RAPPORT Extreme flood estimation of the Grande Rivière du Sud … · 1951-2016 (daily time-series)...

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Pôle Énergies Renouvelables - Division Production Ingénierie HydrauliqueDTGDpt Surveillance - Centre Hydrométéorologique Alpes21, avenue de l'Europe - B.P. 41 - 38040 GRENOBLE CEDEX 09

[MATHEVET Thibault]

RAPPORT

Extreme flood estimation of the Grande Rivière du Sud Est (GRSE) at Sans Soucis (Diamamouve) Dam, Republic of Mauritius

H-44200966-2017-000006 Indice : A 54 Pages 7 annexe(s)

Entité propriétaire : 44200966 - CENTRE HYDROMETEOROLOGIQUE ALPES

Documents associés :

Résumé : The Gradex method has been applied to determine Grande Rivière du Sud Est (GRSE) at Sans Souci dam extreme flood values.

Main results are : - Time step : 6 hours ; - Peak-to-volume ratio : 1.84 (non centered) ; - Rainfall risk (Gradex) : 31 mm/6h ; - 1 000-year return level peak flow : 1352 m

3/s ;

- 10 000-year return level peak flow : 1731 m3/s ;

Catégorie : Enregistrement Accessibilité : Restreint

H-44200966-2017-000006 A approuvé le 22/06/2017 CONSULTABLE EN GED


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Copyright EDF - 2017. Ce document est la propriété d'EDF. Toute communication, reproduction, publication, même partielle, est interdite sauf autorisation

Création - Modifications

Ind. Auteur(s) Vérificateur(s) ApprobateurNom, Visa Nom, Visa Nom, Visa

MATHEVET Thibault

DEVAUCOUP Théo

GARAVAGLIA Federico DAUCHEZ Lorene

Historique des modificationsIndice Date Paragraphes modifiés / Objet

Diffusion

Destinataire(s) pour application Nb Destinataire(s) pour information NbCEB : R. Dhununjoy 1 EDF : R. Garçon, E. Paquet, F. Garavaglia, D. Penot 1

ISL : L. Benberim, S. Chevalier 1 EDF : N. Rouillon, H. Combes 1



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1. INTRODUCTION

1.1. CONTEXT OF THE STUDY

CEB (Central Electricity Board) wants to update the extreme flood estimation of Sans Souci dam due to a project of raising the full supply level of Sans Souci dam up to 244 m asl.

In 2016, EDF-DTG [1] made a review of the hydrological study proposed by SMEC [2], and offered to update the extreme flood estimation study [3]. The main comments of EDF-DTG [1] on SMEC study [2] were the follwing ones :

Improve the data analyses and the estimation of the water balance ; Reconsider the extreme rainfall estimation, taking into account the water balance, more rainfall stations and a

better statistical modelisation of extreme events ; Reconsider the extreme flood estimation, taking into account the dynamic behaviour of the watershed and sub-

daily observations. Improve estimation of flood hydrographs recorded at La Pipe station (E07) ; Take into account if possible, the influence of Midland dams.

From 09/01/2017 to 13/01/2017, EDF-DTG traveled to Mauritius to visit CEB, Hydrological services (WRU), Meteorological Services and the Sans Souci Dam (Figure 1).

Figure 1: Photos of Sans Souci Dam (09/01/2017) from the crest of the dam (top) and from the right bank (bottom)

1.2. OBJECTIVES

The objectives of this study are : Estimation of extreme flood events, up to T=10 000 years ; Estimation of PMF (Probable Maximum Flood) ; Flood hydrograph for T=10 000 years event and PMF.

1.3. APPROACH

This study is based on the Gradex method, used by EDF-DTG for the design of its dam during many decades. Main features of this method are given in Appendix 1. A complete description of the method is given in [4].



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2. AVAILABLE DATA

2.1. WATERSHED & INFLUENCES

As recommended [3], the delineation of GRSE at Sans Souci dam has been updated using ASTER 30m DEM (NASA, [5]) which is more precise than 90m SRTM DEM used by SMEC [2].

Figure 2 : Watersheds of GRSE at Midlands and Sans Souci dams, of Piton du milieu dam and of Rivière Canard at Sans Souci dam.

Figure 3 : Altitude variation over the GRSE at Sans Souci dam (ASTER 30m DEM)



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Table 1 : Summary of watersheds area estimated by EDF

Watershed Area [km²] Source

Midlands dam 17.2 Lahmeyer International 1998 [6]

Midlands dam 17.6 ISL

GRSE at La Pipe (E07) station 24.3 WRU

GRSE at La Pipe (E07) station 24.3 ISL

GRSE at Sans Souci 56.8 SMEC 1979 [5]

GRSE at Sans Souci 61.3SMEC 2013 [2]

90m DEM

GRSE at Sans Souci 62.9 ISL

Table 2 : Estimations of watersheds area by other sourcesThe maximum difference of watershed area estimation is about 5% (EDF & ISL estimation). Given a better expert knowledge of the watershed by ISL, ISL watershed area will used in this study.

2.2. RAINFALL

Available rainfall station from meteorological services (Table 3) :

Station PeriodInterannual mean

[mm/year]Comments

Sans Souci 1961-2016 (daily AMx)3720

(estimated by Met. Office)East of the watershed

Bel Etang 1961-2016 (daily AMx)2880

(estimated by Met. Office)North of the watershed

Vocoas 1961-2016 (daily time-series) 2020 West outside of the watershed

Plaisance1951-2016 (daily time-series)

2013-2016 (hourly & daily AMx)1790

South-east outside of the watershed

Dubreuil 1970-1991 (annual mean) 3820West of the watershed

From Midlands dam report [6]

Belle rive 1970-1991 (annual mean) 3230West of the watershed

From Midlands dam report [6]

AMx : annual maximal value

Table 3 : Available rainfall stations

Mean interannual rainfall amount of stations appear to be coherent with the isohyetal map of Mauritius Island (Figure 4). Given the isohyetal map and rainfall time-series within or around Sans Souci dam watershed, the mean areal rainfall of the watershed could be roughly estimated between 3000 mm/year and 4000 mm/year.

Due to a limited data access (extreme cost of information), a very limited sample of rainfall stations had been collected (and mainly AMx on the GRSE watershed). Other rainfall stations and continuous rainfall time-series could have been used. This would have slightly improved the robustness of this study.

Watershed Area [km²]

Rivière Canard 5.6

Piton du milieu dam 6.2

Midlands dam 16.8

GRSE at La Pipe (E07) station 24.3

GRSE at Sans Souci 60.2



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Figure 4 : Isohyetal map of Mauritius island (Source : Meteorological Office)

2.3. AIR TEMPERATURE

Available air temperature station from meteorological services (Table 4) :

Station PeriodInterannual mean

[°C]

Estimated Potential EvapoTranspiration (PET)

[mm/year]

Comments

Vocoas1961-2016

(daily time-series)21.6 1450

West outside of the watershed

Plaisance1951-2016

(daily time-series)23.9 1380

South-east outside of the watershed

Table 4 : Available air temperature stations (PET estimated from Oudin formula)

2.4. STREAMFLOW

In collaboration with WRU, the following stations have been collected (Table 5). Due to a limited data access, a very limited sample of stations had been collected :

E07, E008a and E13 represent the natural and influenced hydrology of the GRSE ; G09, H02 represent mostly natural hydrology of watershed close to GRSE.

Station locations are represented on APPENDIX 8 - Map of hydrometrical stations.



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Station PeriodInterannual mean [m

3/s & mm/year]

Watershed area [km²]

Comments

E07GRSE at La Pipe

station

1989-2010 (daily mean and maximal value time-series)

0.34 m3/s 24.3

E008aLa Nicollière feeder

canal


1.46 m3/s -

E07+E008aGRSE at La Pipe

station total


1.84 m3/s

2220 mm/year24.3

E07GRSE at La Pipe

station

1967-2002 (40 flood hydrographs)

- 24.3Flood hydrograph

digitised from limnigraphs

E13GRSE at

Beauchamp station

1990-2010 (daily mean and peak AMx)

- 162.3

Represents the main part of the

watershed, before sea

G09Rivière des Créoles

at Riche en Eaustation


3.44 m3/s

2330 mm/year46.7

H02Rivière La Chaux at Beau Vallon station


1.81 m3/s

955 mm/year59.8

AMx : annual maximal value

Table 5 : Available streamflow stations

The GRSE at La Pipe station (E07) is very important for this study. It represents the hydrology of the upper watershed of theGRSE, mostly natural before the construction of Midlands dam in 2002. This station represents a watershed whose dimension and situation is rather close to the Sans Souci dam watershed.

Given the methodology of the study (GRADEX) this limited collection of stations allow a sufficient estimation of moderate flood hydrology. Hence, hourly flood hydrographs significantly improve the robustness of this study.

3. PEAK TO VOLUME RATIO & TIME-STEP OF THE STUDY

3.1. GRSE@LA PIPE FLOOD HYDROGRAPHS

Thank to WRU, 40 flood hydrographs had been digitised. Then, these flood hydrogrpahs had been numerised (example on Figure 6 & Figure 7) and interpolated at an hourly time-step. Thanks to estimation of streamflow absolute peak and daily mean values, hourly water levels had been converted in hourly streamflow values (Figure 5).

Figure 5 : 06/02/1975 & 25/02/1998 streamflow hydrographs



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Figure 6 : 06/02/1975 water level flood hydrograph (Gervaise cyclone)

Figure 7 : 25/02/1998 water level flood hydrograph

The collection of the 40 flood hydrographs is shown in APPENDIX 2 – hourly flood hydrographs.

3.2. PEAK TO VOLUME RATIOS

The aim of the peak to volume ratio study is to characterise the link between a mean flood volume integrated over time and the absolute flood peak. Based on the collection of the 40 hourly flood hydrographs, flood peak to flood volume ratios (Knc) had been estimated for 2h, 4h, 6h, 8h and 24h time-steps.



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The centered peak to volume ratio (Kc) corresponds to the ratio between the peak flood value and the maximum 24h volume, including the peak. The non-centered peak to volume ratio (Knc) corresponds to the ratio between the peak flood value and the 6h volume based on a regular basis.

Table 6 shows the peak to volume ratio for a 6h time-step. This study of peak to volume ratio shows that a 24h time-step(Table 7) is far from the response time of the watershed, with a mean Knc around 3.7. Based on standards in extreme flood studies, the 6h time-step appears to be close to the response time of the watershed with a mean Knc around 1.8.

Peak to volume ratio for a 24h time-step for a sample of flood events is shown in APPENDIX 2 – hourly flood hydrographs, Table 18.

DateQX

(Absolute peak streamflow)

QMc(6h mean streamflow)

Kc(Centered peak to

volume ratio)

Knc(Non centered peak to volume

ratio)06/02/1975 523.9 254.2 2.06 2.0805/01/1987 215.2 135.2 1.59 1.816/04/1981 147.2 100 1.47 1.4729/04/1997 140.1 74.1 1.89 1.8914/03/1988 136 78.4 1.74 1.7427/04/1971 124 90 1.38 1.3814/01/1967 121.7 39.4 3.09 3.1703/03/1990 121.6 86.7 1.4 1.7422/01/2002 119.9 102.5 1.17 1.325/01/1980 118.2 70.1 1.68 1.6810/03/1968 114.3 74.5 1.53 2.2625/02/1998 109.7 72.5 1.51 1.5121/12/1982 107.5 67.3 1.6 1.630/12/1995 101.8 52.5 1.94 2.4103/04/1978 97.7 59.6 1.64 1.6402/02/1987 93.8 44.6 2.1 3.0312/12/1969 93.8 57.4 1.63 1.6330/03/1989 93.8 59.9 1.56 1.5809/01/1973 90.3 48.2 1.87 2.1510/04/1981 76.3 59.7 1.28 1.3629/03/1977 74.9 41.3 1.81 2.1729/03/1970 68.3 47.9 1.42 1.5609/03/1988 59.4 26.9 2.21 2.6221/04/2001 44.6 33.9 1.32 1.8519/03/1989 44.6 28.9 1.55 1.9502/02/1982 41.5 34.6 1.2 1.211/03/1991 41.5 30.9 1.34 1.4713/04/1981 37.5 35.8 1.05 1.15

Mean 1.64 1.84Standard deviation 0.40 0.50

Table 6 : 6h peak to volume ratio

3.3. TIME STEP OF THE STUDY

Time-step (h) 2 4 6 8 24

Knc : Mean 1.15 1.52 1.84 2.17 3.68

Knc : Standard deviation

0.14 0.35 0.5 0.58 1.14

Table 7 : Synthesis of non centered peak to volume ratio (Knc) for time-step ranging from 2h to 24h

Table 7 shows the evolution of the mean and standard deviation of the Knc value for time-steps ranging from 2h to 24h.

Considering results presented in Table 7, the 6h time-step is suitable for an extreme flood study on this watershed. This time-step will be considered for extreme rainfall estimation and extreme flood estimation.



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4. EXTREME RAINFALL ESTIMATION

4.1. WATER BALANCE OF THE WATERSHED & ESTIMATION OF MEAN AREAL RAINFALL

Since rainfall have a high spatial variability, with orographic effects and windward / leeward effects, the water balance of a watershed is often used to estimate mean areal rainfall :

P = R + AET +S~ R + AET (Eq. 1)With :

P : mean areal rainfall (mm/year) ; R : mean runoff (mm/year) ; AET : Actual Evapotranspiration (mm/year) ; S : water stock variation (mm/year), considered as equal to 0 on a long-term mean for this kind of watersheds ;

In the case of the GRSE at La Pipe station : R = 2200 mm/year (Table 5, 1989-2010) ; AET ~ 1500 mm/year, according to Oudin formula (Table 4). This value is homogeneous with values in tropical and

volcanic island environments ;

Hence P is estimated : ~ 3700 mm/year.

This value is rather close from long-term mean rainfall at Sans Souci, Dubreuil and Belle-rive stations.

4.2. CYCLONE TRACKS

Figure 9 shows some cyclone tracks close to Mauritius Island. The track of Gervaise (Figure 8) cyclone, one of most active cyclone since 50 years, cross the Sans Souci watershed. Heavy rainfall amount (>200 mm/day) can be found in the rainfall station time-series.

Figure 8 : Meteorological situation during Gervaise cyclone

Cyclone :12/02/1961

07/01/1966Denise

06/02/1975Gervaise

22/12/1979Claudette

10/02/1994 Hollanda

04/03/2006Diwa

Vocoas 0 226 456 289 / 125

Plaisance 0 70 245 113 / 165

Sans Souci 725 378 368 281 400 261

Bel Étang 494 187 812 348 276 200

Dubreuil / / 484 169 / /

Belle rive / / 368 238 / /

Table 8 : Synthesis of major cyclonic events (maximal daily rainfall during event)



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Figure 9 : Historical cyclone tracks over the 1970-2011 period (source : Global Risk Data Platform, United Nation, UNPE/GRID 2012)

4.3. DAILY RAINFALL GRADEX

In this case, the GRADEX value corresponds to the slope of the Gumbel distribution (Eq. 1), calibrated against maximal annualdaily rainfall values. Gumbel distribution had been calibrated for the available stations of this study (Table 9).

��(�) = �� −�� −��

�� Eq. 1

position parameter ; , scale parameter, which corresponds to the GRADEX ;



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StationMean annual rainfall

[mm/year] [mm/24h]

[mm/24h]GRADEX

Sans Souci 3720 160.0 74.3

Dubreuil 3820 167.0 74.5

Bel Étang 2880 142.8 92.5

Belle Rive 3230 154.4 69.4

« Spatial risk » - 167.1 62.9

Plaisance 1790 113.0 52.3

Vocoas 2020 114.8 70.9

Table 9 : Parameters of the Gumbel distributions calibrated against observations of rainfall stations

Figure 10 : Gumbel distribution of the Sans Souci station



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Figure 11 : 24h Gumbel distribution of the Sans Souci, Dubreuil & Belle rive stations over the 1970-1991 period (spatial risk : mean value of maximal annual values)

Table 9 shows parameters of the Gumbel distribution for Sans Souci, Dubreuil, Bel Étang and Belle Rive stations which are representative of the rainfall over the GRSE river. Rainfall risks are homogenous for Sans Souci, Dubreuil and Belle Rive stations. However, Bel Étang station exhibits a different behaviour, with a lower mean annual rainfall and a larger rainfall risk, mainly due to very heavy rainfall events during cyclonic events (812.8 mm/24h, during Gervaise cyclonic event the 06/02/1975).

Concerning Sans Souci, Dubreuil and Belle Rive stations, the most representative stations over the waterhsed, daily continuous rainfall time-series are not available (only annual maxima for Dubreuil and Belle Rive). In order to represent a mean areal risk, a « spatial risk » had been considered as the mean value of maximal annual values over the 1970-1991 period for Sans Souci, Dubreuil, Belle Rive stations. As an example, for a given year, the annual maximal rainfall is computed as the mean of individual annual maximal values. This hypothesis is conservative since annual maximal values could occur on different days.

Figure 10 shows the representation of the Gumbel distribution for the Sans Souci station. This figure confirms that the fit of the distribution against observations is rather good. This is mostly the case for all the stations (as shown in APPENDIX 4 – 24h gumbel distributions).

Figure 11 shows the representation of the Gumbel distribution for the « spatial risk ». This figure confirms that the fit of the distributions against observations is acceptable. The slope of the distribution (β coefficient) is lower for the spatial due to arealaveraging effects.



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4.4. 6 HOURS GRADEX

In order to realise the GRADEX study at an ideal time-step, it is required to estimate the 6h rainfall GRADEX. Due to a limited availability of hourly data, the 6h GRADEX had been estimated on a station where hourly data are available and transfered to GRSE watershed.

The 6h Rainfall GRADEX had been estimated over the Plaisance station, where hourly data are available since 2003. Gumbel distributions had been fited against annual maximal values at a 1h, 2h, 4h, 6h, 8h time-step.

Figure 12 shows the representation of the Gumbel distribution of 6h rainfall of the Plaisance station. This figure confirms that the fit of the distribution against observations is rather good. This is mostly the case for all the stations (as shown in APPENDIX 4 – 24h gumbel distributions).

Table 10 shows the synthesis of Gumbel distributions for 1h to 8h time-steps. This table shows that there is a large evolution of rainfall risk from 1h to 4h and that the risk slowly evolves from 6h to 8h duration (as show by evolution of and ).

Figure 12 : 6h Gumbel distribution of the Plaisance station over the 2003-2016 period



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Time step [h] [mm/24h] [mm/24h]GRADEX

1 25.9 8.6

2 38.8 13.8

4 51.0 22.4

6 56.8 25.8

8 58.6 28.8

Table 10 : Parameters of the Gumbel distributions of the Plaisance station over the 2003-2016 period for different period

The transfert of the 6h rainfall risk to the GRSE rainfall is made following Eq. 2 :

�� = ��

�� ∗��

��

�� Eq. 2

Eq. 2 means that the 6h rainfall risk over GRSE is equal to the 6h rainfall risk at Plaisance station, multiplied by the ratio of rainfall risk of GRSE over Plaisance.

4.5. GRSE RAINFALL RISK

Considering : ��

�� = 25.8��/6ℎ ;

�� = 62.9��/24ℎ ;

�� = 52.3��/24ℎ ;

Then, the 6h spatial risk :

�� = ��/�� ;

5. EXTREME FLOOD ESTIMATION

5.1. RETURN-PERIOD OF THE FLOOD THRESHOLD

Given the hydrometeorological context and heavy rainfall events during monsoon season, the return period of the flood threshold is considered as rather low, for frequent events of 2 years return-period. This rather strong assumption is confirmed by the empirical flood distribution (Figure 13) and by the fact that the slope of 6h rainfall and 6h streamflow Gumbel distributions are very similar (~30 mm/6h).

The maximal values, observed in February 1975, correspond to one of the major cyclonic events over the east part of Mauritius (Gervaise cyclone) with an estimated spatial rainfall risk of ~400 mm/24h. Given the distribution (Figure 13), this event have an estimated return period between 100 and 200 years.



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Figure 13 : 6h flood Gumbel distribution (in m3/s & mm/6h)



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5.2. FLOOD ESTIMATION UP TO T=10 000 YEARS RETURN LEVEL AT LA PIPE

Considering the following hypotheses : Knc = 1.84 (Table 7) ;

�� = ��/�� ;

Rentention loss limit : T= 2 years Q = 50.7 mm/6h ;

The GRADEX method gives the following results (Figure 14, Table 11) for the GRSE at La Pipe station.

Return period [years]6h Flood volume

Q6h [m3/s]

Flood peakQX [m

3/s]

10 123 227

100 204 377

1000 285 524

10000 365 671

Table 11 : 6h flood volume and flood peak from T=10 years to T=10000 years

Figure 14 : GRADEX of the GRSE at La Pipe, 6h time-step (in mm/6h)



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5.3. FLOOD ESTIMATION UP TO T=10 000 YEARS RETURN LEVEL AT SANS SOUCI DAM(NATURAL WATERSHED)

A classical formulation to extrapolate flood within a watershed is the following :

��(��)�� (��)

� ∗ ��

��

Eq.3

With : (aka Myers coefficient), usually ranging from 0.7 to 1. When this coefficient is far from 1, it represents the possible

spatial reduction of flood specific streamflows (m3/s/km²) from the upper part to lower part of a watershed.

Given information on GRSE at La Pipe and Beau Champ (162.3 km²), it seems that 1. The multiplicative coefficient

is equal to ��

��

=��.�

��.�= 2.58 with watershed area estimated by ISL.

The peak flood estimations are shown on Table 12.

Return period [years]

GRSE at La PipeGRSE at Sans Souci

Natural

Flood peakQX [m

3/s]

Flood peakQX [m

3/s] (ISL area)

10 230 586

100 385 973

1000 538 1352

10000 690 1731

Table 12 : transposition of GRADEX results from La Pipe to Sans Souci dam

5.4. FLOOD ESTIMATION UP TO T=10 000 YEARS RETURN LEVEL AT SANS SOUCI DAM (MIDLANDS IMPACTS)

In the documentation of Midlands dam [6] (partially read at WRU), the hydraulic impact of this dam on flood had been estimated as the following (Table 13) :

Flood inflow [m3/s] Flood outflow [m3/s] Outflow/Inflow ratio [%]

213 110 0.52

422 248 0.59

671 421 0.63

1034 692 0.67

1200 1200 1.00

Table 13 : Impact of Midlands dam on inflow (50m overflow) [6]

Table 14 gives the details of flood estimation of GRSE at Sans Souci, taking into consideration Midlands possible impact.

Return period [years]

GRSE at La Pipe

GRSE at Sans Souciwithout Midlands

contribution (45.3 km²)

Inflow GRSE at Midlands(17.6 km²)

Outflow GRSE at Midlands

(ratio~0.60)

GRSE at Sans Souci

+ Midlands impact

Flood peakQX [m3/s]

Flood peakQX [m3/s]

Flood peakQX [m3/s]

Flood peakQX [m3/s]

Flood peakQX [m3/s]

10 227 423 164 99 522

100 377 703 273 164 867

1000 524 977 380 228 1205

10000 671 1251 486 292 1542

Table 14 : transposition of GRADEX results from La Pipe to Sans Souci dam, taking into account the effect of Midlands dam (ISL area)

Comments about difference between Midlands extreme flood estimation :

Extreme flood estimation are significantly different (Table 15) :



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T [Years]Q [m3/s] (peak)

EDF

Q [m3/s] (peak)Lahmeyer

International [6]

Difference [%]([6] – EDF)/[6]

10 183 200 22%

100 317 420 54%

1000 447 760 100%

10 000 577 1240 155%

Table 15 : Difference of extreme flood estimation of GRSE at Midlands from EDF and [6]The aim of this study is the flood design at Sans Soucis and an estimation is proposed at Midlands, based on GRSE at La Pipe station. Some hypotheses had not been adapted to Midlands, such as mean areal precipitation, representative precipitation stations, etc. Hence, we had a partial access to [6], which prevent us to propose a detailed review of this study.

The main origin of difference between the two estimations comes from the extrapolation of the flood distribution of GRSE at La Pipe station proposed by [6] (Table 16). This estimation is based on Log-Pearson-3 distribution, which is an hyper-exponential distribution (convex form in a Gumbel space). In APPENDIX 7 – Shape of extreme flood hydrograph, the distribution of maximal annual floods of GRSE at Sans Soucis and its Gumbel distribution is shown. For very moderate floods, within observed return periods (T< 20 years), the difference between the empirical distribution and Log-Pearson-3 is already 35% for T=20 years.

T [Years]Q [m3/s]

EDF

Q [m3/s]Lahmeyer

International [6]

Difference [6] - EDF

5 50.3 59 +17%

10 64.1 80 +25%

20 77.3 104 +35%

50 94.4 140 +48%

Table 16 : Difference of extreme flood estimation of GRSE at La Pipe from EDF and [6]Given the difference between [6] and the empirical distribution, we consider that our estimation of floods at Midlands is more appropriate than the estimation based on Log-Pearson-3 distribution [6]. Our estimation might be improved, in testing other hypotheses.

5.5. ESTIMATED PROBABLE MAXIMAL FLOOD

The Probable Maximum Precipitation and Probable Maximum Flood (PMP/PMF) are two concepts which are specific to Anglo-Saxon culture. However, GRADEX method gives extreme flood estimations for specific return periods (up to T=10 000 years).

In the Dam spillway design guidelines recommandations [7], CFBR proposes an approximation of the Qx(PMF)/Qx(T=10000years) ratio which is approximately 1.3.

This mean value will be used to estimate GRSE at Sans Souci PMF (Table 17).

GRSE at Sans SouciNatural

Flood peakQX [m

3/s] (ISL area)

T = 10 000 years 1731

PMF 2251

Table 17 : PMF of GRSE at Sans Souci

5.6. FLOOD HYDROGRAPH

A possible shape of extreme flood hydrograph, based on a selection of observed floods (§3 peak to volume ratio & time-step of the study) is proposed on Figure 15 for T=10 000 years and Figure 16 for PMP.

The dimention less shape of this hydrograph is shown on APPENDIX 7 – Shape of extreme flood hydrograph. This shape could be used for any extreme flood values.



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Figure 15 : Q(T=10 000 years) flood hydrograph

Figure 16 : Q(PMF) flood hydrograph



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6. CONCLUSION

The objective of this study is to estimate the extreme flood at Sans Souci Dam on the Grande Rivière du Sud Est, in Mauritius islands.

In natural conditions, extreme flood estimation at Sans Souci dam are : QX(T=1000 years) = 1352 m

3/s ;

QX(T=10000 years) = 1731 m3/s ;

PMF = 2251 m3/s ;

Due to limited uncertainty on the watershed area, complementary extreme flood estimation (based on ISL area estimations) are also given.

Rainfall and streamflow data sets had been carefully studied and a GRADEX study at a 6h time-step allowed to estimated extreme floods. Given the available data sets thanks to WRU and Meteorological office, this study is considered as robust :

Time-step of the study (6h) adapted to watershed functionning ; Representative collection of flood hydrographs ; Robust estimation of flood peak to volume ratio ; Robust estimation of spatial Rainfall risk at 24h and 6h ;

Overall results appear close to SMEC study [2], but better documented. Data have been used extensively to justify hypotheses. However, due to meteorological data avaibility issues, some uncertainties, that could have been tested with otherexisting data sets, remain.

This study also proposes extreme flood estimations, taking into account Midlands effect. This scenario should be taken into account carefully, given uncertainties on the effective flood reduction due to reservoir. This scenario should be discussed withMidland reservoir management authorities.

7. REFERENCES

[1] Review of hydrology for the assessment of SMEC feasibility study to increase the capacity of Sans Souci Dam (Diamamouve Dam), Mauritius. EDF-DTG (C. JOUET), 16/03/2016, H-44200966-2016-000059-B.

[2] Feasibility Study to increase capacity of Sans Souci Dam, Mauritius - Final Feasibility Report, SMEC, January 2013.

[3] Consultancy Services for Increasing Storage Capacity at Sans Souci Dam, Mauritius - Assignment 1 : Reassessment of site hydrology. EDF-DTG (C. JOUET), 11/07/2016, H-44200966-2016-000195-A.

[4] Design flood : Determination by the Gradex method – 18th

congress ICOLD – N°2 November 1994.

[5] Feasibility Report on L’Etoile Cascade Diamamouve and Champagne Hydroelectric Schemes, SMEC, 1979. United Nations Development Programme, Contract Mar/76/001, Central Electricity Board Mauritius, Volume 2, pp. A-1 to E1-1.

[6] Midlands Dam Project. Consultancy services for Detailed design and Construction supervision. Detailed design, report and drawings. Final version. Lahmeyer International. April 1978.

[7] Recommandations pour le dimensionnement des évacuateurs de crues de barrages. Dam spillway design guidelines. CFBR (Comité Français des Grand Barrages). June 2013.

8. APPENDIX



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1. APPENDIX 1 – MAIN FEATURES OF THE GRADEX METHOD

Main features of the Gradex method given below is an extract of the document « Design flood : Determination by the Gradex method – 18

thcongress ICOLD – N°2 November 1994 ». For further details, the reader can refer it.

The Gradex method is a rainfall-runoff probability approach to computing extreme flood discharges in a river of between 1.10² AEP and 1.10

4AEP, i.e. events with recurrence intervals between one hundred and ten thousand years.

It is used on catchments ranging in size from a few tens to several thousand square kilometers with relatively uniform areal rainfall patterns. The most important factor in flood generation on such catchment is the way rainfall becomes direct overland runoff.The method is based on the general physical process of

but without referring to any precise mechanism, because of its dynamic complexity. This involves considering the space/time processes of precipitation-retention-direct runoff as a statistical process.

The principle of this method based on historical weather records is to find the asymptotic behaviour of the probability model for rare flood volumes from a probability model for cumulative extreme rainfalls. This can be done because the average retention capacity of a catchment tends to reach a constant value during heavy storms. We then find the peak discharge probabiltity with the aid of a relationship which is characteristic of the average shape of the runoff hydrograph. This also makes it possible to construct hydrographs for rare floods.

The Gradex method offers a coherent and plausible basis for computation by reason of its frequency approach to heavy local or regional rainfall. This approach operates through a parameter that is proportional to the standard deviation of heavy storms. This fundamental parameter is called the gradex (gradient of extreme values). The gradex is a seasonal and local climate invariant governed by geographical location. On a daily time-step, it ranges from 5 mm to more than 200 mm.

The first step is to set the unit time for all rainfall and flood events, and to adopt a duration corresponding to the average base time of the direct runoff hydrographs. This base time generally ranges from 4 hours to 72 hours.The duration of the flood hydrograph is an upper bound for the duration of the causal rainfall event. This is due to the routing of the rainfall excess from successive unit storms by the transfer function or unit hydrograph specific to the catchment.

Rainfall assumptions

Strong assumption, the frequency of precipitation P of duration ranging from a few hours to a few days, localised or averaged over the whole catchment (by weighted linear combination of simultaneous localised values) is a simple exponential decay function :

Ln[1-F(P)] = -P/a + constant in wich a is the gradex of annual extreme rainfalls.This assumption implies, mathematically, that the asymptotic distribution function for annual maximum rainfalls is a Gumbel distribution.

Assumptions on retention loss limit and extrapolation to long return periods

Strong assumption, the distribution of direct runoff volumes in extreme annual floods has the same asymptotic behaviour as the distribution of precipitations (all data is expressed in mm). The volume of direct runoff is equal to the volume of total causal rainfall less some random retention loss D. When rainfall increases as the storm progresses, retention loss tends towards some upper limited associated with antecedent soil moisture in the catchment.

Flood hydrographs

The last strong assumption arises from the principle of the invariance of the unit flood hydrographs or average transfer function from rainfall excess to streamflow, regardless of the magnitude of the rainfall. The probability of peak discharge is derived from the probability of the mean of extreme flood flows by a ratio r, the average shape factor of direct runoff hydrographs.

Total Rainfall

Rainfall Excess

Transfer Function

Flood Volume, Peak, Shape



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2. APPENDIX 2 – HOURLY FLOOD HYDROGRAPHS



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DateQX

(Absolute peak streamflow)

QMc(24h mean streamflow)

Kc(Centered peak to

volume ratio)

Knc(Non centered peak to

volume ratio)23/12/1979 206 54.8 3.76 4.1606/02/1982 158.6 74.2 2.14 2.1516/04/1981 147.2 48.8 3.02 3.5827/04/1971 124 44.1 2.81 2.8214/01/1967 121.7 19.5 6.25 6.3103/03/1990 121.6 54.8 2.22 2.6925/01/1980 118.2 39 3.03 3.0510/03/1968 114.3 37 3.09 4.9825/02/1998 109.7 27.9 3.93 4.6121/12/1982 107.5 27.3 3.94 3.9430/12/1995 101.8 21.4 4.75 4.8903/04/1978 97.7 30.8 3.17 3.5712/12/1969 93.8 20.4 4.61 4.9330/03/1989 93.8 29.6 3.17 3.2929/01/2000 89.5 46.3 1.93 2.2408/02/1972 87.8 37 2.37 4.1329/03/1977 74.9 17.5 4.29 4.7329/03/1970 68.3 31.5 2.17 2.711/03/1991 41.5 16.4 2.53 2.7302/02/1982 41.5 22.3 1.86 1.8823/04/2001 35.6 13.1 2.72 3.92

Mean 3.23 3.68

Standard deviation 1.10 1.14

Table 18 : 24h peak to volume ratio



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3. APPENDIX 3 – 6H FLOOD PEAK TO VOLUME RATIO STUDY



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4. APPENDIX 4 – 24H GUMBEL DISTRIBUTIONS



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5. APPENDIX 5 – 1H,2H,4H,6H,8H GUMBEL DISTRIBUTIONS



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6. APPENDIX 6 – 24H FLOOD DISTRIBUTION OF GRSE AT SANS SOUCIS



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7. APPENDIX 7 – SHAPE OF EXTREME FLOOD HYDROGRAPH

Time (hours) Non-dimentionnalQ [-]

Time (hours) Non-dimentionnalQ [-]

-5 0.16 4 0.29

-4 0.18 5 0.25

-3 0.21 6 0.23

-2 0.29 7 0.22

-1 0.46 8 0.21

0 1.00 9 0.21

1 0.74 10 0.20

2 0.59 11 0.18

3 0.51 12 0.18

The value non-dimentionnal hydrograph had to be multiplied by the flood peak (in m3/s) to represent an extreme flood event.



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8. APPENDIX 8 - MAP OF HYDROMETRICAL STATIONS


© EDF -2017. Ce document est la propriété d'EDF. Toute communication, reproduction, publication, même partielle, est interdite sauf autorisation.

Page d'approbation

Extreme flood estimation of the Grande Rivière du Sud Est(GRSE) at Sans Soucis (Diamamouve) Dam, Republic of Mauritius

Réf. : H-44200966-2017-000006 Indice : A Date : 22/06/2017 Accessibilité : Restreint

Rédacteur(s) :■ MATHEVET Thibault - 14/06/2017

Vérificateur(s) :■ GARAVAGLIA Federico - 16/06/2017

Approbateur(s) :■ DAUCHEZ Lorene - 22/06/2017


RAPPORT Extreme flood estimation of the Grande Rivière du Sud … · 1951-2016 (daily time-series)...

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