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The hydrological response ofheadwater and sideslope areas /La réponse hydrologique deszones de cours supérieurs etdes zones de pente latéraleKEITH BEVEN aa Institute of Hydrology , Wallingford, Oxon, OX108BB, UKPublished online: 25 Dec 2009.

To cite this article: KEITH BEVEN (1978) The hydrological response of headwaterand sideslope areas / La réponse hydrologique des zones de cours supérieurs etdes zones de pente latérale, Hydrological Sciences Bulletin, 23:4, 419-437, DOI:10.1080/02626667809491821

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Hydrological Sciences-Bulletin-des Sciences Hydrologiques, 23, 4, 12/1978

The hydrological response of headwater and sideslope areas

K E I T H B E V E N Institute of Hydrology, Wallingford, Oxon, 0X10 8BB, UK

Received 30 March 1978;revised 14 July 1978

Abstract. This paper shows that the hydrological response of convergent headwater and divergent sideslope areas, within a broadly homogenous basin, may be expected to be significantly different. A field study of three headwater and two sideslope areas of the order of 0.25 km2 in the Crimple Beck catchment, Yorkshire, England, is described. Spatial variations in gauged rainfall inputs to the sub-basin areas are shown to be small relative to differences in hydrological response. Results from winter and spring storms show that the headwater areas will generally provide significantly higher and earlier peak flows per unit area, and more total storm discharge, than the sideslope areas. Areas of surface saturation of the soi are most commonly found during and between storms in convergent hollow areas associated with ephemeral channels, expanding as variable contributing areas of surface flow during storm rainfall. In this basin, however, there was also a tendency for both headwater and sideslope sub-basins to generate surface flow on large areas of saturated soil during storms. Measured unchannelled surface flow velocities were very slow (~20 m/h) and suggest that, in this particular situation, the differences in the response of headwater and sideslope areas may be largely due to the role of the network of minor channels commonly found in convergent headwater areas. These, often ephemeral, channels transmit surface water to the permanent stream network efficiently and rapidly. In the sideslope areas, generally lacking such channels, surface water will be delayed, and may be delayed sufficiently to reinfiltrate before reaching a channel when rainfall ceases.

La réponse hydrologique des zones de cours supérieurs et des zones de pente latérale

Résumé. Cette mémoire montre qu'on peut s'attendre à ce que la réponse hydrologique des zones des cours supérieurs convergents et des zones de pente latérale sur un bassin versant pour la plupart homogène soit sensiblement différente. On décrit une étude sur terrain de trois zones de cours supérieurs et de deux zones de pente latérale de l'ordre de 0.25 km2 dans le bassin versant de Crimple Beck, Yorkshire, en Angleterre. Les variations spatielles des entrées jaugées de précipita­tion aux zones des bassins versants secondaires se montrent de moindre importance par rapport aux différences de réponse hydrologique. Les résultats des averses d'hiver et de printemps montrent que les zones de cours supérieurs fourniront généralement des débits maximaux qui sont plus forts et plus rapprochés par aire unitaire et un écoulement d'averse plus appréciable que les zones de pente latérale. Pour la plupart on trouve les zones de saturation superficielle du sol pendant et entre les averses dans des zones creuses et convergentes associées aux canaux éphémères et elles s'étendent sous la forme des apports intermédiaires variables au ruissellement de surface pendant les averses. Dans ce bassin versant cependant, les bassins secondaires du cours supérieurs et aussi ceux de pente latérale ont montré une tendance à générer du ruissellement de surface sur des zones extensives de sol saturé pendant les averses. Les vitesses superficielles mesurées dans des zones sans lits de cour d'eau étaient très lentes ( -20 m/h) ce qui suggère que, dans cette situation particulière, les différences de réponse des zones de cours supérieurs et celles de pente latérale pourraient être

*Formerly at: School of Geography, University of Leeds, UK.

0303-6936/78/1200-0419$02.00 © 1978 Blackwell Scientific Publications 419

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420 Keith Beven

dues au rôle du réseau des canaux secondaires qu'on trouve ordinairement dans les zones de cours supérieurs convergentes. Ces canaux souvent éphémères apportent l'eau de surface au réseau permanent des cours d'eau d'une manière efficace et rapide. Dans les zones de pente latérale où il manque de ces canaux en général, l'eau de surface sera retardée de telle manière qu'elle reinfiltre avant de parvenir à un cours d'eau quand la pluie cesse.

1. THE EFFECT OF HILLSLOPE SHAPE ON BASIN HYDROLOGICAL RESPONSE

This study is not concerned with large scale differences in bulk relief between basins in different areas, or between the headwater and flood plain areas of large basins. This investigation is restricted to an examination of the effect of topographical configura­tion, or the shape of slopes (at scales of the order of 0.01-1 km), on the details of basin hydrology within a broadly homogenous area. The results presented here suggest that differences in topography are a major factor in the hydrology of storm response which is often markedly non-uniform over short distances. Convergent headwater areas, draining to the head of a permanent stream channel, are distinguished from sideslope areas, draining to the side of a channel. Sideslope areas may have straight or divergent contours in plan. The effects of slope convexity or concavity in section will also be noted. Sideslope areas may form a significant proportion of the total basin area, which will generally increase with increasing basin size.

There have been few studies that have explicitly considered the hydrological signi­ficance of slope convergence/divergence. In a theoretical study, Kirkby & Chorley (1967) noted that hillslope convergence in plan, concavity in section, and decreasing soil thickness would all tend to increase the outflow discharge from a slope segment, and in particular, the likelihood of occurrence of surface flow. The classic field experi­ments of Dunne & Black (1970a, b) on a grassed basin in Vermont, tried to distinguish the response of three adjacent slope units, in all some 80 m wide within a sideslope section, one convergent, one divergent and one straight sloped in plan. Measurements were also made on a seep draining from a convergent concave hollow. The results suggest that for all the areas subsurface flow was too late and too little to make a significant contribution to the measured channel hydrograph. Stormflow reaching the channel appeared to derive from direct channel precipitation and from precipitation on areas where the water table had risen sufficiently to intersect the surface. There was also a significant contribution from subsurface return flow coming to the surface where saturated, with a consequent marked increase of velocity of flow towards the channel. Dunne & Black stressed this threshold in flow velocity between subsurface and surface flow and recorded that the areas most likely to generate surface flow were the convergent slope segment and the seep hollow area. They also noted that with increasing storm rainfall the saturated areas spread further into the hollows. The con­tribution of discharge to the storm hydrograph from the divergent and straight sloped areas was reported as rare and relatively insignificant. Subsurface flow rates were also less per unit width of slope in these areas. Some of the differences were undoubtedly due to differences in soil conditions between the slopes but the fact that these re­flected the slope form is also indicative of the importance of topography in the details of slope hydrology (Dunne et al., 1975).

At a similar scale the studies of Anderson & Burt (1977) on a grass with bracken sideslope in the Quantock Hills, Somerset, have provided more detailed information

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Hydrological response of headwater and sideslope areas 421

on the spatial variation of saturated conditions in a small convergent topographic hollow and adjacent spurs. The experiment showed that the dynamic response of saturated conditions within the soil was most strongly marked in the hollow area where, for the storm considered, the water table rose to come close to the surface. On the adjacent spurs, only at one site did the water table rise above 60 cm below ground level. Anderson & Burt, however, report that the brown earth soils on the slope were generally deeper but stonier in the hollow area in comparison with the adjacent spurs. No details were given of comparative discharge from the different slope segments.

Moving up towards the scale of large slope segments, the work of Weyman (1974) in the Mendips, Somerset, enabled a direct comparison of a small headwater basin (0.11 km2) of gently convex slopes, with a sideslope area immediately downstream (0.10 km2) with much steeper convex slopes and divergent contours. The distinction between the two areas was made more marked by soil and vegetation differences, with a peaty-gleyed podzol under grass and heather in the upper convergent basin, and predominantly free draining brown earth soils under dense bracken in the lower divergent section. The two areas showed a distinct contrast in hydrological response, the upper basin having a much earlier and higher peak discharge. Immediate storm runoff from the lower area could be accounted for by precipitation directly into the channel and a small immediately adjacent area that remained saturated throughout the winter. The bulk of the outflow, however, was extremely delayed with a low and diffuse peak at a minimum of 24 h after the storm rainfall. The shape of this lower area hydrograph was closely correlated with throughflow hydrographs measured at several small slope segments within the lower area, although rates of flow into the channel were distinctly non-uniform across the slopes (Weyman, 1970). Weyman postulated that flow from the upper basin was generated by rainfaU excess overland flow on areas of low infiltration capacity, together with surface flow on saturated areas in shallow hollows above the stream head. It was found that during a storm the surface flow extends into the network of hollows, thereby increasing the length of drainage net. No surface flow was observed in the lower basin.

Most field experiments are subject to a plethora of complicating factors such that it is difficult to define and separate the effects of soils, hillslope shape, initial and storm conditions on the overall response of a basin or slope area. Using a theoretical simula­tion model, Beven (1977a, 1977b) has tried to isolate some of these effects and examine the sensitivity of the subsurface flow system to a range of imposed slope conditions. The results confirm that it is convergent slopes, and in particular convergent slopes concave in section, that deliver the highest peak rates of subsurface flow and are also most likely to generate saturated conditions and return flow at the soil surface. These experiments also suggest that, for the limited range of soil and storm conditions considered, peak subsurface flow rates could occur within minutes of the end of the rainfall. In addition while convergent areas generally gave rise to higher peak flow rates and storm flow volumes per unit length of slope, the amounts were such that divergent and straight slopes, with a greater width of slope adjacent to the channel, might yield a greater overall contribution to the basin subsurface hydrograph, albeit relatively delayed.

2. OBJECTIVES OF THE STUDY

This study into the hydrological response of different areas of the Crimple Beck basin

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422 Keith Beven

was undertaken as part of a project with the wider aim of developing a simple but physically based model of basin hydrology that was applicable to medium sized basins. The theoretical basis of the model was firmly rooted in the variable contri­buting area concepts of basin response (Hewlett, 1974) and a theoretical framework was provided to model the effects of topography and soils on the dynamic variation in saturated area in a basin (Beven & Kirkby, 1979). To test the model, however, data were required for comparable basins of differing topography. Such data were not available elsewhere and consequently the programme of field work described below was set up to distinguish the response of headwater and sideslope areas within the basin at a scale suitable for model testing. Results of the modelling exercise are reported in Beven & Kirkby (1979).

3. THE CRIMPLE BECK

The headwaters of the Crimple Beck, a tributary of the River Nidd, lie to the south­west of Harrogate, Yorkshire, and some 15 miles north of Leeds (Fig. 1). The area under study covers some 8 km2, the lower limit of the basin being delimited by a flat-vee crump weir installed by the Yorkshire Water Authority (grid reference SE 284518). The basin ranges in altitude from 115 to 250 m OD and has an average annual preci­pitation of about 800 mm. The underlying bedrock is mostly sandstones and inter-calcated shales of the Carboniferous MiËstone Grit series, with an inlier of calcareous Harrogate Roadstone in the north, close to the village of Beckwithshaw. Most of this bedrock, however, is overlain by Pleistocene glacial till, periglacial and fluvial deposits.

FIG. 1. Location and topographic maps of the Crimple Beck basin.

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Hydrological response of headwater and sideslope areas 423

The drainage network is incised predominantly into these deposits and bedrock sections are rare. There are a small number of minor springs but their contribution to stream-flow is small. The quality of the surficial deposits varies greatly from unweathered impermeable blue glacial clay, to localized lenses of sand in the headwater area on Stainburn Moor, and lobes of head deposits with angular rocks in a fine compact matrix in the lower part of the basin. Over most of the area the subsoil is relatively impermeable and the basin as a whole shows a fast response to storm rainfall, with a typical time between peak rainfall intensity and peak discharge at the outlet of 2-10 h.

4. HEADWATER AND SIDESLOPE AREAS IN THE CRIMPLE BECK

With the aims of the overall modelling project in mind, this present study required the separation of headwater and sideslope areas at a larger scale than those described in section 1. The distribution of discharge and rainfall measurement sites enabled three headwater sub-basins and two sideslope sub-basins to be isolated as indicated on Fig. 2. Details of these sub-basins are as follows.

H I : The Lanshaw sub-basin (0.22 km2} This headwater area lies in the highest part of the Crimple Beck and remains largely an unimproved area of rough grazing dominated by rough grasses (Nardus, Festuca, Agrostis spp.). There are Juncus rushes with bog mosses in the wetter flush areas and in the relatively flat hollow area in the centre of this sub-basin. Heather communities are found on the drier localized sand lenses noted above. Elsewhere the soils are developed over till and are predominantly stagno-gley soils. A typical profile consists of 10 cm of loamy peat, over some 15 cm of yellowish firm clay, over a compact grey

F I G . 2. Instrumentation, headwater and sideslope sub-basins in the Crimple Beck basin. H I : Lanshaw sub-basin; H2: Tatebaek sub-basin; H3: Swires sub-basin; SI: Hemingway sub-basin;S2: Knowles sub-basin, v, Discharge measurement sites; o, raingauge sites; , sub-basin boundaries.

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424 Keith Beven

or blue-grey clay to below auger depth. There Is evidence along the channel section above the outflow for a podzolic soil with interbedded layers of peaty and stony sand. The sectional form of this sub-basin is gently convex, the slope increasing to about 8° close to the 90° V-notch weir at the outflow. During the winter months, the subsoil is generally saturated and the hydrologically active layer is confined to the humose topsoil, which may become saturated over wide areas during storm rainfall.

H2: The Tateback sub-basin {0.23 km2) This sub-basin is mostly under permanent pasture with some arable land: it has a long history of improvement and drainage. Nearly the full length of the natural channel within the area has been enclosed in drains of stone slabs, dating at least from the nineteenth century. There are also ditches at field boundaries and some more recent tile drainage. The former stream channels are here more marked than elsewhere in Crimple Beck and the drains lie in steep sided gullies. The drains appear to be as effective as open stream channels in removing surface runoff and, because of the position in natural gullies, probably have a restricted influence on the occurrence of saturated conditions on adjacent slopes.

The soils in the Tateback basin have been examined in some detail by Harris (1975) and are indicative of patterns found elsewhere on the improved agricultural land of the Crimple Beck, reflecting drainage conditions and parent material at a point. Most of the relatively flat upper slopes in the basin are characterized by cambic stagno-gley soils, especially where the parent material is shale or till. A typical profile consists of 10-20 cm of compact humose loam becoming grey white with depth, over a firm yellow clay or clay loam. At a depth of about 1 m this is underlain by a grey gritty clay. This soil may have a very low infiltration capacity (as low as ~1 mm/h). On steeper slopes while the soils may still be classified as stagno-gieys they generally appear better drained with up to 60 cm of sandy loam overlying a gleyed sandy clay or clay. With a further improvement in drainage over sandstone and on the steepest slopes the soils tend towards brown podzolic and typical brown earth profiles. The slopes are again broadly convex in section.

Discharge measurements from the Tateback sub-basin were made using a 90° V-notch weir.

H3: The Swires sub-basin (0.25 km2! The third convergent headwater area also reflects the long history of agricultural use to which the majority of the Crimple Beck basin has been subjected. Much of this sub-basin is again under improved permanent pasture, the remainder being used for an arable/fallow grass rotation. There has been some underdraining In the sub-basin in addition to older ditches at field boundaries. The soils exhibit a similar pattern to that in the Tateback sub-basin. Again there was a significant area with gleyed soils on the relatively flat upper slopes. The slopes in this sub-basin show more of a basal concavity as the area narrows towards the outflow, where discharge was again measured with a 90° V-notch weir. Flow was found to be maintained between storms by a small spring, but the contribution was small relative to the storm response of the sub-basin. The buildings of Highmoor Farm sited in the centre of this basin provide an impermeable area of roofs, yard and track.

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Hydrological response of headwater and sideslope areas 425

S1: The Hemingway sub-basin (0.175 km2) Outflows from this sub-basin were determined by subtraction of discharges measured at two 90° V-notch weirs on a tributary of the Crimpie Beck. The slope on the south side of the tributary is a short steep scar and most of the area of the sub-basin consists of convexo-concave slopes with a long straight or concave section at the base. The con­tours are slightly divergent in plan. The soils are mostly gjeyed, improving on the mid slope areas. Part of the sub-basin had been tile drained and two minor ditches enter the tributary stream at field boundaries.

S2: The Knowles sub-basin (0.56 km2I This was the least satisfactory of the sub-basins in terms of accurately measuring the contributions to streamflow. The size of the Crimpie Beck here is such that the upper and lower measurement sites on the mainstream were both rated sections at minor con­trols. The situation was also further complicated by the inflow from the Swires sub-basin to the mainstream within this section. The contribution at steady flows from this side-slope area amounted to some 20-30 per cent of the flow at the downstream station. Calibration of the mainstream sites was carried out using repeated dilution gauging measurements. The rating curves appeared to remain reasonably constant during the period of study, changes only being necessitated by the large storm hydrograph on 2 January 1976, which also damaged weirs in other parts of the Crimpie Beck basin.

The shape of the slopes were broadly straight contoured, and concave over most of their length to the north of the mainstream, with two areas of divergent, convexo-concave slopes to the south. Again, the pattern of soils was similar to that described in Tateback, though close to the stream they were in places developed on lobes of head material into which the stream had incised.

It must be realized in what follows that the determination of the hydrological response of the sideslope areas from two or three measurement sites has a number of disadvantages at this scale. The effects of travel time within the stream channel are introduced and will give rise to error in the subtraction of discharges for sites some distance apart. More importantly, the effects of measurement errors at each site are also included in the determination of the incremental discharge of the sideslope areas. Particularly in the case of the S2 Knowles sub-basin the length of stream channel and three measurement sites involved result in some uncertainty in the storm hydrograph as calculated by subtraction. The comments on sideslope response that follow have consequently concentrated on the SI Hemingway sub-basin.

5. HYDROLOGICAL INPUTS

In an examination of spatial variations in hydrological response, it is first necessary to examine possible variations in the hydrological inputs to the area under study. Rainfall data were measured at a maximum of five ground level gauge sites in the basin, with measurements taken at weekly intervals. Two of the sites, Rl in the Lanshaw sub-basin and R2 in the Tateback sub-basin were also equipped with tilting syphon autographic gauges with strip charts changed weekly. In addition data were available from a standard daily raingauge and a tilting syphon autographic gauge at the Yorkshire Water Authority site at Harlow Hill (grid reference SE 250541) outside the basin.

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426 Keith Seven

TABLE 1. Rainfall totals foi the period 8.10.75 to 2.11.76

Gauge site Total rainfall (mm)

Rl R2 R3

Harlow Hill

866.7* 850.5* 864.0* 777.2f

*Gro«nd level gauge with anti-splash grid tMeteorological Office standard gauge, 30 cm above ground level

The annual rainfall totals (luring the period of study are given in Table 1 for four of the sites. Only one storm (that of 1-2 January 1976) had a significant contribution from precipitation in the-form of snow. This storm (storm 2 in Table 2) resulted in the largest hydrograph during the period (3.37 m3/s at the basin outlet) and caused the failure of several measurement sites. This event has consequently been excluded from the analysis of storm response that follows.

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Hydrological response of headwater and sideslope areas All

( a ) , V ^ ^___800mm

FIG. 4(a) A map of total measured rainfall for the period 3.12.75 to 2.11.76 (4 weeks missing data interpolated for gauge R5). Co) À map of measured rainfall for the week commencing 4.5.76. Dashed lines represent basin boundary, circles represent the raingauge sites.

An examination for spatial variation in the rainfall input was made first by com­paring double mass curves for the individual raingauges (Fig. 3). This plot suggests that differences between the sites are relatively small, but there is a tendency for the gauge in the Lanshaw sub-basin (Rl), at the head of Crimple Beck, to catch more than the other gauges except the R4 gauge. The R4 gauge at Beckwithshaw sewage works was the most sheltered of all the gauges. The R5 gauge near Valley Farm at the bottom of the basin often recorded the lowest catch of all the gauges. A map of rainfall totals (Fig. 4a) emphasizes the general trend across the basin, with rainfall decreasing with altitude from the watershed to the outflow. The differences, however, are relatively small and the pattern for individual storms was variable (e.g. Fig. 4b). The spatial variation in rainfall inputs should not therefore have a dominant influence on any variations in hydrological response in the basin. The reader should note, however, that 1975/1976 was an abnormally dry winter and that this conclusion may not always hold.

6. THE HYDROLOGICAL RESPONSE OF THE CRIMPLE SUB-BASINS

The study covered the period November 1975 to June 1976. A list of significant storm hydrographs with well defined peaks considered in the analysis is given in Table 2. The hydrological response of the sub-basins was analysed in terms of the timing and amount of the discharge peak, and the volume of storm discharge.

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428 Keith Beven

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Hydrological response of headwater and sideslope areas 429

FIG. 5. A plot of peak discharges from the headwater and sideslope areas for storms in the period November 1975 to May 1976.

Peak discharges A comparison of peak discharges (expressed in mm per unit area per half hour time increment) from the headwater and sideslope sub-basins is given in Fig. 5, relative to the outflow from the Lanshaw sub-basin. The peak discharge values for the area S2 show the greater scatter and, as noted above, are undoubtedly the least certain. If these are excluded the consistency in the ordering for the remaining areas for different storms suggests that these differences are a true reflection of the variations in response between the areas. This consistency extends even to the closest of the areas, H2 and SI, with the sideslope area giving the lowest discharge for all but one storm. The Lanshaw sub-basin produces generally higher peak discharges than the other areas and there is some tendency for differences between the areas to increase with increasing discharge.

Peak flow timing The time of the peak (accurate to the nearest half hour) has been plotted relative to that of the main weir outflow from the whole basin. Figure 6a shows that the head­water areas always peak earlier or at the same time as the main weir but that this difference tends to decrease with increasing peak flow. A comparison with Fig. 6b shows that the areas H2 and S1 now differ markedly in respect of peak flow timing, the sideslope area generahy peaking later than the main weir with some tendency for the delay to decrease with increasing peak flow. The timing results for area S2 were particularly difficult to define from the three measurement records and are again equivocal.

Volume of discharge An objective procedure to calculate the volume of discharge resulting from a single, but possibly complex, period of storm rainfall, is not easy to define. Since this study was mostly concerned with the storm response rather than the recession period the following procedure was adopted. The volumes were calculated from the start of the

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430 Keith Seven

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FIG. 6(a) A plot of peak discharge timing (relative to the main Crimple Beck weir) with peak magnitudes for the three headwater sub-basins for seven storms with complete data, (b) A plot of peak discharge timing (relative to the main Crimple Beck weir) with peak magnitudes for the two sideslope sub-basins for seven storms with complete data.

hydrograph rise at each site to arbitrary cut-off points of 12 and 24 h after the peak of the hydrograph at the Crimple Beck main weir site. To exclude the influence of pre-existing flow, a constant rate of flow, equal to that immediately prior to the start of the hydrograph rise, was subtracted from the total runoff volumes. Five storm periods were chosen for study (storms la and lb were taken together for this purpose with the 12 and 24 h period starting from the second, higher peak) on the basis of being relatively isolated so that the effect of the initial flows was small and no further significant rainfalls occurred within the maximum 24 h period after the main weir peak. After 24 h, the discharge had generally fallen to the order of 10 per cent of the peak or less. This procedure is admittedly arbitrary but makes minimum assumptions about the nature of the processes involved. The results are presented in Table 3, expressed as percentages of the total storm rainfall.

The results show that there is a tendency for the headwater areas to produce a greater volume of storm discharge, to both 12 and 24 h after the main weir peak, than the sideslope areas. The incremental volume between the 12 and 24 h times, also tends to be greater from the headwater sub-basin. With the notable exception of storm 1, the sideslope sub-basins tend to produce less storm discharge than the basin as a whole and the headwater areas more. Area S2 is again the more variable of the two sideslope sub-basins. The Tateback area (H2) is something of an exception to this pattern. In the two storms (1 and 7) for which the sub-basin is wetting up after a dry spell, this headwater area produces much less storm discharge than the sideslope areas and the whole basin. It would appear that under such conditions the artificial drainage in this basin has the result of allowing the effect of initial losses to predominate over the effect of topography. Once the basin has wetted up, this sub-basin produces more discharge volume than the sideslope areas.

À further impression of the differences between the areas is gained from a plot of the hydrographs for two of the sub-basins relative to the main weir. The areas HI

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Hydrological response of headwater and sideslope areas 431

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432 Keith Seven

FIG. 7. Discharge hydrographs for the headwater sub4>asin HI, the sideslope sub-basin SI and the whole Crimple Beck basin,

and SI are plotted in Fig. 7 and show that, for this particular area, differences in flow quantities throughout this storm are far more significant than differences in timing.

Saturated area In the basin of the Crimple Beck a major part of the early storm discharge and hydro-graph peak appears to be generated as surface flow on areas of topsoil saturation, and on unsaturated areas of low infiltration capacity. Large areas are maintained at or close to saturation throughout the winter due to low subsurface flow rates. The saturated contributing areas expand and contract dynamically during and between storm rainfalls in a manner that reflects the complexities of soil and topography. These factors are strongly correlated and in places in the basin, changes in soil and natural drainage conditions, and the dynamic changes in contributing areas, are conditioned by very minor changes in topography. In this study apparent saturated areas were mapped by a foot survey of the sub-basins HI, H2 and SI. The results from the three areas are shown in Figs 8, 9 and 10. It should be noted that the maps for each area were necessarily based on surveys from different periods and are not strictly com­parable. A number of interesting points are suggested by the maps. The restricted spread of contributing area close to channels and into seep areas, as reported by Dunne et al. (1975) is present but in addition, in all three sub-basins, areas of low uniform slope associated with stagno-gley soils saturate easily over wide areas. These areas may be far from a stream channel (or drain) and the basin outlet. The effects of drainage in reducing the omet of saturated conditions are clearly seen in the lowest field of the Hemingway sub-basin (Fig. 10), the only field drained in that area.

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Hydrological response of headwater and sideslope areas 433

V Weir

Catchment boundary

~ ~ - - Minor channels

: ' : ' . ' ' . : Saturated area at g = 3 t / s

FIG. 8. Observed saturated area at different discharge rates for part of the HI Lanshaw sub-basin.

In the Lanshaw sub-basin (Fig. 8), the present results confirm the earlier studies of Kirkby et al. (1976) who used a network of crest saturation tubes to determine the percentage of storms during which an area becomes saturated. The area of saturation extends from the head of the channel into flush lines that connect with a broad area of low slope in the centre, that is saturated throughout the winter. The more detailed, if less rigorous, map presented here shows, however, that the pattern is more complex than previously presented with the spread restricted by minor elevation differences within the central area of the sub-basin. In addition a number of small flush areas in hollows in the lower part of the basin, not necessarily connected directly to the stream network appear to be saturated throughout the winter, as a result of both convergent flow and more impermeable soil conditions. The minor channels and flushes of the upper area continue to channel water to the stream head for considerable periods after rainfall has ceased.

7, DISCUSSION OF RESULTS

These results have revealed that differences in the hydrological response of headwater and sideslope areas may be clearly distinguished. These differences have been shown to be a function not only of topography but also of soil and rainfall conditions. Dif­ferences in rainfall input to the sub-basins were small but the overall trend across the area may have accentuated the differences between the sub-basins. It would appear,

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434 Keith Beven

> Weir

Catchment boundary

Minor channels

-X-:::;::'. Saturated area at q = 8 L/

Additional saturated area at C; » 30 L/s

FIG. 9. Observed saturated area at different discharge rates for the H2 Tateback sub-basin.

V Weirs

Catchment boundary

Saturated area at q = 20 L/s

Additional saturated at q = 65 L/s

FIG. 10. Observed saturated area at different discharge rates for part of the SI Hemingway sub-basin.

however, that the likelihood of the topsoil becoming saturated is more important and that this is strongly related to the details of topography within the sub-basins. In general, sub-basin areas convergent in plan were reyealed to yield higher and earlier peak discharges than the SI sideslope area studied. The differences between sub-basin peak discharges showed some tendency to increase with increasing storm rainfall while the small differences in peak timing decreased.

Within each area, areas of saturation were shown to expand into convergent hollow areas, some of which contain ephemeral streams and are directly linked to the channel system. There were also broad areas of saturation associated with relatively poorly

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Hydrologicaï response of headwater and sideslope areas 435

drained soils on low slopes. Even the sideslope area SI showed a tendency for saturated conditions to spread over most of the basin under winter storm conditions. This occurred even during the smaller storms which would help to explain the similarity in peak flows of the areas H2 and SI shown in Fig. 5. Once this saturated area is established, however, peak discharge might be expected to increase less rapidly with increasing storm rainfall than in areas where the saturated area continues to expand, as is particularly true of the HI Lanshaw area. Thus the difference in peak flow between the areas would, as shown, increase with the size of the peak.

The extent of saturation alone cannot fully explain the results presented. For the sideslope area SI in particular there is a discrepancy between the large area of basin apparently saturated and the much smaller proportion of rainfall input contributing to streamflow within the peak and early recession of the hydrograph. It is suggested that the differences between the areas are predominantly a result of differences in the routing of the surface runoff within the sub-basins. In part this may be a result of slope differences between the areas, headwater areas being broadly convex, suggesting an increasing velocity of flow downslope, and the sideslope areas concave with low slopes close to the channel. This cannot be a fully satisfactory explanation, however, when, even in the headwater areas, most of the apparent saturated area which must generate most of the surface runoff, lies on the flatter slopes and may be far from the outflow.

What is markedly different between the areas is that the convergent areas have developed a far greater network of ephemeral and minor channels that become effective during storm periods and can efficiently transmit surface water from far into the basin area to the outflow. The sideslope areas have no such channels, and even where ditches have been dug to intercept the water their zone of influence is restricted, lacking the ramifications and convergent contributing areas of the minor channel network in the headwater areas. To account for the differences in peak flow rates and timing it is, however, necessary then to invoke very slow velocities of overland flow, in comparison with that in the channels. Certainly a considerable volume of water remains stationary in depression storage in all the areas, but flow rates measured by tracing during natural storms and under a sprinkling in fil tr orne ter, were indeed slow, ranging from the order of 0.005 m s-1 through short grass and 0.05 m s-1 for the smallest channels to 0.1 m s-1 in the first order streams within the study areas. Even if these are only of the correct order of magnitude the length of flow path within the time to peak of the sub-basin hydrograph (say 3 h) is only of the order of 50-60 m for strictly overland flow. Certainly flow has been observed to continue over some of the area saturated during a storm after rainfall has ceased, particularly in the convergent hollows supplying water to the minor channels. It follows that all direct surface flow should reach a channel within 6-10 hours, so that subsurface flow, inclu­ding reinfiltrated water and return flow, must make a possibly significant contribution to the hydrograph peak and early recession. At this scale, none of the sub-basins provided a secondary peak that could be attributed directly to subsurface flow, as reported for example by Weyman (1974) and Anderson & Burt (1978).

8. CONCLUSIONS

(1) Convergent headwater areas yield earlier and higher peak flows per unit area though peak flow timing differences decrease with increasing discharge.

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436 Keith Beven

(2) Areas in which moisture conditions are maintained at or near saturation between storms in winter are found in small convergent hoËow areas often associated with ephemeral channels. These areas generate surface runoff early in a storm and were found predominantly in the headwater sub-basins. Such areas of convergence also tend to maintain saturated conditions and flowing surface water after rainfall has ceased, maintaining higher flows from the headwater areas during the early part of the hydrograph recession.

(3) In addition all the Crimple Beck sub-basins exhibited a widespread extent of surface saturation during periods of storm rainfall on areas of low slope where lateral subsurface removal of water is slow. Such areas did not necessarily lie close to the permanent channel network.

(4) At the scale considered, differences between the sub-basins may be largely due to the network of ephemeral minor channels found in the convergent headwater areas which facilitates the collection and transmission of surface water to the basin outflow. Velocities of flow in these minor channels may be an order of magnitude faster than shallow overland flows. Sideslope areas have few such minor channels and peak flows may be delayed in consequence. In addition it may be expected that more surface water will reinfiltrate in sideslope areas after rainfall has ceased, increasing delays and reducing the runoff percentage.

The effects of soils and topography on hydrological response cannot be clearly distinguished but are closely and genetically related within the areas studied. It is likely that differences between headwater and sideslope areas will be accentuated in areas of better drained soils where the extent of saturated surface conditions will be more limited. Even within Crimple Beck the differences in response of headwater and sideslope areas are such that spatial variation in hydrological response must significantly affect outflows from the complete basin. This will grow in importance with increasing basin size, as the contribution of sideslope areas and routing of flow through the permanent channel network become increasingly significant.

ACKNOWLEDGEMENTS

This work was funded by a grant from the Natural Environment Research Council under the supervision of Prof. M. J. Kirkby. Dick Iredale and Martin Kew were closely involved with running the instrumentation in the Crimple Beck basin. This work has gained from all the previous research effort in Crimple Beck, especiaUy that of John Lockwood, who originally instigated the setting up of a research basin, John Wood, Pete Midgely, and Graham Harris. Mark Robinson and Gilly Marsh also helped with field work.

REFERENCES

Anderson, M.G. & Burt, T.P. (1977) Automatic monitoring of soil moisture conditions in a Mil-slope spur and hollow./. Hydrol. 33, 27-36.

Anderson, M.G. & Burt, T.P. (1978) Time synchronized stage recorders for the monitoring of incre­mental discharge inputs in small streams. J! Hydrol. 37,101-110.

Beven, K.J. (1977a) Hillsiope hydrographs by the finite element method. Earth Surf. Process. 2, 13-28.

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Hydrologicaï response of headwater and sideslope areas 437

Beven, K.J. (1977b) Experiments with a finite element model of hillslope hydrology: the effect of topography. Paper presented to the 3rd Int. Hydrol. Symp., Fort Collins, Colorado.

Beven, K.J. & Kirkby, M.J. (1979) A simple, physically based, variable contributing area model of basin hydrology. Hydrol. Set Bull. 24, No. 1. (In press).

Dunne, T. & Black, R.G. (1970a) An experimental investigation of runoff production in permeable soils. Wat. Resour. Res. 6,478-490.

Dunne, T. & Black, R.G. (1970b) Partial area contributions to storm runoff in a small New England watershed. Wat. Resour. Res. 6,1296-1311.

Dunne, T., Moore, T.R. & Taylor, C.H. (1975) Recognition and prediction of runoff producing zones in humid regions. Hydrol. Sci. Bull. 20, No. 3, 305-327.

Harris, G. (1975) Modelling rainfall-runoff relationships in a very small catchment within the Crimple Beck Basin, Yorks. Working Paper No 102, School of Geography, University of Leeds.

Hewlett, J.D. (1974) Comments on letters relation to 'Role of subsurface flow in generating sur­face runoff 2. Upstream source areas' by R. Allen Freeze. Wat. Resour. Res. 10, 605-607.

Kirkby, M.J. & Chorley, R.J. (1967) Throughflow, overland flow and erosion. Bull. Int. Ass. Scient. Hydrol. 12, No. 3, 5-21.

Kirkby, M.J., CaEen, J., Weyman, D.R. & Wood, J. (1976) Measurement and modelling of dynamic contrib uting areas in very small catchments. Working Paper 167, School of Geography, University of Leeds.

Weyman, D.R. (1970) Throughflow on hillslopes and its relation to the stream hydrograph. Bull. Int. Ass. Scient. Hydrol. 15, No. 3, 25-33.

Weyman, D.R. (1974) Runoff process, contributing area and streamflow in a small upland catch­ment. In: Fluvial Processes In Instrumental Watersheds. IBG Special Publication No 6, 33-42.

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