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Initial contributing area of a small watershed
Journal of Hydrology, 118 (1990) 387-403
387
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
[3] INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED 1
WILLIAM J. GBUREK
Northeast Watershed Research Center, ARS-USDA, University Park, PA, 16802, (U.S.A.) (Received December 10, 1988; accepted after revision August 30, 1989)
ABSTRACT Gburek, W.J., 1990. Initial contributing area of a small watershed. J. Hydrol., 118: 387-403. The initial contributing area (ICA) of a watershed at the onset of rain is defined as consisting of the stream surface and the area of surface saturation caused by the groundwater table intersecting the land surface above the elevation of the stream. Subsurface flow discharges upward within this area, so the ICA exhibits zero infiltration capacity and potential storage for rainfall. Thus, the ICA is the initial runoff-producing area in variable-source-area generation of storm runoff. The ICA of a 42-ha east-central Pennsylvania watershed is shown to be a function of prestorm baseflow; a prediction equation is developed using rainfall-runoff data from small rainstorms. This equation could be incorporated directly into a continuous streamflow model where a baseflow value is part of the simulation, or into an event-based hydrograph model where prestorm baseflow is specified as a design parameter. INTRODUCTION
The variable-source-area (VSA) concept of hydrologic analysis, recently reviewed by Ward (1984) and Bernier (1985), has become widely accepted as a descriptor of upland watershed response to precipitation under humid-climate conditions. The basic premise of this concept is that there is a 'contributing subwatershed' within the topographically defined watershed, the dimensions of which expand and contract seasonally and in response to precipitation. Storm runoff from the contributing subwatershed is envisioned to be dominated by saturation overland flow and/or rapidly responding subsurface flow. Physically based quantification of this dynamic runoff-producing area is necessary to understand the VSA concept and employ it as a basis for watershed runoff models. As with any modeling endeavor, specification of the initial state of the watershed is important. The most simple initial runoffproducing area is the stream surface since it produces the channel precipitation component of a storm hydrograph. However, quantification of channel
1This paper is a contribution from the U.S. Department of Agriculture, Agricultural Research Service, in cooperation with the Pennsylvania Agricultural Experiment Station, The Pennsylvania State University, University Park, PA (U.S.A.)
0022-1694/90/$03.50
© 1990 Elsevier Science Publishers B.V.
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w.J. GBUREK
precipitation (direct interception, stream interception) has largely been ignored, its supposed lack of importance rooted in traditional hydrologic concepts where watersheds were analyzed as lumped systems. In a lumped analysis, increase in streamflow during the storm hydrograph is considered to result from a small percentage of the rainfall depth running off the entire watershed. Since the stream surface is a minimal part of watershed area, the importance of the channel precipitation component is discounted, although even as early as 1941, Hursh and Brater (1941) stated, "It is believed that the importance of channel-precipitation as a component of the flood-hydrograph has not been fully appreciated". In VSA hydrology however, storm runoff is assumed to result from a relatively high percentage of the rainfall depth running off only a small percentage of the watershed area. This increases the significance of the channel precipitation component, in that stream surface area is proportionally a much larger part of the active watershed area (i.e. the contributing subwatershed), which is itself only a relatively small portion of total watershed area. Under humid-climate conditions, there is an additional facet to the direct interception component which also must be considered. Following groundwater recharge events, the subsurface flow system is typically unable to move all groundwater discharge to the stream through the area of the stream bed. Consequently, the water table along the base of hillslopes (flowlines converging in the vertical) and in the vicinity of swales (flowlines converging in the horizontal) attempts to move above the land surface to increase the cross-sectional area of discharge. This results in an increased area of subsurface discharge to the land surface manifested as seeps and/or springs. This area is, of course, saturated to the land surface, and has zero infiltration capacity and potential storage. Rain falling on zones of surface saturation produces overland flow (termed 'saturation overland flow'), and because these zones are usually adjacent to the stream, saturation overland flow is coincident in time with the channel precipitation component of storm runoff. Since the saturated areas effectively increase the surface area of the stream, this redefined and expanded direct interception source-area of storm runoff further increases in importance in VSA hydrology. BACKGROUND The following definitions are understood. ~Baseflow' is streamflow derived from relatively slow long-term drainage of the groundwater body at the watershed scale. This drainage sustains streamflow between storms and also provides a continuing flow component during the storm hydrograph. The 'storm hydrograph' includes all flow when the stream is affected by precipitation; i.e. it is the total hydrograph during this time period. On the other hand, 'storm runoff', also termed 'direct runoff" or 'quickflow', is only the increase in streamflow above baseflow resulting from precipitation; it may include channel precipitation, surface runoff, and flow from subsurface sources other than continuing baseflow.
INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED
389
The VSA concept of hydrology has implied an expanded 'effective' stream surface area from its inception. This expanded area can result from a number of conditions: regional groundwater discharge (seepage) to the land surface; high water tables and their associated capillary fringe intersecting the land surface (Gillham, 1984); drainage from water tables perched on fragipans or other impermeable layers in the near-stream vicinity (Roulon et al., 1985); and zones of high soil water content created by down-slope unsaturated moisture movement (Hewlett and Hibbert, 1963; Zaslavsky and Sinai, 1981a,b). Earlier studies of VSA hydrology (e.g. Hewlett and Hibbert, 1967), or the related partial-area hydrology (Betson, 1964), were generally concerned only with total storm runoff, envisioning it to originate from areas riparian to the stream or from the lower elevations of the watershed. Without defining specific mechanisms, implications were that storm runoff generation was greatly influenced by the degree of saturation of soils in these locations. Two interrelated lines of research continue. One consists of efforts to mathematically model the geometry and processes ranging from the earlier work of Freeze (1972a,b) to the more recent works of Bernier (1985) and Hornberger et al. (1985). The other consists of field-oriented attempts to either quantify the effects of the variable-source area or to observe it directly. Investigations of the latter type are of concern here. Betson and Marius (1969) found that saturated conditions developed most frequently in areas of a small North Carolina watershed having soils with relatively shallow A-horizons, and only infrequently in the larger portion of the watershed having deeper A-horizon soils. They provided a field-based demonstration that surface runoff was produced preferentially dependent on moisture status over the watershed, rather than only on precipitation characteristics. Bissell and Ragan (1969) provided a comprehensive overview of partial-area hydrology to that date, and also presented extensive data from a forested Vermont watershed. Inflow to and outflow from a channel reach were gaged, as were separable inputs from small wet areas (seeps) contributing perennial flow at defined points along the reach. The storm runoff-rainfall ratio for the entire experimental watershed was typically an order of magnitude less than runoff-rainfall ratios from the seep areas. Rawitz et al. (1970) showed that direct interception by the stream surface accounted for 3-61% of storm runoff from a small Pennsylvania watershed, emphasizing the potential importance of this component in small-watershed VSA hydrology. Hewlett and Troendle (1975) discussed the need to incorporate the extent of surface saturation at the beginning of a rainstorm into a VSA-based watershed model, this area being allowed to expand during the course of the storm with the resultant storm hydrograph composed of runoff integrated from the entire area. A common thread in a number of field-based investigations has been the effect of landform on source-areas of surface runoff. Kirkby and Chorly (1967) suggested that overland flow tends to occur where subsurface water is forced to the surface, as in topographic hollows. Dunne et al. (1975) mapped the extent
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of saturated areas (stream surface plus seeps and springs) on four watersheds in Vermont and Ontario, Canada, by field observations during non-storm periods. The large seasonal variation in saturated area found (3% of the basin in the summer to 50% immediately after periods of snowmelt) was related qualitatively to topography, soils distribution, and vegetation on the watersheds. Anderson and Burt (1978) showed that potential source-areas of runoff during a storm can be delineated by monitoring equipment, and that hollows (subsurface flowlines converging arealty) may be significant sourceareas of runoff during all stages of drainage. Subsequent studies (Beven, 1978; Anderson and Kneale, 1980, 1982; O'Loughlin, 1981; Heerdegen and Beran, 1982; Beven and Wood, 1983) report analytic and/or field-based studies of the effects of landform (generally referred to as hollow and spur configurations) on the convergence or divergence of subsurface flowlines and the resultant areas of surface saturation. Finally, VSA concepts have been incorporated into watershed models such as TOPMODEL (Beven and Kirkby, 1979) and VSAS2 (Bernier, 1985), as well as an aquifer model (PLASM, modified by Potter and Gburek, 1987). The studies noted generally emphasize source-areas during and after precipitation events. Consequently, there remains a need to define the source-area at the onset of rain. Here, a simple technique for quantifying the extent of surface saturation at the start of a rainstorm is presented. Following the statement in Linsley et al. (1958) that "Channel precipitation is the only increment of streamflow during the initial period of rainfall", and in keeping with VSA terminology, this area is referred to as the 'initial contributing area' (ICA) of the watershed. The ICA is understood to include, but not distinguish between, stream surface per se and all zones of surface-saturation (zero or greater pressure head) hydraulically connected to the stream. Consequently, it will produce storm runoff from any rainfall event. Additional runoff may result from continuing rainfall on a source-area expanded beyond the ICA owing to increased groundwater discharge from below, filling of limited soil water storage by infiltrated precipitation from above, or Hortonian surface runoff from upslope. But the area of concern here is only the initial contributing area, the starting point for growth of the variable-source area. QUANTIFYING ICA Rationale The most basic expression for the initial contributing area of a small upland watershed is a constant stream surface area independent of flow. However, in small watersheds (e.g. < ~ 15 km 2) in the humid northeastern U.S.A., stream surface area varies appreciably, ranging from nearly zero under late summer baseflow conditions to well over bankfull (e.g. > 5m) in the spring. These extreme conditions are not just temporary, but can continue for days. This variability in ICA should at least be included in a small watershed VSA model,
INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED
391
perhaps simply expressing stream surface area as a function of flowrate. But many of the studies previously discussed noted the importance of near-stream surface saturation zones in producing storm runoff. Thus, a technique should be developed to delineate ICA as defined previously. Small moderate-intensity rainfalls on relatively dry watershed conditions produce no overland flow of the Hortonian type since precipitation intensity does not exceed soil infiltration capacity. Likewise, there is little or no subsurface contribution (interflow, throughflow) to storm runoff from these events. Even man-made impermeable surfaces, such as roads, parking lots, etc. generally produce no runoff from very small rainstorms because of their inherent depression storage, retention storage, and distance from the stream. Thus, the only areas producing storm runoff from this type of event will be the stream surface and zones of surface saturation adjacent to, and hydraulically connected to the stream. The stream surface will, of course, produce 'storm runoff' at 100% of the rainfall depth. The previously discussed seeps and springs bordering the stream and forming the surface saturation zone are above the stream surface elevation, but precipitation falling on them will not infiltrate since they are zones of groundwater discharge with flow exiting the soil under positive pressure. This continually emerging flow fills all potential depression storage within the saturation zone and moves d i r e c t l y t o the stream to sustain baseflow. Consequently, precipitation falling on this area is assumed to also produce a storm runoff component at or near 100% of the rainfall depth. Interception and some limited depression storage may occur within the zone of saturation, but for this study these losses are neglected. The basic assumptions of this analysis then are: (]) All storm runoff from a relatively small rainfall is derived only from precipitation impinging on the stream surface and the near-stream saturation zone; (2) this source-area of runoff remains constant in areal extent throughout the duration of the small rain; (3) storm runoff contributions from both the stream and zone of saturation are at 100% of rainfall depth. So if storm runoff volume from a small rainfall can be determined, the effective area contributing this storm runoff can be estimated by simply dividing runoff volume by rainfall depth: ECA
=
V/P
(1)
where ECA is the effective contributing area (L2), V is storm runoff volume (L3), and P is precipitation depth (L). The ECA is a consequence of the water table intersecting the land surface at some distance from the stream; higher water table elevations result in larger values of ECA. Since baseflow is also a function of general groundwater levels within the watershed (higher baseflow rates are associated with higher groundwater levels), a relationship between ECA and baseflow may be expected. The ECA derived from small storm data under the assumptions given is identical to the ICA for a larger event as defined previously. That is, the stream surface and near-stream zone of saturation contributing all storm runoff from
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w.J. GBUREK
a small storm (ECA) is also the initial contributing area of runoff production (ICA) which would expand if the rain were to continue. So hereafter, the area of concern will be referred to only as the ICA, regardless of whether it is the effective contributing area for the small storms analyzed or the ICA which is the objective of this study. Also, the relationship between effective contributing area and baseflow derived from the data will be presented in terms of ICA. This relationship is developed by applying eqn. (1) to a large number of small storms representing a wide range of precipitation depths and baseflow conditions on an east-central Pennsylvania watershed.
Experimental watershed and instrumentation The 42-ha Paul Watershed is a small upland agricultural subarea of the 420-km 2 Mahantango Creek Watershed, the primary location for field research of the Northeast Watershed Research Center. Mahantango Creek is within the non-glaciated portion of the Appalachian Ridge and Valley Physiographic Province and is tributary to the Susquehanna River approximately 50 km north of Harrisburg, Pennsylvania. Generalized hydrology and water quality
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responses of upland watersheds in this area have recently been presented by Pionke et al. (1988). The Paul Watershed is typical of upland watersheds in the Ridge and Valley Province in its landform, hydrology, soils, geology, and rural land use. Figure 1 shows the location of the watershed within the Mahantango Watershed and Pennsylvania, as well as its topography, channel system, cultural features, and basic hydrologic instrumentation. The Paul Watershed is underlain mainly by steeply dipping interbedded shales and siltstones. Its soils are shallow residual silt loams, the characteristics of which indicate similar development and parent materials, as well as a moderate range in permeabilities. From the hydrologic viewpoint, the major distinguishing feature between soil series is the existence or absence of a fragipan. Fragipan soils tend to border stream channels or established drainage ways, while those without fragipans are at higher elevations further removed from the channels. Rainfall and runoff records have been collected on this watershed since it was first instrumented in 1967. A single Belfort-type weighing raingage provided the rainfall intensity and depth records from which this dataset was extracted. For a watershed of ~ 4 0 h a in Pennsylvania, one raingage gives adequate representation of total storm characteristics over the watershed, even during severe thunderstorms. The gage was equipped with a two-day clock, completing one revolution every 48 hours. Charts were changed at the same two-day intervals, making the resultant records easy to interpret. Because of the frequent gage servicing, the records are of high quality, and the charts can be read to + 0.25 mm of precipitation and to _+2 min. Thus, even the smallest storms are accurately characterized with regard to total depth. Streamflow at the watershed outlet was monitored using a 90° sharp-crested V-notch weir equipped with a float-activated FW-1 water level recorder, giving good gage sensitivity to low flow changes. The FW-1 recorder was also equipped with a two-day clock and serviced at two-day intervals, resulting in high-quality runoff records easily read to ± 2 min and ± 1.5mm gage height. Flow is calculated using a standard weir equation relating gage height to flowrate, giving an accurate characterization of total runoff rates and volumes.
Data analysis Rainfall records from 1967 to 1976 were screened for storms suitable for this analysis. All non-winter single events of ~<6 mm of moderate to low intensity rainfall were initially considered. Events were deleted from consideration when they occurred d u r i n g an active storm hydrograph recession or when subsequent precipitation obscured the end of their recession. After checking streamgage records to see that the storm hydrograph resulting from the event was recorded properly (no gage malfunctions), 116 rainfall-runoff combinations were found which met the above criteria. Total precipitation depth for each event was tabulated, and breakpoint analyses were used to develop the resulting storm hydrographs. These
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hydrographs generally consisted of a simple rise from prestorm baseflow to peak flow and a relatively quick recession to very near prestorm baseflow; this indicates that the baseflow regime of the watershed was altered little or not at all by these small events. Unlike storm hydrographs resulting from larger rainfalls where the point of storm runoff cessation may not be obvious, the break in slope between these recessions and the return to baseflow was usually quite distinct. Therefore, storm runoff volumes were separated by the commonly used technique of continuing prestorm baseflow to the time of the hydrograph peak, then extending the separation line to the break in slope on the recession. The areas above the baseflow separation lines were planimetered to determine storm runoff volumes, and dividing volume by depth of causative rainfall gives the ICA value as per eqn. (1). The final dataset developed consists
INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED
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of rainfall depth, resultant volume of storm runoff, calculated runoff contributing area (ICA), and baseflow at the start of the event for each of the 116 storms. Figure 2 shows two typical storm hydrographs from the dataset, one for a rather small rainfall and the other for one of the larger depths considered. Also shown for each storm is precipitation depth, the baseflow separation line used for separating the hydrograph into continuing baseflow and storm runoff, storm runoff volume resulting from the rain, initial contributing area, and prestorm baseflow. An additional assumption critical to this analysis is that these small storm hydrographs can be realistically separated into their basefiow and storm runoff components. Many VSA-related studies have addressed the question of storm hydrograph components from either the hydrologic viewpoint (e.g. Dunne and Black, 1970a,b) or by use of natural tracers (e.g. Sklash and Farvolden, 1979; Pearce et al., 1986; Sklash et al., 1986), but these studies generally focused on storms much larger than those considered here. Objective hydrograph separation of small storms has not, therefore, been addressed directly, but using differing wording, both Dunne and Black (1970b) and Pearce et al. (1986) concluded that for small storms on small watersheds, direct rainfall on the saturation area generates the bulk of the runoff and alone controls storm hydrograph generation. In concurrence with their observaticlns, it is instructive to note that most of the smaller rainfalls considered here (i.e. events up to about 1.5 mm) caused virtually no observed increase in baseflow; the resultant storm hydrographs generally returned to prestorm baseflows within about one hour of the event. This observation implies that the overall hydrologic status of the watershed remained unchanged after the brief episode of storm runoff generation. That is, there was no increase in the baseflow component during the storm hydrograph and the zone of surface saturation did not expand to any great degree. So separation of these particular storm hydrographs into their storm runoff and baseflow components appears simple. The larger storms analyzed did alter the watershed flow regime, but only to a limited extent. The slope breaks on the hydrograph recessions apparently indicating cessation of storm runoff and return to baseflow were generally distinct and only slightly elevated from prestorm baseflow levels. So by extension from the very simple smaller storm separations, application of the basic hydrograph separation technique described previously seems justified. RESULTS AND DISCUSSION Recognizing that the goal of this study is the determination of the relationship between ICA and baseflow, it must first be shown that the dataset represents the variability of the system. Figure 3 shows precipitation depth plotted against baseflow at the time of each storm. The rectangular pattern of points indicates that the dataset represents the full range of rainfalls considered (0.86.3mm) applied to the full range of corresponding baseflows (0.03-601s1), thereby containing an unbiased distribution of storm depthbaseflow combinations.
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Fig. 7. ICA as a function of baseflow. calculation. Figure 6 shows storm runoff volume as a function of baseflow. There is a trend in the data, with higher baseflow values tending toward higher runoff volumes. However, there is also a large degree of scatter; storm runoff volume varies up to three orders of magnitude at a given baseflow. Figure 7 shows ICA as a function of baseflow, the relationship we are concerned with. Since ICA is simply storm runoff volume 'normalized' by causative precipitation, Fig. 7 can be compared visually with Fig. 6 to see if the ICA calculation reduces scatter. The two figures are plotted with the same y-axis scale, and there is somewhat less scatter in the relationship of Fig. 7. The maximum range of ICA values is approximately two orders of magnitude for given baseflow values, compared with the three-orders-of-magnitude range in storm runoff volumes at the same baseflows. Statistics also indicate a tighter relationship. The correlation coefficient for Fig. 6 is 0.51, while that of Fig. 7, including precipitation to calculate ICA, is raised to 0.65. The F-value is raised from 40.4 for Fig. 6 to 81.7 for Fig. 7, significant at the 0.05 level. The equation of the best-fit straight line to Fig. 7 is: ICA = 1240 Q~b? '7
(2)
where ICA is initial contributing area (m2) and Qbfis baseflow (1 s-l) at the time of the storm. The ICA values from eqn. (2) make sense when examined in context of Paul Watershed geometry. Baseflows observed prior to the storms used in this analysis ranged from ~ 0.03 to 60 1s -1, and corresponding ICA values are 215 and 9600m '~, respectively. Since the watershed area is 4.2 x 105m2, these ICA values range from ~0.1% (stream channel only) to 2% of the watershed area. Based on quickflow-precipitation ratios reported
INITIAL CONTRIBUTING A R E A O F A SMALL W A T E R S H E D
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in the literature (e.g. Hewlett et al., 1977; Dunne, 1978), the source-area contributing total storm runoff from larger storms may itself be only 20% or less of the total watershed. In this light, the maximum ICA is significant in that it comprises ~ 10% of the active source-area. The ICA values may also be examined in terms of stream length. Perennial stream channel within the Paul Watershed totals ~ 900m. Dividing ICA by stream length gives an average width of the initial contributing area. Widths corresponding to the range of ICA values given above are ~ 0.2-10.7m. The 0.2-m value, the minimum average width of ICA, corresponds closely to stream surface width at low flow. Conversely, the maximum average ICA width calculated, about l l m, is somewhat larger than the width of the small flood plain bordering the main stream channel. When considering the maximum width indicated, it must be remembered t h a t this width is only an average of the extreme variability encountered in the natural system. The average is calculated using the approximate length of stream channel supporting perennial flow, and consequently does not reflect either upstream increase in channel length during periods of higher baseflow, or lateral preferential (concentrated) expansion of seep areas or small channels perpendicular to the main stream. Because they increase total effective stream length, such conditions tend to reduce the average effective width of ICA calculated for higher baseflow levels, thereby making the width more in line with the observed physical features of the watershed. Even neglecting these considerations, the range and magnitude of the ICA dimensions indicated by eqn. (2) correspond favorably with the physical characteristics of the Paul Watershed.
Variability of results Figure 6, storm runoff volume against baseflow, contains a high degree of variability. Normalizing volume by rainfall to give ICA reduces the variability as evidenced by the higher correlation and F-value of Fig. 7. However, with an r 2 of ~ 0.40, Fig. 7 still exhibits substantial unexplained variability. Limited additional analyses of the data were made in an attempt to explain the variability. The influence of precipitation depth within the relationship of Fig. 7 was examined. Storms were grouped by depth into three categories, < 2.5mm, 2.5-5 mm, and > 5 mm. Visual examination of Fig. 8, which shows this grouping, indicates that larger precipitation may be associated with larger ICA values for the same baseflow levels. However, statistical analysis indicated no significant difference between the data in each group. While shedding no light on variability of the results, this finding tends to reinforce the assumptions detailed earlier regarding baseflow-stormflow separations. The storm hydrographs which required no judgement in their separation (those with no observed increase in baseflow) are statistically part of the same population as those which required a slightly more complex separation. Data from a limited range of baseflows (0.3~.51s ') were also examined.
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points), plotted as Fig. 9, indicate that storm runoff volume does increase with rainfall depth as expected for the smaller rains, but it also shows an increased degree of scatter at larger precipitation depths. This same analysis was repeated using data selected from other narrow ranges of baseflow, and similar results were found. Such results imply that the larger precipitations sampled, > 5mm, may be the beginning of the range where ICA-only hydrology is undergoing the transition into storm runoff production controlled by a sourcearea expanding during the storm. Figure 10 shows ICA plotted against rainfall depth only for the data used in Fig. 9. Ideally, the slope of this plot should be zero, since the hypothesis is that similar baseflow values have similar ICA values. However, there appears to be a slight positive slope to these data, implying that precipitation depth influenced ICA at these same baseflow values. As mentioned previously, a similar analysis including all data (all baseflow values) did not statistically support a relationship between precipitation and ICA. There may be other methods to examine these data, but as in most investigations of natural phenomena using field data, a certain degree of variability always remains unexplained. The purpose of this study was to investigate the potential for developing a relationship between initial contributing area, as calculated from storm runoff volume and precipitation depth, and concurrent baseflow. Figure 7 and its associated statistics indicate that there is a defensible relationship, and eqn. (2) is its quantitative expression. SUMMARY
The initial contributing area of a watershed is defined as consisting of the
402
w.J. GBUREK
stream surface area and the area of surface saturation caused by the water table intersecting the land surface above that of the stream. Because subsurface flow is discharging to the land surface within this area, the area provides zero storage capacity and infiltration potential for rainfall, producing storm runoff at nearly 100% of the rainfall depth. The ICA is the initial area of runoff production in a variable-source-area analysis of the dynamics of storm runoff generation on a watershed. This study shows that the ICA of the 42-ha Paul Watershed can be expressed as a function of prestorm baseflow. The prediction equation presented (eqn. (2)) was developed using small-storm rainfall-runoff data from the watershed. The equation is in a form which could be easily incorporated into either a continuous streamflow model, where the baseflow value is available from the simulated recessions, or an event-based model, where prestorm baseflow is specified as a design parameter or probability function. The technique developed here can be applied simply and quickly to watersheds where rainfall-runoff records exist, and thus is a valuable addition to the growing body of knowledge related to the mechanisms of variable-source-area storm runoff generation on humid-climate upland watersheds. REFERENCES Anderson, M.G. and Burt, T.P., 1978. Toward more detailed field monitoring of variable source areas. Water Resour. Res., 14(6): 1123-1131. Anderson, M.G. and Kneale, P.E., 1980. Topography and hillslope soil water relationships in a catchment of low relief. J.Hydrol., 47:115 128. Anderson, M.G. and Kneale, P.E., 1982. The influence of low-angled topography on hillslope soil water convergence and stream discharge. J. Hydrol., 57: 65-80. Bernier, P.Y., 1985. Variable source areas and storm-flow generation: An update of the concept and a simulation effort. J. Hydrol., 79:195 213. Betson, R.P., 1964. What is watershed runoff?. J. Geophys. Res., 69(8): 1541 1552. Betson, R.P. and Marius, J.B., 1969. Source areas of storm runoff. Water Resour. Res., 5(3): 57~582. Beven, K.J., 1978. The hydrological response of headwater and sideslope areas. Hydrol. Sci. Bull., 23(4): 419437. Beven, K.J. and Kirkby, M.J., 1979. A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24(1): 43-69. Beven, K.J. and Wood, E.F., 1983. Catchment geomorphology and the dynamics of runoff contributing areas. J. Hydrol., 65: 139-158. Bissell, V.C. and Ragan, R.M., 1969. The determination of zones of intense contribution to stream flow as related to the concept of partial area contributions. Tech. Rep. 21, Water Resour. Res. Center, University of Maryland, College Park, MD, 188 pp. Dunne,T., 1978. Field studies of hillslope processes. In: M.J. Kirkby (Editor), Hillslope Hydrology. Wiley, New York, pp. 227 294. Dunne, T. and Black, R.D., 1970a. An experimental investigation of runoffproduction in permeable soils. Water Resour. Res., 6(2): 47~490. Dunne, T. and Black, R.D., 1970b. Partial area contributions to storm runoff in a small New England watershed. Water Resour. Res., 6(5): 1296 1311. Dunne, T., Moore, T.R. and Taylor, C.H., 1975. Recognition and prediction of runoff-producing zones in humid regions. Hydrol. Sci. Bull., 20(3): 305 327. Freeze, R.A., 1972a. Role of subsurface flow in generating surface runoff, 1. Baseflow contributions to channel flow. Water Resour. Res., 8(3): 6094~23.
INITIAL CONTRIBUTINGAREAOF A SMALLWATERSHED
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Freeze, R.A., 1972b. Role of subsurface flow in generating surface runoff, 2. Upstream source areas. Water Resour. Res., 8(3): 1272-1283. Gillham, R.W., 1984. The capillary fringe and its effect on water-table response. J. Hydrol., 67: 307-324. Heerdegen, R.G. and Beran, M.A., 1982. Quantifying source areas through land surface curvature and shape. J. Hydrol., 57: 359-373. Hewlett, J.D. and Hibbert, A.R., 1963. Moisture and energy conditions within a sloping soil mass during drainage. J. Geophys. Res., 68:1081 1087. Hewlett, J.D. and Hibbert, A.R., 1967. Factors affecting the response of small watersheds to precipitation in humid areas. In: W.E. Sopper and H.W. Lull, (Editors), International Symposium on Forest Hydrology. Pergamon Press, New York, pp. 27~290. Hewlett, J.D. and Troendle, C.A., 1975. Non-point and diffused water sources: A variable source area problem. Proceedings of a Symposium on Watershed Management, Am. Soc. Civ. Eng., New York, pp. 65 83. Hewlett, J.D., Cunningham, G.B. and Troendle, C.A., 1977. Predicting stormflow and peakflow from small basins in humid areas by the R-index method. Water Resour. Bull., 13:231 253. Hornberger, G.M., Beven, K.J., Cosby, B.J. and Sappington, D.E., 1985. Shenandoah Watershed study: Calibration of a topography-based, variable contributing area hydrological model to a small forested catchment. Water Resour. Res., 21(12): 1841 1850. Hursh, C.R. and Brater, E.F., 1941. Separating storm-hydrographs from small drainage-areas into surface- and subsurface-flow. Trans. Am. Geophys. Union, 22: 863-871. Kirkby, M.J. and Chorly, R.J., 1967. Throughflow, overland flow and erosion. Bull. Int. Assoc. Sci. Hydrol., 12(3): 5 21. Linsley, R.K., Jr., Kohler, M.A. and Paulhus, J.L.H., 1958. Hydrology for Engineers. McGraw-Hill, New York, 340 pp. O'Loughlin, E.M., 1981. Saturation regions in catchments and their relations to soil and topographic properties. J. Hydrol., 53: 229-246. Pearce, A.J., Stewart, M.K. and Sklash, M.G., 1986. Storm runoff generation in humid headwater catchments, 1. Where does the water come from? Water Resour. Res., 22(8): 1263 1272. Pionke, H.B., Hoover, J.R., Schnabel, R.R., Gburek, W.J., Urban, J.B. and Rogowski, A.S., 1988. Chemical hydrologic interactions in the near-stream zone. Water Resour. Res., 24(7): 1101 1110. Potter, S.T. and Gburek, W.J., 1987. Seepage face simulation using PLASM. Ground Water, 25(6): 722-732. Rawitz, E., Engman, E.T. and Cline, G.D., 1970. Use of the mass balance method for examining the role of soils in controlling watershed performance. Water Resour. Res., 6(4): 1115 1123. Roulon, J.J., Rodway, R. and Freeze, R.A., 1985. The development of multiple seepage faces on layered slopes. Water Resour. Res., 21(11): 162~1636. Sklash, M.G. and Farvolden, R.N., 1979. The role of groundwater in storm runoff. J. Hydrol., 43: 45-66. Sklash, M.G., Stewart, M.K. and Pearce, A.J., 1986. Storm runoff generation in humid headwater catchments, 2. A case study of hillslope and low-order stream response. Water Resour. Res., 22(8): 1273-1282. Ward, R.C., 1984. On the response to precipitation of headwater streams in humid areas. J. Hydrol., 74: 171-189. Zaslavsky, D. and Sinai, G., 1981a. Surface hydrology: III--Causes of lateral flow. J. Hydraul. Div., ASCE, 107(HY1): 37-52. Zaslavsky, D. and Sinai, G., 1981b. Surface hydrology: IV--Flow in sloping, layered soil. J. Hydraul. Div., ASCE, 107(HY1): 53~4.
387
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
[3] INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED 1
WILLIAM J. GBUREK
Northeast Watershed Research Center, ARS-USDA, University Park, PA, 16802, (U.S.A.) (Received December 10, 1988; accepted after revision August 30, 1989)
ABSTRACT Gburek, W.J., 1990. Initial contributing area of a small watershed. J. Hydrol., 118: 387-403. The initial contributing area (ICA) of a watershed at the onset of rain is defined as consisting of the stream surface and the area of surface saturation caused by the groundwater table intersecting the land surface above the elevation of the stream. Subsurface flow discharges upward within this area, so the ICA exhibits zero infiltration capacity and potential storage for rainfall. Thus, the ICA is the initial runoff-producing area in variable-source-area generation of storm runoff. The ICA of a 42-ha east-central Pennsylvania watershed is shown to be a function of prestorm baseflow; a prediction equation is developed using rainfall-runoff data from small rainstorms. This equation could be incorporated directly into a continuous streamflow model where a baseflow value is part of the simulation, or into an event-based hydrograph model where prestorm baseflow is specified as a design parameter. INTRODUCTION
The variable-source-area (VSA) concept of hydrologic analysis, recently reviewed by Ward (1984) and Bernier (1985), has become widely accepted as a descriptor of upland watershed response to precipitation under humid-climate conditions. The basic premise of this concept is that there is a 'contributing subwatershed' within the topographically defined watershed, the dimensions of which expand and contract seasonally and in response to precipitation. Storm runoff from the contributing subwatershed is envisioned to be dominated by saturation overland flow and/or rapidly responding subsurface flow. Physically based quantification of this dynamic runoff-producing area is necessary to understand the VSA concept and employ it as a basis for watershed runoff models. As with any modeling endeavor, specification of the initial state of the watershed is important. The most simple initial runoffproducing area is the stream surface since it produces the channel precipitation component of a storm hydrograph. However, quantification of channel
1This paper is a contribution from the U.S. Department of Agriculture, Agricultural Research Service, in cooperation with the Pennsylvania Agricultural Experiment Station, The Pennsylvania State University, University Park, PA (U.S.A.)
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© 1990 Elsevier Science Publishers B.V.
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precipitation (direct interception, stream interception) has largely been ignored, its supposed lack of importance rooted in traditional hydrologic concepts where watersheds were analyzed as lumped systems. In a lumped analysis, increase in streamflow during the storm hydrograph is considered to result from a small percentage of the rainfall depth running off the entire watershed. Since the stream surface is a minimal part of watershed area, the importance of the channel precipitation component is discounted, although even as early as 1941, Hursh and Brater (1941) stated, "It is believed that the importance of channel-precipitation as a component of the flood-hydrograph has not been fully appreciated". In VSA hydrology however, storm runoff is assumed to result from a relatively high percentage of the rainfall depth running off only a small percentage of the watershed area. This increases the significance of the channel precipitation component, in that stream surface area is proportionally a much larger part of the active watershed area (i.e. the contributing subwatershed), which is itself only a relatively small portion of total watershed area. Under humid-climate conditions, there is an additional facet to the direct interception component which also must be considered. Following groundwater recharge events, the subsurface flow system is typically unable to move all groundwater discharge to the stream through the area of the stream bed. Consequently, the water table along the base of hillslopes (flowlines converging in the vertical) and in the vicinity of swales (flowlines converging in the horizontal) attempts to move above the land surface to increase the cross-sectional area of discharge. This results in an increased area of subsurface discharge to the land surface manifested as seeps and/or springs. This area is, of course, saturated to the land surface, and has zero infiltration capacity and potential storage. Rain falling on zones of surface saturation produces overland flow (termed 'saturation overland flow'), and because these zones are usually adjacent to the stream, saturation overland flow is coincident in time with the channel precipitation component of storm runoff. Since the saturated areas effectively increase the surface area of the stream, this redefined and expanded direct interception source-area of storm runoff further increases in importance in VSA hydrology. BACKGROUND The following definitions are understood. ~Baseflow' is streamflow derived from relatively slow long-term drainage of the groundwater body at the watershed scale. This drainage sustains streamflow between storms and also provides a continuing flow component during the storm hydrograph. The 'storm hydrograph' includes all flow when the stream is affected by precipitation; i.e. it is the total hydrograph during this time period. On the other hand, 'storm runoff', also termed 'direct runoff" or 'quickflow', is only the increase in streamflow above baseflow resulting from precipitation; it may include channel precipitation, surface runoff, and flow from subsurface sources other than continuing baseflow.
INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED
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The VSA concept of hydrology has implied an expanded 'effective' stream surface area from its inception. This expanded area can result from a number of conditions: regional groundwater discharge (seepage) to the land surface; high water tables and their associated capillary fringe intersecting the land surface (Gillham, 1984); drainage from water tables perched on fragipans or other impermeable layers in the near-stream vicinity (Roulon et al., 1985); and zones of high soil water content created by down-slope unsaturated moisture movement (Hewlett and Hibbert, 1963; Zaslavsky and Sinai, 1981a,b). Earlier studies of VSA hydrology (e.g. Hewlett and Hibbert, 1967), or the related partial-area hydrology (Betson, 1964), were generally concerned only with total storm runoff, envisioning it to originate from areas riparian to the stream or from the lower elevations of the watershed. Without defining specific mechanisms, implications were that storm runoff generation was greatly influenced by the degree of saturation of soils in these locations. Two interrelated lines of research continue. One consists of efforts to mathematically model the geometry and processes ranging from the earlier work of Freeze (1972a,b) to the more recent works of Bernier (1985) and Hornberger et al. (1985). The other consists of field-oriented attempts to either quantify the effects of the variable-source area or to observe it directly. Investigations of the latter type are of concern here. Betson and Marius (1969) found that saturated conditions developed most frequently in areas of a small North Carolina watershed having soils with relatively shallow A-horizons, and only infrequently in the larger portion of the watershed having deeper A-horizon soils. They provided a field-based demonstration that surface runoff was produced preferentially dependent on moisture status over the watershed, rather than only on precipitation characteristics. Bissell and Ragan (1969) provided a comprehensive overview of partial-area hydrology to that date, and also presented extensive data from a forested Vermont watershed. Inflow to and outflow from a channel reach were gaged, as were separable inputs from small wet areas (seeps) contributing perennial flow at defined points along the reach. The storm runoff-rainfall ratio for the entire experimental watershed was typically an order of magnitude less than runoff-rainfall ratios from the seep areas. Rawitz et al. (1970) showed that direct interception by the stream surface accounted for 3-61% of storm runoff from a small Pennsylvania watershed, emphasizing the potential importance of this component in small-watershed VSA hydrology. Hewlett and Troendle (1975) discussed the need to incorporate the extent of surface saturation at the beginning of a rainstorm into a VSA-based watershed model, this area being allowed to expand during the course of the storm with the resultant storm hydrograph composed of runoff integrated from the entire area. A common thread in a number of field-based investigations has been the effect of landform on source-areas of surface runoff. Kirkby and Chorly (1967) suggested that overland flow tends to occur where subsurface water is forced to the surface, as in topographic hollows. Dunne et al. (1975) mapped the extent
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of saturated areas (stream surface plus seeps and springs) on four watersheds in Vermont and Ontario, Canada, by field observations during non-storm periods. The large seasonal variation in saturated area found (3% of the basin in the summer to 50% immediately after periods of snowmelt) was related qualitatively to topography, soils distribution, and vegetation on the watersheds. Anderson and Burt (1978) showed that potential source-areas of runoff during a storm can be delineated by monitoring equipment, and that hollows (subsurface flowlines converging arealty) may be significant sourceareas of runoff during all stages of drainage. Subsequent studies (Beven, 1978; Anderson and Kneale, 1980, 1982; O'Loughlin, 1981; Heerdegen and Beran, 1982; Beven and Wood, 1983) report analytic and/or field-based studies of the effects of landform (generally referred to as hollow and spur configurations) on the convergence or divergence of subsurface flowlines and the resultant areas of surface saturation. Finally, VSA concepts have been incorporated into watershed models such as TOPMODEL (Beven and Kirkby, 1979) and VSAS2 (Bernier, 1985), as well as an aquifer model (PLASM, modified by Potter and Gburek, 1987). The studies noted generally emphasize source-areas during and after precipitation events. Consequently, there remains a need to define the source-area at the onset of rain. Here, a simple technique for quantifying the extent of surface saturation at the start of a rainstorm is presented. Following the statement in Linsley et al. (1958) that "Channel precipitation is the only increment of streamflow during the initial period of rainfall", and in keeping with VSA terminology, this area is referred to as the 'initial contributing area' (ICA) of the watershed. The ICA is understood to include, but not distinguish between, stream surface per se and all zones of surface-saturation (zero or greater pressure head) hydraulically connected to the stream. Consequently, it will produce storm runoff from any rainfall event. Additional runoff may result from continuing rainfall on a source-area expanded beyond the ICA owing to increased groundwater discharge from below, filling of limited soil water storage by infiltrated precipitation from above, or Hortonian surface runoff from upslope. But the area of concern here is only the initial contributing area, the starting point for growth of the variable-source area. QUANTIFYING ICA Rationale The most basic expression for the initial contributing area of a small upland watershed is a constant stream surface area independent of flow. However, in small watersheds (e.g. < ~ 15 km 2) in the humid northeastern U.S.A., stream surface area varies appreciably, ranging from nearly zero under late summer baseflow conditions to well over bankfull (e.g. > 5m) in the spring. These extreme conditions are not just temporary, but can continue for days. This variability in ICA should at least be included in a small watershed VSA model,
INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED
391
perhaps simply expressing stream surface area as a function of flowrate. But many of the studies previously discussed noted the importance of near-stream surface saturation zones in producing storm runoff. Thus, a technique should be developed to delineate ICA as defined previously. Small moderate-intensity rainfalls on relatively dry watershed conditions produce no overland flow of the Hortonian type since precipitation intensity does not exceed soil infiltration capacity. Likewise, there is little or no subsurface contribution (interflow, throughflow) to storm runoff from these events. Even man-made impermeable surfaces, such as roads, parking lots, etc. generally produce no runoff from very small rainstorms because of their inherent depression storage, retention storage, and distance from the stream. Thus, the only areas producing storm runoff from this type of event will be the stream surface and zones of surface saturation adjacent to, and hydraulically connected to the stream. The stream surface will, of course, produce 'storm runoff' at 100% of the rainfall depth. The previously discussed seeps and springs bordering the stream and forming the surface saturation zone are above the stream surface elevation, but precipitation falling on them will not infiltrate since they are zones of groundwater discharge with flow exiting the soil under positive pressure. This continually emerging flow fills all potential depression storage within the saturation zone and moves d i r e c t l y t o the stream to sustain baseflow. Consequently, precipitation falling on this area is assumed to also produce a storm runoff component at or near 100% of the rainfall depth. Interception and some limited depression storage may occur within the zone of saturation, but for this study these losses are neglected. The basic assumptions of this analysis then are: (]) All storm runoff from a relatively small rainfall is derived only from precipitation impinging on the stream surface and the near-stream saturation zone; (2) this source-area of runoff remains constant in areal extent throughout the duration of the small rain; (3) storm runoff contributions from both the stream and zone of saturation are at 100% of rainfall depth. So if storm runoff volume from a small rainfall can be determined, the effective area contributing this storm runoff can be estimated by simply dividing runoff volume by rainfall depth: ECA
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where ECA is the effective contributing area (L2), V is storm runoff volume (L3), and P is precipitation depth (L). The ECA is a consequence of the water table intersecting the land surface at some distance from the stream; higher water table elevations result in larger values of ECA. Since baseflow is also a function of general groundwater levels within the watershed (higher baseflow rates are associated with higher groundwater levels), a relationship between ECA and baseflow may be expected. The ECA derived from small storm data under the assumptions given is identical to the ICA for a larger event as defined previously. That is, the stream surface and near-stream zone of saturation contributing all storm runoff from
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a small storm (ECA) is also the initial contributing area of runoff production (ICA) which would expand if the rain were to continue. So hereafter, the area of concern will be referred to only as the ICA, regardless of whether it is the effective contributing area for the small storms analyzed or the ICA which is the objective of this study. Also, the relationship between effective contributing area and baseflow derived from the data will be presented in terms of ICA. This relationship is developed by applying eqn. (1) to a large number of small storms representing a wide range of precipitation depths and baseflow conditions on an east-central Pennsylvania watershed.
Experimental watershed and instrumentation The 42-ha Paul Watershed is a small upland agricultural subarea of the 420-km 2 Mahantango Creek Watershed, the primary location for field research of the Northeast Watershed Research Center. Mahantango Creek is within the non-glaciated portion of the Appalachian Ridge and Valley Physiographic Province and is tributary to the Susquehanna River approximately 50 km north of Harrisburg, Pennsylvania. Generalized hydrology and water quality
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responses of upland watersheds in this area have recently been presented by Pionke et al. (1988). The Paul Watershed is typical of upland watersheds in the Ridge and Valley Province in its landform, hydrology, soils, geology, and rural land use. Figure 1 shows the location of the watershed within the Mahantango Watershed and Pennsylvania, as well as its topography, channel system, cultural features, and basic hydrologic instrumentation. The Paul Watershed is underlain mainly by steeply dipping interbedded shales and siltstones. Its soils are shallow residual silt loams, the characteristics of which indicate similar development and parent materials, as well as a moderate range in permeabilities. From the hydrologic viewpoint, the major distinguishing feature between soil series is the existence or absence of a fragipan. Fragipan soils tend to border stream channels or established drainage ways, while those without fragipans are at higher elevations further removed from the channels. Rainfall and runoff records have been collected on this watershed since it was first instrumented in 1967. A single Belfort-type weighing raingage provided the rainfall intensity and depth records from which this dataset was extracted. For a watershed of ~ 4 0 h a in Pennsylvania, one raingage gives adequate representation of total storm characteristics over the watershed, even during severe thunderstorms. The gage was equipped with a two-day clock, completing one revolution every 48 hours. Charts were changed at the same two-day intervals, making the resultant records easy to interpret. Because of the frequent gage servicing, the records are of high quality, and the charts can be read to + 0.25 mm of precipitation and to _+2 min. Thus, even the smallest storms are accurately characterized with regard to total depth. Streamflow at the watershed outlet was monitored using a 90° sharp-crested V-notch weir equipped with a float-activated FW-1 water level recorder, giving good gage sensitivity to low flow changes. The FW-1 recorder was also equipped with a two-day clock and serviced at two-day intervals, resulting in high-quality runoff records easily read to ± 2 min and ± 1.5mm gage height. Flow is calculated using a standard weir equation relating gage height to flowrate, giving an accurate characterization of total runoff rates and volumes.
Data analysis Rainfall records from 1967 to 1976 were screened for storms suitable for this analysis. All non-winter single events of ~<6 mm of moderate to low intensity rainfall were initially considered. Events were deleted from consideration when they occurred d u r i n g an active storm hydrograph recession or when subsequent precipitation obscured the end of their recession. After checking streamgage records to see that the storm hydrograph resulting from the event was recorded properly (no gage malfunctions), 116 rainfall-runoff combinations were found which met the above criteria. Total precipitation depth for each event was tabulated, and breakpoint analyses were used to develop the resulting storm hydrographs. These
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hydrographs generally consisted of a simple rise from prestorm baseflow to peak flow and a relatively quick recession to very near prestorm baseflow; this indicates that the baseflow regime of the watershed was altered little or not at all by these small events. Unlike storm hydrographs resulting from larger rainfalls where the point of storm runoff cessation may not be obvious, the break in slope between these recessions and the return to baseflow was usually quite distinct. Therefore, storm runoff volumes were separated by the commonly used technique of continuing prestorm baseflow to the time of the hydrograph peak, then extending the separation line to the break in slope on the recession. The areas above the baseflow separation lines were planimetered to determine storm runoff volumes, and dividing volume by depth of causative rainfall gives the ICA value as per eqn. (1). The final dataset developed consists
INITIAL CONTRIBUTING AREA OF A SMALL WATERSHED
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of rainfall depth, resultant volume of storm runoff, calculated runoff contributing area (ICA), and baseflow at the start of the event for each of the 116 storms. Figure 2 shows two typical storm hydrographs from the dataset, one for a rather small rainfall and the other for one of the larger depths considered. Also shown for each storm is precipitation depth, the baseflow separation line used for separating the hydrograph into continuing baseflow and storm runoff, storm runoff volume resulting from the rain, initial contributing area, and prestorm baseflow. An additional assumption critical to this analysis is that these small storm hydrographs can be realistically separated into their basefiow and storm runoff components. Many VSA-related studies have addressed the question of storm hydrograph components from either the hydrologic viewpoint (e.g. Dunne and Black, 1970a,b) or by use of natural tracers (e.g. Sklash and Farvolden, 1979; Pearce et al., 1986; Sklash et al., 1986), but these studies generally focused on storms much larger than those considered here. Objective hydrograph separation of small storms has not, therefore, been addressed directly, but using differing wording, both Dunne and Black (1970b) and Pearce et al. (1986) concluded that for small storms on small watersheds, direct rainfall on the saturation area generates the bulk of the runoff and alone controls storm hydrograph generation. In concurrence with their observaticlns, it is instructive to note that most of the smaller rainfalls considered here (i.e. events up to about 1.5 mm) caused virtually no observed increase in baseflow; the resultant storm hydrographs generally returned to prestorm baseflows within about one hour of the event. This observation implies that the overall hydrologic status of the watershed remained unchanged after the brief episode of storm runoff generation. That is, there was no increase in the baseflow component during the storm hydrograph and the zone of surface saturation did not expand to any great degree. So separation of these particular storm hydrographs into their storm runoff and baseflow components appears simple. The larger storms analyzed did alter the watershed flow regime, but only to a limited extent. The slope breaks on the hydrograph recessions apparently indicating cessation of storm runoff and return to baseflow were generally distinct and only slightly elevated from prestorm baseflow levels. So by extension from the very simple smaller storm separations, application of the basic hydrograph separation technique described previously seems justified. RESULTS AND DISCUSSION Recognizing that the goal of this study is the determination of the relationship between ICA and baseflow, it must first be shown that the dataset represents the variability of the system. Figure 3 shows precipitation depth plotted against baseflow at the time of each storm. The rectangular pattern of points indicates that the dataset represents the full range of rainfalls considered (0.86.3mm) applied to the full range of corresponding baseflows (0.03-601s1), thereby containing an unbiased distribution of storm depthbaseflow combinations.
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INITIAL CONTRIBUTING A R E A O F A SMALL W A T E R S H E D
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in the literature (e.g. Hewlett et al., 1977; Dunne, 1978), the source-area contributing total storm runoff from larger storms may itself be only 20% or less of the total watershed. In this light, the maximum ICA is significant in that it comprises ~ 10% of the active source-area. The ICA values may also be examined in terms of stream length. Perennial stream channel within the Paul Watershed totals ~ 900m. Dividing ICA by stream length gives an average width of the initial contributing area. Widths corresponding to the range of ICA values given above are ~ 0.2-10.7m. The 0.2-m value, the minimum average width of ICA, corresponds closely to stream surface width at low flow. Conversely, the maximum average ICA width calculated, about l l m, is somewhat larger than the width of the small flood plain bordering the main stream channel. When considering the maximum width indicated, it must be remembered t h a t this width is only an average of the extreme variability encountered in the natural system. The average is calculated using the approximate length of stream channel supporting perennial flow, and consequently does not reflect either upstream increase in channel length during periods of higher baseflow, or lateral preferential (concentrated) expansion of seep areas or small channels perpendicular to the main stream. Because they increase total effective stream length, such conditions tend to reduce the average effective width of ICA calculated for higher baseflow levels, thereby making the width more in line with the observed physical features of the watershed. Even neglecting these considerations, the range and magnitude of the ICA dimensions indicated by eqn. (2) correspond favorably with the physical characteristics of the Paul Watershed.
Variability of results Figure 6, storm runoff volume against baseflow, contains a high degree of variability. Normalizing volume by rainfall to give ICA reduces the variability as evidenced by the higher correlation and F-value of Fig. 7. However, with an r 2 of ~ 0.40, Fig. 7 still exhibits substantial unexplained variability. Limited additional analyses of the data were made in an attempt to explain the variability. The influence of precipitation depth within the relationship of Fig. 7 was examined. Storms were grouped by depth into three categories, < 2.5mm, 2.5-5 mm, and > 5 mm. Visual examination of Fig. 8, which shows this grouping, indicates that larger precipitation may be associated with larger ICA values for the same baseflow levels. However, statistical analysis indicated no significant difference between the data in each group. While shedding no light on variability of the results, this finding tends to reinforce the assumptions detailed earlier regarding baseflow-stormflow separations. The storm hydrographs which required no judgement in their separation (those with no observed increase in baseflow) are statistically part of the same population as those which required a slightly more complex separation. Data from a limited range of baseflows (0.3~.51s ') were also examined.
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Under the hypotheses of the overall investigation, this implies looking at watershed response under similar ICA values (common baseflow values). Storm runoff volumes for events segregated this way should be proportional to rainfall depth, with the constant of proportionality being ICA. The data (21 ~0
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points), plotted as Fig. 9, indicate that storm runoff volume does increase with rainfall depth as expected for the smaller rains, but it also shows an increased degree of scatter at larger precipitation depths. This same analysis was repeated using data selected from other narrow ranges of baseflow, and similar results were found. Such results imply that the larger precipitations sampled, > 5mm, may be the beginning of the range where ICA-only hydrology is undergoing the transition into storm runoff production controlled by a sourcearea expanding during the storm. Figure 10 shows ICA plotted against rainfall depth only for the data used in Fig. 9. Ideally, the slope of this plot should be zero, since the hypothesis is that similar baseflow values have similar ICA values. However, there appears to be a slight positive slope to these data, implying that precipitation depth influenced ICA at these same baseflow values. As mentioned previously, a similar analysis including all data (all baseflow values) did not statistically support a relationship between precipitation and ICA. There may be other methods to examine these data, but as in most investigations of natural phenomena using field data, a certain degree of variability always remains unexplained. The purpose of this study was to investigate the potential for developing a relationship between initial contributing area, as calculated from storm runoff volume and precipitation depth, and concurrent baseflow. Figure 7 and its associated statistics indicate that there is a defensible relationship, and eqn. (2) is its quantitative expression. SUMMARY
The initial contributing area of a watershed is defined as consisting of the
402
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stream surface area and the area of surface saturation caused by the water table intersecting the land surface above that of the stream. Because subsurface flow is discharging to the land surface within this area, the area provides zero storage capacity and infiltration potential for rainfall, producing storm runoff at nearly 100% of the rainfall depth. The ICA is the initial area of runoff production in a variable-source-area analysis of the dynamics of storm runoff generation on a watershed. This study shows that the ICA of the 42-ha Paul Watershed can be expressed as a function of prestorm baseflow. The prediction equation presented (eqn. (2)) was developed using small-storm rainfall-runoff data from the watershed. The equation is in a form which could be easily incorporated into either a continuous streamflow model, where the baseflow value is available from the simulated recessions, or an event-based model, where prestorm baseflow is specified as a design parameter or probability function. The technique developed here can be applied simply and quickly to watersheds where rainfall-runoff records exist, and thus is a valuable addition to the growing body of knowledge related to the mechanisms of variable-source-area storm runoff generation on humid-climate upland watersheds. REFERENCES Anderson, M.G. and Burt, T.P., 1978. Toward more detailed field monitoring of variable source areas. Water Resour. Res., 14(6): 1123-1131. Anderson, M.G. and Kneale, P.E., 1980. Topography and hillslope soil water relationships in a catchment of low relief. J.Hydrol., 47:115 128. Anderson, M.G. and Kneale, P.E., 1982. The influence of low-angled topography on hillslope soil water convergence and stream discharge. J. Hydrol., 57: 65-80. Bernier, P.Y., 1985. Variable source areas and storm-flow generation: An update of the concept and a simulation effort. J. Hydrol., 79:195 213. Betson, R.P., 1964. What is watershed runoff?. J. Geophys. Res., 69(8): 1541 1552. Betson, R.P. and Marius, J.B., 1969. Source areas of storm runoff. Water Resour. Res., 5(3): 57~582. Beven, K.J., 1978. The hydrological response of headwater and sideslope areas. Hydrol. Sci. Bull., 23(4): 419437. Beven, K.J. and Kirkby, M.J., 1979. A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24(1): 43-69. Beven, K.J. and Wood, E.F., 1983. Catchment geomorphology and the dynamics of runoff contributing areas. J. Hydrol., 65: 139-158. Bissell, V.C. and Ragan, R.M., 1969. The determination of zones of intense contribution to stream flow as related to the concept of partial area contributions. Tech. Rep. 21, Water Resour. Res. Center, University of Maryland, College Park, MD, 188 pp. Dunne,T., 1978. Field studies of hillslope processes. In: M.J. Kirkby (Editor), Hillslope Hydrology. Wiley, New York, pp. 227 294. Dunne, T. and Black, R.D., 1970a. An experimental investigation of runoffproduction in permeable soils. Water Resour. Res., 6(2): 47~490. Dunne, T. and Black, R.D., 1970b. Partial area contributions to storm runoff in a small New England watershed. Water Resour. Res., 6(5): 1296 1311. Dunne, T., Moore, T.R. and Taylor, C.H., 1975. Recognition and prediction of runoff-producing zones in humid regions. Hydrol. Sci. Bull., 20(3): 305 327. Freeze, R.A., 1972a. Role of subsurface flow in generating surface runoff, 1. Baseflow contributions to channel flow. Water Resour. Res., 8(3): 6094~23.
INITIAL CONTRIBUTINGAREAOF A SMALLWATERSHED
403
Freeze, R.A., 1972b. Role of subsurface flow in generating surface runoff, 2. Upstream source areas. Water Resour. Res., 8(3): 1272-1283. Gillham, R.W., 1984. The capillary fringe and its effect on water-table response. J. Hydrol., 67: 307-324. Heerdegen, R.G. and Beran, M.A., 1982. Quantifying source areas through land surface curvature and shape. J. Hydrol., 57: 359-373. Hewlett, J.D. and Hibbert, A.R., 1963. Moisture and energy conditions within a sloping soil mass during drainage. J. Geophys. Res., 68:1081 1087. Hewlett, J.D. and Hibbert, A.R., 1967. Factors affecting the response of small watersheds to precipitation in humid areas. In: W.E. Sopper and H.W. Lull, (Editors), International Symposium on Forest Hydrology. Pergamon Press, New York, pp. 27~290. Hewlett, J.D. and Troendle, C.A., 1975. Non-point and diffused water sources: A variable source area problem. Proceedings of a Symposium on Watershed Management, Am. Soc. Civ. Eng., New York, pp. 65 83. Hewlett, J.D., Cunningham, G.B. and Troendle, C.A., 1977. Predicting stormflow and peakflow from small basins in humid areas by the R-index method. Water Resour. Bull., 13:231 253. Hornberger, G.M., Beven, K.J., Cosby, B.J. and Sappington, D.E., 1985. Shenandoah Watershed study: Calibration of a topography-based, variable contributing area hydrological model to a small forested catchment. Water Resour. Res., 21(12): 1841 1850. Hursh, C.R. and Brater, E.F., 1941. Separating storm-hydrographs from small drainage-areas into surface- and subsurface-flow. Trans. Am. Geophys. Union, 22: 863-871. Kirkby, M.J. and Chorly, R.J., 1967. Throughflow, overland flow and erosion. Bull. Int. Assoc. Sci. Hydrol., 12(3): 5 21. Linsley, R.K., Jr., Kohler, M.A. and Paulhus, J.L.H., 1958. Hydrology for Engineers. McGraw-Hill, New York, 340 pp. O'Loughlin, E.M., 1981. Saturation regions in catchments and their relations to soil and topographic properties. J. Hydrol., 53: 229-246. Pearce, A.J., Stewart, M.K. and Sklash, M.G., 1986. Storm runoff generation in humid headwater catchments, 1. Where does the water come from? Water Resour. Res., 22(8): 1263 1272. Pionke, H.B., Hoover, J.R., Schnabel, R.R., Gburek, W.J., Urban, J.B. and Rogowski, A.S., 1988. Chemical hydrologic interactions in the near-stream zone. Water Resour. Res., 24(7): 1101 1110. Potter, S.T. and Gburek, W.J., 1987. Seepage face simulation using PLASM. Ground Water, 25(6): 722-732. Rawitz, E., Engman, E.T. and Cline, G.D., 1970. Use of the mass balance method for examining the role of soils in controlling watershed performance. Water Resour. Res., 6(4): 1115 1123. Roulon, J.J., Rodway, R. and Freeze, R.A., 1985. The development of multiple seepage faces on layered slopes. Water Resour. Res., 21(11): 162~1636. Sklash, M.G. and Farvolden, R.N., 1979. The role of groundwater in storm runoff. J. Hydrol., 43: 45-66. Sklash, M.G., Stewart, M.K. and Pearce, A.J., 1986. Storm runoff generation in humid headwater catchments, 2. A case study of hillslope and low-order stream response. Water Resour. Res., 22(8): 1273-1282. Ward, R.C., 1984. On the response to precipitation of headwater streams in humid areas. J. Hydrol., 74: 171-189. Zaslavsky, D. and Sinai, G., 1981a. Surface hydrology: III--Causes of lateral flow. J. Hydraul. Div., ASCE, 107(HY1): 37-52. Zaslavsky, D. and Sinai, G., 1981b. Surface hydrology: IV--Flow in sloping, layered soil. J. Hydraul. Div., ASCE, 107(HY1): 53~4.