMENT = SOILWET SOIL-ST-MEDIUM: SOIL-PER-POOR = GT-SANDSILT =

606256 m 146745 m 28.752 km* 1852 m 1312m 2692 m 1382 m 1.0 % 33.8 % 4.5 96 1.800 “C -2.72 “C Adelboden 5270 1325 m 3879 m 1727 mm 923 mm 804 mm 1.330 0% 0.0 % 38.1 % 0.8 % 17.0 % 27.5 96 3.5 % 47 6 %

GT-KIESSAND = 0.6 % GTISILTTON = 0.0% Mode1 A) REGIO-GIUB Q347S-GIUB Q347 GIUB Mode/ 8) REGIO-LHG NQ-TYPE Q-Y QS-Y PC-MIN Q-MIN QS-MIN Q347-LHG QS347 LHG

= 5 = 8.26 Vs km’ = 237 Ils

= 1 = 9 = 1104mm = 38.4 Ils km2 = 0.208 = 230 Vs = 8.0 I/s km2 = 171 Vs = 5.9 Ils km’

Figure 5: Extract from the map ,,Basic elements for the estimation of Q95” completed with a calculation for a basin under investigation (QS5 as l/sec; measured data indicated by different triangles, modelled values by spots).

61

The map represents both the lead-in to the assessment of discharge Q95 and the concept appropriate for a rough estimate of many river sections of concern. The map is a synthesis of measuring sites and spots in the hydrometric network which have been subject to Q95 estimation by means of statistical approaches. Thus discharge Q95 detïned at measuring sites as well as calculated for mode1 spots is represented in the map. TO obtain a more consistent description the Q95 values calculated were rounded according to specifïc rules and correlated with the measuring sites considered which are though a crucial element of the map. The representation comprises measuring sites for which discharge Q95 based on at least 3 years of measurement cari be calculated and where streamflow is not signifïcantly influenced. For purposes of comparison values measured during the period of 1983 - 1993 are particularly emphasised. By numerical order measuring sites and mode1 spots are referred to in a table which contains a11 information essential for a useful interpolation between the points determined.

A GIS application to determine Q95

One of the diffculties in applying the above mentioned and described procedure cornes from the fact that the necessary mode1 input data are complex and that their elaboration without the use of a GIS cari hardly be put into practice. The SNHGS has therefore developed a GIS- application on the basis of the ARCDNFO macro language, which supports the user as far as possible. Starting from a pair of coordinates and a search radius as only input values the delimitation of the catchment by means of a digital elevation mode1 is first automatically carried out. The catchment under investigation is then presented at the screen together with a pixel map. This allows the user to modify the delimitations. In the next step the mode1 inputs as well as the calculation of discharge Q95 are provided. Apart from a compilation in table form, the program plots an extract from the map ,,Basic elements for the estimation of Q95“, completed with both the catchment and intermediate and final results of the calculations (cf. Fig. 5). The expertise of the hydrologist starts at this point: he has to evaluate the calculated Q95 and to interprete it regarding a wider area.

OUTLOOK

The mentioning of Q95 in the Swiss Water Protection Law had the effect that for a very long time low flow studies were focussed on one discharge value derived from the duration curve. Investigations carried out clearly show that on the one hand there is a lack in the comprehension of low flow processes and that on the other hand the data base for further research in this field is too small. Therefore the SNHGS decided to invest into further projects on low flows (Aschwanden & Kan, 1998b). The fïrst aims at a systematical low flow statistics, the second at the elaboration of a methodology to assess and quantify the human impacts on river systems.

Low flow statistics of Switzerland

The project’s objective is the realisation of an extensive low flow statistics for Switzerland. Conceptual work on the project was started in 1997. In a current pilot approach few long- standing measurement series are evaluated according to methods generally known until recently to ensure suficient data information for conceptualising the final extent of the statistics and probable complementary work. The selected measurement series caver different

62

discharge regimes, such as glacial, nival, pluvial, and different regions - the Alps, Midland, Jura, southern parts of the Alps - as well as two examples under anthropogenic influence, In this way it Will be possible to infer whether current statistics are likely to make inhomogeneity and inconsistency of data visible. The following units Will be incorporated into the low flow statistics: Low flow characteristics according to DVWK (1983, 1992), supporting points of the duration curve (Q50, Q75, Q90, Q95, NQ) and parameters of the recession curve. While precipitation and temperature data are equally included in the pilot approach a correlation analysis is due to reveal whether the low flow statistics should as well consider climatic variables.

Elaboration of a methodology to assess and quantify the human impacts on river systems

Humans and their activity are influencing river systems in various ways. Many questions in the fïelds of hydrology, water management and conservation require a sound knowledge of the impacts on the water cycle and their effects on rivers. Adequate typology on the influences and a methodology to assess, record and quantify human impacts for any catchment are unfortunately still missing. Low flow is most sensitive to impacts on the river, In connection with the project ,,Low flow statistics“ described above as well as in view of its measuring networks the Swiss National Hydrological and Geological Survey is strongly motivated in developing such methodology. It is for this reason that this body strives to start the project ,,Assessment and quantification of human inpacts on river systems“ in coordination with the Federal Office for the Environment, Forestry and the Landscape. Results are due not only to evaluate the present measuring networks in view to human impacts but to relate the characteristics identifïed from the low flow statistics to the degree of impacts.

CONCLUSION

Switzerland has no long-standing tradition in low flow analysis and regionalisation. The only experience concerns the discharge Q95 derived from the longterm duration curve. The investigations show that that a regionalisation of low flows is possible as long as the approach is general and at an overview scale. As soon as going into details concerning time and space the low flow processes must be taken into account. However the presented projects, and low flow statistics in particular, permit to establish a sophisticated nationwide database suitable for increased perception of low flow processes and for application in discharge modelling. Methodology in quantifying human impacts on river systems Will clear the ground to a new understanding not only in the field of low flow but in many questions on water balance.

LITERATURE

Aschwanden H., Kan C. (1998a): Die Abflussmenge 4347 - eine Standortbestimmung. Hydrologische Mitteilungen der Landeshydrologie und -geologie , Nr. 27, in preparation, Berne.

Aschwanden H., Kart C. (1998b): Status of low flow analysis in Switzerland. FIUEND - Low flows expert meeting, 10-12 june 1998, BelgradeMJ, Faculty of Civil Engineering, University of Belgrade,

Aschwanden, H. (1992): Die Niedrigwasserabflussmenge 4347 - Bestimmung und Abschatzung in alpinen schweizerischen Einzugsgebieten. . Hydrologische Mitteilungen der Landeshydrologie und -geologie . Nr. 18, Berne.

63

Aschwanden, H. (1996): Einzugsgebietskenngrossen der hydrologischen Untersuchungsgebiete der Schweiz. Hydrologische Mitteilungen der Landeshydrologie und -geologie , Nr. 23, Bem

DVWK: Niedrigwasseranalyse. Teil 1: Statistische Untersuchung des Niedrigwasser-Abflusses, DVWK-Regeln 120/1983 und Teil II: Statistische Untersuchung der Unterschreitungsdauer und des Abflussdefizits. DWK-Regeln 121, 1992. Verlag Paul Parey, Hamburg.

GEOSTAT (1992): Benutzerhandbuch. Bundesamt für Statistik, Bem. Landeshydrologie und -geologie (1999): Niedrigwasserstatistik der Schweiz. Hydrologische Mitteilungen,

Landeshydrologie und -geologie, in preparation, Berne. Swiss National Hydrological and Geological Survey (1992, 1995, 1997): Hydrological Atlas of Switzerland.

EDMZ, Berne. *

64

REGIONAL ANALYSIS OF LOW FLOWS IN GEDIZ AND B. MENDERES RIVER BASINS

M. BAYAZIT, B. ONOZ, B. OGUZ Istanbul Technical University, Faculty of Civil Engineering

ABSTRACT

The subject of this study is regional low flow analysis which has significance in water ressources engineering. With this purpose 7-day non-zero annual minimum flows of 11 stations in two neighbouring basins in Western Turkey are analyzed. As the result of simple scaling investigation and discordancy analysis, the two basins cari be considered as a single region and a unified probability distribution function cari be accepted for minimum flows. For this unified distribution, power distribution, which is a physically based distribution, is accepted. Power distribution is applied using regional LL-moments (Lm,m=O, 1,2,3,4) giving weight to the lower tail. Regional power distribution is compared to Weibull 2 and lognormal 2 distributions graphically. For the goodness-of-fit of regional power distribution probability plot correlation coefficient test is applied and the best-fit is obtained for m=l case.

Introduction

Recently analysis of low flows has gained importance related to water ressources management. Low flow analysis is used for determining the amount of downstream release of reservoirs with energy, irrigation, water supply purposes and that of cooling-plants. Low flows of a river are expressed as the annual minimum average of d-day (d=l, 3, 7, 10, 15, 30,. ,) flows. In order to make an estimate for the d-day minimum flow (a random variable), corresponding to a certain return period (T=5, 10, 15, 20, years), the pdf of this variable must be known. This pdf must especially fit well to the observations of the lower tail. In this study the objective is to make a regioanl low flow analysis in Gediz and B. Menderes river basins in Turkey (Fig. 1).

Regional Analysis

The 7-day annual minimum flows at 6 stations in Gediz basin and 5 stations in B. Menderes basin with a record period of 14-57 years are used (Table 1). These stations are chosen SO that there are no zero 7-day minimum flows. In the region mk, k = 1, 2, 3, 4 statistical moments and qp(p = 0.10, 0.15, 0.20, 0.25) quantiles are determined at each station. Simple scaling investigation is made between the logarithms of these parameters and the logarithms of the catchment areas of each station. The results are given in Table 2 from which it is seen that in the relations of mk values with area, simple scaling is valid, i.e. as ck increases the power of A also increases as ck (mk-AO.gk), similarly, when the relations of quantiles with areas are investigated, the power of A remains almost constant (qp-Ao,‘).

65

-- --

Table 2. Statistical moments and quantiles are directly proportional to the given powers of basin area

ml

m2

m3

m4

Statistical mc A”.%,

Al.84

272 A

A3.60

lents

R=O.69

qo.10

qo.15

qo.20

qo.25

Quantile S

AO.

~0.87

R=O.57-0.62

When dealing with the data of a group of sites coming fiom a large geographical area a discordancy analysis cari be performed to flag as discordant the sites of which the data stand out f?om the other sites. Di is a standard discordancy measure for multivariate observations (Hosking and Wallis, 1993). Discordancy measures for all stations are calculated and shown in Table 1.

It is not easy to choose a single value of Di that cari be used as a criterion for decidmg whether a site is unusual. Thus it is tentatively suggested that Di < 3 is a criterion for declaring a site to be unusual (Hosking and Wallis, 1993). Considering this criterion, the region cari be assumed as homogeneous and a unifïed probability distribution function for minimum flows cari be accepted. The candidate 2 parameter probability distribution fùnctions for this unified probability distribution cari be Weibull-2 , lognormal-2 and power distribution functions.

Power Distribution

A study has been done by Gottschalk and Perzyna (1989) for determining the distribution of low flows considering the physical aspect of the phenomenon. During a dry period the flows of the river decrease following the recession curve and at the end of this period (t=T) minimum flows are observed. Fx(x) distribution fùnction of minimum flows X cari be obtained as follows:

Fx(x)=P[X<x]=P[T>t]=l-FT(t; (1)

Dry period length, when considered as a discrete variable taking integer values, cari be expressed by geometric distribution (Bayazn,Sen,1979). In case it is considered as a continuous variable it may be expected that the exponential distribution corresponding to the geometric distribution will be valid. Hence the distribution of the dry period length cari be expressed as (onoz and Bayazn ,1998):

FT(~) = 1 - exp(-ht)

x(t) = xo.exp(-t / k)

(2)

(3)

66

Fig 1. Gediz and B.Menderes river baslns in Western Turkey with the stations of Table 1.

Table 1. Stations, their record lengths, means and discordancy measures Di in Gediz and B .Menderes river basins

Basins

Gediz

Stations Record Length MfXll 501 17 1.57 509 33 0.16 510 24 0.64 514 30 0.05 515 30 0.06 524 22 0.39 701 57 1.22

1 B.Menderes / ii 1 - i 5.19 8.95 0.52 1.05

0.33 0.98 2.21

1 1.14

67

.,...

When equ 2 and equ 3 are substituted in equ 1, power distribution with parameters ~0 and c for the distribution of minimum flows X is obtained.

Fx(x) = (x1 x0)’ x 5 x0 (4)

Parameter estimation by L-moments:

1 Ll c=y c-1 ( 1

cc + Wl x0 = (5)

2 C

When observations belonging both to high flows and to low flows are plotted on a x-F(x) plane, the impression is that all the data do not fit the same distribution. The most important part of the problem is finding the distribution which fit the data for high flows and the data for low flows. Thus in the analysis of low flows LL-moments km) have been defmed which give larger weight to the lower tail i.e. data at the lower tail are given larger weights (onoz, Bayaztt,1998). These moments are similar to LH-moments defïned by Wang,1997 for floods. They are based on expectations for the r smallest elements of a sample of size r+m (m=1,2,....). As m increases the weight of smaller data in parameter estimation also increases. For m=O, LL- moments are reduced to L-moments. The expressions of the parameters of the power distribution in terms of Lrn moments are given below:

(6)

x0 = (c+ 1)(2c+ l)...[(m + l)c+ l]LTp

(m + l)! cm+l (7)

For m=O,1,2,3,4 the parameters of the power distribution and L-CV (L-coefficient of variation) and L-CS (L-coefficient of skewness) are given in Table 3. The L-moments and the LL-moments for the calculation of these magnitudes are the weighted averages of the at site L- moments and LL-moments.

Table 3. Regional L-and U-moments as weighted averages of at-site parameters

m x0 C L-CV L-cs 0 2.27 0.79 0.39 0.12 1 3.24 0.91 0.42 0.07 2 4.93 0.83 0.44 0.04 3 7.33 0.76 0.45 0.04 4 10.49 0.71 0.47 0.04

When the data of the stations are analyzed, it is seen that 3 elements at each of the 4 stations remain larger than the Upper limit ~0. Mer elimination of these data the goodness-of-fit test of the data to the power distribution is done by Probability Plot Cor-relation Coefficient (PPCC) test. Number of stations passing the PPCC goodness- of-fit test for power distribution at the

68

.” .._ .____-- -.-- -..-. -.

level of significance a=?/o5 is given in Table 4. It is seen that the best fit is for the case m=l with three stations failmg the test.

Table 4. No. of stations passing the PPCC goodness-of-fit test for power distribution at the level of significance o=O.O5

m 0 1 2 3 4 No. of stations 7 8 7 6 6

For m=O, 1 and 2 at-site L-CV versus L-CS are plotted (Figs. 2-4). On this plot also the theoretical curves of power, Weibull 2 and lognormal 2 distributions are drawn. Regional values of these coefficients are also plotted. When these figures are examined carefùlly considering the regional value it is seen that power distribution fits better than Weibull 2 and lognormal2 distributions in general.

The regional pdf for 7-day minimum flows and the estimation of the at-site quantile X+, will be the ones for m=2 case.

F(x) = (x / 324)“.91

x = 3.24 x IL; x Fp/‘.” (8) I

0.8

0.6

L-CV 0.5

0.4

0.3

0.2

. . .

REGIONAL VALUE 1

r 1 M=O _--

I !

-0.3 -0.1 0.1 . 0.3 0.5 0.7 0.9 1.1

L-cs

1

l

/

I

l _-

Fig. 2. At site L-CV versus L-CS plots and the theoretical curves of power, Weibul12 and lognormal distributions for m=O case

69

0.8

0.7

0.6

-L-CV 0.5

0.4 -

0.3 -

c --- -.-POWER -1

I

.

0.2 I -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1

LL-cs

Fig. 3. At site L-CV versus L-CS plots and the theoretical curves of power, Weibul12 and lognormal distributions for m=l case

L

-

0.8 - .

0.7 - I ---

--POWER 1 -cwEImJLL 2 0.6 - r, . REOIONU VALUE

\

LL-cv 0.5

cl M=2

0.4 .

0.3

0.2 1 8 1 l l I -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1

LL-CS

Fig. 4. At site L-CV versus L-CS plots and the theoretical curves of power, Weibul12 and lognormal distributions for m=2 case

70

Conclusions

1. By a simple scaling analysis it is shown that a regional lowflow analysis will be appropriate for Gediz and B. Menderes river bas&.

2. By a discordancy analysis it is shown that Gediz and B.Menderes basins for-m a homogeneous region.

3. For the distribution of 7-day minimum flows the goodness-of-fit of power distribution is tested by the PPCC test. According to the test the power distribution for m=l case is the best distribution among all, with 8 stations passing the test at a=O.O5 signifïcance level.

4. At site L-CV versus L-CS are shown graphically together with the theoretical curves of power, Weibull 2 and lognormal 2 distributions. The regional values of these magnitudes are also plotted on these figures (Figs 2-4). It is seen that for all cases regional values are closer to power distribution.

Refmences

Bayazn, M., Seri,, 2. (1979). “Dry period statistics of monthly flow models”. Modeling Hyrologic Processes, ed.H.T. Morel-Seytouk, Water Resour. Publications.

Gottschalk, L., Perzyna, G. (1989). “Derivation of low flow distribution tùnctions using recession curves”, J. Hydrology, 194:23 9-262.

Hosking, J.RM.,Wallis,J.R., (1993).“Some statistics usefùl in regional fiequency analysis”, Water Resources ResearchVol.29, NO.~, pp.271-28 1.

Onoz,B., Bayazn M., (1998)“Power distribution for low flows”, Proceedings of II National Hydrology Meeting, June 1998, pp. 175-181 (in Turkish).

Wang, Z.J. (1997). “LH moments for statistical analysis of extreme events”, Water Resour. Res., 33(12):2841-2848.

71

FREQUENCY ANALYSIS TECHNIQUES IN LOW FLOW HYDROLOGY

Atil BULU Istanbul Turkey Universit, Civil Engineering Faculty, Hydraulics Division 80626 AYAZAGA, Istanbul- Turkq

ABSTRACT This manuscript was intended to summarise what was done till now by the research team of the author as the International Coordinator of the Low flow Group in the FRIEND-AMHY project on the statistical analysis of low flows. Parameter estimation techniques of the generally accepted and applied 2-parameter Weibull (W2) distribution were given. For the case of the hydrologie data containing zero flows, frequency analysis techniques were given by using the total probability theorem. Regional analysis techniques were given to check the applicability of the chosen W2 distribution for the whole region under consideration.

INTRODUCTION

Low flow discharges occur at some period of the year and sometimes get dry, especially in arid and cold regions.This usually occurs during the summer season when irrigation is primary importance in the arid regions. From the dilution point of view, this has important consequences for the discharge of waste water into the river flows during the low flow period. If the flow decreases below a certain value, there is direct effect on the aquatic life of the surface flow under consideration. Low flow statistics are also used in water planning to determine allowable water transfers and withdrawals. Other applications of low flow frequency analysis include determination of minimum downstream release requirements from hydropower, water supply, cooling plants and other facilities.

In examining low flows, different Duration-days (D-days) of flows are taken into consideration. For instance, in calculating 7-day of low flows of N year of observations, mean value of the seven days of succeeding flows are calculated and exceedance probabilities are determined. By the help of flow duration curve of a D-day flow, one cari find out the percentage of time during which specifïed discharges are equaled or exceeded during the period of record.

Also probability distribution fùnctions are used in low flow analysis. While the flow duration curve is concerned with the proportion of time during which a flow exceeded, the low flow frequency analysis shows the proportion of years when a flow is exceeded, or equivalently the average interval in years that the river flow falls below a given discharge. In USA 7-day lO- year low flow (Q7,10) value is accepted as a low flow criteria. This value coincides with mean seven day minimum flows for a year and with a lO-year retum period. Some researchers accept 7-day 2-year low flow (Q~,z) as a low flow criteria (Task Committee, 1980).

FREQUENCY DISTRIBUTION OF LOW FLOWS

Different distribution fùnctions and parameter estimation techniques have been investigated for many years to predict Q~,HJ low flow discharge value (Gumbel, 1954, 1958; Matalas, 1963; Condie and Nix, 1975). In a study using lognormal (LN2), Weibull (W2) and Gumbel distribution performed by Vogel and Kroll (1989) in the USA, they came to the conclusion

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LN2 distribution is the best for estimating Q~,io discharge at a station and on a regional basis. In an other study, Bulu and Onoz (1997) found out that W2 distribution conformed better to the low flows of the selected rivers in Turkey. In the FRIEND study group, the Weibull distribution has been adopted for low flow analysis (Gustard et al., 1989). In this paper, W2 distribution and its parameter estimation techniques Will be given.

The probability density function of W2 distribution has the form of,

fW=Qx a-p exp _ 5 a r;)l P

x20 CZ,p20

where a is the scale and l3 is the location parameter. Thus the cumulative frequency function is,

(2)

The mean, variante and the skewness coefficient have been given respectively as (Bulu, 1998)

E(x)= pr[1+;) \

Var(x) = /?’ [r(1+;)-I-2(1+;)]

YZ++;)-3++;)r(I+;)+2P(I+;)

[,(,t g-P(li ;Il”

(3)

(4)

(5)

Parameter Estimation by the Method of Moments (MOM)

The parameters of the W2 distribution cari be estimated by the MOM by substituting the calculated mean and variante of the sample respectively in Eqs. (3) and (4) and then solving the two equations simultaneously for â and p

Parameter Estimation by the Maximum Likelihood Method ( MLE )

The estimation of â and B parameters by MLE has been given by Haan (1977). These estimates cari be determined by letting,

a=p-ff (6)

74

and then solving

and

&= N ** N

3°C x” Lnx, - C Lnx, ,=I I=i

simultaneously for â in which N is the sample size. P n is then given by,

B = (q’”

(8)

(9)

Parameter Estimation by the Probability Weighted Moments (PWM)

In the recent years, L-moments and PWM methods were preferred for the parameter estimation of the probability distribution fùnctions. As was mentioned in Stedinger et al. (1993) L-moments provide simple and reasonably efficient estimators of the hydrologie data and of a distribution’s parameters.

The estimates of â and p parameters by PWM are,

In these equations, Li is the mean of Ln(x) series and LZ is the L2-moments calculated from the ordered Ln(x) series. The information related to the PWM and L-moments are given in Stedinger et al. (1993).

Once â and p parameters are estimated by any of the methods given above, low flow value for a taken T return period cari be computed by

as given in Kite (1974)

PROBABILITY ESTIMATION OF ZERO FLOWS

On semi-arid and arid regions, hydrologists may encounter data series that contain zero values. The same problem arises in the cold regions when the rivers are frozen during the winter season. Such data sets are called censored saamples (Stedinger et.al., 1993).

75

These zero flows have to be taken into consideration in estimating the probabilities of low flows (Haan, 1977; Bulu, 1997; Bulu and Aksoy; 1997, 1998). According to the theorem of total probability

P(x2x)=P(x2x~x=o)P(x=o)+P(x2x~x#o)P(x#o) (13)

Since P(X > x 1 X = 0) is zero, the relationship reduces to

P(x~x)=P(x2xpY#o)P(x#o) (14)

In this relationship P(X + 0) would be estimated by the fraction of non-zero values , k, and P(X 2 x 1 X + 0) would be estimated by a standard analysis of the non-zero values with the same size taken to be equal to the number of non-zero values. This relation cari be written as a function of cumulative probability distributions

1- F(x) = k[ 1- F’(x)] (15)

or

F(x)=+k+kF’(x) (16)

where F(x) is the cumulative probability distribution of a11 X [P(X I x 1 X 2 o)], k is the

probability that X is not zero, and F*(x) is the cumulative probability distribution of the non-

zero values of X, [P(X I XI X # 0)] Th is is a mixed distribution which has a finite

probability for X=0 and a continuous distribution of probability for X>O. Bulu et al. (1995) and Bulu and Aksoy (1997) have applied this method for the frequency analysis of low flows. Eq. (16) cari be used to estimate a magnitude of an event with return period T by solving fïrst for F*(x) and then using the inverse transformation of F*(x) to get the value of X. This merely depends on the probability distribution fùnction applied to the non-zero flow values.

F(x)-l+k F”(x) k

Since the return period of the flow cari be estimated by

1

T = F(x)

(17)

(18)

Eq. (17) takes the form of

(19)

The applicability of Eq. (19) depends upon to get positive values of probabilities, F’(x). SO that, the application of the total probability theorem to the low flows depends on the relations

76

between T and k. For the common used return periods, the fractions of non-zero values, k, that would be greater were given on Table 1.

Table 1. k Values Depending on Return Periods

T(years) 2 5 10 20 50 100 k> 0.50 0.80 0.90 0.95 0.98 0.99

For different return periods, k fractions should be

k>T-l T

(20)

for the application of this theorem. Actually, if we obtain negative F' (x) values by Eq. (19), it means that for that return period T and fraction k, the probability of seeing that flow is zero for the river under consideration.

Since the calculation of F’(x) by Eq. (19) is distribution free, the values of F*(x) cari either be calculated from Eq. (19) or cari be taken from Fig. 1 depending on T and k values (Bulu, 1997).

77

-.

F*(x)

0.50 0.60 0.70 0.80 -0.90 1.00 k

0 06

F'(x) 004

0 02

0 90 0 92 0 94 k 0 96 0.98 1 .oo

0 020

0 015

F*(x)0 010

0 005

0 000 0 980 0 985 0.990 0 995 1 000

k

015

F*(x) o IO

0 05

0 00 0 90 0 95 1 00 k

0 05

004

003

F’(x)

F’(x

0950 0960 0.970 0980 0990 1000 k

0008

0 006

1) 0004

0002

0 000

0990 0992 0994 0996 0998 1000 k

Figure 1. F*(x) and k Relation for Different T Return Periods

GOODNESS OF FIT TESTS

Rigorous statistical tests are available and are useful for assessing whether or not a given set of observations might have been drawn from a particular family of distributions. Generally three statistical tests are widely used for this purpose. The fïrst of these , the x2 (Chi-Square) test divides the data into class inter-vals and cari be used only for large samples. The other two, K-S (Kolmogorov-Smirnov) test and PPCC (Probability Plot Correlation Coefficient) test may also be used for small samples. In this paper, PPCC test Will be given.

Probability Plot Correlation Coefficient (PPCC) Test

The Probability Plot Correlation Coefficient (PPCC) is a test statistics to measure the linearity of the probability plot. The correlation coefficient test statistic, r, is calculated between the

78

.--.__-~ P_l^-^-.-. -.

ordered observed values and the inversed of the cumulative distribution functions of the fitted distribution. If the observed values conform to the applied distribution, the r statistic should be greater than the critical value for the selected significance level. The equations that give unbiased estimates of the inverse values, have been obtained by different researchers, with the r test statistic defined as

5 (xi - Xxm, - E)

r=/$qq (21)

in which x,(x, I . . . . . I x, 5 . I xN) is the ordered ith value and x is the mean of observed

values.

mi = Fi’ (~9,) (22)

in which F(.) is the cumulative probability value and pi is the value estimated by unbiased equations for different probability distributions.

PPCC Test for the Two Parameter Weibull Distribution (W2)

The probability density function and cumulative distribution function of the W2 distribution were given in Eqs. (1) and (2) respectively. The estimate of PPCC test statistic, r is calculated by Eq. (21) between the yi=Ln(xi) values and the inverse values determined by

mi = F;‘(p,)= Ln/?+iLn[-ln(l-p,)]

pi values in Eq. (23) cari be estimated by

i - 0.44

” = N+O.12

(23)

(24)

that was proposed for Gumbel distribution (Gringorten, 1963) since there is a hmctional relationship between Weibull and Gumbell distributions. If the x variate is distributed as Weibull then the z =-Ln(xJ variate is distributed as Gumbell. Therefore, the equations used for one of these distributions cari also be used for the other one (Stedinger et al., 1993).

The estimates of â and â parameters by the probability weighted moments were given in Eqs. (10) and (1 l), respectively. The information related to the probability weighted moments and L-moments are given in Stedinger et al. (1993). Critical values for this distribution were given in Table 2 (Vogel and Kroll, 1989).

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Table 2 Critical Values for the Weibull Distribution

n 0.01 0.05 10 132.0 90.9 15 107.0 72.6 20 97.2 61.6 25 86.0 54.0 30 77.1 47.5 35 71.9 44.1 40 66.6 40.1 45 62.6 37.0 50 60.1 35.3 55 55.5 33.1 60 53.2 30.7 65 51.1 29.1 70 48.2 27.8 75 48.1 26.7 80 44.8 25.8 90 42.1 23.4 100 39.4 22.3 200 24.1 13.2

a (Signifïcance Level) 0.10 0.25 0.50 0.75 0.90 0.95 0.99 73.8 49.6 31.9 20.0 12.7 9.66 5.80 58.0 39.4 25.6 16.5 11.0 8.65 5.59 48.9 33.3 21.7 14.2 9.71 7.68 5.09 I 42.3 28.7 18.9 12.6 8.70 6.97 4.75

- 37.5 25.5 16.8 11.2 7.85 6.32 4.24 34.4 23.2 15.3 10.2 7.14 5.83 3.98 31.3 21.1 13.9 9.28 6.59 5.36 3.70 28.7 19.3 12.8 8.64 6.12 4.97 3.42 27.2 18.2 12.0 8.06 5.71 4.71 3.24 25.5 17.0 11.3 7.61 5.40 4.42 3.15 23.8 16.1 10.6 7.18 5.14 4.21 2.96 22.5 15.1 9.99 6.80 4.86 4.00 2.78 21.4 14.4 9.53 6.45 4.62 3.78 2.69 20.5 13.7 9.06 6.11 4.40 3.62 2.54 19.7 13.2 8.63 5.87 4.20 3.47 2.46 17.9 11.9 7.93 5.41 3.88 3.20 2.27 16.9 11.3 7.41 5.06 3.62 2.99 2.11 10.1 6.68 4.43 3.04 2.22 1.86 1.35

PPCC Test for the Uniform Distribution

If the random variable takes every value with the same probability for a given inter-val then it is distributed as uniform. The probability density function f(x) and cumulative probability

function F(x) for (a,b) inter-val are

F(x) = E a<x<b (26)

The mean and variante of the uniform distribution are

E(x) = $f

Var(x) = (b y;)

(25)

(27)

(28)

The estimate of the PPCC test statistic, r, cari be determined from Eq. (21) between the ordered observed values and the inverse values of the uniform distribution. The inverse value of this distribution cari be calculated by

m, = FXm’(p,)=a+(b-a)p, (29)

and pi values by

80

The PPCC test statistic is free of parameter estimation techniques used to estimate a and b parameters and Eq. (21) cari be defined as (Vogel and Kroll, 1989)

cov(xi > Pi )

Y = [var(x,)var(j, )y 5 (31)

Critical values of the test statistic have been given for the uniform distribution on Table 3 (Vogel and Kroll, 1989).

Table 3. Critical Values for the Uniform Distribution

n 0.01 0.05 0.10 10 124.0 81.0 64.0 15 83.6 56.3 44.4 20 63.3 42.4 34.0 25 50.9 34.2 27.4 30 43.2 28.8 23.1 35 36.8 24.8 19.9 40 32.1 21.8 17.5 45 28.7 19.4 15.5 50 25.9 17.6 14.1 55 23.8 15.9 12.8 60 21.7 14.6 11.7 65 20.0 13.4 10.8 70 18.4 12.5 10.0 75 17.3 11.8 9.45 80 16.4 11.0 8.86 90 14.4 9.84 7.92 100 13.2 8.78 7.09 200 6.58 4.45 3.58

a (Signifîcance Level) 0.25 0.50 0.75 42.7 27.3 17.4 30.2 19.6 12.8 23.1 15.2 10.1 18.8 12.4 8.29 15.8 10.5 7.03 13.6 9.04 6.10 12.0 7.98 5.40 10.7 7.12 4.81 9.71 6.43 4.37 8.80 5.87 3.98 8.09 5.39 3.66 7.48 4.99 3.39 6.96 4.65 3.17 6.53 4.35 2.96 6.11 4.07 2.78 5.45 3.64 2.47 4.91 3.27 2.24 2.47 1.65 1.13

0.90 0.95 0.99 11.7 9.18 5.79 8.94 7.21 4.87 7.09 5.80 4.02 5.88 4.82 3.39 5.02 4.13 2.95 4.36 3.62 2.55 3.88 3.21 2.30 3.47 2.88 2.08 3.15 2.61 1.90 2.87 2.40 1.72 2.65 2.21 1.61 2.46 2.05 1.49 2.30 1.91 1.39 2.15 1.79 1.30 2.01 1.67 1.23 1.80 1.49 1.09 1.63 1.36 0.995

0.824 0.690 0.503

REGIONAL ANALYSIS

TO check the validity of results found at the selected stations and regions, the D-day low flows cari be taken for regional analysis. Afier calculating the PPCC test statistics and their corresponding a signifïcance levels, regional analysis was applied. Significance levels a corresponding to the PPCC test statistic, r, are the cumulative probabilities of the distribution of r. The distribution fùnction of a is uniform at (0,l) interval (Vogel and Kroll, 1989). The theoretical mean and standard deviation of a should be 0.5 and 0.289 according to Eqs. (27) and (28). Mean and standard deviation values of the a values are calculated by taking into account the number of stations on the region taken. For the first check, theoretical and observed mean and standard deviation values are compared for the fitted W2 distribution, if they are close together then the fit cari be accepted as good. As the second check, the PPCC test statistic, r, are calculated by Eq. (3 1) for the a significance levels and compared with the critical value taken from Table 3 for the uniform distribution. If the calculated r2rcr, the

81

selected W2 distribution cari be applied for the selected region on low flow statistical analysis. This method was applied by Bulu and Onoz (1997) to the selected regions on Turkey.

CONCLUSIONS

This manuscript was intended to summarise the state-of-art on the statistical analysis of low flows which was done till now by the working team of the author as the International Coordinator of the Low Flow Group in the FRIEND-AMHY project. The following conclusions cari be written.

1. The 2-parameter Weibull (W2) distribution is the generally accepted and applied distribution fùnction for the frequency analysis of low flows.

2. Three parameter estimation techniques were given for the W2 distribution. Since L- moments provide simple and reasonably escient estimators of the characteristics of hydrologie data and of a distribution’s parameters, L-moments method was proposed.

3. If the hydrologie data series contain zero values which is the usual case for arid and cold regions, the total probability theorem cari be used for the frequency analysis of low flows. The application of this method was given briefly.

4. Regional analysis techniques were given to check the applicability of the chosen W2 distribution for whole the region under consideration in the frequency analysis of low flows.

REFERENCES

Bulu, A. (1997) Statistical Analysis of low flows with zero discharges, FRIAND, 3rd Report : 1994- 1997, Cemagref Editions, 167- 170.

Bulu,A. (1998) Statistical techniques in low flow hydrology, Lowflows Expert Meeting, 10-12 June 1998, Belgrade, Yugoslavia, 39-46.

Bulu, A. and Aksoy, H. (1997) Frequency analysis of low flows on arid regions. International Satellite Conference on Water & Statistics, 28-30 August 1997, Ankara, Turkey.

Bulu, A. and Aksoy, H. (1998) Low Flow Drought Studies in Turkey, Low Flows ExpertMeeting, 10-12 June 1998, Belgrade, Yugoslavia, 133-142.

Bulu, A. and Onoz, B. (1997) Frequency analysis of low flows by PPCC test in Turkey, Proceedings of Postojna, Slovenia Conference, September- October 1997, IAHS Publ. No. 246,133-140.

Bulu, A., Cigizoglu, H.K. and Cokgor, S. (1995) Statistical analysis of low flows on Thrace region. FRIEND-AMHY Conference, 1995, Thessalonique, Greece.

Condie, R and Nix, G.A. (1975) Modelling of low flow frequency distributions and parameter estimation, Int. Water Resou. Symp. Water for Arid Lands, Teheran, Iran.

Gumbel, E. J. (1954) Statistical theory of droughts, Proc. Hydraul. Div. , ASCE, 80, l-10.

Gumbel, E. J. (1958) Statistics ofExtreme.s, Columbia Univ. Press, New York, N.Y. Gringorten, 1.1. (1963) A plotting rule for extreme probability paper, J. Geophys.

Res., 68(3), 813-814.

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Gustard, A., Roald, L. A., Demuth, S., Lumadjeng, H. S. and Gross, R (1989) Flow Regimes From Experimental and Network Data (FEND)), Vol, 1, Hydrological Studies, Institute of Hydrology, Wallingford.

Haan, CT. (1977) Statistical Metho& in Hydrology, The Iowa State University Press, Ames, Iowa.

Kite, G.W. (1974) Flood Frequency and Risk, Inland Waters Directorate, Water Resources Branch, Ottawa, Canada.

Matalas, N.C. (1989) Probability distribution of low flows, Professional Paper 434-A, U.S. Geological Survey, Washington D. C.

Stedinger, J. R., Vogel, R. M. and Foufoula-Georgiou, E. (1993) Frequency analysis of extreme events. Chapter 18 in Handbook of Hydrology, ed. by D. Maidment, McGraw Hi11 Book company, New York.

Task Committee on Low-Flow (1980) Characteristics of low flows, ASCE, journal of Hydraulics Division, 106 (HY5), 7 17-73 1.

Vogel, R.M. and Kroll, C.N. (1989) Low-flow frequency analysis using probability plot correlation coefficients. J. Water Resour. Planning and Management, 115 (3), 338-357.

83

THE MINIMUM MEAN MONTHLY FLOW OF MARITZA RIVER

Dakova, Sn. Hydrologist Neykov, N. Statistician

Both from National Institue of Meteorologv and Hydrologv, Bulgarian Academy of Sciences, 66 Tsarigradsko Shause Boul., Soja 1784 - Bulgaria

Beginning from the Maritza lacks situated under the peak Manche in Rila mountain to the frontier, the length of Maritza river is 321 km having a difference of the altitude level 2337 m. The catchment area (A) of Bulgarian part of Maritza river is 21084. km* Maritza river has about 35 tributaries. The biggest are : Tchepelarska river (A=889,6 km* ), Topolnitza river (a=1789 km * ), Strjama river (A= 395 km * ), Rakitnitza river (3293 km* ).

The values of the main water balances elements are given in Table 1, where the values of runoff are restored to the natural ones. The natural runoff is the one which is formed on the catchment area and which would be reach to some cross-section of the river if there are no water users.

According to Mandadjiev (1994) if the meteorological effect on the catchment area are noted by Xl(t), X2 (t),..., Xl(t) then the process river flow cari be presented in the general view by the following formational model:

QtU) = S PW, X2 (9, X3 (t),.. .,X(t)].

Here Xi(t) for i=l ,...,l are random process, S is an aggregate of the mathematical and logical operations through which the accordance between the input and output of the system river basin are conformed and cari be named its structure.

If S is a constant for some time period and haven’t appreciable influence of man-made activities then the streamflow is natural. If S is a variable then the flow is disturbed. In respect to the hydrological response to human activities the flow is homogeneous in the period with permanent structure (obviously, the possibility of the natural inhomogeneous is not excluded).

The low flow and especially the minimum monthly flow is this part of the streamflow, which is the most vulnerable on the changes of the transforming system structure river basin and particularly on the activities related directly with the river network.

The water of Maritza river have been utilised for irrigation since the time when Bulgaria was include in the Otoman empire. The total about 30 m3 is the volume of a11 existing from this period water - intakes with discharge over 600 Vs.

Accepting a hypothetical possibility for a total guarantee of a11 needs (including the rice-fïelds), now the water demands are between 90 and 100 mil.m3. It is a negligible small value about 2% from the natural mean annual flow. However, these are volumes which are intakes from the river in the period of low flow and influent on the a11 low flow characteristics including the minimum monthly flow.

The structure of the transforming system river basin is keeping to the beginning of fiftieth when the intensive building of the big hydraulic constructions have started. A part of

85

them has a complex destination (for hydroenergetic, irrigation, water supply), the others are small ones, with the local importance. The distribution of the hydrotechnical construction along the river are illustrated on the table 2.

As a result of the human activities, more than 500 big and small reservoirs have been built on the Maritza river basin with the total volume of 1,5 mlrd.m3 and about 356 water intake structures with or without equipment of pumping plants, having a total discharge over 220 m3/s.

The structure of the transforming system was changing significantly for a long time. In the end, a number of changes are set in the cathment area, the more essential of them are:

1) A signifïcant redistribution of the stremflow in the time comparing with this one in natural conditions.

2) The function M = F(A) corne interrupts (except of karst), where A is the surface of the cathment area in km* This indicate that the data observed on the existing now gauging stations are not to be utilised for characterisation of the runoff and especially of low flow, because of the fact that their situation is not confirmed with the coming/advancing runoff changes.

3) In the period of low flow the runoff in the river is to be generated not only from the ground water but from the water remain of the fimction of the complete water managing system (the significant volumes of water are transferred into Maritza basin from the Strouma, Mesta and Toundja rivers.

The buts of this investigations are follow: 1) TO estimate the degree of influence of the river basins. 2) TO try to find a methods for interpolations on the territory (on the space) 3) TO assess a degree of possibility for regionalisation of low flow on the Maritza river

basin, in assumption that after 1975 the transforming system river basin has a relatively steady parameters.

The fïrst gauging stations have been founded since year 1909 to 1912. Water level has been observed to the 1935. AAer that, the systematically gauges of the water discharge were started. SO, the available hydrological data information dates from 1935 on. Since 1935, 93 gauging stations have Iùnctioned during a different time periods.

Now, 60 gauging stations fùnction, but only 4 stations on the main river and 4 on the tributaries have a fùll period (from 1935 up to now). These stations was utilised as a base in this study.

The preliminary analyses of the water discharge data, of the a11 water managing systems and of the hydraulic structures which have been built on the Maritza basin show that there are 3 groups of river sections concerning the mean monthly follow:

The first one: the natural regime of the streamflow is keeping on. Unfortunately, the adjacent catchments cari be joint in one area because they are sppoty throw on the Maritza river basin. The standard statistical methods of obtaining the temporaries and spaces statistical characteristics of flow without doubt are applicable. In the process of choice of the representative calculating period it is not exist other criteria than the statistical.

If we talk in the absolutely classical sense about regionalisation through the distributions curves it reflect to these section only.

86

The second group of sections has a diverted streamflow by water draw-of. Usually they are situated under the water -intakes constructions or the reservoirs. The drawn water from the river length closely near to the constructions could be reach to 95% from the mean annual flow.

The third group sections have a streamflow arised from the seepage waters here. The water utilised for different purposes is to be inflow back into the river by the surface or by underground way. The example for that cari be Maritza river from Plovdiv to the boundary. The sections cari be divided on a few different subsections, where in the each following one the part of the returned water is bigger.

Alter a11 talked here, it is clearly that the choice of the returned (computation) period is the most important one in the dynamic structure of the transforming system river basin. The choice of the returned period have to be conformity as follow:

- to present the last status of the transforming system-river basin; - to be homogenise regarding to the human activities; - to include wet and dry series; - After the detail analyse of the human activities in the period 1975 -1995 is

accepted as an computed (returned ) period.

Towards 1975 the biggest water-managing systems have been built. Looking to the natural flow, the accepted period include the series bolts of wet and dray years. These acceptances is approximated, especially for the period afier 1992 when the water intakes for irrigation and for water supply decrease, also 1993 and 1994 are very sec years.

The period 1975- 1995 is more sec than the period 193 5- 1974. The proportion between the flow in these two periods is about 0,8. This value is bigger in the mountains and smaller in, the plains.

The minimum monthly flow series may be obtained from various procedures: - The minimum monthly flow is chosen from each calendar year and is one sample

(element) of the time series. If the streamflow regime has a winter and summer low flow phases, the series for each phase are to compose. i.e. three series of winter, summer and annual minimum mean monthly flow are to compose;

- The hydrographs including the mean monthly discharges are considered as a realisation of the random function and the it sections with the minimum values are developed.(This method is hard for exploitation.)

- screening method, which utilise the lowest monthly flow in a period of year or more, regardless of when they occurred. By these methods the overlapping of the data is to avoid (UNESCO ,1982).

The applying of the above mentioned methods is illustrated for the gauging station 301 on Maritza river near Plovdiv town. In the zone of highest probability (over 80%) the three curves constituted by any of these methods are overlapped. In this reason and also because of the easier applying of the tirs method it is chosen for further work.

The characteristics of mean monthly flow of Maritza river are calculated for the gauging stations situated on the main river (from Belovo to Svilengrad) and are shown on table 3. Obviously the logic common for the natural conditions is missing here i.e. the increase of the water discharge with the growing of the catchment area due to a human activities.

87

The analyse of the empirical probability curves shown their very complicated configuration. This is due to a different role of the surface and the ground water in the river supply in wet and dray years and also to a human activities. In this reason, except the traditional distributions of Gumbel, Pearson 3 (computing their parameters by methods of the moments ), but in addition 11 distributions (applying the L-moments) are tested The evaluated frequency distributions are : Exponential, Gamma, Generalised extreme-value, Generalised logistic, Generalised Normal (Log-normal, Normal), Generalised Pareto, Gumbel, Kappa, Normal, Pearson Type III, Wakeby.

The reasons to use these distributions are as follow: (i) special cases of the generalised extreme value distribution (also known as the Von Mises- Jenkinson distribution) are the Exponential, the Gumbel-Frechet-Tippett and Weibull types distributions; (ii) the Kappa distribution has four parameters and includes as special cases the generalised logistic, generalized extreme-value and the generalised Pareto distributions; (iii) the Wakeby distribution is a generalisation of the generalized Pareto distributions and it has five parameters and cari mimic the shapes of many widely used skew distributions (e.g., extreme value, log-normal, Pearson type III).

The reason to consider distributions with enough free parameters that cari mimic a wide range of plausible frequency distributions as candidate frequency distributions is that the data record is often short or frequency distributions cari be heavy-tailed.

In the present study the method of L-moments is used for fïtting distributions to data (see, Hosking, 1990; Hosking and Wallis, 1997). L-moments are analogous to ordinary moments. The advantages of the method of L-moments over the conventional methods of moments and maximum likelihood are the smaller impact of outliners (atypical values, anomalous observation, gross error) and more reliable inference from small samples, as the sample L-moments are a linear combination of ordered observations. The more suitable distributions are shown on fig. 1 to 4.

The obtaining the interpolation relationships on the space is to be realised on two manner:

- by using the parameters of the distribution curves; - through the quantiles of the distribution curves.

presented in the specific discharge coefficients

The first manner is suitable in the cases of 2 or 3 parametric distributions. The second one is convenient in applying the more parametric distributions which are accomplished here.

The gauge stations involved in the study are too few and are physically and statistically (according to the test statistic H, derived by Hosking and Wallis, 1997) quite heterogeneous. Although this we formally identified and fitted the regional frequency distribution to the data following the approach developed by Hosking and Wallis (1997). The advantage of their approach is that a well-conducted regional frequency analysis remains far superior in quantile estimates to at site analysis under a wide variety of physically realistic deviations from exact homogeneity with a range of at site frequency distributions.

In regional frequency analysis data are assumed to corne from homogeneous regions. TO aid the presentation a forma1 definition is given. Let Qij, j=l,..., ni be observed data at N sites of a region, with sample size ni at site i, and let Qi(F), O<F<l, be the quantile function of

88

the distribution at site i. A region of N sites is called homogeneous if Qi(F)=piq(F), i=l,...,N, where ui is the site dependent scale factor and q(F) is the quantile fimction of the regional frequency distribution, common distribution of the data qi=Qij/b,. Here fi, is an estimate of ui, for example the mean of the at site frequency distribution. It is assumed that q(F) is a known function that depends on p unknown parameters 8i,...,8,. The quantile estimates are given by GI(F) = b,ij(F), where q(F) denotes the estimated regional quantile function. The unknown at site parameters are estimated separately at each site whereas the regional estimates are the weighted average of these at site estimates with weights proportional to sample size ni.

CONCLUSIONS

The investigation performed on the zone with Sign&ant human activities confit-m the impossibility to obtain the space and temporal characteristics of the minimum monthly flow by traditional approaches.

The river network have to be divided into sections with homogeneous conditions of for forming the runoff. Unfortunately, the existing observing networks are not fit for decision of this question, This calls to search for a new interpolate methods.

In the result of the human activities the minimum mean monthly flow is increase almost 2 times near the boundary.

It is difficult to use the characteristics of Low flow (base flow and BFI) to characterised the underground river supply in the sections with the seepage water and intake waters. This is especially important in the river sections with the linear distribution of the return waters from the irrigation and the towns sewerage networks.

In spite of the attempting of a many distributions including these ones using the L- moments, there are not enough reason to maintain that the regionaisation over a large territories is possible At now, it is possible to accomplish the regionalisation only on the river sections.

Acknowledgements

We are grateful to Dr P. Neytchev for producing the figures in the text.

References

1. Hosking, J.R.M. (1990) L-moments: Analysis and estimation of distributions using linear combinations of order statistics. J. R. Statist. Soc. B, 52, 10.5-124. 2. Hosking, J.R.M. and J.R.Wallis. (1997). Regional Frequency Analysis: An Approach Based on L-moments, Cambridge University Press. 3. Mandadjiev,D.( 1994). Water Resources of the Bulgarian Rivers. Sofia. NIMH Press. 4. UNESCO,1982, Methods of computation of low slow, Mc.Mahon T.A., A.Diaz Arenas

(eds.)

89

The mean values in mm of the water balance

Table 1. (according Mandadjiev, 1994)

Precipi- Runoff Evapo elements tation Total Surface Under - transpiration

ground Without 680 191 125 66 481

correction With correction 748 191 125 66 557 0.255

Table.2

G.st. N. 1 309 1 307 1 304 1 301 1 252 1 248

1 Distance from the frontier 18.20 52.25 138.0 188.8 222.2 255.2

2 Reservoirs - number 580 543 297 104 43 6

3 Reservoirs -total volume 1483 1469 1154 924 603 146.3 (mil.m.cub.)

4 Water intakes - number 356 346 225 153 104 58

5 Water intakes total debit 221.7 218.1 189.1 124.3 60.6 5.200 (m.cub./s)

Table 3

Distance from the frontier

7 Q min abs (m.cub./s) 0.660 0.630 2.040 0.076 0.250

8 Ocuring in year 1945 1968 1946 1952 1985

9 Qmin ocured in 1994 6.690 9.420 4.940 0.360 0.830

10 Qmin 95%P 6.200 6.200 4.900 0.350 0.400

90

Mmimum Mean Mountly Flow Mwitza river/304/1938-1974 At-me Requency Analysis based on L-moments

P

2

a 0

. w&

- - pe3

- - - -kap

- -gum -gev

=a

, ,100 ,50 JO ,5 ,4 ,3 ,2 ,3 , ‘.O 1

4 ,5 JO ,50 ,100 ‘.05 ‘.l ‘.25 ‘.5 ‘Y75 ‘.9 ‘.95 ‘99

Normal Probabihty Plot

Minimum Mean Mountly Flow Mantza river/304/1975-1995 At-site Frequency Anabsis based on L-moments

x

3

2 0

_______ w&

- - pe3

----kap

- - gdm

-gev

a

,100 ,50 JO ,5 ,4 ,3 Retmô pe;Fod

,2 ,3 ,4 ,5 JO ‘.O 1 ‘.05 ‘.l ‘.25 ‘.5 ‘.75 ‘Y9 ‘.95 ‘99

Normal Probability Plot

Fig. 1.

91

Minimum Mean Mountly Flow Maritza river/309/1936-1974 At-site Frequency Analysis based on L-moments

..___.. wak

- - pe3

- - - -kap

- -gum -&V

E

riod ,100 ,50 ,lO ,5 ,4 ,3 ,2 ,3 ,4 ,5 ,lO ,50 ,100 ‘.O 1 ‘!OS ‘.l ‘!25 ‘.5 ‘.75 ‘.9 ‘.95 ’ 99

Normal Probabihty Plot

0;

Minimum Mean Mountly Flow Maxitza river/309/1975-1995 At-site Frequency Analyris based on L-moments

. . . . . . . ?y&

- - pe3 - - - -kap

- -gum

-gev

? riod

,100 ,50 ,lO ,5 ,4 ,3 ,2 ,3 ,4 ,5 ,lO ,50 ,100 ‘.O 1 ‘!OS ‘.l ‘.25 ‘.5 ‘.?5 ‘.9 ‘.95 ‘99

Normal Probabillty Plot

Fig. 2

92

<. .” ,_ _, .-.,..” _..._. I .

4

Minimum Mean Mountly Flow Maritza river/304/1938-1974 Regional Frequency Analysis based on L-moments

._____. w,&

- - pe3 - - - -kap

- -gum -gev

________... a.’

c> 9

Return period

’ .Ol .05 .l .?5 .Y ‘.9 .99 ,100 ,50 JO ,5 ,4 ,3 ,2 ,3 ,4 ,5 I ,50 , 100

Normal Probability Plot

Minimum Mean Mountly Flow Maritza river/304/1975-1995 Regional Frequency Analysis based on L-moments

. . ..___ w&

- - pe3

- -kap - -

- -gum -gev

,100 ,50 JO ,5 ,4 ,3 ,2 ,3 ,4 ,5 ,lO Retc;; pe;kod

‘.O 1 ‘.05 ‘.I l.25 ‘.5 ‘.75 ‘.9 ‘.95 ‘.99 Normal Probability Plot

J

Fig. 3.

93

Minimum Mean Mountly Flow Maritza river/309/1936-1974 Regional Frequency Analysis based on L-moments

_______ wak

- - pe3

- - - -kap

- -gum

-gev

; riod

,100 ,50 JO ,5 ,4 ,3 ,2 ,3 ,4 ,5 JO ,50 ,100 ‘.O 1 1.05 ‘.l ‘.25 ‘.5 ‘.75 1.9 ‘.95 1.99

Normal Probabillty Plot

Minimum Mean Mountly Flow Maritza river/309/1975-1995 Regional Frequency Analysis based on L-moments

_.____. ,q&

- - pe3 - - - -kap

- -gum

-gev

Return period ,100 ,50

‘!OS III” ,5 ,4 ,3 ,2 ,3 ,4 ,5 JO ,50 ,100

‘.O 1 ‘.25 ‘.5 ‘.?5 ‘.9 ‘Y95 ‘.99

Normal Probability Plot

Fig. 4.

94

\

Long Range Forecasting Of Hydrological Aspects Of Droughts

Valentina UNGUREANU, Mary-Jeanne ADLER National Institute of Meteorology and Hydrology. SOS. Bucuresti-Ploiesti, nr 97, Sector 1, Bucharest, Remania

Summary

The methods used for long term forecast of trends of discharges are statistical, statistical- physical, analogue and physical numerical. Almost each method is based on the weather long term forecasting. The availability of long term records is one of the key requirements for this purpose. Suitable analogous are selected based on hisorical data process which are used in the hydrological forecast. Two such methods are presented. There have been attempts to use statistical techniques for analysis of annual and monthly discharges in order to evaluate that there follow a particular process such as the Bow Jankins ARMA/ARIMA Model. Another approach for drought forecast uses statistical-physical methods. The results using a deterministic mode1 are emphasized. In the end of the paper the improved forecast using a multimodel method of monthly data derived by different techniques is presentd.

1. Introduction

Drought hazard is one of the most serious problems in many countries, affecting even wider ranges of regions on the earth than flood hazard. In order to alleviate the drought problems, various counter measures are in practice,, not only engineering structural means or agricultural and bio-genetic means but also socioeconomic and human adjustment means. Many of these counter measures are based upon the statistical knowledge of drought and on the forecasted characteristic of that.

The statistical occurrrences and drought severness are most seriously investigated and actually applied in drought damage prevention management.

Low flow forecasts are based mainly on the presence of a relationship between the river and its associated groundwater storage. The effect of the preceding hydro- meteorological conditions upon the river discharge at the time under consideration are determinant.

A great influence on low flows and herin on the precision of the forecast is due to availability of stored water from natural storage on and below the ground surface. Knowledge of this practices are indispensable in low flow forecast.

The reliability of low flow forecast depends not only on whether they are local or regional in extent but also whether they are short- or long-range forecast. Depending of the characteristics of the droughty period different models should offer best results in forecasting. The general idea is to apply a11 the methods in use and to give a greater importance to those which offerd a best results to anterior time of forecasting. In short, a multimodel method is preferable than to adopt one single mode1 in forecasting practice.

97

2. Low flow forecasting methods

A dictionary definition of a mode1 is given by Webster as “a system of postulates, data and interfaces, presented as a mathematical description of an entity or state of affairs”. The major objective in modelling the hydrologie behaviour of a watershed is to simulate its stream flow hydrograph in response to an input of precipitation. TO accomplish this, the hydrological cycle is analysed and expressed as a collection of mathematical formulations based on rational parameters that may be adjusted alter tria1 simulations with known input and output. This may be continued until the mode1 is judged to be an adequate representation of the hydrologie cycle for a study area - for low flows in our case. The testing gauging station was Bals on Oltet River, from an endemic droughty area of the south-eastern part of Romania.

Statistical-determinist mode1 The statistical-determinist mode1 simulates separately the two main components of the

monthly mean discharge: the mean pluvial discharge and the base flow. The base flow is forecasted using the recession curve during low flows. The mean

discharge of the base tIow is:

where T is the number of days of the considered month, Q, is the initial value at the beginning of the each month and a the recession coefficient. The a parameter is a function depending of Q, :

In Q,, - In Q( t) a=

t For each basin the a = f(QCb) re a ions are calculated for each month or groups of months. 1 t’

In our case, two distinct cases were found (Table 1).

Table 1. llie recession parameters for each characteristic intersai Q,, a

I I

1.00 I 5.6 l 3.2 1 2.00 6.3 3.9 3.00 6.9 4.5 4.00 7.3 4.7 5.00 7.8 4.9 6.00 8.1 5.1 7.00 8.3 5.3

In a forecast situation (2, is known, the coefficient a is determined from Figure 1 and using Q, equation, the monthly mean discharge of the base flow is calculated.

98

In view to determine CI, a multiple regression QP = f( Q, ,P) was used for each month

(Figure 2).

Figure 1. a = f(Q,,)

Long ter-m meteorological forecast is usually qualitative one (excessive droughty period, drought, normal droughty period), and similar for rainy periods. The transformation in numeric values was obtained using the tiequency of the mean precipitation in the basin associating to the each forecasted meteorological situation an probabilistic interval:

- excessive drought : p=90-95% - drought : p=80-90% - normal drought : p=60-80% - normal rainy: p=20-40% - rainy: p=lO-20% - normal rainy: p=5-10%

From the probability curve of each basin, the rainy inter-val is obtained for each meteorological prevision (Table 2).

At the end, considering the superposition of effects, the mean monthly discharge is forecasted:

An application of this mode1 for the year 1994 is presented in Table 3.

99

Table 3. The ntean monthlv foret

1994

X 68.4 1.86 6.9 0.784 1.00 1.78 2.98 XI 7.84 1.70 4.5 0.820 0.20 1.02 1.71

Mode1 using hydre-meteorological analogues The forecasting mode1 based on the hydro-meteorological analogues suppose the following

stages: + the definition of the characteristic space, of the quantitative and/or qualitative variables,

determining the analogy with an anterior stage; + the definition of the position in the space of characteristics in the forecasting moment; + the search of an analogue position using the theory of shapes.

The forecasting algorithm estimates two regime tendency using: + the hydrological information, + the information fiom the analogue years fiom the meteorological point of view furnished

by the meteorological prevision (M. Matreata, 1997). The first tendency is obtained usin, 0 the percentage from the mean multiyear discharge

( Q,,,) of the forecasted discharge ( Q,,b,): C, = % - meLin

The mean monthly forecasted discharge C&, is obtained tiom the annual hydrograph of

droughty type (adimensioned by the mean annual discharge- Qi,,, ) or excessive droughty type for the physicogeographical work space and re-dimensioned using the mean annual forecasted discharge Q$,m,ti,. An example of the adimensioned hydrograph is presented in Figure 3.

Figure 3 . Regiottal droughty years use as an ina’ex qf the hdvdroIogicai drorlght

100

The estimation of the second tendency is based on the evolution of the mean monthly discharges from the meteorological analogue year, for each month, using the relation:

1 V

where Q,, is the monthly mean discharge of the jth month from the i’” analogue year from the

meteorological point of view. The droughty analogue characteristic years were determined using the deciles method

(Figure 4)

methods (analysed interval: I93 1-I99jj

The final forecast is obtained using the relation:

Q& = (0.6 x Ch + 0.4 Y :-J x cl;,,

In Table 4 is presented an application of this mode1 for the year 1994

Table 4. The mean monthly forec&t discharge qf the vegetation period, using the aflalogue mode1

Year Month 0~ 1 rlw log ue 0’ d mean C?l Q&,, Ch o.fi, Qobs

( m3/s) (m3/s) ( m3/s) (m3/s) (m3/s)

1994 VI 5.77 4.53 0.676 4.03 0.473 3.12 3.61 VII 1.66 4.28 0.200 1.23 0.148 3.80 3.18

VIII 1.02 3.38 0.302 0.532 0.157 0.727 1.19 IX 0.922 2.02 0.456 0.406 0.201 0.624 0.474 X 1.67 2.06 0.811 0.669 0.325 1.50 2.98

XI 2.30 3.66 0.628 0.947 0.259 1.49 1.71

101

Stochastic models usedfor the mean monthly discharges during low flows period The non-stationary and seasonal nature of the monthly flows are modelled using ARIMA

class of models. A step-by-step procedure was used to obtain valid models through proper mode1 identification, parameter estimation, performance evaluation, mode1 parsimony and validation of residual. In building the mode1 and of special importance was to obtaining the parsimonious models with white residuais. This procedure have been applied for few Romanian basins and the zones presented in Figure 5 was obtained

! \

‘h____

Figure 5 Zones qf the recommenciez stochastic models

The procedure was applied for the monthly flows of Oltet at Bals and at the end was obtained a valid mode1 capable of acceptable prediction results: ARIMA(2,1,1). The forecasted monthly mean discharges are presented in Table 5.

Table 5. The riean monthly forecasted discharges rrsirfg an ARIA44 ( Year Month 1 &,, (m’W 1 Qobs (m”N 1

1994 VI 3.80 3.61 VII 3.26 3.18

VIII 1.26 1.19 l

I IX I 0.55 l 0.747 l -X 3.20 2.98 XI 2.02 1.71

A determinist model for the mean monthly !orv fiows.forecast The types of mode1 used was the Stanford Watershed Simulation Mode1 (Crotiord and

Linsley, 1966), a mathematiçal mode1 programmed for a PC, synthesising a continuous hydrograph (watershed outflow vs. time) of stream flow from climatological data (precipitation and evaporation), and watershed parameters (soi1 surface moisture and retention properties, interflow storage and flow conditions, ground water storage and flow conditions, and the physical state and geomorphological properties of the basin)

102

The computer program was carefùlly studied, flow diagrammed in detail, and a carefùl calibration for low flows was obtained, using mainly the facilities of the multiple recession constants.

CB - infiltration index, LZSN - soi1 moisture storage index, UZSN - soi1 surface moisture index, K24L - parameter indicatino b groundw-ater slow leaving the basin, KK24 - daily base recession constant and GWF - base tlow w-ere determining for low tlows period caiibration of the model.

The 1990-1993 period was used for calibration and June - November 1994 low flow period was forecasted (Table 6).

Table 6. d Model

3. MULTIMODEL DECISION PROCEDURE

In real time cari occur a lot of perturbations like: lack of information necessary to the mode1 (problems of data transmission), errors of measurement or errors of representation of the variables, a particular situation that cari not be simulated with good results by the model.

SO, the forecast hydrologist has to pet-foi-m several operations more or less hazarded thus, he needs some good software which include both forecasting models and a decision nrocedure. In this way, the forecaster will have moor time to look for supplementary data and make a better analysis of the existing situation. The diminution of subjectivity and a better understanding of the situation Will lead to the improvement of forecast.

Some theoreticai aspects A simple description of the problem is the following:

+ we have several forecast models; + it is presumed that each mode1 checks a hypotheses group; + the forecast quality for each mode1 is not guarantied but only if it cheeks these hypotheses; + in real-time is no possible to check the whole of these hypotheses; + the relative quality of the results of various models depend on the situation (operating

configuration) where the system is situated at the time. During the time several researchers have tried to salve this problem using different

procedures (Newbold and Granger, 1974, Makridakis and Wincler, 1983, Cavadias and Morin, 1985,) but a11 those attempts have some inconveniences when we try to apply them for the real- time forcast

In this paper a simple real-time estimating procedure of the weight given to each mode1 (Roche and Tamin, 1986a, b, Roche et al., 1987) is applied. This procedure, named multimodel procedure, presume that the errors registered on the last time steps allow to construct an operating

103

configuration available for the given moment and different from the normal operating configuration of the system. This procedure uses in its computing the mode1 errors on the last time step, SO that the models weight whose quality degrades, decrease allowing, at the same time, the increase of the ones which match the best actual data.

The weight computing formula is:

( 7’ ei Wk=m

a 1 e-

-1 J

j=1

where m is number of models used for flow forecast and e(lc) is the forecast error of the A!h model. Evidently the sum of a11 models weight is:

m

c Wk = 1.0 k=i

Application of the multimodel procedure The multimodel procedure has been applied to compute the forecasted mean monthly

discharges during June - November 1994 low flow period using the results provided by the four models presented in the paper.

In June. the first month of the forecast inter-val, the forecast errors of the four models for May (the previous month) are unknown and ‘we have consider the same value for ail the models ( ek = 1.00 w-here k = 1,2,3,4). In this case, the weight of each k mode1 calculated with the weight

formula is: wk = 1 + 1 l+ 1 + 1 = f = 0.25 and the forecasted mean monthly discharge for June is:

Q” = 3.03 x 0.25 + 3.12 x 0.25 + 3.80 x 0.25 + 3.50 x 0.25 = 3.36

In July, the forecast errors of the four models for June have been calculated and those values have been used to compute the weight of each mode1 like in the following example:

l measured discharge in June: 3.6 1 m”/s l forecasted discharges for June:

- Statistical-determinist model: - Hydrometeorological analogues method: - Stochastic mode1 ARJMA type: - Stanford model:

l forecast errors in June: - Statistical-determinist model: - Hydrometeorological analogues method: - Stochastic mode1 ARMA type: - Stanford model:

l weight of the models computed for July: - Statistical-determinist model:

3.03 m3/s 3.12 m3/s 3.80 m3/s 3.50 m3/s

-16.066 % -13.573 %

5.263 O/’ 0

-3.047 %

((- 16.066)‘)--1

““” = ((- 16.066)‘)-’ +((- 13.573)‘)-’ +(5.263:)-l + ((- 3.047)‘)-’ = o’o253

- Hydro-meteorological analogues method:

104

((- 13.573):)-l

“” = ((- 16,066)')~~' +((- Ij,j73)')-' + (j.263') -' +((- 3)47)')-! = o.o

- Stochastic mode1 AEUMA type:

I - (5.263') -'

M’3 - [(- 16,066)‘)-’ +((- 13.j73)')-' +(5,263’)-’ +i(-3,047)‘)-’ = o.2358

- Stanford model:

((- 3.o47)-)m1 ‘,‘!A =

((- 16,066)‘)’ +((- 13.573)‘).-’ + (5.263’)~’ + ((- 3.047j’)-’ = o.7035

Having the weight of each model. the forecasted mean monthly discharge for July provided by the multimodel procedure was computed using the formula:

Q;c = 3.36 x 0.0253 + 3.80 x 0.0354 + 3.26 x 0.2358 + 3.20 x 0.0253 = 3.24

The same procedure have been applied for August, September, October and November. The computed weights are presented in Table 7 and Figure 6 and the forecasted mean monthly discharges provided by the multimodel procedure are presented in Table 8.

Tub/e 7. Models weights comprrted bv the mz~itimodel procedure

Year I 1994 I VI / VII l VIII I IX I x I XI

1 Statistical-determinist 1 0.2500 / 0.0253 1 0.0115 1 0.0164 1 0.0140 1 0.0117

I mode1 (1) I

I Hydro-meteorologjcal 0.2500 0.0354 0.0010 0.0012 0.0013 0.0010 analogues method (2) 1 / / / / /

Stochastic mode1 ARIMA type (3)

Stanford mode1 (4) Sum of the weights

0.2500 0.2358 0.0581 0.0676 0.0635 0.0539

0.2500 0.7035 0.9295 0.9148 0.9212 0.9334 1 .oooo 1 .oooo 1.0000 1 .oooo 1 .oooo 1 .oooo

. ci c : é : : :

1

: : : 3 : : I

: e : : i/ : .: I t El B i :

~ : : E : .

:: :: :: :: 1:: ;E . . 1 . :: 1

:: :: :: E! :: ii :i VI “II VIII IX x xi

Month

IWeighimodel 1 q Weight mode1 2 I We!qm odel 3 q Weiqht mode1 4‘

Figure 6, Representatiorz of the weights of the four mnthematical models

105

1 yrocedw-e

The calcuius of the weight of each mode1 and of the forecasted mean monthly discharge provided by the multimodel procedure is automatically done using a computer program which compute also, the forecasted mean monthly discharge provided by the four mathematical models described in the paper.

4. Analysis of the low flow forecast results

An comparativ-e analysis of the results provided by the four mathematical models and by the multimodel procedure has been performed (Table 9 and Figures 7 and 8)

The results of this analysis are the following: 0 The models which match the best the data are the stochastic mode1 (ARIMA type) and

Stanford mode1 which forecasting errors are smaller that 10% in four cases. In two cases the forecasting errors of the ARIMA mode1 are smaller than 20% and those of the Stanford mode1 are bigger than 20%.

l The forecasting errors calculated for the other models are bigger. The forecasting errors of the statistical deterministic mode1 are smaller than 10% in two cases, between 10% and 20% in one case and bigger in three cases and those of the hydro-meteorological analogues method are between 10% and 20% in three cases and bigger in three cases.

106

l The multimodel procedure provide the best results, its errors being smaller than 10% in fïve cases in the sixth case the forecast errer being 24.4%.

4.0 - .---_. --__ /’ ‘\

1.0 -

0.5 -

0.0

VI VII VIII IX X Xi Month

-Qobs ~ Qfor mode1 1

- - - Qfor mode1 3 - - Qfor mode1 4

- - - Qfor mode1 2

- ‘Qfor multimodel

Figure 7. Forecasted discharges using four forecast modefs md the ntulhnodel yroced

80

60

40

0 oc z 20 w

0

-20

-40

Month

?gure 8. Forecast en-ors of the, jôur mathrmcrrical mode1.s and qf the mrrltimodel yrocedwe

q Er mode1 1 q Er mode1 2 n Er mode1 3 Q Er mode1 4 q Er multimodel

107

5. CONCLUSIONS

1. Four mathematical models have been applied to forecast June - November 1994 low flow period.

2. The models which match the best the data are the stochastic mode1 (ARIMA type) and Stanford mode1 ( the forecasting errors are smaller that 10% in four month) but the multimodel procedure provide the best results (in tive month the forecast errors are smaller that 10%).

3. The multimodel procedure is very efficient, the weight of the mode1 which had provided the worse result in a month decrease ver-y much in the following month, while, the weight of the mode1 which had provided the best result in a month increase ver-y much in the following month.

4. The application of the multimodel procedure is ver-y usefùl the result being the improvement of the forecast.

REFERENCES

1. Cavadias, G., Marin, G. (1985) “Amélioration des performances des modèles hydrologiques par combinaison des débits simulés”, Revue internationale des sciences de l’eau, vol. 1, no. 1/4.

2. Makridakis, S., Wincler, R.L. (1983) “Average of forecast: some empirical results”, Manag. Sci., no. 29.

3. Matreata M. (1997) “Dinamico-statistic mode1 for low slows”, Studii de hidrologie, INMH 4. Newbold, P., Granger, C.W.J. (1974) “Experience with forecasting univariate time series

and the combination of forecasts”, J.R. Statist. Soc. A, 137. 5. Roche, P.A., Tamin, R(1986) “Procédures de décision en temps réel pour la prévision des

crues”, CERGRENE. 6. Roche, P.A., Tamin, R.(1986) “Procédures de décision multi-modèles applicables à la

prévision des crues en temps réel”, CERGRENE. 7. Roche, P.A., Torterotot, J.P. (1987) “Prévision des crues sur la Haute-Garonne. Utilisation

d’une procédure Multi-Modèles. Méthodologie et critique des données”, CERGRENE.

108

DOMAINS OF APPLICABILITY OF THEORETICAL PROBABILITY DISTRIBUTION FUNCTIONS IN LOW FLOW FREQUENCY ANALYSIS

V. Vukmirovic and D. Pavlovic Faculty of Civil Engineering, University of Belgrade, PO Box 89.5, 11000 Belgrade, Yugoslavia

Abstract

The low flow frequency analysis has a great importance for water ressources problems, especially when considering streamflow antipollution measures. Statistical analysis is commonly performed by applying the annual minima method. In this procedure there are certain problems related to the choice of an appropriate theoretical distribution fùnction of low flows, since the domain of low flows is limited to the postive values (O,+a) and some of theoretical distributions are applicable in the range (-C/C, +a). Application of such distributions to some low flow samples may yield negative values for greater return periods (20 years or more years), which is unacceptable. Domains of applicability of some common two-and three- parameters probability distribution functions (PDFs) are investigated by analyzing values of the parameters Cs and Cv (skew and coefficient of variation).

INTRODUCTION

The low flow fiequency analysis has a great importance in the decision-making process for solving water ressources problems, especially when considering streamflow antipollution measures. Statistical analysis is commonly performed by applying the annual minima method. In this procedure there are certain problems related to the choice of an appropriate theoretical distribution function of low flows, since the domain of low flow is limited to the positive values (0, +a) and some of theoretical distributions are applicable in the range (-a, +a). Application of such distributions to some low flow samples may yield negative values for greater return periods (20 years or more years), which is unacceptable.

THE ANNUAL MINIMA MEHTOD

This method is based on the analysis of observed annual minimum low flows (one value per year) over N years of record. Sorting this data according to their magnitude, a statistical series of the hydrological random variable X is formed :

The goal of the analysis is to determine the probability of occurrence of the hydrological random variable.This cari be achieved by defïning its probability distribution function (PDF) :

F(x) = P{X~x), x ER (2)

PDf represents completely probabilistic characteristics of a random variable. This means that a11 characteristics of the random variable X cari be obtained from the PDF.

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In hydrological practice, the return period for minimum values is defined by the following expression:

R(x) = J- F(x) (3)

The application of the annual minima method on random variable X comprises the following basic steps:.

l determination of empirical distribution fùnction, l calculation of numerical characteristics of the statistical sample (mean, standard

deviation, variation and skew coefficients, curtosis, etc.), l calculation of parameters of chosen theoretical PDF, l conduction of goodness-of-lit tests between empirical and theoretical PDF. Theoretical PDF cari be expressed in the form:

F(~;a&c >...) = P(x), x ER (4)

which emphasise dependence of PDF on parameters a, b, c, etc. An application of theoretical PDF gives an opportunity to extrapolate empirical distributions by objective statistical methods.

THEORETICAL PROBABILJTY DISTRIBUTION FUNCTIONS OF THE GAMMA TYPE

The general gamma distribution (also referred to as the three-parameter gamma, or Kritski- Menkelj PDF) has the probability density function:

f(x) = A(k,a) xk-’ exp[ - B(k,a) x”], x e R = (O,+ 00) (5)

Coefficients A and B are expressed through probability distribution fùnction parameters p, k and a:

Some one-parameter PDFs (exponential, Rayleigh’s, Erlang’s) or two-parameters PDFs (Weibull, 2-parameter gamma) are special cases of the general gamma PDF, for certain values of k and a. Table 1 presents these special cases with corresponding values of parameters k and a. In this table I(k) and T(l+l/a) reprsent the complete gamma function (Euler’s integral of the first type), while I*(kx/u, k) represents the incomplete gamma function.

Figure 1 shows dependence between the ratio of Cs and Cv (skew and variation coefficients) and Cv (variation coefficient) as the indication of the optimal domain of applicability of some of PDFs derived from the general gamma PDF.

One-parameter PDFs are represented as points on the graph in Fig. 1 with the following values:

- Exponential CKV = 2 cv= 1 - Rayleigh C&v = 1.207 Cv = 0.523 - Erlang cs/cv = 2 cv = 1k.h

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4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

0

CSJCV

I

s

0.1

: 0.0

Figure 1, Relations between the Cs/Cv ratio and Cv, variation coefjcient.

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The optimal domain for the two-parameters PDFs is represented with curves in Fig. 1. For the two-parameters gamma PDF, the ratio Cs/Cv is constant (Cs/Cv = 2). The two- parameters Weibull PDF is characterised with the curve for kla = 1. The one-parameter exponential PDF is a special case of the two-parameters Weibull PDF (k = a = 1) or the two- parameters gamma PDF (k = 1). The Rayleigh PDF is the Weibull PDF with parameters k = a = 2, while the Erlang PDF is the special case of the two-parameters gamma PDF.

The three-parameters PDFs are presented in Fig. 1 with a family of curves for different values of parameters or their ratios. The three-parameters gamma PDF is represented with either thick curves for different values of the parameters ratio kla (in the range from 0.05 to 20), or with thin curves for different values of lia (ranging from 0.1 to 3.0). Since the domain of these distributions is limited to the positive values of the random variable X, there are no limitations in the application of beforementioned PDFs in low flow frequency analyses.

Table 2 shows the values of Cv as a function of Cs/Cv and K = XI% / u, where Xl% is the quantile for F(x) = 0.01.

Table 1. PDF originated PDF Parameters Exponential k=a=l

Ray leigh k=a=2

Erlang k=2;a= 1

Weibull k=a

Gamma 2 a=1

Gamma 3 a, b, k

iom the neneral pamma PDF. Ffx)

l-exp -? ! 1 P

2

l-exp -E 5 i 01 4 P L J

il-(1+2;) exp(-2:)

Table 2. Cv as the fünction of ratios Cs/Cv and I&. I cv 3

cs/cv K = 0.01 K = 0.005 K = 0.001 1.0 0.75 0.79 0.90

1.30 l 2.5 1.22 1.33 1.50 3.0 1.42, 1.57 1.80 3.5 1.62 1.80 >2.00 4.0 1.78 1.95 B2.00

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q / Gamma2

, / / / / / / , / / / / / /

1 I 1 ‘

Figure 2. Relations between the Cs/Cv ratio and Cv, variation coefjcient, for some theoretical PDFs (shaded area is not recommendedfor application of encompassed curves i.e. PDFs)

Regarding values of a, b and c parameters, as it is shown by Bobeé (1975) and Rao (1980), probability density function may be of different shapes: bell-shaped (unimodal), U- shaped, J-shaped and reverse J-shaped. Areas of different shapes as the fùnctions of Cs and Cv are presented in Fig. 3. The bell-shaped probability density function appears in the areas marked with Zr and Z2, which are bounded by the curve determined by parameter values b = 0 and Csy = 0. This boundary line repres.ents two-parameters log-normal PDF. Table 4 shows domains of parameters a and b for different areas in Fig. 3.

Rite (1977) claims that only the unimodal shape of the log-Pearson type III probability density function satisfies conditions for frequency analysis of hydrological random variables. If this criteria is adopted for the definition of applicability domain, the corresponding area in Fig. 3 is bounded by the following expressions:

cv I 2a 43-a -4-a

cs 2-a -31-a +21-2a -2 cv 22a

c 3-av2-2a 2

>

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Table 4. Domains ofparameters a and b. Area Parameter a Parameter b

21 a>1 b>O

22 a>1 -l<b<O U aCI b<-1 J a<1 -l<b<O

RJl a< 1 b>O

RJ2 a>1 b c-1

6

Figure 3. Domains of different shapes of Log-Pearson Type 3 PDF:

COMPARISON OF THEORETICAL PDFs

The comparison of theoretical PDFs Will be illustrated for several values of Cs/Cv and Cv for which two-parameters PDF curves in Fig. 2 intersect (Vukmirovic, 1990). This gives an opportunity to compare two-parameters PDFs with three-parameters PDFs. Four different cases are chosen:

0 intersection of the Gumbel and the log-normal 2 PDFs (Cv = 0.364, Cs/Cv = 3.131),

0 intersection of the Gumbel PDF curve with the line for the two-parameters Gamma PDF (Cv = 0.570, Cs/Cv = 2)

0 intersection of the Gumbel and the Weibull two-parameters PDFs (Cv = 0.703, Cs/Cv = 1.621),

0 intersection of curves for the two-parameters log-normal and the two-parameters exponential PDFs (Cv = 0.596, Cs/Cv = 3.356).

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Table 5 presents comparison of two two-parameters PDFs (Gumbel and log-normal) and three three-parameters PDFs (Gamma, Weibull, Pearson and log-Pearson), for p = 1.0, Cv = 0.364 and Cs = 1.14. The values in Table 5 are quantiles of the probability P(X) ranging from 0.10% to 99.9%. For probabilities between 0.1% and 95% similar quantile values are obtained by the Gumbel, Log-normal 2, Gamma 3 and Log-Pearson III PDFs. The greatest differences are in comparison with the Weibull PDF (0.5% for P(x)=O.l%). The most significant differences are encountered for probabilities P(X) over 95%; Weibull 3 PDF (with the shift c = 0.4823) gives the quantile which is 70% higher then Gumbel PDF value. General conclusion is that for these values of Cs and Cv and large probabilities (P(X) over 90°A) one should be cautious of PDF used in the hydrologie minima frequency analysis.

Table 6 compares quantiles of probabilities P(X) from 0.1% to 99.9% according to two-parameters PDFs (Gumbel and Gamma) and three-parameters PDFs (log-normal, Weibull and Log-Pearson) for p = 1 .O, Cv = 0.57, Cs = 1.14. The biggest quantile for P(x)=O. 1% is obtained by the Gumbel PDF and it is 6% larger than the smallest value obtained by the Weibull PDF. The 99% quantiles for the Gumbel and log-normal PDFs are negative. For these values of Cs and Cv, an attention has to be paid in choice of theoretical PDF.

Table 7 presents comparison of quantiles of two two-parameters PDFs (Gumbel and Weibull 2) and three three-parameters PDFs (log-normal, Pearson III and log-Pearson III) for ~1 = 1 .O, Cv = 0.703 and Cs = 1.14. For probability P(X) = 0. lO%, similarly to the previously mentioned cases, the greatest quantile is obtained with the Gumbel PDF and it is 10% higher in magnitude than the smallest quantile (log-Pearson III PDF). For probabilities over 99%, negative quantile values are obtained with the Gumbel, log-normal 3 and log-Pearson III PDFs. This means that these PDFs are hardly acceptable for minima frequency analysis regarding statistics Cs and Cv.

I P(x) Table 5. Comparison ofPDFs with p = 1.0, Cv = 0.364, Cs = 1.14. 1 Gumbel 1 Log- 1 Pearson II 1 Gamma III 1 Log- 1 Weibull3 1

W) 0.1 0.5 1.0 5.0

2.797 2.339 2.142 1.679

normal 2 2.795 2.33 1 2.135 1.679

2.722 2.801 2.3 14 2.333 2.133 2.146 1.692 1.679

Pearson III 2.786 2.327 2.132 1.678

2.657 2.292 2.125 1.702

10.0 1.475 1.477 1.488 1.476 1.477 1.499 20.0 1.262 1.264 1.269 1.265 1.265 1.267 30.0 1.129 1.130 _ 1.130 1.130 1.132 1.131

t 50.0 I 0.940 0.940 1 0.932 1 0.939 i 0.940 1 0.925 70.0 0.784 0.781 0.772 0.781 0.781 0.762 80.0 0.701 0.698 0.692 0.699 0.698 0.684 90.0 0.599 0.598 0.600 0.599 0.598 0.602

I 95.0 ) 0.525 0.526 1 0.539 1 0.527 0.525 0.555 99.0 0.403 0.413 0.457 0.416 0.412 0.506 99.5 0.363 0.379 0.436 0.381 0.377 0.497 99.9 0.288 0.316 0.404 0.320 0.3 14 0.487

Table 8 compares quantiles of two two-parameters PDFs (log-normal and exponential) and two three-parameters PDFs (Gamma 3 and log-Pearson) for IA = 1 .O, Cv = 0.596 and Cs = 2.00. The Gumbel quantiles are also shown in the table although its Cs of 1.14 is signifïcantly

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different than one used in other PDFs (Cs = 2.00) causing serious quantile deviations from others in comparison. Quantiles according to Pearson III and Weibull 3 PDFs are identical to the Exponentia12 PDF, which is the reason to exclude them from the table. It cari be seen that exponential-type PDF quantiles (i.e. Pearson III or Weibull) are different from those of log- normal 2, Gamma 3 and log-Pearson III which are almost the same.

Table 6. Comparison ofPDFs with p = 1.0, Cv = 0.57, Cs = 1.14.

P(x) Gumbel Log- Gamma 2 Log- Weibull 3 (%) normal 3 Pearson 111

0.1 3.813 3.811 3.696 3.662 3.595 0.5 3.097 3.085 3.057 3.059 3.024 1.0 2.788 2.777 2.774 2.783 2.762 in ? fi/” 2.063 2.083 2.094 2.099 7

1.747 1.764 1.770 1.781 20.0 1.410 1.414 1.422 1.422 1.432 30.0 1.202 1 1.204 1.201

0.889 0.640 0.517

0.627 1 0.506 1 0.377 1

I 95.0 1 0.256 I 0.258 I 0.279 I 0.288 I 0 304 I 99.0 0.065 0.081 0.150 0.165 0.226 99.5 0.002 0.027 0.117 0.133 0.212 99.9 -0.115 -0.072 0.067 0.083 0.197

99.5 -0.230 -0.200 -0.089 0.048 0.028 99.9 -0.376 -0.322 -0.151 0.022 0.009

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Trrhle 8 Clomnarison of P = = Cs = 2.00 _________ -... -...-- ~ - ‘DFs with p 1.0, Cv 0.596,

P(x) Gumbel Log- Exponential Gamma 3 Log- W) normal 2 2 Pearson III 01 3 942 4 721 4.521 4.724 4.695 1<- -._ .- 0.5 3.193 3.555 3.562 3.585 3.545 1.0 2.870 3.098 3.149 3.113 3.092

7 13!2 5.0 1 2.112 1 2.128 2.189 1 2.133 1 10.0 1.778 1.741 1.776 ( 1.746 1 1.743 20 0 1429 1 1.366 1 1.363 1 1.366 1 1.368 50.0 0.902 0.859 0.817 0.858 0.859 70.0 0.646 0.643 0.617 0.641 0.643 80.0 0.5 11 0.540 0.537 0.537 0.539 90.0 0.344 0.424 0.467 1 0.421 1 0.422 97 0 I 0 37.7 I 0 347 0.435 I 0.344 I 0.345

t 90 _-.- n I n - ,--- n73

I I

0 23x 0.410 I 0.235 l 0.233 1 t 99.5 , , .- I 1 -0.043 -.--- 1 I

_.-- - I I I

0.208 0.407 ) 0.205 1 0.205

I 99.9 1 -0.166 1 0.156 1 0.403 1 0.155 1 0.153

CONCLUSION

The choice of a theoretical probability distribution function (PDF) in the process of statistical analysis of low flows present a very delicate task. It is necessary to keep an attention about the domain of applicability of every PDF in consideration. Examples presented show that very different values of low flow quantiles are obtained from used PDFs for the same probability and for adopted values of skew coefficients (Cs). Positive values of skew indicate the two-parameters gamma PDF as the most appropriate.

Finally, it is to remind both on delicacy of determinition of skew coefficient on the basis of a sample of low flow observations and on the need for a regional statistical analysis.

REFERENCES

Bobeé, B. (1975) : The Log Pearson Type 3 Distribution and Its Applicability in Hydrology, Water Resources Research, Vol. 11: 68 1-689. Kite, G. W. (1977) : Frequency and risk analyses in hydrology, Water Resources Publications, Fort Collins, Colorado. Rao, D.V. (1980) : Log-Pearson Type 3 Distribution: Method of Mixed Moments, Journal of Hydraulic Engineering, ASCE 106: 999-l 0 19. Vukmirovic, V. (1990) Frequency Analyses of Hydrologie Values (in Serbian), Faculty of Civil Engineering - Naucna knjiga, Belgrade.

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4. THEME VII : EROSION ET TRANSPORT SOLIDE

INTRODUCTION PAR PHILIPPE RAMEZ

Les problèmes liés à l’érosion des sols et au transfert des fines vers la rivière sont de plus en plus préoccupants. D’ailleurs l’article de Tidjani A. est très clair en ce qui concerne l’envasement des barrages algériens. La situation est alarmante (durée de vie très courte, ressource en eau compromise) et les chiffres (taux d’érosion, concentrations en crue) place ce pays en tête devant les autres pays d’Afrique du Nord. L’auteur précise que pour lutter contre ce phénomène il ne faut pas systématiquement draguer mais rechercher les causes et traiter le mal dès son origine. C’est bien là le cœur du sujet car pour traiter les causes il faut d’abord les comprendre. L’article de Vukmirovic V., basé sur un constat relativement pessimiste de l’état de l’art en matière de transport solide (théorie peu avancée, essais en laboratoire et mesures in situ difficiles) est assez réaliste sur ce plan là.

Différentes méthodes existent pourtant pour cerner le problème et nous retrouvons dans les articles présentés les deux grandes approches habituelles : déterministe et statistique. Le premier groupe est représenté par un article sur l’analyse des causes entraînant l’envasement des retenues (Tidjani A. et al.), un article sur les mécanismes de base du transport solide et sa mesure (Vukmirovic V.) et un article sur le dépôt des fines dans un réservoir et sa modélisation (Bessenasse M. et al.). Le deuxième groupe est représenté par un article sur les corrélations débit liquide / débit solide basées sur des mesures en rivière (Touaïbia B. et al.), un article sur les processus stochastiques appliqués aux débits solides (Bulu 1. et ai.) et un article sur la prise en compte des seuils et durées dépassées pour estimer le charriage (Vukmirovic V. et al.). Il existe cependant un troisième groupe, moins habituel dans ce domaine, qui pose le problème en terme d’analyse du risque et de l’optimisation d’un système (Bekkouche A. et al.).

Le domaine de l’érosion est très vaste et de nombreux mécanismes doivent être envisagés. Tidjani A. analyse l’érosion à l’échelle du bassin versant. Il constate, qu’en Algérie, les facteurs climatologique (pluies torrentielles), pédologique (sols friables), agronomique (couvert végétal) et topographique (forte déclivité) entraîne une forte production en sédiments sur les versants. Par contre, dans le talweg, il présente un bilan entre forces érosives liées à l’écoulement et résistance à l’érosion liée au substrat. Il insiste sur le rôle particulier de l’argile aussi bien pour son effet sur l’augmentation des forces résistantes (cohésion) que pour le fluage possible qu’elle induit lorsque le niveau de l’eau baisse trop rapidement. Enfin il décrit l’effet des aménagements et surtout le cas du barrage et les mécanismes de dépôt qui en résultent. De son côté, Bessenasse M. propose une distinction entre deux types de transport solide : celui des grains formant le lit relié à l’hydraulique locale (capacité de transport) et celui des fines provenant de tout le bassin versant corrélé aux variables climatologique, pédologique et hydrologique. Il rappelle la difficulté à estimer le volumes des fines transférées jusqu’à la rivière.

L’estimation des apports est possible par les approches statistiques appliquées sur un site

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particulier. Ainsi Touaïbia B. a établi des corrélations entre débit solide et débit liquide à différents pas de temps (année, saison, mois) à partir de données hydrauliques et de données en concentration mesurées dans deux stations hydrométriques à l’amont du barrage de Sidi Mohammed Ben Aouda (en zone semi-aride). L’érosion spécifique annuelle au droit des deux stations ainsi que la modulation intra-annuelle des apports liquide et solide sont présentées. Ces résultats permettent d’estimer le volume de sédiment entrant en moyenne annuellement au barrage. De son côté, Vukmirovic V. propose une analyse statistique du charriage en tenant compte à la fois du seuil de mise en mouvement et de la durée pendant laquelle un événement est soutenu ou dépassé. Cette méthode est appliquée à la rivière Sava à Skopice sur 49 années de données hydrologiques et de mesures de débit solide charrié, de nombreuses sorties sont proposées à différentes échelles de temps. Enfin la génération de débits solides peut aussi être envisagée. Bulu 1. constate que les modèles stochastiques (type ARMA) appliqués habituellement aux variables hydrologiques, donnent de bons résultats pour des débits solides mesurés périodiquement. Le modèle ARMA appliqué aux débits solides mensuels sur deux rivières américaines a permis de générer des événements « solides » synthétiques. Une bonne corrélation entre débit liquide et débit solide a ainsi pu être mise en évidence. Ce résultat permettrait donc d’utiliser les longues séries de mesure concernant les débits liquides pour les débits solides. Certains mécanismes du transport solide sont modélisables aussi bien en ce qui concerne la stabilité des lits (dans ce cas le transport e’st ramené à une simple déformation) qu’en ce qui concerne le transfert de fines en provenance du bassin versant. Vukmirovic V. propose une analyse du transport par charriage basée sur deux méthodes de mesures in situ : par la nasse et par traceurs. Une combinaison de ces deux méthodes appliquée à la rivière Save à Skopice près de Krsko a permis de déterminer le débit solide charrié en fonction des caractéristiques hydrauliques et granulométriques du tronçon. Les résultats obtenus sont en accord avec les lois classiques du transport solide. Il ressort de cette analyse que le choix d’un tronçon représentatif de la dynamique du cours d’eau est primordiale pour l’extrapolation à l’ensemble de ce cours d’eau. Bessenasse M. cherche à évaluer le coefficient de restitution des fines vers l’aval en fonction de la gestion d’une retenue algérienne (Zardezas) par une modélisation numérique. Le modèle utilisé est développé à partir du code 2-D horizontal RUBAR20. La dynamique des dépôts est analysée en fonction du pic et de la durée de la crue, de la concentration en sédiment et du niveau d’eau à l’arrivée de la crue. Les inconvénients du transport solide ont un coût et dans le cas de pays relativement pauvres ce critère devient vite prépondérant. Dans son article, Tidjani A. précise que plusieurs barrages algériens ont une durée de vie comprise entre 30 et 40 ans. Ces résultats n’étaient pas prévisibles lors de la construction des ouvrages en raison d’une sous-estimation des apports solides. L’exemple du barrage de Fergoug montre qu’il est difficile de mettre en place un protocole réaliste de dragage et que le gain obtenu ne compense pas les pertes considérables d’eau utilisée pour les opérations.

Bekkouche A. propose une méthode originale d’aide à la décision pour contrôler les coûts en matière de lutte contre l’érosion. Il s’agit en fait d’un système d’optimisation pour calculer le risque « érosion ». Trois approches (déterministe, semi-probabiliste et probabiliste) sont proposées pour déterminer la performance du système en fonction des mécanismes de base de l’érosion. Une quatrième approche (décisionnelle) permet de tenir compte des enjeux économiques. L’analyse des causes de l’érosion et des conséquences pourrait se faire à travers cette analyse ce qui permettrait en particulier de réduire le coût des conséquences de l’érosion. Un processus d’optimisation est proposé dans ce sens.

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AMPLEUR DE L’ENVASEMENT DANS LES BARRAGES ALGERIENS

TIDJANI Abdellatif El-Bari, YEBDRI Djilali, CHERIF El-Amine Maîtres assistants chargés de cours à l’Institut d’Hydraulique, Université des Sciences et de la Technologie d’Oran,BP. 1505 El-M’Naouer 3 1000 Oran Algérie.

Résumé :

Les retenues sont souvent exposées au problème d’alluvionnement. A long terme, cela compromet leur fonctionnement et leur rentabilité. L’Algérie est caractérisée sur l’ensemble de ses bassins versants, par le taux d’érosion le plus élevé de l’Afrique du Nord, estimé à 5000 Tonnes /Km2 /An, au niveau du bassin d’oued Agrioun qui alimente le barrage d’Iri1 Emda. Ce fort taux d’érosion a entraîné une diminution considérable, de l’ordre de 20 Millions de m3 par an, dans les capacités de stockage du pays. Une projection faite à l’an 20 10, montre que le volume envasé passe de 11% en 1990 à 24% en 2010 de la capacité initiale totale des barrages mis en exploitation. Ces chiffres nous confirment la gravité du problème. Il en ressort que la majorité des barrages algériens ont une durée de vie très courte, de l’ordre de 30 à 40 ans, ce qui ne correspond guère à la garantie de service établie au préalable. Pour illustrer ce phénomène, on présente dans cet article le cas du barrage Fergoug, vu l’importance de l’apport annuel de vase qui est de l’ordre de 800.000 m31 an où le seuil critique est largement dépassé. Pour y remédier, plusieurs solutions ont été proposées dont le dragage constitue l’intervention d’urgence et qui a été entreprise en 1990. Enfin, il en ressort de cet état des lieux que seule une connaissance approfondie des facteurs d’érosion, afin de guérir le mal à son origine, pourra contribuer à accroître efficacement la durée de vie de nos barrages sans passer par la technique de dragage qui ne se justifie pas toujours.

I/ INTRODUCTION :

L’érosion est à l’origine de tous les types de transport solide qui se développent dans un système constitué d’une part d’un élément principal qui est le bassin versant ou la rivière et d’autre part de l’élément moteur qui est l’eau. Ce phénomène d’érosion reste cependant très complexe du fait qu’il est lié à plusieurs facteurs.

En Algérie, le taux d’érosion atteint les valeurs les plus importantes de l’Afrique du Nord

Atlas Tellien (Rhiou, Sly, Fodda, Isser, ,)

Bassin de l’oued Agrioun qui alimente le

Fig. No 1 : valeurs du taux d’érosion dans quelques régions d’Algérie [l]

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L’intensité du phénomène se manifeste essentiellement en période de crue, c’est ainsi que des concentrations très élevées en matières en suspension sont souvent enregistrées pendant les crues.

FigN”2 : valeurs des concentrations en matières en suspension des eaux des oueds dans quelques régions d’Algérie[ 11.

L’envasement des retenues constitue la conséquence la plus dramatique de l’érosion. Il entraîne une diminution des potentialités hydrauliques du pays. En Algérie cette diminution atteint en moyenne 20 Mm3/an. D’autre part l’érosion entraîne : - Une défertilisation des terres agricoles, - Ensablement des ports. - Rehaussement des lits des rivières favorisant ainsi l’inondation. - Endommagement des infrastructures (pont, route, conduite . etc.).

II/ ANALYSE DU MECANISME D’EROSION :

Sous l’action du courant d’eau, les particules solides du fond et des berges des rivières sont arrachées et entraînées. En effet les particules solides ne sont arrachées que si la contrainte de cisaillement z y exercée par le courant d’eau dépasse un seuil appelé contrainte critique de cisaillement ~~~~ , donc z > 7cr.

z = pgR,I

où p : masse volumique de l’eau. g : pesanteur. RH: rayon hydraulique du cours d’eau. 1 : pente du cours d’eau. h : épaisseur de la couche de fond. ys , ye: densité du sol et de l’eau. <p : coefficient de frottement interne du sol. ,

Il faut noter que cette contrainte de cisaillement critique augmente avec le pourcentage en argile des sédiments et la finesse des particules. Le débit .des particules érodées est fonction de la différence entre la contrainte de cisaillement exercée z et la contrainte de cisaillement critique zCr., PARTHENIADES propose une formule empirique pour le calcul de ce débit[5].

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où M est une constante qui dépend de la concentration C&/l) des particules érodées. Elle est donnée par la formule empirique de BONNE-FILLE.

M = 5,5. lO-“.C3

II-l/Erosion dans les bassins versants :

En Algérie, l’érosion des bassins est très répandue car toutes les conditions lui sont favorables. Au moment des pluies, une forte érosion est engendrée par plusieurs facteurs. Pour ne citer que quelques-uns uns de ces facteurs : - Le relief: une forte déclivité entraîne une forte vitesse de ruissellement. - irrégularité : les pluies torrentielles supérieures à 300 mm par 24 heures sont très fréquentes sur les bassins de l’atlas tellien. Ce qui contribue à accroître l’agressivité sur le terrain. - La Géologie : en Algérie, l’argile et la marne, qui ont une très faible résistance aux forces érosives, forment 75 % du crétacé supérieur tellien. - Absence du couvert végétal favorise la dégradation des terrains.

Tous ces paramètres liés entrent simultanément en jeu, et, il est difficile d’en isoler un, pour qu’il soit le seul à considérer dans l’érosion des bassins versants pendant la crue.

II-2/Erosion dans les rivières :

Les particules qui forment le fond et les berges d’une rivière sont arrachées lorsque la vitesse de l’eau est très élevée.

Dans certains terrains argileux, au moment de la décrue, le fluage peut engendrer une dégradation du talus à cause d’une baisse rapide du niveau de l’eau dans la rivière.

Toutes ces particules arrachées du bassin versant et du lit de la rivière, sont transportées vers l’aval par le cours d’eau, soit en suspension pour les particules fines (sable fin, argile,...), soit en charriage sur le fond pour les grosses particules (sable, graviers, galets).

II-3/Envasement des retenues et consolidation des vases :

A l’état naturel, les rivières transportent progressivement jusqu’à la mer des quantités importantes de sédiments. En aménageant ces rivières, le transit naturel de ces sédiments est modifié, c’est ainsi que les matériaux grossiers transportés par charriage sont freinés dans la zone de remous caractérisée par la présence d’objets flottants et formant un delta en queue de la retenue. Les particules fines traversent cette zone de remous et forment un courant de densité qui s’écoule au fond de la retenue transportant ainsi la vase jusqu’au pied du barrage. En absence de soutirage de fond, il se forme un dépôt de vase (Fig.3).

En réalité, le mécanisme d’envasement des retenues est très complexe, vu l’influence de diverses caractéristiques de la retenue. Parmi les facteurs principaux qui modifient le schématique précédent (Fig.3) on cite : - La topographie de la retenue modifie les conditions d’écoulement. - Les affluents chargés en matières en suspension et rejetés dans la retenue modifient le mécanisme d’envasement - La végétation existante au fond de la retenue retient une grande partie de sédiments et accélère la consolidation de la vase par drainage.

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Zone de remous

sédiments grosiers

densité

Lac de vase barrage

Fia.No : Schéma du mécanisme d’envasement des retenues

Les particules érodées et transportées arrivent au niveau de la retenue où elles commencent à se décanter selon les conditions d’écoulement et leurs grosseurs granulométriques.

Le débit de dépôt a été évalué par KRANE par une formule empirique où il montre qu’au-dessus d’une certaine contrainte de cisaillement de fond (TO&, il n’y a pas de dépôt. Il a proposé une loi donnant un débit de dépôt proportionnel au pourcentage de cette contrainte, à la concentration C et à la vitesse de chute des particules VC [5].

/ \

0 -dépôts

Pour les vases marines, cette contrainte limite est de l’ordre de 8. 10m2N/m2

Après cette phase de décantation, la vase se consolide sous la charge des couches déposées, en évacuant les eaux interstitielles. Les espaces interparticulaires sont ainsi diminués et la concentration du dépôt augmente avec le temps.

C(t) = C, + a logt

où a est un coefficient qui dépend de la taille des particules.

Cette consolidation peut être plus accélérée en présence d’un drainage naturel assuré par la présence de sous couches de sable ou une végétation. Il existe aussi un gradient de concentration entre la surface et la profondeur h, tel que :

C(h) =C, + m.logh

La consolidation varie d’un matériau à un autre. Certains restent à l’état fluide pendant des mois, alors que d’autres se consolident en quelques jours.

III/ ETAT D’ENVASEMENT DES BARRAGES EN ALGERIE :

Un état des lieux sur l’envasement des 37 barrages mis en exploitations (1990) montre que la capacité totale initiale de ces barrages qui est 3886.5 M.m3, sera envasé à 24% d’ici l’an 2010,.ce qui explique un déficit énorme en capacité de stockage des ressources en eau du PaY s.

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L’ampleur du phénomène varie d’une région à une autre, dans le tableau suivant on présente l’état d’envasement de quelques barrages algériens.

Barrage Année Capacité Superficie Apport Capacité Taux Volume Volume de Mise initiale du bassin Solide actuelle d’envasement envasé envasé

en (Mm’) versant Moyen (Mm3) Actuel Actuel prévu service @Qn*) annuel W) (Mm31 en 2010

(Hm3) (Mm3)

BENI-BAHDEL 1 1940 j 63 1 1016 1 0.22 1 56.50 ) 10 1 6.50 1 11.78 MEFROUCHE 1 1963 j 15 1 264 1 0.017 1 14.60 / 2 I 0.40 / 0.74 SARNO I 1954 I 22 1 264 1 0.021 1 21.30 / 3 I 070 I 112

BOUHANIFIA 1944 73 7850 0.58 51.60 29.30 2-1.4; 35.32 FERGOUG 1970 18 420 0.83 3.90 78.30 14.10 30.70 BAKHADA 1963 56 1300 0.45 45.10 19.50 10.90 21.70 SMBA 1978 235 4890 1.34 225.60 4 9.40 41 56 OUED EL FODDA 1932 BOUGHZOUL 1934 GHRIB 1939 HAMIZ 1935

DJORF TORBA 1 1969

I 228 I 800 55 20500

280 2800 21 139 Cr 31 570 31 1500 47 1300

1 350 1 22000

132.70 42 20 63.60

165.60 40.90 16.40 21.90 20.20 34.80 26.40 14.80 26.50 43.60

316.40 9.60

Fia.No : Etat récapitulatif de l’envasement de quelques barrages exploités en Algérie[ l]

Ces chiffres nous confirment la gravité du problème. Ils montrent que plusieurs barrages ont une durée de vie très courte qui est de l’ordre de 30 à 40 ans. Une durée qui ne correspond point à la garantie de service établie au préalable, ceci est dû essentiellement à une mauvaise estimation du transport solide dans nos bassins versants.

III-l/Cas du barrape Fergoug :

Pour illustrer le problème d’envasement des retenues des barrages algériens, on présente dans cet article le cas du barrage Fergoug où l’apport annuel solide de l’ordre de 800.000 m3/an a largement dépassé le seuil critique d’envasement qui permet une gestion rationnelle des eaux. Il ressort d’une projection faite à l’horizon 2010 que ce barrage finira par périr si des dispositions radicales ne soient pas prises dans les plus brefs délais.

A cet effet, une opération de dévasement de 12 Mm3 par dragage hydraulique a été lancée en mars 1990. Pour cela on a procédé dans une première étape aux levers balthymétriques afin de mesurer le taux d’envasement et le niveau de la vase en différents points de la retenue. La retenue de Fergoug est alimentée principalement par deux oueds en l’occurrence oued Fergoug et oued Hammam. Les profils en long des deux oueds permettent d’estimer le taux d’envasement (Fig.5).

125

Ê

a! OI

102,5

d >

100,o m d

(a>

ar 97,5

d

il 95,0 3 u d c

92,5

0 w 0 90,o u LL

87,s

E

0 m

:

m rl

m d

4 3 a! d c 0 u 0 L( PI

I I I I I I I I I I I I 0 0 500 500 1000 1000 1500 1500 2000 2000 2500 2500 3000 3000

102,5

100,o

97,5

95,o

92.5

90,o

87,5

Distance au mur du barrage (In)

y,,-/ --+--.c/-

_,.....__~_.~ .. :. ,,._....... .__.

0 I I I

500 1000 1500 2000

Distance au mur du barrage (ml

FiE.No :Levers balthymétriques avant et après dévasement. (a) Oued Hammam. (b) Oued Fergoug

A cause des années déficitaires et successives en eau ces derniers temps, l’opération de dévasement prévu pour 36 mois n’a duré que 6 mois, vu qu’elle s’accompagne d’une perte d’une quantité considérable d’eau évacuée avec la boue (40%vase + 60%eau). Le volume dévasé est estimé à 4.071.730 m3

A cause des années déficitaires et successives en eau ces derniers temps, l’opération de dévasement prévu pour 36 mois n’a duré que 6 mois, vu qu’elle s’accompagne d’une perte d’une quantité considérable d’eau évacuée avec la boue (40%vase + 6O%eau). Le volume dévasé est estimé à 4.071.730 m3

IV/ LUTTE CONTRE L’ENVASEMENT DES RETENUES :

Il s’avère donc impératif d’utiliser des moyens de lutte adéquats pour allonger la durée de vie des barrages. La première idée qui vient à l’esprit pour éviter l’envasement est la prévention, d’une façon schématique, on agit sur trois fronts :

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IV-l/ Lutte au niveau du bassin versant :

- Diminuer l’impact des gouttes d’eau de pluie sue le sol en augmentant la résistance du sol au ruissellement par paillage ou intensification de la culture. - Diminuer la pente par billonnage, terrasses, bandes d’arrêt, etc. - Création de zones de dépôts par des haies et des digues en terre favorisant la décantation d’une grande quantité matières solides. Il faut signaler qu’en Algérie un programme a été lancé dans cette perspective. Il projette l’aménagement d’une superficie de bassins versants de 1.5 Mha d’ici l’an 2010, avec un rythme de 67000 ha/an.

IV-2/ Lutte au niveau de la rivière :

Le fond et les berges d’une rivière doivent être protégés contre les forces érosives des courants d’eau torrentiels. On procède en général de deux manières : - Une protection continue par plantation, enrochement, matelas de bitume ou gabionnage et parfois des palplanches pour protéger les berges. - Une protection discontinue qui consiste à éloigner le courant érosif du fond et des berges d’une rivière par des épis placés sur les berges et qui repoussent les courants érosifs vers le centre de la rivière ou des seuils implantés en travers limitant ainsi l’approfondissement du fond. En général, on emploie les protections discontinues sur les rivières larges alors que les protections continues sont mieux adaptées aux rivières étroites

IV-3/ Lutte au niveau de la retenue :

Les eaux chargées de densité supérieure à la densité des eaux claires, arrivent dans la retenue par un courant de densité qui s’écoule au fond. Il transporte la vase jusqu’au pied du barrage En absence de soutirage de fond, elle s’y accumule. Le soutirage du courant de densité est donc une possibilité de réduire l’envasement. En Algérie, les résultats de dévasement les plus remarquables par ce procédé ont été obtenus au barrage d’Ighil-Emda, le premier barrage algérien d’organes spéciaux de soutirage. On a pu évacuer en dix (10) jours de crue par an 50% de l’apport solide annuel. Dans le cas où le barrage ne serait pas équipé d’organes de soutirage, on utilise les vidanges de fond c’est ce qu’on appelle « chasse ». Cette solution est peu utilisée, vu qu’elle entraîne des pertes de quantités considérables d’eau.

VKONCLUSION :

En Algérie, le phénomène d’envasement des retenues a pris suffisamment d’ampleur. Par conséquent, le potentiel hydraulique du pays chute sans cesse au cours des dernières années. La capacité de stockage déjà insuffisante de nos barrages sera réduite de l’ordre de 1/4 au début siècle, ce qui nous rend inquiet quant à l’avenir de nos barrages. Face à cette situation, il devient absolument urgent et primordial d’agir selon les étapes suivantes qu’on juge très efficaces, à savoir : - A cours terme, en ce qui concerne les barrages existants et envasés, il faut absolument procéder au dévasement par une intervention mécanique ou hydraulique et ce, selon l’importance de la retenue.

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- A long terme, , Quant aux barrages à construire, il faut, d’une part les doter d’organes de soutirage bien dimensionnés afin d’améliorer les conditions de soutirage pour un dévasement par le courant de densité, et d’autre part limiter l’érosion qui est le facteur principal de l’envasement des retenues en aménageant les bassins versants et les oueds.

La solution technique proposée pour le dévasement du barrage Fergoug, ne se justifie pas toujours économiquement. Seules une exploitation et une gestion dynamique et rationnelle de nos barrages, basées’ sur une étude approfondie des facteurs d’érosion, pourra contribuer à accroître efficacement la durée de vie de nos barrages.

VI/REFERENCES BIBLIOGRAPHIQUES :

[l] Rapport de l’Agence Nationale des Barrages, Envasement des barrages algériens : Stratégie de gestion des eaux Horizon 2010, 1990 [2] J.CLAUDE et R.CHARTIER, Mesure de l’envasement dans les retenues de six barrages en Tunisie, Cahier d’orstom, série hydrologie, Volume XIV, n”l, 1977. [3], M.URECHET et M.BRUTTIN, Définition des retenues sur l’oued NECKOR au Maroc, 14eme Congrès des grands barrages, Rio de Janeiro, 1982. [4] C.PERIGAUD, Mécanique de l’érosion des vases, la houille blanche, n”7/8, 1983. [5] PKEUER et J.P.BOUCHARD, Etude bibliographique de l’alluvionnement des retenues par sédiments fins, Bulletin de la direction des études et recherches, n”1, 1986. [6] C. MIGNIOT, Action des courants de la houle et du vent sur les sédiments, La houle

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TRANSPORT DES SÉDIMENTS CHARRIÉS PAR LES RIVIÈRES

Vojislav Vukmirovic Faculte de Génie Civil, Université de Belgrade, Yougoslavie

Résumé

Dans les études du transport de sediments charriés par les rivières, l’idée principale est qu’on doit connaître les propriétés du courant d’eau et du sédiment charrié. A la base de celles-ci on peut éstimer le débit du sédiment charrié ainsi que les effets provoqués par les ouvrages hydrauliques sur les rivières. Les mesures sédimentologiques complètes comprennent des mesures des caractéristiques morphologiques, des vitesses d’eau, des mesures du sédiment en suspension et du sédiment charrié. On a appliqué des mesures conventionnelles du sédiment charrié, ainsi que des mesures par des traceurs radioactifs. On donne la description des techniques appliquées, quelques résultats des mesures et les conclusions à la base des expériences.

INTRODUCTION

Les études des sédiments fluviaux se heurtent souvent à de sérieux obstacles parce qu’il n’existe pas encore de théorie pleinement satisfaisante sur le transport des sédiments et il faut encore surmonter un bon nombre de difficultés quant à son évaluation pratique. La solution apparaît dans les procédés utilisant en même temps des analyses théoriques, des essais de laboratoires et des mesures sur les rivières. Les mesures in situ sont d’importance particulière parce qu’il est indispensable de bien connaître les caractéristiques hydrologiques, morphologiques, hydrodynamiques et sédimentologiques d’une rivière afin d’y étudier les processus de transport des sédiments.

MESURES SUR LE TRONÇON REPRÉSENTATIF

Les recherches des sédiments fluviaux demandent un équipement parfait et une organisation excellentes des mesures. Les mesures sédimentologiques complètes sont coûteuses. Elles sont souvent menées pour résoudre des problèmes posés par des ouvrages hydrauliques. Le choix du tronçon des mesures d’une rivière est limité par le lieu de la construction hydraulique projetée. Cependant, il faut tâcher de choisir un tronçon de la rivière où l’écoulement est uniforme, des trajectoires rectilignes et des caractéristiques hydrauliques, morphologiques et sédimentologiques représentatives pour une région très large. Un choix correct du tronçon donne la possibilité de vérifier quelques relations entre des facteurs hydrodynamiques et le transport solide. Ceci permet une extrapolation des résultats des recherches pour un intervalle de temps plus long et pour d’autres portions du cours d’eau.

Les mesures sur le tronçon de la rivière doivent donner les informations complètes pour les analyses hydrologiques, morphologiques, hydromécaniques et sédimentologiques de la rivière. Elles comprennent:

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(a) des observations quotidiennes des niveaux d’eau et des concentrations de sédiments en suspension,

(b) des mesures périodiques le long du tronçon (les sections transversales, les pentes de la ligne d’eau, l’hydrométrie sur plusieurs sections, les analyses granulométriques de sédiment du fond, les formes de lit),

(c) des séries de mesures sédimentologiques complètes dans des conditions hydrologiques différentes comprenant des mesures de la pente de la ligne d’énérgie, des vitesses d’eau, du sédiment en suspension (concentrations et granulométrie) et du sédiment de fond charrié.

MESURES DU SEDIMENT CHARRIE

Les mesures de débits du sédiment charrié représentent un problème dont la solution n’est pas complète. Deux méthodes de mesures sont souvent pratiquées: par la nasse et par les traceurs radioactifs ou fluorescents.

Les mesures du sédiment charrié par la nasse demandent une station hydrométrique bien équipée et un degré élevé d’entraînement de l’équipe. On utilise un point, une plate-forme, ou le bateau pour réaliser les mesures avec équipements très lourds. Il faut descendre la nasse au fond en plusieurs points de mesure à la section. A chaque point, la mesure se répète plusieurs fois.

Les problèmes des mesures par la nasse sont: le contact au fond, les vibrations de la nasse, les difficultés à réaliser des mesures pendant les crues, le coefficient de rendement des mesures. Malgré tout, on peut dire que les mesures par la nasse donnent des résultats corrects de la composition granulométrique du sédiment charrié et des informations approximatives du débit du sédiment charrié.

Les traceurs sont un moyen important dans les recherches des caractéristiques cinématiques et dynamiques de l’eau et des sédiments. L’application des traceurs dans les recherches du mouvement du sédiment charrié a été orientée vers trois problèmes: la vérification des directions des déplacements des sédiments, la détermination de la dispersion du sédiment et les mesures du débit du sédiment charrié.

Les mesures par traceur sont basées sur les méthodes d’intégration des masses du sédiment entre les détections. Le principe des mesures par traceur est assez simple: il faut déposer une certaine quantité de sédiment marqué sur le fond et suivre leur déplacement par détection. Le transport ( TB) du sédiment charrié est défini par l’expression

TB =pB X, EL

où: pB - densité de sédiment charrié, X,,, - déplacement moyen de l’onde du traceur, E - épaisseur d’enfouissement du sédiment, L - largeur de la zone de charriage.

La méthode du “bilan de taux de comptage” de Sauzay-Courtois permet dans le cas d’application des traceurs radioactifs de déterminer l’épaisseur d’enfouissement E sans les échantillons du sédiment du fond (Sauzay, 1967).

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La technique de préparation des traceurs radioactifs pour les recherches en sédimentologie est très développée, en premier lieu grâce aux chercheurs français du CEN de Saclay, France. On prépare le traceur de granulométrie voulue, entre une dizaine de micron et 2 mm, avec des caractéristiques de transport, semblabes à celles du sédiment sablonneux fluvial, On utilise deux techniques: le verre broyé et le marquage du sable naturel par l’adsorbtion en surface. On peut également préparer le traceur pour le gros matériel (diamétre supérieur à 20 mm) par le perçage de trous et l’introduction d’un morceau de fil radioactif. Il faut enfin noter qu’il y a des problèmes dans la préparation du traceur radioactif pour les sédiments de granulométrie entre 2 et 20 mm.

L’expérience yougoslave des trente dernières années, dans les mesures de sédiment charrié, montre que les mesures par la nasse donnent les meilleurs résultats sur les rivières moyennes (largeur de lit entre 50 et 250 m), avec le sédiment charrié de granulométrie non uniforme, en vue du mélange de sables et graviers. Il est souhaitable de faire les mesures du sédiment charrié par les traceurs radioactifs en même temps.

Dans les études de charriage des petites rivières, l’hydrologie spécifique avec les ondes de crue éphémères et les caractéristiques specifiques du sédiment (mélange de sables, graviers et galets) créent de grandes difficultés à la fois dans la réalisation technique des mesures et dans l’interprétation des résultats. L’expérience a montré que dans ce cas, la technique la plus efficace, et quelques fois la seule possible, pour mesurer le sédiment charrié est la méthode des traceurs.

En comparant les résultats obtenus par les deux différentes méthodes, nous devons exprimer un certain doute quant aux résultats du débit de sédiment charrié obtenus par la nasse, parce qu’ils représentent le débit instantané en un point. Considérant que le mouvement de sédiment charrié est constitué de déplacements discrets de grains insolés, successivement interrompus par des périodes longues de repos, il est évident que la méthode d’intégration volumétrique et spatiale, offre des résultats plus sûrs.

Evidemment, les traceurs sont un moyen puissant dans les recherches du sédiment charrié. D’autre part, il est important de souligner que l’application des traceurs n’exclut pas des mesures hydrométriques et sédimentologiques conventionnelles ni des analyses hydrauliques. Il ne s’agit pas d’une concurrence entre les méthodes conventionnelles et la méthode du traceur. Ces méthodes se complètent mutuellement. Leur application parallèle garantie de meilleurs résultats.

MESURES SUR LA RIVIERE SAVE PRES DE KRSKO

Les mesures hydrométriques et sédimentologiques sur la rivière Save à Skopice près de Krsko en période mai-juin 1975 sont organisées par l’Institut d’eau Jaroslav Cerni de Belgrade. Les mesures ont servi pour les besoins de construction de la prise d’eau pour la Centrale nucléaire de Krsko.

Le choix de tronçon représentatif de la rivière des mesures est fait d’après l’analyse des plans, des sections transversales et la reconnaissance par la visite. La portion de 5 km est stabilisée avec un régime équilibre de sédiment charrié. Pour le besoin des mesures on a construit une plate-forme, qui se déplace à travers la section à l’aide d’une corde transversale.

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Par les mesures hydrométriques on a obtenu les informations géometriques et hydrauliques de la section hydrométriques. Paralèllement on a mesuré le sédiment en suspension (les concentrations et débits, les changements de concentration et granulométrie en section).

Les mesures de sédiment charrié ont compris: la prise d’échantillons de fond pour la granulométrie, les mesures par la nasse mécanique (type hongrois) et les mesures par traceurs radioactifs. Les mesures par la nasse ont été faite au cinq sept verticales en répetant les mesures plusieures fois (min trois fois). Les echantillons mesurés ont donné les éléments pour le débit de sédiment et la granulométrie. A la figure 1 on donne l’exemple d’une mesure par la nasse. La table 1 présente des résulats des mesures de sédiment charrié par la nasse.

Figure1 . Mesure de sédiment charrié par la nasse sur la rivière Save à Skopice.

ANALYSE DES RESULTATS

Le procédé préliminaire a pour but de déterminer des liaisons fonctionelles entre la hauteur du niveau d’eau et les paramètres hydrauliques et sédimentologiques. Il faut construire des fonctions du débit liquide (courbe de tarage), de la vitesse moyenne à la section, de la surface de la section, du rayon hydraulique, de la pente de la ligne d’énergie, de la rugosité, du débit de sédiment charrié mesuré par la nasse, des caractéristiques des courbe sgranulométriques du sédiment charrié, des caractéristiques des courbes granulométriques du matériel du lit qui dépendent de la hauteur du niveau d’eau (Fig. 2). Ce procédé élémentaire sert à vérifier les mesures et à préparer les éléments pour le procédé complémentaire, permettant d’analyser les données du débit du sédiment charrié et d’extrapoler la fonction du débit du sédiment charrié.

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No Table 1. Résultats de mesures de sédiment charrié

Date Niveau Débit d’eau Vitesse Profondeur Débit (m’/s) moyenne de séd. ch.

1975 H (cm) v hds) h (4 GB (kds)

EL- 1 ’ 505 2.10 3,‘lO y25 1,90 2,74 3,94 1,68 2,45 0,510

2 10-5 138 400 3 11-5 110 315 4 12-5 102 302 1,66 2,39 0,340 5 14-5 86 270 1.56 2,28 0,040 6 1 17-5 83 251 1.54 2.15 0.025

I 7 / 19-5 / 75 250 8 1 29-5 71 237 9 1 21-5 80 248 10 j 22-5 79 248

1154 2,14 1,54 2,04 1,52 2,16 1:53 2,14

11 1 24-5 j 130 1 380 1.87 2.64 1,220 12 1 3-6 1 296 1 820 2.44 4.15 43.5

232 640 2:25 3.80 12,o 173 485 2,ll 3,26 1,50 144 415 1,98 2,28 0,27

1 140 1 405 1,92 2,80 0,193 [ 17 1 19-6 1 170 1 480 2,02 3,04 11,50

H (cm) i

600

500

400

300

200

100

/

/ I

/ /

,'Q /

/ d I /

P

JP

I

4x0 looo/ ,Bp 2:do1:B~),[4,,.. i

+/ +040608

Q(m3's) IOO 200 300 400 ‘oo> (m2)

Figure 2. Les caractéristiques de la section.

Dans ce procédé, il faut d’abord passer aux nombres nondimensionnels. Entre plusieurs possibilités nous avons utilisé (l’exemple présenté, Fig. 3) la relation entre la fonction du sédiment et la fonction du courant, qui a été obtenue par la méthode des moindres carrés:

133

où: @ = G, / Lfp, dg la fonction du sédiment, 8 = U, / Jp’gD est la fonction du

courant, G, débit de sédiment charrié, p, - densité du sédiment, p’ = (p, - p) / p - densité

relative, g - gravité, D - diamètre du grain, U, - vitesse dynamique.

2000

1000

? 800

-3 = 600 0,

400

300

Figure 3. La fonction de sédiment en relation de la fonction du courant

m - mesuré ’ ~- E - Einstein

MPM - Meyer Peter C - Chamov L - Levi G - Gontcharov

0.1 1 248 10 20 40 60 100 200 300 GB (kg/9

50

Sur la même figure nous avons présenté les essais de laboratoire (Gontcharov, 1954) aves les sédiments charriés de diamétre supérieurs à 2 mm (indiqués par les points vides). On constate quelques différences entre les mesures realisées en laboratoire et les mesures faites sur la rivière, mais nous donnous plus d’importance aux mesures sur le terrain. Nous considérons aussi que les spécificités locales (la forme des grains, la non uniformité de la granulométrie etc.) ont de l’influence sur les mesures sur place.

On utilise la relation (2) pour extrapoler la fonction entre le débit liquide et le débit du sédiment charrié (Fig. 4). On a également, evalué le débit du sédiment charrié par les formules d’Einstein (E) Meyer Peter-Muller, Levy (MPM) (L). Gontcharov (G) et Chamov (cr). On voit que les résultats obtenus par les formules s’écartent des résultats des mesures dans le domaine d’eaux moyennes. Mais, nous sommes loin de conclure que ces formules ne soient pas d’une grande validité; tout simplement, dans les conditions spécifiques étudiées, la relation (2) donne une description satisfaisante du processus et sert pour l’extrapolation et la simulation d’une série sédimentologiques.

134

0.5 CP

0.4

0.3

0.2

0.1

0

0

0 0

00” o/

00

/ 8 0 0 0

0

0 .o b. 0 O

/

0

0 0

0 0

. 080 _ 000.

/ 0

0

l 0

0.15 0.20 0.25

Figure 4. La relation entre le débit de sédiment charrié et le débit d’eau.

Les mesures par les traceurs donnent la masse du sédiment entre les deux détéctions, réalisées pratiquement pendant l’étiage, parce que les conditions sont idéales et la précision des mesures maximales. Cela signifie qu’on obtient la masse transporté par une onde de crue. Un procédé de déconvolution doit être alors appliqué pour déterminer la relation entre le débit du sédiment et les paramètres hydrauliques (débit liquide, par exemple). Pratiquement, il faut ajuster une courbe intégrale du sédiment charrié à la courbe intégrale mesurée par les traceurs.

La comparaison entre ces deux méthode est présentée à la table 2, pour les quatre périodes caractéristiques.

Il faut indiqué que les difficultés des mesures d’enfouissement de sédiment ont été causé pur la crue de 2000 m”/s au début du Juillet 1975. Les mesures de l’épaisseur d’enfouissement ont été complétés par les résultats des mesures plus complète sur la rivière Savinja (l’influence de la rivière Save) et par la calibration avec des mesures par la nasse dans la période du 14 au 25 mai.

Malgré les différences entre les mesures par traceurs radioactifs et par la nasse on peut accepter l’analyse obtenu par les mesures sur place (par la nasse) et par les essais au laboratoire (Gontcharov).

Table 2: Transport de sédiment charrié par traceurs (TTR) et par la nasse (TN~ formule 2)

Date de la détection

10 Mai 21 Mai

X?l TTR TNZ

(m (t) (t) 12 59 60 20 98 86

25 Mai 90 441 426 21 Juin 3350 16400 14400

135

REGIME DE SEDIMENT CHARRIE

Suite aux observations hydrologiques à la station Rade-e (en amont de Kr{ko) et la correspondance entre les observations à Skopice et Rade-e on a évalué les débits d’eaux quotidiens à Skopice pour la période 1926-1974. Ensuite, on a éstimé des débits journaliers de sédiments charriés. La masse annuelle de sédiment charrié par la rivière Save près de Kr{ko peut s’ exprimer par la moyenne de 115700 t/a, l’écart-type de 77340 t/a, max 388.300 t/a et min 4760 t/a.

La construction proposée pour la prise d’eau avec le dragage (une solution possible) a demandé une analyse statistique des masses, de sediment charrié, maximalles annuelles pendant trois et pendant sept jour. On a appliqué la méthode des maxima annuel (la loi de Gumbel). Les statistiques sont pour trois jours: moyenne T,j = 26,600 t/3; l’écart-type Sj = 17,360 t/3j et pour sept jours Tm7 = 34420 t 5’: = 21,940 t.

CONCLUSIONS

On peut constater que, malgré quelques défauts des méthodes de mesures du débit du sédiment charrié, on peut obtenir des informations satisfaisantes en combinant des méthodes conventionnelles et celles des traceurs avec les résultats des essais aux laboratoires et les analyses théoriques.

REFERENCES

Gontcharov, V.N. (1954) Osnovy Dinamiky Ruslovyh Potokov, Gidrome-teorologichesko Izdatelstvo, Leningrad.

Sauzay, G. (1967) Méthode du bilan des taux de comptages d’indicateurs radioactifs pour la détermination du débit de charriage des lits sableux. Thése d’ingénieur-Docteur, Faculté des Sciences de Toulouse.

Vukmirovic, V., Vukotic, R. (198 1) Mesure des sédiments charriés par les rivières, Erosion and Sediment Transport Measurement (Proceedings of the Florence Symposium, June 1981) IAHS Publ. no. 133.

136

SEDIMENT DEPOSITS IN A RESERVOIR POSSIBLE METHODS OF ESTIMATION AND CHOICE

M. Bessenasse’, A. PaquieS, P. Ramez2, S. Massart’

Abstract The estimate of the deposition rate in reservoirs and then their ltfe duration requires from one hand the determination of the sediment inputs and from the other hand the analysis of the mechanisms of transfer and deposit upstream from the dnm. Globally, the ain: i.2 the estimate qf a trapping coefficient in the reservoir and then the effect on the sediment Io;ld fransported by the reach of the river downstream from the dam. Local& the effiency of the opening of the gates for the evacuation of the sediments located upstream may be the main objective. Then, modelling the deposits might use simplified relation but also ID, 20 or 30 hydrodynamic models. In any case, it is essential to collect enough precise data in order to estimate properly the water and sediment inputs and to follow the evolution of deposits. An illustration of these various aspects is proposed for the case of the Zardezas reservoir (Algeria).

Difficulties in estima ting sedimen t deposits

Sediment deposits in reservoirs become a very disturbing problem in countries of Northern Africa and particularly in Algeria. The estimate of the deposition rate in these reservoirs and then their life duration requires from one hand the determination of the sediment inputs and from the other hand the analysis of the mechanisms of transfer and deposit upstream from the dam.

Methods that provide an estimate of the sediment inputs coming from the upstream basin cannot be trusted. First, the classical methods from mechanics only estimate the transport capacity limited to the exchanges between the grains deposited and those in movement inside the water ; they do not include the very small particles that stay suspended in the flow. Secondly, the hydrological or statistical approach does not separate easily the direct phase - particles withdrawn and carried away by rains - and the movement of sediments previously deposited in the beds or flood plains (Ramez and Kellal, 1994).

Thus it is necessary to perform measurements of sediment transport upstream of the reservoir. The difficulty to obtain reliable values of bed load discharge leads to propose an estimate of this discharge by a computation of the maximal capacity of transport of the river upstream using a relation such as Meyer-Peter Miiller’s. Such an estimate Will be reliable if the bed load sediment size is known and if the reach of the river upstream the reservoir cari be considered as in equilibrium. Anyhow, in the cases considered, bed load is generally much lower than suspended load. Then, only, the suspended sediment concentration should be measured by suitable sampling methods. It is essential that these measurements should be performed

’ UNIVERSITÉ DE BLIDA. INSTITUT DE GÉNIE CIVIL ET RURAL, ROUTE DE SOUMAA BP270 BL.IDA ALGÉRIE Fa : 213.3.43.38.64 ’ CEMAGREF, DIVISION HYDROLOGIE-HYDRAULIQUE, 3 BIS, QV CHAUVEAU, CP 220 69336 LYON CEDEX 09 FRANCE F.~v; 33.4.78.47.78.75

137

regularly several times during flood periods. Later on, the results of these measurements cari be treated statistically in relation with rains and water discharges in order to build some scenarios of sediment inputs. The analysis of the transfer and deposition of sediments inside the reservoir may have several objectives with various scales. Main point Will be the estimate of a trapping coefficient which Will provide the volume of sediment deposited. If you tare about the river downstream, you Will estimate the distribution of this volume along the year in relation with the distribution of the discharges. The localisation of the deposits inside the reservoir may have some importance, particularly, if there are some populations along the reservoir. The uses of the reservoir are linked with various intakes which should be kept out of the sediment deposits as long as possible; it means that specifïc devices should be designed and their operation modelled.

Any way it is always required to follow up the deposits inside the reservoir (topography, characteristics of sediments) and the sediment outputs during usual discharges, floods, flushes and emptying.

The case to be treated is a situation ofien met, particularly in Algeria: measurements of inputs, outputs and deposits exist but their quantity and quality are not suffïcient to provide local (in space and time) estimates; the objective is an estimate of the trapping coefficient in various scenarios differing by management and volumes of sediment inputs. More or less detailed models cari be used to reach that aim.

Selection of models

A selected mode1 should meet 3 requirements: - to be able to bring an operational answer which means enough simplicity to be used several times in order to compare scenarios in an uncertain future; - to be adaptable to various levels of knowledge of the reservoir; - to include the exchanges of sediments between the suspension and the bottom in an adapted way.

The 3-D models request a detailed topography and a detailed behaviour of the clays at various stages of settling. Moreover, the behaviour of the particles near the bottom is not completely described even in the theory. Such a mode1 should thus be excluded immediately.

An horizontal Z-D mode1 provides a field of velocities above any point of the bottom. It makes possible the localisation of the deposits if a suitable exchange term cari be defined. This term should integrate the concentration distribution on the vertical axis. Its use is complicated above a11 when no detailed data are available. However, it cari take into account the heterogeneity inside the cross section.

The vertical 2-D and the 1-D models do not provide information on the lateral transfer which prevents to precise any localisation of the deposits inside the cross section. However 2-D may represent the stratification on the vertical direction.

Simplified mode/

Yet, in some cases in which data are not enough, 1-D mode1 may be the suitable tool to bring a global answer (trapping coeff%zient for instance) of the reservoir afier a flood. The mode1 then cari be very simple (as Hazen’s mode1 for settling tanks (Lafond, 1995)) but the

138

horizontal velocity in the reservoir should be computed as it is the essential parameter. Thus, the minimal proposa1 should be a coupling between a mode1 solving de Saint Venant equations with a relation giving the behaviour of the particles: for instance, uniform fa11 velocity for one class of particles. Then, to obtain spreading of the deposits, it is supposed that particles are introduced at various depths and that horizontal velocity depends of the position of the particles in the vertical direction. Obviously, the mode1 should be calibrated; then, it could provide an answer in case of a long reservoir in which the essential problem is the evacuation of the sediments downstream. The use of several classes of particles is possible but it complicates the calibration. If the deposits are thick, the change of topography should be included in order to take into account the induced changes in the velocity.

An other way to complete a 1-D mode1 may be achieved by introducing a transport equation for the sediments : sediment discharge for bed load but rather convection - diffusion for the concentration of suspended sediment. But then, it is advisable to use a 2-D (horizontal) mode1 which does not need to integrate on cross sections where the homogeneity of the concentrations is not verifïed.

2-D mode/ Cemagref developed RUBAR 20, a code that solves shallow water equations by an explicit second-order Godunov type finite volume scheme (Paquier, 1995). Adding an equation of convection - diffusion equation for concentration of suspended sediment is possible. The source term should include the definition of the exchanges between the particles in the liquid and those present on the bottom but should also take into account the settling of the deposits with time. Till now, in RUBAR 20, two types of source terms have been implemented: one computes the deposits by comparing the concentration to an equilibrium concentration; the other one uses the comparison of bottom shear stress to a critical shear stress. The first type of source term seems to be convenient for deposition whereas the second one corresponds to erosion.

Shallow water equations and convection - diffusion equation for sediment are written as follows in orthogonal co-ordinates :

139

d(hC) + d(huC) + d(K) 6’ a hk

~ =--(hrxg)+$&,$)-sr (4)

in which h is water depth, u and v are velocities along x and y-axis, zb is bottom level, n is Manning’s roughness coefficient, g is gravity acceleration, v,fis effective cinematic viscosity, C is concentration of sediment, TX and rY are coefficients of diffusion for sediments oflen linked to v,fby a multiplying coefficient called Schmidt number. The source term &is computed either from (5) in case of deposition:

Sd =@&(c-c.)

or from (6) in case of erosion:

(5)

(6)

in which ws is fa11 velocity, C* is equilibrium concentration, Q: is a non-dimensional coefficient to be calibrated from measurements, z is bottom shear stress, rcR is critical shear stress and M is a coefficient to be calibrated.

The parameters of the relations should always be carefùlly calibrated for the case considered. Solver for the convection - diffusion equation may be of the same type as the one for hydrodynamics. Numerically, the difficulty Will appear if an effective coupling of the equations is required in order to change the topography for hydrodynamics during the computation : this option is generally not necessary as the thickness of the sediments deposited during a flood is much smaller than the water depths.

Zardezas reservoir

Zardezas dam is situated on river Saf-Saf in the North Eastern Algeria. It is 64 m high and the volume of the reservoir is 20 millions m3. The period studied is from 1975 to 1986 as two topographies are available at these dates (GEOKART-IMGW, 1987). They are constituted of 17 cross sections distributed along the 5.5 kilometres of the reservoir.

140

Dam

Fig. 1 - Localisation of the cross sections

A management of the dam that prevents the sediments coming with high floods to pass through the dam caused huge settling of sediments. The deposits are less thick in the steeper areas (Fig. 2).

141

-=. - Bottom bel measurd in 1975 ’

195 -I . Bottom lwel measured in 1966 ~ -..

-.--____

190

200

180

175

170

0 1000 2000 3000 4000 5000 6000

Distance (m)

Fig.2 - Deposits between 1975 and 1986

First step of modelling was to Select the floods to be modelled. As the data concerning concentrations and discharges were not available completely over the 11 years studied and as the computations with a 2-D mode1 of a 11 years’ period would have been very long, it was decided to Select the highest floods to be computed in the hydraulic model. From the concentration measurements performed at the upstream end of the reservoir, it appears that about 90% of the sediment inputs may be due to the 20 highest floods. We finally grouped these floods to define some characteristic situations that differ by the peak and base discharges, the duration of the flood, the concentration of sediment and the level of the reservoir when the flood occurs. This last point is very important as the global balance and the localisation Will be completely different if the flood occurs when the reservoir is nearly empty or at highest level. The concentration of sediment during a flood was modelled as constant as the measurements were not enough to precise the variation of the concentration during a flood; the analysis of these measurements shows that the peak of concentration might be strongly delayed compared to the peak discharge but there were also cases in which the concentration peak occurs slightly before the peak discharge. The concentrations varied from 5 to 20 g/l and the size of sediment was about 0.1 mm. The discharge during the floods was supposed to rise during 4 hours and then to decrease linearly to the base discharge to reach a total flood duration of 24 to 48 hours.

The second step of modelling is the use of an hydraulic model. We used the two models described here above. Strickler coefficient was always equalled to 40. In Fig.3, the results of the simplified mode1 for the flood 5 are shown (thickness of the deposits is multiplied by 10). Several computations were performed with a different number of classes of sediment. Deposits are concentrated in the middle of the reservoir except if a large number of classes is used but, then, the coarser sediments settle too rapidly.

142

z

f 2 185

0

a m

170 4

0 1000 2000 3000 4000 5000 6000

Distance (m)

Fig. 3 Results of the simplified mode1 for flood 5

In Fig. 4, the results of the 2-D mode1 (lower ce11 of every cross section) for the same flood are shown (thickness of the deposits is multiplied by 10). Few sediments are found in the steeper areas; the thicker deposits are concentrated in the flat area upstream and near the dam.

195

190

E 165

2 2 E i? 2 180

175

170

-0ottom level in 1975

Wth depaslt camputed by RUBAR 20

0 1cQo 2000 3030 4M)o 5530 6COO

Distance(m)

Fig. 4 Results of the 2D mode1 for flood 5

143

For higher initial water level (the selected floods always fil1 the reservoir), the deposits are generally met in the upstream half of the reservoir. More generally, for both models and a11 the selected floods, the deposits are located too upstream which may be due either to a too large size of sediments in the mode1 or to some complementary process which was not taken into account in the computations.

Conclusions _

In the case of Zardezas reservoir, the uncertainties concerning the input data are such that it is difficult to assert that the 2-D mode1 provides more precise results that the simplified model. This point which was already illustrated for 3-D models and settling tanks (Lafond, 1995) is right when only the absolute value of the trapping coefficient is computed. When some alternative management should be tested and when the localisation of deposits is an important point, more sophisticated models may have some advantages. The 2-D mode1 makes possible the comparison of the thickness of deposits a11 over the bottom of the reservoir but in case of Zardezas reservoir, it does not appear as a determining advantage as the data were not suffrcient. This case in which input data are not enough is oRen met. This involves that the models presented cannot then provide an answer to the duration life of the reservoir ; however, when various input scenarios are defined, they cari compare several types of management and contribute to a choice suitable to adapt the reservoir management to the defined objectives. This also points out the necessity of a carefùl follow-up of the present reservoir management and inputs.

References

GEOKART-IMGW, 1987. Expertise de l’envasement de la retenue du barrage de Zardezas. Lafond, J.M., 1995. Comparaison de modèles de transport en suspension : application à des

ouvrages de stockage - dépollution. Ph. D Thesis, Université Claude Bernard Lyon 1, Paquier, A., 1995. Modélisation et simulation de la propagation de l’onde de rupture de

barrage. PhD Thesis, Université Jean Monnet de Saint Etienne. Ramez, P. and Kellal, M., 1994. Production et transfert de sédiments à l’échelle du bassin

versant. Comptes rendus de l’Académie d’Agriculture de France, 80(9).

144

STOCHASTIC MODELING OF MONTHLY SEDIMENT DISCHARGES

Atil BULU & Tanju AKAR Istanbul Technical University Civil Engineering Faculty 80626, Maslak, Istanbul, Turkey

Abstract

Stochastic modeling techniques have been given to apply to the monthly sediment discharges. ARMA models, their parameter estimation techniques and goodness of fit tests are explained. As a case study, monthly river and sediment discharges of 2 rivers in USA were used. It was seen that monthly sediment discharges have periodic and stochastic components as in river discharges. ARer the periodicity is removed, sediment discharges cari be modeled by Moving Average (MA) type of models which shows random effect more soundly as was expected. High cross cor-relation was found between the monthly river and sediment discharges.

Keywords : Stochastic Models, ARMA Models, Sediment Discharge

Introduction

Stochastic modeling techniques have been succesfùlly applied till now to the hydrologie variables for generating and forecasting purposes. These modeling techniques were generally developed for river discharges. If the sediment discharge of a river is measured periodically as river discharges, time series modeling techniques cari also be applied to the historical values for generating and forecasting purposes. Afier a mode1 is constructed, the total amount of sediment that may deposit in a water storage structure during the project life cari be predicted. One cari more precisely estimate the dead volume of the storage by the help of the estimated total sediment volume that cari accumulate.

In this study, monthly river and sediment discharges were used on the same river and their cross cor-relation coefficients were investigated to find out their dependence structure.

In 2 studies accomplished by ( Skoklevski & Velickov; 1995,1998), they came to a conclusion that runoff and suspended load transformation cari be studied as composed processes both deterministically and stochastically. They also showed that suspended load transformation process has much random effect and autoregressive type mode1 cari be erected. (Phien; 1981) used annual sediment and river discharges to forecast the sediment volume in a reservoir by using the Box-Jenkins models. (Bulu & Akar;l998) applied time series modeling techniques to annual sediment and river discharges.

1. ARMA Modeling of Monthly Sediment Discharges

Periodic hydrologie time series are those for which the time intervals are less than one year.

Let us consider the monthly sediment discharges x,,, where v denotes year, z=l,. . .,w and w is the number of time in the year which is 12 for monthly values. Assuming that the distribution of the series is skewed, an appropriate transformation is used to transform x”,~ to the normal series y,,, cari be written as

145

Y v,5 = Pu, + ~SZV,, (1) where pr and CY~ are the periodic mean and standard deviation which are the Fourier Series fit (Salas, et. al.; 1980). z y,T may be represeented by an ARMA mode1 with either constant or time varying coefficients.If we consider the series z”,~ by zt with t=(v-l)w+z , the ARMA(p,q) mode1 with constant coefficients is

P 4

z, = c 4, zt-, + E, - C+c,

r=l j=l

(2)

In which, p is the number of autoregressive parameters and q is the number of moving average parameters. The parameters of the mode1 are u, oE2, $1,. . ,&,, 81,. .,8,. A total of p+q+2 parameters must be evaluated from data.

Mode1 identification and parameter estimation techniques were given in detail by ( Salas, et.al., 1980; Box & Jenkins, 1970).

2. Goodness of Fit for ARMA Models

The goodness of fit tests of ARMA models fitted to the sediment discharges cari be accomplished by testing on the assumptions for the ARMA model. In addition, a test needs to be made for checking whether the order of the fitted mode1 is adequate SO as to obtain a parsimonius model.

a) Tests on the Assumptions of the Mode1

Two assumptions of the mode1 need to be checked, i.e., the independence and normality of of the residuals of the fitted model. Th residuals Et of the fitted ARMA(p,q) mode1 may be determined from Eq.(2). Therefore, Et may be written as

E, = z, - &4& +&$Etwj (3) 14 j=I

Porte Monteau lack of fit test in which the autocorrelations of the Et is used to test whether the residuals of the mode1 are uncorrelated.

L

e = NC rk” (4 (4) k=l

is applied to determine the statistics Q with L may be order of 10-30 percent of the sample size N. The statistics Q is approximately X~(L-p) distributed with (L-p) degrees of freedom. If Q < X~(L-P) then Et is independent which in turn implies that the selected ARMA(p,q) mode1 is adequate. Qtherwise, the mode1 is inadequate and another mode1 should be selected for analysis.

A test of normality is required to check whether the residuals are normal. For this purpose, Probability Plot Correlation Coefficient (PPCC) test may be used ( Stedinger, et.al.; 1993).

b) Test for the Parsimony of Parameters

The Akaike Information Criterion (AK) may be used to check whether the order of the fitted mode1 is adequate compared with other orders models. The AIC for an ARMA(p,q) mode1 is

146

AWP, 4) = NLn(d > + 2~ + 4) (5)

where N is the sample size. The preferred ARMA(p,q) mode1 is that which yields the minimum value of AIC of Eq.(5).

3. Generation and Forecasting Using ARMA Models

Once the parameters of the ARMA mode1 are determined and the goodness of fit tests indicate that the mode1 is appropriate, then the mode1 cari be used for generating synthetic sediment discharges.

For generation monthly sediment discharges, periodic mean and standard deviation Fourier fit components should be used to obtain y,,,.

and P 9

Z, = C+izl-I +‘, - CejE,-j

I=l J=l

(7)

where t=(v-l)w+z and Et is normal with zero mean and variante ag2 . Thus, Eqs. (6) and (7) cari be used to generate the synthetic periodic series xv,r=exp(yv,r).

4. Case Study

The monthly flow and sediment discharges of the Juaniata River at Newport, PA, USA which has a record of 38 years and of the Potomac River at Cumberland, NR, USA which has a record of 14 years were taken for modeling purposes. The statistical moments of the monthly sediment discharges are given on Table 1 and 2.

Tablel. A4onthly Sediment Discharge Statistics of Juniata River.

Month Original Series Transformed Series Mean 1 St.Dev. 1 Skewness Mean 1 St.Dev. 1 Skewness

8 104.81 155.14 1.786 3.59 1.53 0.235 9 124.65 373.90 4.918 3.00 1.76 0.826 10 318.06 626.13 2.821 3.45 2.37 0.596 11 351.72 563.79 2.543 4.58 1.85 -0,159 12 346.69 409.03 1.463 4.83 1.72 -0.336

147

Table 2. Monthly Sediment Discharge Statistics of Potomac River.

Probability Plot Cor-relation Coefficient (PPCC) test was applied to check the normality of these data. Logaritmic transformation was applied. Test results were given on Table 3. a=0.05 signifïcance level was selected. Critical value was taken from the Table 18.3.3 at ( Stedinger, et. a1.;1993). For N>lOO , rcr= 0.987. Logaritmically transformed sediment discharges passed the normality tests.

Table 3. PPCC Test Results for Normal Distribution.

Juniata River Potomac River

Monthly (yt=ln xt) Monthly (yt=ln xt)

Fourier Coefficients were estimated for the mean and standard deviation of the monthly sediment discharges for both rivers. Cumulative periodograms were sketched on Fig. 1. & 2.

09

06

07

06

05

04

03

02

01

0 i

0 1 2 3 4

09

06

07

06

05 Mean SI Dev 04

03

02

Ill 01

5 6

P,

/ /” /,’ /

hkan 9 Dev

m

0 1 2 3 4 5 6

Figure 1. Cumulative Periodograms for Figure 2. Cumulative Periodograms for Juniata River Potomac River

Estimated Fourier Coefficients were given on Table 4. As cari easily be seen from the periodograms, one harmonie was found to be signifïcant for the mean and also for the

148

standard deviation of Juaniata River and one harmonie for the mean and two harmonies for the standard deviation were found to be significant for the Potomac River.

Table 4a. Fourrier Cot@certts of Juniata River.

Number of Harmonies

Mean Standard Deviation Esplained Explained

A B, Variantes A, Bi Variantes

1 -0.13929 1.71134 0.94035 0.25929 -0.30737 0.74175

2 -0.01941 -.025 136 0.02027 0.00363 -0.02287 0.00246

l 3 ( -0.01036 1 -0.23907 1 0.01827 / -0.19933 1 -0.00776 1 0.1825-l 1

4 0.05684 / -0.23949 1 I 0.01933 -0.03754 1 0.05806 1 0.02193 / / I /

5 -0.03766 / !

-0.03766 ; I

0.00133 0.04070 0.01654 1 0.00885 ~

6 0.05350 0.05350 0.00046 / 0.13078 0.00000 0.042-17 : C Variantes - 1 .OOOOO 1.00000 1

Table 4b. Fourrier Coefficents of Potornac River.

Number of Harmonies

1

Mean Standard Deviation

-1.2633 0.42846 0.93444 -0.06868 -0.11118 0.23542

/ 2 0.13072 0.14025 / 0.01930 / -0.13093 / 0.09998 / 0.37412 j

I 3 1 0.01850 1 -0.07790 1 0.00337 / 0.03648 ~ 0.01780 / 0.02271 1

l 4 1 0.10264 1 -0.01009 / 0.00556 / -0.05922 / 0.08528 ( 0.14859 /

5 1 -0.18160 / 0.19478 1 0.0372-l 1 0.03179 / 0.10854 ! 0.17633 1

l 6 1 -0.01922 ( 0.00000 / 0.00010 1 -0.07883 1 0.00000 / 0.04288 1

C Variantes -

l

1.00000 - 1 .ooooo

After the periodic components are removed, correlograms of the monthly sediment discharges were sketched on Fig. 3 and 4.

Figure 3, Correlogram of Juniata River for Figure 4. Correlogram of Potomac River for Monthly Sediment Discharges Monthly Sediment Discharges

149

-. -

Maximum Likelihood Estimation Method was used to estimate the parameters of the ARMA models. AIC yielded MA(2) mode1 for the monthly sediment discharges of the Juaniata River. For Potomac River, MA(3) mode1 gave the smallest AIC value. According to the fitted models. Porte Monteau Lack of Fit test was applied to the residuals and a11 2 models passed the test at the 5% significance level. Test results were given on Table 5. Parameters of the fitted models were given on Table 6.

Table 5 Porte Monteau Lack of Fit Tests Results of Juniata and Potomac Rivers (a = %5)

T&e 6. Pnrmneters of the Fitted Models

,- -~ ----- ~-- -_.-~. -

Cross correlation coefficients were estimated between the monthly sediment and river discharges for both rivers and were given on Fig. 5. The mean of the cross correlation coeflicients were close to ro,s=0.80 for both rivers.

0.i 02 01 Yonths

0 0

12 3 4 5 6 7 a 9 10 11 12 1 2 3 L 5 6 7 a 9 10 11 12

Figure 5a. Figé 5b. Relation Between Discharges and Relation Between Discharges and Sedirnent Discharges of Juniata River Sediment Discharges of Potornac River

5. Conclusions

Time series modeling techniques were applied to the monthly sediment discharges in this study and the following results were obtained

Periodicity was seen in monthly sediment discharges like in monhtly river discharges. High cross correlation was found between the monthly sediment and river discharges. Since river discharger rn-e measured for longer periods, reliable time series models cari be constructed

‘50

among them. Using these river discharge models, one cari obtain the mode1 of sediment discharges for forecasting purposes to estimate the dead volume of the water storage structures.

As was expected, Moving Average Models tïtted better than the other models between the stochastic components. Since in Moving Average Models, stochastic components are the weighted sum of the normally distributed random variables, random effect was seen more soundly.

The total amount of sediment that may deposit cari be forecasted if a water storage structure was constructed there by the help of generating series and with the use of the constructed mode1 among the sediment discharges.

References

Box, G.E.P. & Jenkins, G. (1970). Time Series Analysis, Forecasting and Control, San Fransisco, Holden-Day.

Bulu, A. & Akar,T. (1998). Time Series Modeling of Sediment Discharges, XIX Corzfereme of the Danube Countries, Proceedings, 15- 19 June, 1998, Osijek, Crotia, pp. 74 l-747.

Phien, H.N. (198 1). Reservoir Sedimentation With Correlated Inflow, Journal of Hydrology, 53, pp. 327-341.

Salas, J.D., Deleur, J.W., Yevjevich, V. & Lane, W.L. (1980). Applied Modeling of Hydrologie Time Series, Water Resources Publications, Littleton, Colorado,USA:

Salas, J.D. (1993). Analysis and Modelling of Hydrologie Time Series, In D. Maidment (Editor), Handbook of Applied Hydroiogy, Chapter 19, McGraw-Hill, New York.

Skoklevski, Z. & Velickov, S. (1995). lOta/ Suspendeu Load Transport as a Natural Stochastic Process, IAHS Publication, No.226.

Skoklevski, Z. & Velickov, S. (1998). Suspended Load Transportation Process Within Vardar River Basin in the Republic of Macedonia, XIX Conference of the Danube Countries, Proceedings, 15- 19 June, 1998, Osijek, Crotia, pp. 7 17-727.

Stedinger, J.R., Vogel, R.M. & Foufoula-Georgiou, E. (1993). Frequency Analysis of Extreme Events, In D. Maidment (Editor) Handbook of Applied Hydrokogy, Chapter 18, McGraw-Hi11 Book, New York.

151

Application of Renewal Processes to Characteristics of the Riverbed Sediment Load

Vojislav Vukmirovic, Dragutin Pavlovic and Jasna Petrovic E’amlty of Civil Engineering, IJniversiQ of Belgrade, Yugoslavia

Abstract The paper presents the theoretical background and an example of statistical analysis of the bed load using the peaks over tlueshold (POT) method. The POT method is based on the theory of renewal processes. The advantages of the POT method over the commonly used ammal maxima method are: inclusion of a11 significant values in the sample rather than only one value per year. and the possibilities for analysis of other important v.ariables such as duration of flood/low flow and volume of water surplus or deficit. The example presented in the paper deals with the maximum bed load yield and the duration (number of days) of flow with bed load flux greater than some base value.

1 Introduction

The bed load transport cari be described as a discrete random process. During the low flow, when the shear stress at the riverbed are smaller than some critical value, the riverbed sediment is not in motion. During the flood flow, the river carries a significant amount of sediment that cari sometimes be greater than a half of the annual sediment yield.

Extreme values of hydrological variables (maximum and minimum flow rates, water levels, precipitation) are usually statistically analyzed on the basis of annual maxima/minima series. This approach takes only one value per year into the sample and ignores some other values, which cari be more signifïcant than annual extremes in some years. The peaks over threshold (POT) method, which is based on the theory of the renewal processes (Todorovic, 1970; Zelenhasic, 1970) takes into account a11 peaks exceeding certain threshold value. The POT method also offers broader possibilities for analysis of other characteristic variables, such as the duration of the flood wave or dry period, time to peaks or volume surplus or defïcit.

2 Theoretical Background

The series of peaks considered in the POT method consists of a11 values X in the N-years record that exceed a chosen threshold value XE. Two main variables in the POT method are the number of peaks in each year v and the exceedance over threshold Z = X - XB. The occurrence of the annual maximum value is a random process defined with:

x(t) = sup z,, Z” = X - Xg (1) v> 1

Distribution fùnction of annual maxima is

F(x) = P{X(t) I x} (2) TO obtain this distribution fùnction it is necessary to combine probabilities of occurrence of the two main variables: number of peaks v and exceedance (or peak) Z.

153

2.1 Number of peaks

The number of peaks during interval (0, t) - one year in this analysis - is random variable t-k which cari take values 0, 1, 2, with probabilities p,(t) = P{qt = v>. The occurrence of peaks during a time inter-val cari be described as a Markov renewal process with intensity function:

h(t 7 v) = lim ‘{ [rl(t + At> - rl(t)l = v> Af+O At

(3)

The probability of occurrence of peak exceedance is given with

P’” w = w v - UP”-, w - w, V>P, (t>

P’L w = -4tA9P, w (4)

The solution of equations (4) represents the probability law of occurrence of peaks and depends on the form of the intensity function h. This function cari take different forms (Vukmirovic, 1990):

Poisson

Bernoulli (binomial)

Pascal (negative binomial) (5)

Table 1 summarizes the major characteristics of the number of peaks for the three different forms of intensity function. It is of practical importance to note that the dispersion index is unity for the Poisson law, it is smaller than 1 for binomial law and greater than 1 for negative binomial law.

Table I: Three d&Serent models for the number of peaks.

mode1 for the number Poisson Bernoulli Pascal of peaks (binomial) (negative binomial) intensity h(t, v) h(t) h(t)(1- via) A.(t)(l+ vlb)

number of peaks Aye-A C;e-* (pu - 1)” CV b+v-le -A(l-e-AibY

P”(f) r(v + 1) mean Eh) A a(1 - e-*‘O) Ne AJb - 1)

variante Y(TJ~) A a(1 - e-A’a - l)e-*la W A’b - l)eAlb dispersion index 1 eeAJa < 1 ehlb > 1 I(r, 1

2.2 Peaks over tbreshold

Distribution fùnction of peak exceedances is defined with:

H(z) = P(Z I z} (6)

154

This distribution cari be generalized as three-parameter gamma distribution with density function:

(7)

Distributions like two-parameter gamma, Weibull’s, Rayleigh’s, Erlang’s or exponential are special cases of this general distribution. The exponential and the Weibull distributions are usually employed to describe the magnitude of peaks over threshold. Characteristics of some of these distributions are given in Table 2.

Table 2: Characteristics ofsome distributions usedfor.fitting peaks over chosen threshold

Exponential Weibull d.f. d.f.

3-par. gamma d.f. - -

distribution function H(z)

lwe-“‘P 1_ ,-wo” Lr* zai bG, b ‘a l() 1

density function h(z)

‘,-WP)

CL

a-l a z e-(zib)”

-0 b b 0 k-l a z - - e-(2’ b)”

bG, b

bl-1 -5 bG0

coefficient of variation Cv(z) 1 &-T

G

relative skew Cv(z)lCs(z) 2 r,(r,-3r,r,+2rt)

u-, - W G,(G;G, -3G,G,G, +2G;)

(G,G, -G:J2 Note:

r, =r(l+lla), r, =r(1+2/a), r, =r(l+3/a)

[() 1 (zi b)’

r* ‘k

i ,- = tk/a-le-tdt

b a 0

2.3 Annual maxima

Distribution of annual maxima is obtained by combining the distributions of number of peaks and distributions of peak exceedance over threshold value (Todorovic, 1970):

F(x) = Po + ~WWPvW (8)

If the number of peaks follows the Poisson law, distribution fimction F(x) reduces to:

F(x) = exp{- A[1 -H(x)]) (9)

This simple form has found a wide application, but some problems may arise concerning the choice of the threshold value. A lower threshold in some cases cari give numbers of peaks

155

whose distribution is not Poissonian. A greater threshold allows the Poisson law, but the total number of peaks included in analysis W than reduced and affects the reliability of statistical inference.

This problem is resolved by introducing the binomial (Bernoulli’s) or negative binomial (Pascal’s) distributions for the number of peaks (see Table 1). For these cases, distribution of annual maxima (8) reduces to the following expressions (Vukmirovic, 1995; Vukmirovic and Petrovic, 1997):

- binomial distribution for the number of peaks:

F(x)=e-“[l+(e”‘n -l)H(x)]’ (10)

- negative binomial distribution for the number of peaks:

I;(X)=~-A[l-(l-e-“-b)H(x)]-b (11)

2.4 Application of the renewal processes

If the chronological series of bed load flux X during N years is avalable (Fig. la), the values above a chosen threshold x~ are considered. Analysis of the folowing variables is of practical importance:

- maximum daily bed load flux (Fig. lb); - maximum 2-days, 3-days, . . . . IO-days mean bed load flux; - bed load volume during the event X> x~ (Fig. lc); - duration of the event X > XB (Fig. 1 d); - time to peak for the event X> XB (Fig. le).

Al1 these variables may be analyzed using the POT method using the procedure described in previous sections, in order to obtain distributions of annual maxima for the characteristic processes.

3 Example of Application of the POT Method

According to the results of field measurements of the bed load and hydrological observations on the Sava river at Skopice, a sample of the daily bed load yield was established for the period 1926-1974 (total of 49 years). This data was used for analysis of the bed load transport needed in the design project of the water withdrawal structure for the nuclear power plant Krsko. The project included the statistical analysis of daily, 3-days and 7-days maximum bed load yield, as well as of duration of bed load transport with fluxes greater than .20, 30 and 50 kg/s. The POT method was applied to a11 these variables.

For the daily maximum bed load yield, a threshold value of 100 kg/s (8640 tons per day) was chosen; for the 3-days maximum bed load yield the threshold of 150 kg/s was chosen. The number of peaks for both daily and 3-days bed load yield follows the negative binomial (Pascal) law, as indicated by the dispersion index value of 1.569 and 1.545, respectively. Two graphs at the top in Fig. 2 present sample distributions of the number of peaks for these two variables, together with the Poisson? and Pascal’s distributions. For the peaks over threshold, the 2-parameters Weibull distribution was applied (Fig. 2 in the middle) for both variables.

156

z=x-x, x(t) = max 2,

0 b

21 23

ZZ

I I I I I I I I I I I >

X,,(t) = max d,

X,(t) = max 6,

0 e , , , l I I >

Figure 1: Description of different processes which may be analyzed using the POT method.

157

The distributions of the annual maxima for the two variables were calculated via equation (11) using parameters of the Pascal and Weibull distributions, and presented on the bottom graph in Fig. 2.

0123456789 012345678

number of peaks number of peaks

90000 80000 70000

60000

50000 N

40000

30000

20000

10000

0

Peak values

/- 1 -- - 3-days (Weibull dist.)

‘X ./I( ,~

+ 1 -day (emp. dist.)

0.5 0.8 0.9 0.95 0.98 0.99 0.995 0.959

H(z)

Annual maxima

- - 3-days (Weibull dist.)

0 .-m _ ~_

0.5 0.8 0.9 0.95 0.99 0.99 0.995 0.929

Figure 2: Application of the POT method to the daily and 3-days maximum bed load yield at Skopica on the Sava river: distributions of the number ofpeaks (top), values ofpeaks (middle) and annual maxima (bottom).

The analysis of the duration of bed load transport with fluxes greater than 20, 30 and 50 kg/s is illustrated here only for the fluxes greater than 50 kg/s. The results are presented in Fig. 3. The number of peaks follows the negative binomial law, according to the dispersion index of 1.626. The Weibull distribution was the best fit for the values of peaks, SO that the final distribution of annual maxima is again calculated using equation (11).

158

12

10 n ’ w empirical :;

0 1 2 3 4 5 6 7 a 9 1011

number of peaks

Peak values ;

-----If ~-~ ~~

0.5 0.8 0.9 9.95 0 98 0.99 0.995 0.999

H(z)

Annual maxima

0.5 0.8 0.9 0.95 0.98 0.99 0.995 0.999

F(x)

Figure 3: Application of the POT method to the duration of the bed loadflux greater than 50 kg/s at Skopica on the Sava river: distributions of the number ofpeaks (top), values ofpeaks (middle) and annual maxima (bottom).

This analysis has proved that the POT method, based on the renewal processes, is suitable fod the analysis of hydrological and sediment-related variables, especially for the analysis of the occurrence of extreme values.

159

-.-...- .-.._--_

4 References

Todorovic, P. (1970) On some problems involving random number of random variables, Ann. Math. Statistics, 14 (3): 1059-1063.

Vukmirovic, V. (1990) Analiza verovatnoce pojave hidroloskih velicina (Analysis of probability of occurrence of hydrologie variables - in Serbian), Faculty of Civil Eng. and “Naucna knjiga”, Belgrade.

Vukmirovic, V. (1995) Analysis of maxima using renewal processes, Int. Conf. in honor of Jacques Berme?, Paris, UNESCO.

Zelenhasic, E. (1970) Theoretical probability distributions for flood peaks, Hydrology paper No. 42, Colorado State University, Fort Collins.

Vukmirovic, V. and Petrovic, J. (1997) Flood flow analysis using renewal processes, Annual FRIEND-AMHY Meeting, Thessaloniki (September 1995); UNESCO IHP-V Technical Documents in Hydrology, No. 11, pp. 159-169.

160

Quantification de l’érosion au droit d’un barrage, à partir de

stations hydrométriques, en zone semi-aride.

Touaïbia B.*,Aïdaoui A.** Achite M.***

* Ecole Nationale Supérieure de I’Hydraulique. BP 3 1. 09 000. Blida. Algérie

** Ecole Nationale Supérieure des Sciences Agronomiques. Ex. INA. El-Harrach. Alger. Algérie

*** Ecole Nationale Supérieure de 1’Hydraulique. BP 31. 09 000. Blida. Algérie

RESUME

Nous examinons ici, une approche statistique de traitement et d’homogénéisation des données de transport solide de deux sous bassins versants adjacents contrôlés par des stations hydrométriques en zone semi-aride. L’objectif à atteindre, consiste en l’estimation de l’érosion spécifique au droit du barrage de Sidi M-Hammed Bénaouda à partir des données de Transport solide de deux stations hydrométriques situés à son amont. L’approche méthodologique adoptée consiste à rechercher un modèle régressif pouvant expliquer la relation débit solide - débit liquide mesurés au droit des stations, et ce à travers différents modes de traitement de la banque de données disponible sur une période de 23 ans (1972/73 à 1994/95). Quelque soit le type de traitement, le modèle puissance semble le mieux adapté bien que le modèle parabolique lui soit compétitif. L’approche statistique de traitement des données par mois reste la plus significative vu l’irrégularité saisonnière et inter-annuelle des écoulements liquide et solide.

INTRODUCTION

En Algérie, l’estimation de l’érosion spécifique au droit d’un barrage pose des problèmes sérieux lors du dimensionnement de l’ouvrage quant au calcul de la tranche morte. De ce fait, nous nous intéressons à la quantifkation de l’érosion spécifique au droit d’un barrage en partant des mesures de concentrations en éléments fins effectuées par l’Agence Nationale des Ressources Hydrauliques au droit de stations hydrométriques et compilés sur plusieurs années. L’analyse statistique de l’information constitue l’étape la plus importante pour une homogénéisation fiable de la donnée manquante, notamment celle du transport solide. Plus la taille de l’échantillon est importante dans la recherche du modèle, plus l’homogénéisation des données reste significative. Pour mettre en valeur cette homogénéisation, nous avons pris deux stations hydrométriques appartenant au bassin versant de l’oued Mina (Figure1 .) qui sont : la station hydrométrique de Sidi A.E.K. Djillali contrôlant le bassin versant de Oued El- Haddad ; la station de Oued El-Abtal contrôlant le bassin versant de l’oued Mina ; et pour lesquelles, nous disposons de longues séries de mesures de concentration instantanée sur 23 années (1972/73 à 1994/95).

161

La Figure 1. schématise la structure spatiale des différents sous bassins versants de l’oued Mina et donne non seulement la position des différentes stations hydrométriques mais aussi les surfaces en % du bassin versant au droit de chacune de ces stations.

Figure 1. Schématisation du bassin versant de l’oued Mina

S=6200Km2 Vers Oued Cheliff

1

2.: 3. 4. 5 6

Barrage de Sidi M’Hammed Bénaouda ( SMB ) Station Hydrométrique de Sidi A.EK Djillali Statmn hydrométrique de Oued El-Abtal Station hydrométrique de Ain Hamara Station hydrométrique de Kef Mahboula Barrage de Bakhadda

N

T

1. Présentation des données

La mise en forme des données pour leur traitement constitue l’étape la plus longue et la plus diffkile. A partir des données de hauteurs d’eau, de concentrations instantanées mesurées et des barèmes d’étalonnage fournis par l’Agence Nationale des Ressources Hydrauliques, nous avons établit un fichier de données instantanées compreriant (( date - heure - hauteur d’eau (H en mm) - concentration en sédiments (C en g/l) - débit liquide(Q1 en m3/s)- débit solide(Qs en Kgk.), servant de base à la recherche de modèles mathématiques pouvant expliquer la relation QS-Ql au droit des stations.

2. Traitement des données

Différentes approches de traitement des données de débits liquides et solide quant à leur manipulation, ont été entreprises (Touaïbia, 1986), à savoir : - en regroupant les données dans leur totalité sur la période d’observations ; - en regroupant les données par année ; - en regroupant les données par mois ;

162

- en regroupent les données par saison ; - en regroupant les données par années humides et années sèches ; et pour lesquelles les modèles : linéaire, logarithmique, puissance, exponentiel et parabolique leur ont été ajustées(Dagnellie, 1992).

En Figures 2 et 3, nous avons présenté les diagrammes de dispersion donnant la relation débit solide - débit liquide respectivement pour les 2 stations en prenant les données dans leur totalité soit 1909 couples pour la station de Sidi A.E.K. Djillali et 2586 couples pour la station de Oued EL-Abtal. L’allure du graphe oriente le choix du modèle.

r 25000 T

Sidi A.E.K Djillali

1972113 à 1994195

20000 t

Gl 2 15000 A

0 A A A

2 51

2 10000 a

5000

0 0 30 60 90

Débit liquide m’/s

A

A

Figure 2. Relation débit liquide - débit solide : Sidi A.E.K Djillali

Station Oued El-Abtal

1972il3 à 1994195

80000 0 0 a 2 60000 ‘0 a

A A A A ti AA

A A ~~

A A A

A

400 600 800 iooo 1200

Débit liquide m’/s

Figure 3.. Relation débit liquide - débit solide : Oued El-Abtal

163

Les résultats de ce traitement quant à la valeur du coeffkient de détermination R2 , calculé pour tous les modèles et pour les différentes approches statistiques avec une erreur de lère espèce a = 5 % (Dagnellie, 1992) sont donnés dans les Tableaux 1 et 2 respectivement pour la station de Sidi A.E.K et Oued El-Abtal.

3. Homogénéisation des données

L’approche mensuelle a été retenue pour l’homogénéisation des données de transport solide, au vu de la valeur de R2 (Tableau 1. et 2.) dont le modèle puissance semble le mieux adapté. Les modéles retenues sont présentés dans le Tableau 3. pour les deux stations

Tableau 3. Modèles retenus : station Sidi A.E.K Djillali et station Oued El Abtal. Période 1972/73 à 1994/95

Relation QS = f (QI)

Mois

Septembre

Octobre

Novembre

Décembre

Janvier

Février

MalT

Avril

Mai

Jllin

Juillet

Août

Sidi A.E.K Djillali

21.305 Ql 15637

14.594 Ql ‘.4767

15.458 Ql ‘.+w

16.478 Ql ‘.3792

15.383 Ql 1.s80’

10.686 Ql ’ 4’oz

11.835 Ql ’ 3605

13.322 Ql ’ s646

20.286 Ql 1.4611

15.634 Ql ’ 4248

5.793 Ql ’ 7413

25.128 Ql 1.4g35

Oued El-Abtal

6.8074 Ql ’ 4o52

3.6073 Ql ’ 5271

4.1442 QI ’ 4227

3.6330 Ql ’ 375g

2.8173 Ql ’ 4738

1.0514 Ql 1703’

1.5343 Ql ‘*C+I’

1.8075 Ql ’ 4558

2.5236 Ql ’ 4’4g

10.0.97 Ql ’ 284’

4.5459 QI 1.4277

6.3051 Ql ’ s326

164

Tableau l.Valeur de R2 pour différents types de traitement : station Sidi A.E.K Djillali

Type de traitement

Ensemble des données

Nombre Observa

1909

Linéaire

0.76

Logarithmique

0.24

Modèles Puissance

0.81

Exponentiel Parabolique

0.33 0.77

Annuel : 1972/73* 1973/74* 1974/75* 1975/76* 1976/77* 1977178

1978/79* 1979/so* 1980/8 l* 1981/82

1982183’ 1983184 1984/85 1985186

1986/87* 1987188

1988/89* 1989/90* 1990/9 1* 1991/92 1992193 1993194 1994/95

Mensuel : Septembre

Octobre Novembre Décembre

Janvier Février

Mars Avril

Mai Juin

Juillet Août

Saisonnier Automne

Hiver Printemps

Eté Années :

Humides Sèches

* Années humides

30 0.53 0.29 0.49 0.49 0.67 55 0.98 0.38 0.71 0.27 0.98 30 0.78 0.43 0.90 0.44 0.78 83 0.90 0.45 0.83 0.51 0.91 49 0.61 0.46 0.67 0.46 0.76 64 0.89 0.50 0.86 0.58 0.90 110 0.80 0.51 0.90 0.53 0.80 102 0.76 0.45 0.81 0.58 0.82 85 0.78 0.34 0.71 0.66 0.93 61 0.93 0.60 0.84 0.60 0.96 94 0.88 0.36 0.86 .0.37 0.90 76 0.98 0.28 0.81 0.23 0.99 70 0.89 0.36 0.91 0.54 0.97 166 0.46 0.36 0.73 0.39 0.56 170 0.84 0.28 0.84 0.41 0.94 130 0.85 0.37 0.87 0.50 0.90 84 0.90 0.47 0.82 0.46 0.95 114 0.85 0.32 0.90 0.35 0.87 109 0.60 0.27 0.87 0.43 0.62 38 0.75 0.74 0.64 0.46 0.83 48 0.94 0.32 0.88 0.38 0.94 95 0.79 0.42 0.91 0.48 0.79 76 0.94 0.10 0.89 0.25 0.97

111 092 0.34 0.83 0.39 0.94 221 0.84 0.36 0.87 0.48 0.85 212 0.80 0.27 0.83 0.29 0.80 189 0.83 0.46 0.76 0.51 0.84 241 0.88 0.40 0.81 0.42 0.90 308 0.57 0.35 0.77 0.40 0.62 295 0.75 0.31 0.81 0.39 0.75 104 0.71 0.47 0.58 0.38 0.74 130 0.78 0.33 0.86 0.34 0.80 36 0.94 0.47 0.88 0.46 0.94 47 0.79 0.40 0.87 0.51 0.82 15 0.95 0.63 0.88 0.43 0.96

544 0.81 0.30 0.85 0.38 0.82 738 0.72 0.31 0.77 0.41 0.74 529 0.70 0.28 0.78 0.35 0.70 98 0.85 0.42 0.85 0.45 0.86

1131 0.79 0.25 0.82 0.37 0.83 748 0.79 0.20 0.81 0.29 0.79

165

Tableau 2.Valeur de R2 pour différents types de traitement : station Oued El-Abtal r

Type de traitement

Ensemble des données

Annuel : 1972/73* 1973/74* 1974175’ 1975/76* 1976/77* 1977/78* 1978/79* 1979/80* 1980/81* 198 1/82

1982/83* 1983184 1984185

1985/86* 1986/87* 1987188 1988/89

1989/90* 199019 1 1991192 1992193 1993194

1994195 * Mensuel :

Septembre Octobre

Novembre Décembre

Janvier Février

Mars Avril Mai Juin

Juillet Août

saisonnier Automne

Hiver Printemps

Eté Années :

Humides --Il Sèches * années humides

Nombre Observa

T Linéaire Logarithmiq

Modèles

Puissance Exponentiel Parabolique

2586 0.61 0.19 0.80 0.34 0.62

32 0.72 0.50 0.67 0.69 0.85 54 0.69 0.56 0.81 0.65 0.70 53 0.85 0.66 0.86 0.64 0.86 81 0.56 0.44 0.64 0.53 0.62 100 0.44 0.30 0.83 0.65 0.44 99 0.60 0.42 0.86 0.73 0.64 154 0.79 0.24 0.71 0.44 0.93 163 0.72 0.19 0.89 0.42 0.90 108 0.53 0.24 0.57 0.49 0.74 70 0.82 0.69 0.88 0.71 0.82 91 0.61 0.28 0.77 0.68 0.70 76 0.54 0.39 0.67 0.58 0.57 81 0.51 0.44 0.72 0.39 0.58

207 0.88 0.45 0.83 0.38 0.88 235 0.72 ‘0.25 0.89 0.40 0.78 158 0.44 0.33 0.73 0.49 0.45 115 0.82 0.42 0.83 0.54 0.85 132 0.91 0.43 0.90 0.37 0.92 143 0.70 0.47 0.89 0.42 0.76 74 0.80 0.35 0.87 0.55 0.95 116 0.92 0.35 0.90 0.37 0.93 135 0.84 0.48 0.87 0.34 0.94 109 0.57 0.25 0.96 0.37 0.60

254 0.53 0.26 0.89 0.43 0.54 491 0.77 0.21 0.89 0.30 0.77 217 0.51 0.26 0.78 0.47 0.53 158 0.38 0.22 0.74 0.49 0.38 213 0.67 0.40 0.84 0.58 0.70 345 0.76 0.31 0.82 0.35 0.76 293 0.75 0.52 0.84 0.46 0.77 208 0.32 0.17 0.63 0.51 0.33 242 0.70 0.34 0.67 0.39 0.75 56 0.97 0.38 0.77 0.49 0.98 53 0.97 0.59 0.93 0.53 0.98 56 0.55 0.47 0.81 0.48 0.59

962 0.64 0.20 0.87 715 0.67 0.28 0.80 743 0.61 0.24 0.73 165 0.35 0.32 0.83

0.34 0.64 0.39 0.67 0.37 0.61 0.38 0.68

1586 0.60 0.19 0.81 968 0.68 0.23 0.83

0.36 0.60 0.33 0.69

166

4. Quantification de l’érosion spécifique

4.1 Quantifïcation au droit des stations hydrométriques

L’application des modèles retenus (Tableau 3.) a permis de quantifier les apports solides et d’estimer l’érosion spécifique annuelle au droit des stations et du barrage comme le montre le Tableau 4.

Les débits moyens journaliers donnés dans les annuaires hydrologiques fournis par l’Agence Nationale des Ressources Hydrauliques ont servi de base pour l’homogénéisation des données de débit solide.

Tableau 4.Quantité de sédiments apportés en Tonnes et Erosion spécifique estimée en T/Ha: Période 1973/74 à 1994/95

L’érosion spécifique a varié annuellement de 0.11 à 7.60 T/Ha à la station de Sidi A.E.K. Djillali et de 0.32 à 10.84 T/ha à la station de Oued El-Abtal.

167

En moyenne sur les 22 années, l’érosion. spécifique est stimée oannuellement à 3 et 2.10 T/Ha respectivement aux stations de Sidi A.E.K et de Oued El-Abtal.

Bien que l’érosion spécifique reste faible, sa variabilité temporelle est très significative.

En terme de variabilité, nous avons illustré en Figure 4. La modulation intra-annuelle des apports liquide et solide sur la périodes 1973/74 à 1994/95.

-a-

30 30

$:: 25 s T$a, s

“z+ ‘= 15 ô 15 VI e L & 10 10 a $5 58

0 0 SONDJFMAMJJA

mi!3

-b-

l - *” zzi-

\o 25

0

ii a 10

$5

0

30

25 <

cl ‘c

15 -j

10 f :

5 4

0 SONDJFMAMJJA

Mi!3 -A-A -S-A

Figure 4. Modulation intra-annuelle des apports liquide et solide au droit des stations hydrométriques : période 1973174 à 1994195.

Il y a lieu de constater que le maximum atteint en apport solide (Figure 4) arrive au mois d’octobre, avec les premières pluies et les premiers labours. L’effet du couvert végétal semble être très manifeste en automne.

Pour mieux cerner cette variabilité temporelle de l’écoulement, nous avons comparé la variation annuelle de l’érosion spécifique et le coeffkient d’écoulement sur la période d’observations comme le montre la Figure 5.

Au vu de la Figure 5.;l’érosion spécifique Es varie proportionnellement avec le coeffkient d’écoulement Ce durant ces différentes années, à l’exception de l’année 1994/95 où on relève une disproportionalité entre Es et Ce à la station de Oued El-Abtal. L’écoulement

168

L’écoulement observé cette année là, provient des lachées du barrage Bakhadda(Figure 1) transitant par le cours d’eau principal qu’est l’oued Mina et non du ruissellement.

-a-

l Mi A.EK DjîUali 10 - -10 i

82/83 85/86 88189 91192 94195

Année I---O---k %a;

-b-

Oued El-Abtal

Q

73174 76177 79/80 82/83 85186 88189 91192 94195

Année 1 -ce% ! ---A--- EsT/Ha

Figure 5. Variation interannuelle de l’érosion spécifique annuelle et du coeffkient d’écoulement

4.2 Quantifïcation de l’érosion au droit du barrage

Le barrage de Sidi M’hammed Bénaouda reçoit comme le montre la Figure l., les apports liquide et solide des bassins versants de Oued Mina et de Oued El-Haddad contrôlés respectivement par les stations hydrométriques de Sidi A.E.K Djillali et Oued El-Abtal.

L’érosion spécifique estimée au droit des stations hydrométriques a permis de déterminer l’érosion spécifique moyenne interannuelle au droit du barrage [calculée sur la période 1980/81(pratiquement de sa mise en service) à 1994/95] ; soit à 5.42 T/Ha an.

Si la densité des sédiments est de 1. 6 T/m3 (AN& 1976), nous estimons, pour une surface du bassin versant au droit du barrage de 4900Km2, à 1.66 Mm3 le volume de sédiment entrant en moyenne annuellement au barrage, ce qui bien appréciable.

169

Conclusion

L’érosion est un phénomène très complexe. L’exploitation des données de mesures fournies par l’Agence Nationale des Ressources Hydrauliques reste très insuffisante quant à l’explication des causes de l’érosion. Cependant les conséquences sont visibles et l’estimation exacte de l’érosion spécifique reste la principale voie de dimensionnement adéquat d’un ouvrage d’art. Quelque soit le mode de traitement des données de transport solide, le modèle puissance semble le mieux adapté. L’approche mensuelle d’homogénéisation des données reste la plus fiable vu l’irrégularité intra-annuelle de l’écoulement. L’érosion spécifique moyenne interannuelle au droit des stations hydrométiques est estimée à 3 et 2.10 T/Ha.an respectivement aux droit des stations de Sidi A.E.K et Oued El-Abtal. Au droit du barrage l’érosion spécifique moyenne interannuelle est de 5.42 T/Ha.an.

Bibliographie

* Agence nationale des barrage @NB), 1976. Avant projet détaillé du barrage de Sidi-M-Hammed Bénaouda. Ministère de YHydraulique. Alger

* Dagnellie, P. ,1992 Théorie et Méthodes statistiques. Volume 2. Presses Universitaires Agronomiques de

Gembloux (Huitième impression). Belgique

*TOUAIBIA B., 1986 Quantifïcation de la salinité et du transport solide :Cas du bassin versant de l’oued

Deurdeur.Ain-Defla . Thèse de Magister. INA .El-Harrach .Alger

170

RISQUE «CALCULE » ASSOCIE A L’EROSION

Abdelmalek BEKKOUCHE*, Abdelkader DJEDID* ‘Université Abou Bekr Belkaïd, Institut de Génie Civil, B.P. 119, Tlemcen, 13000 ALGERIE Tél-Fax: 213.7.20.86.37

Mots clés: Erosion, état critique, arbre des causes, arbre des conséquences, optimisation.

Résumé: L’érosion des sols comme état critique a pour origine plusieurs causes qui, classées sur

plusieurs niveaux, permettent la construction de l’arbre des causes. Quant aux conséquences de l’apparition de ce phénomène, elles peuvent se développer suivant différent scénarios. La construction de l’arbre des conséquences permet de décrire la progression de l’état critique.

Bien qu’irréaliste, l’hypothèse binaire permet, en affectant des coûts et des probabilités afférentes aux différents scénarios, l’estimation du risque “calculé” associé à l’érosion et donne une possibilité d’optimisation.

1. INTRODUCTION:

L’érosion des sols est considérée comme la forme de dégradation des sols la plus sérieuse et la moins réversible. L’enclenchement de ce processus pourrait avoir des conséquences très importantes. Ces conséquences peuvent être directement liées au sol comme la défertilisation et/ou la dégradation, comme elles peuvent agir sur les ouvrages appartenant au même bassin versant et/ou situés à son environnement (envasement des retenues, ensablement des ports, ect...).

Atténuer de l’effet de l’érosion implique un investissement qui pourrait être très important. Pour lutter contre l’érosion et les préjudices affectant les différents les ouvrages, il est impératif d’établir un compromis économique. C’est donc un problème décisionnel où une optimisation est tout à fait possible.

Avant l’affectation des coûts, il faudrait pouvoir évaluer la performance du sol vis à vis de l’érosion (fiabilité du sol), opération difficile mais pas impossible. Les récentes applications de la théorie de fiabilité dans le domaine des structures nous laissent optimiste quant à son application dans le domaine de l’érosion des sols.

II OUANTIFICATION DE LA PERFORMANCE: [ 1,3]

Une structure (sol ou autre) est considérée comme devenue impropre quant elle atteint un état particulier, dit état limite, pour lequel elle transgresse un des critères conditionnant son comportement.

H.l- Approche déterministe: “Niveau 0”

L’approche déterministe de la performance est conduite à partir d’un coeffkient qui n’est autre que le rapport d’une grandeur agissant sur la structure (sollicitation) à une grandeur résistante

171

maximale (résistance) qu’elle peut lui opposer. Ce rapport a une justification peu précise et son importance dépendra de la variabilité des efforts appliqués, des paramètres de résistance et des incertitudes sur les différents paramètres et modèles. Chaque utilisateur y transmet ses craintes et ses ignorances suivant la destination du projet, du temps de reconnaissances effectuées, l’élément étudié, l’état critique considéré et ses conséquences et ceci d’une manière subjective basée uniquement sur le jugement et l’expérience.

Ce coefficient de sécurité a été souvent traité comme étant un coeffkient d’ignorance car sa valeur dépendra du degré de connaissance vis à vis de l’état critique considéré.

a 11.2- ADDroche semi-probabiliste: “Niveau 1”

Cette approche exige que la résistance calculée à partir des valeurs minorées des paramètres de base soit supérieure à la sollicitation calculée à partir des valeurs majorées des actions. Ces coefficients “de majoration et de minoration” sont obtenus à partir d’une modélisation probabiliste des coeficients de sécurité partiels. Les valeurs utilisées pour ces derniers seront des fractiles de leurs lois de distribution et ceci en tenant compte d’une manière subjective des considérations économiques.

11.3- Approche probabiliste: “Niveau 2 et 3”

Si R et S sont respectivement la résistance et la sollicitation agissante, on définit une fonction de performance g(R,S) par:

g(R, S)=R-S

R et S sont des variables aléatoires de base. Si de plus R et S sont indépendants et fa(r) et fs(s) sont leurs densités de probabilités respectives, la probabilité de ruine P, sera:

Pr=P(g(R,S)<O)

P((R - S) < 0) = +fFR(S).f,(S)dS

-m

où Fa(s) est la fonction de répartition de R pour le champs s.

D’une manière générale R et S sont dépendants et la probabilité de ruine sera fonction de la distribution conjointe f&:

Pr = I;( g?,, (r,sW)dS

La résolution probabiliste (niveau 3) nécessite la connaissance totale des lois marginales et conjointes des variables de base et la disponibilité d’un outil permettant de calculer la probabilité de ruine (méthodes numériques ou simulation de Monté Carlo).

172

L’approche “Niveau 2” nécessite seulement la connaissance des paramètres statistiques estimés. L’évaluation des indices de fiabilité de Corne11 (1969) ou d’Hasofer et Lind (1974) permet d’estimer la probabilité de ruine. Il reste que ces méthodes d’analyse de fiabilité, basées sur un critère ponctuel de ruine, sont très mal adaptées au sol où les volumes concernés par la ruine sont importants. La variation spatiale des paramètres de base doit être prise en compte.

11.4- Approche décisionnelle: [ 1,2]

Il est très important pour l’ingénieur concepteur de pouvoir se définir un niveau de performance permettant de solutionner le problème posé mais sans perdre de vue les aspects économiques. Dans les quatre niveaux d’approche, l’aspect économique est ignoré sauf dans l’approche dite semi-probabiliste où l’utilisation des fractiles (des coeffkients de sécurité) tient compte de ces aspects mais d’une manière subjective.

L’approche décisionnelle tient compte d’une part des différents paramètres constituant les fonctions de performance et d’autre part, des coûts directs et indirects. Le niveau de performance sera fixé par une simple optimisation

si Cd et Cind sont respectivement les coûts directs et indirects intervenant dans un problème d’érosion, le risque total & n’est autre que l’espérance de ces coûts:

Les coûts indirects étant liés à l’apparition de l’état critique, on a donc:

De l’analyse de cette équation, il apparaît que si elle est établie d’une manière explicite en fonctions des différents paramètres ai, alors l’optimisation par rapport au niveau de performance sera donné par:

a* seront les paramètres décisionnels.

III. ETAT CRITIOUE D’EROSION:

Les causes constituant les événements précurseurs à la réalisation de l’état critique sont très diverses et il est très difficile d’établir une équation de performance globale. Néanmoins, la possibilité d’établir les équations de performance n’est pas à exclure. L’utilisation d’un arbre de causes [1,2] (figure 1) permet:

l D’identifier l’état critique. l D’identifier les événements initiateurs et leurs causes premières. 0 D’attirer l’attention de l’ingénieur et par conséquent d’éviter les oublis dont les

ctinséquences pouvant être catastrophiques. l D’estimer le poids de chaque événement et de consacrer son attention au plus

lourds.

173

FIGURE 1: ARBRE DES CAUSES DE L’EROSION

-EFFETSPLASH

I -COMPOSITION CIIIMIQUE DE L'EAU

-NATUREDUSOL -FISSURES -COUVERTURE

VEGETALE -PENTE

-ETATDESURFACE

EROSIONCONCENTREEOUI~AVIEMENl EROSIONENMASSEOUROULLEMENTGLISSEMENT

EROSIONDIJSOL

IV. ANALYSE DES CONSEOUENCES:

L’analyse des conséquences liées à l’érosion [ 1,4] (figure 2) montre que cette dernière peut se développer sous plusieurs scénarios. Chacun de ces scénarios engendre des coûts en fonction de la probabilité de sa réalisation. Si le problème est posé en terme de scénario, il faudrait donc chercher les risques ” calculés “.

Bien entendu, à chaque fois que le risque calculé associé à l’érosion est très faible, il est raisonnable de prendre une décision rapide sans le bénéfice d’aucune méthode formelle.

Cette méthodologie exige:

l L’identification des scénarios succédant l’état critique d’érosion l Estimer les magnitudes des probabilités. l Estimer les risques calculés associés à chacun des scénarios.

V. OPTIMISATION: [ 1,4]

L’optimisation des aménagements et ouvrages de lutte contre l’érosion exige la formulation du risque total associé à l’érosion. On pourrait distinguer deux types de coûts; l’un associé directement aux actions entamés et l’autre aux éventuelles conséquences. L’affectation des probabilités de réalisation de ces coûts permet l’évaluation des risques.

V.l- Risaue direct: La probabilité d’occurrence des coûts directs étant égale à l’unité, le risque direct sera:

&= E[Cd]= cd

Les coûts directs seront constitués essentiellement par les coûts d’investissement dans le bassin versant considéré (barrage, port, etc.. .) et qui seront affectés éventuellement par les sols érodés, des coûts des’ aménagements et des mesures palliatives à l’érosion.

V.2- Risaue indirect: Si l’on se place dans le cas ou seul un barrage est concerné par les sols érodés, les

principaux coûts pouvant être déduit des conséquences sont constitués essentiellement de:

l Coût lié à la dégradation des sols Cd (défertlisation etc...) l Coût lié aux vidanges de fond des ouvrages de mobilisation C,, l Coûts des pertes de production C, (envasement des barrages, ensablement des

ports, ect...) l Coût des mesures palliatives C,. l Gain de production G = -C, (fonctionnement normal des différents ouvrages

concernés par les sols érodés)

Partant des scénarios retenus par l’arbre des conséquences (figure 2) les différentes probabilités qui affectent les coûts indirects seront:

l Pr: Probabilité d’apparition de l’état critique. l P2: Probabilité d’échec des mesures palliatives. l PS: Probabilité pour que l’apparition de l’état critique et l’échec des mesures

palliatives entraîne la perte des différents investissements.

175

FIGURE 2: ARBRE DES CONSEQUENCCES DE L’EROSION

SENSIBILISATION DES PAYSANS CORRECTION TORRENTIELLE

(I-P,) pï?pzq p, ‘17 NON OUI I 1 1

14 ECI IEC DES MESUR ET/0 u

- (l-PI)C,

PALLIATIVES I

P?

ENVASEMENT TOTAL PA - OUI - (l-P41 NON

P3

v ENVASEMENT TOTAL

(l-P,)

P,(l-1’2) PJ P,(l-P2)(1-P4) P,P,P;

177

l Pa: Probabilité pour que malgré la réussite des mesures palliatives, il y a perte de l’ouvrage.

l PS: Probabilité pour que malgré l’échec des mesures palliatives, l’ouvrage n’est pas envasé.

Ainsi, les probabilités de réalisation des différents scénarios (figure 1) seront:

l Scénario 1: Pas d’état critique (1 -PI). l Scénario 2: L’état critique est atteint en l’échec des mesures palliatives PI( l-Pz)Pd. l Scénario 3: Pas d’état critique et ceci malgré l’échec des mesures palliatives h(l-p2)(1-p4).

l Scénario 4: L’état critique est atteint et ceci malgré la réussite des mesures palliatives Pr.P2.P3.

l Scénario 5: L’état critique est atteint partiellement et ceci malgré la réussite des mesures palliatives PI .Pz( 1 -P~).Ps.

l Scénario 6: Pas d’état critique après la réussite des mesures palliatives PlP2(1-P3)(1-P5).

Dans ce cas, le risque indirect sera:

Rind = - (l-Pr)C, + PI( J-P2)P4(Cr+Cd) + PI( I-P2)( I-P4)(Cpl+Cd+Cv) + P1PZP3(Cp+Cd+Cm) + P&( 1-P3)Pj(Cpl+Cm+Cd+C”) + P$2( 1 -P3)( l-P&,

L’optimisation consiste à rechercher la stratégie minimisant le risque indirect d’une part et d’autre part son adéquation avec le risque direct.

CONCLUSION:

Les actions de lutte et de prévention contre l’érosion des sols nécessitent souvent des investissements importants. La méthodologie proposée constitue une aide à la décision sur les actions à entreprendre permettant de prévenir contre l’érosion tout en optimisant le risque. Elle constitue aussi un élément pour convaincre les décideurs qui souvent n’accordent pas d’importance à ces projets surtout dans les pays ayant des difficultés économiques.

Cette approche mérite d’être enrichie tout en préparant les outils nécessaires à son élaboration. Les modèles de performance restent à établir, les paramètres à modéliser par des variables ou des fonctions aléatoires, les fonctions de coûts à déterminer et enfin penser à son application à des cas réels.

Au stade actuel, bien que qualitative, l’approche permet d’éviter les oublis, met en évidence les actions à entreprendre et oriente les décideurs.

REFERENCES BIBLIOGRAPHIOUES

1- A Bekkouche (1987) “Sécurité des grands barrages en terre. Approche probabiliste des problèmes d’écoulements liés aux reconnaissances et contrôles”. Thèse de Doctorat, Ecole Centrale des Arts et Manufactures de Paris, France. 2- N.J Schniter (1982) “Contributions and discussions” 14ièm” Congrée des Grands Barrages, Page 86-88, Rio de Janeiro, Brésil. 3- P. Thoft-Christensen, M.J. Baker (1982) “Structural reliability theory and it’s applications”. Printed in Germany, Nato Asi Séries. 4- M. Tribus (1972) “Décisions rationnelles dans l’incertain”. Traduit de l’anglais par J.Pelzer, Edition Maçon et Cie.

177

ANNEXES

179

ANNEXES

A) Summarv of the Content for the topics IV (Rare Floods) and IV (Hea- rains) joint session on “Heavy rains and flash floods”, edited through a specifïc report, by the topic IV (Pasquale Versace. Cosenza University) and VI (Carmen Llasat, Barcelona University) International Coordinators. Request them for obtaining the proceedings volume.

Prrrt I : Methodologic contribution .Y~>.WIOI? : Analysis of Precipitations

Joint estimation of IDF curves by maximum likelihood method by F. Frances and 1. Caskova

A multifractal explanation for Rainfall Intensity-Duration-Frequency Curves by P. Hubert, H. Bendjoudi, D. Schertzer and S. Lovejoy

Application of PWM method in the regional estimation of parameters for the SQRT-ET max distribution fünction

by J. Ferrer .se.s.sion : Statistical problems for floods

Use of historical information for flood frequency studies: the example of river Guiers by M Lang, D. Couer, C. Lallement and R. Naulet

Modelling of design hyetograph as a input to hydrologie models by E. Kupczyk and R. Suligowsky

Application of the rainfall-nmoff models to design flood computation by U. Soczynska, B. 12iowicka and 1,: Somorowska

General formulation of QdF mode1 by P. Javelle

Stochastic characteristics of long series by Z. Radie and J. Petrovic

Part II : Case studies Recent flood disasters at north western Black Sea region of Turkey

by 1. Gurer Flash-floods in the Northwest of the Meditemmean Area : tlie 27th -28th September 1992 event

by M. C. Llasat, C. Ramis and L. Lanza Heavy rainfall intensities in small basins: the flood of Crotone (October 1996. Italy)

b-y E. Ferrari and P. Versace Flood flows in the Kolubara catchment during June 1996

by A. Vukmirovic, B. Kapor and K Vukmirovic Flood behaviour on a small Mediterranean basin in French Cevennes

bUy C. Cosandey

B) List of the communications presented by AMHY participants at the joint session with the IDNDR and PIARC meeting (Maçka Hotel, Thursday 15 October) : “Floods and Roads”. PIARC meeting proceedings a\failable by Georges Pilot, LCPC Paris (georges.pilot@lcpc.fr).

Available assessment methods on floods in Mediterranean area (key note lecture) b-v P. Versace

Road embankment overflooding effects by A. Paquier

Specifïc methods to be applied for exceptionnal floods : consequences of epicentral phenomena along roads.

byA4. Lang

C) Participants’ directory (seefurther)

181

---.-

w

LIST OF PARTICIPANTS

NAME

ADLER, Marie Jeanne

FULL ADDRESS

National Institute of Meteorology and Hydrology 97 Bucuresti-Ploiesti 71552 Bucharest ROMANIA

PHONE NIMBER FAX NUMBER (with country and (with country and E-MAIL ADDRESS area code) area code)

40 12303116 40 12303143 adler@meteo.inmh.ro

AKAR, Tanju Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division 80626 Ayazaga, Istanbul 90 212 2853720 90 212 2853710 akar@itu.edu.tr TURKEY

AKSOY, Hafzullah Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division 80626 Ayazaga, Istanbul 90 212 2856577 90 212 2853710 haksoy@itu.edu.tr TURKEY

ASCHWANDEN, Hugo Swiss National Hydrological and Geological Survey (SNHGS) CH-3003 Berne S WITZERLAND

41 313247670 41313247681 Hugo.Aschwanden@BUWAL.admin.ch

BAYAZIT, Mehmetcik Istanbul Technical Univers@, Civil Engineering Faculty, Hydraulics Division 80626 Ayazaga, Istanbul 90 212 2856739 902122853710 mehmet@rain.hydro.itu.edu.tr TURKEY

BEKKOUCHE, Abdelmalek

BENDJOUDI, Hocine

Universite Abou Bakr Belkaid Institut de Genie Civil BP 119 13000 Tlemen ALGERIA

Universiti Paris 6, Lab. Geologie Applique Case 123, 4 Place Jussieu, 75252 Paris Cedex 05 FRANCE

213 7 208637 213 7 208637

33 144276326 33 144275125 bdj@biogeodis.jussieu.fr

BERNTSEN, Einar J. Faculty of Mathematics and Nat. Sciences, University of Oslo, PO BGX 1032 Blindem 03 15 OSLO NORWAY

4722858187 4722856339 Einar.bemtsen@matnat.uio.no

BULU, Atil Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division 80626 Ayazaga, Istanbul 902122853735 902122853710 buh@itu.edu.tr TURKEY

CENGIZ, Taner Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division 80626 Ayazaga, Istanbul 902122856845 90 212 2853710 tcengiz@?itu.edu.tr TUFKEY

PHONE NUMBER FAX NUMBER NAME FULL ADDRESS (with country and (with country and E-MAIL ADDRESS

area code) area code)

CHAOUCHE, Keltoum ENGREF 19, avenue du Maine 75015 Paris 33 1 45498960 chaouchekeltoum@engref.fr FRANCE

COSANDEY, Claude CNRS geography 1 pl A Briand 92 190 Meudon 33 145075578 33 1 45075830 Cosandey@cnrs-bellevue.fr FRANCE

National Institute of Meteorology and Hydrology DAKOVA, Snejana Tzarigradsko Chosse 66 Sofia 35929753986 3592884494 Snejana.Dakova@neteo.bg

BULGARIA . (285, internal)

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ALGERIA

Univers@ of Calabria FERRARI, Ennio Dipartimento di Difesa del S~olo, Cosenza 39984934316 39 984 934245 ferrari@dsserver.unical.it

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Confederation Hidrografica del Jucar Avda Blasco FERRER, Javier Ibanez 48,460lO Valencia 34 96 3938925 34963938801 ChjophQctv.es

SPAIN

Universidad Politechnica de Valencia FRANCES, Felix Apdo. 22012, 46071 Valencia 34963877612 34963877618 ffrances@hma.upv.es

SPAIN

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Gazi Univers&, Faculty of Engineering and GURER, Ibrahim Architecture Dept of Civil Engineering Ankara 9031223192223 90 3 12 2308434 Ibral~im@mikasamn~.gazi.edu.tr

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POLAND

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Istanbul Technical University, Civil Engineering OGUZ, Beyhan Faculty, Hydraulics Division 80626 Ayazaga, Istanbul 902122853725 902122853710 boguz@srv.ins.itu.edu.tr

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SERVAT, Eric ORSTOM BP 5045 - 34032 MONTPELLIER Cedex 33 4 67416400 SERVAT@ADIOPO.ORSTOM.CI FRANCE

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NATIONAL INSTITUTE OF METEOROLOGY STANESCU, Viorel AND HYDROLOGY SOS BUCURESTI PLOIESTI 40 1 2309507 40 1 2303143 Stanescu@meteo.inmh.ro Alexandru NO:97 BUCHAREST 71552 ROMANIA

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