in Southern Ontario. It was calibrated on the Grand River watershed and then applied to the three other watersheds without further calibration of the hydrologic.
G R O U P E D R E S P O N S E U N I T S FOR D I S T R I B U T E D HYDROLOGIC MODELING a
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By N. Kouwen,l Member, ASCE, E. D. Soulis, 2 A. Pietronirofl J. Donald,4 and R. A. Harringtons ABSTRACT: This paper introduces a method for distributed hydrologic modeling that eliminates the need for small computational areas while maintaining the requirement of computing runoff for homogenous watershed subareas. The model is designed from the ground up as a georeferenced model that can make maximum use of remotely sensed data such as rainfall from weather RADAR and land cover characteristics from LANDSAT or SPOT satellites. Other remotely sensed data such as snow-cover extent and initial soil moisture can also be based on satellite data and be directly incorporated in the model. The method consists of grouping hydrologic response units that have similar response characteristics on the basis of classifiedland-cover maps. Model parameters are unique to individual land-cover classes. This reduces the need for model calibration and allows for the transfer of model parameters in both time and space. The model was applied to four watersheds in Southern Ontario. It was calibrated on the Grand River watershed and then applied to the three other watersheds without further calibration of the hydrologic parameters. Only the river roughness was adjusted. INTRODUCTION
Distributed models are most likely to p r o d u c e the next increment of progress in streamflow modeling (Link 1983). The importance of considering the unique contribution of each type of land cover to a watershed's hydrologic response has been recognized ( D u c h o n et al. 1992; Tao and Kouwen 1989). Most models in current use are l u m p e d conceptual models that use basin averages for meteorological inputs and watershed characteristics. These models are extremely useful but in m a n y cases do not o u t p e r f o r m simpler statistical or empirical models (Naef 1981). D i s t r i b u t e d models, on the other hand, incorporate the spatial variability of watershed and meteorological processes and permit m o r e fundamental representations of the hydrological processes and therefore should be far less p r o n e to the calibration and extrapolation p r o b l e m s of their l u m p e d predecessors. E x a m p l e s of the m a n y distributed models u n d e r d e v e l o p m e n t are S H E ( E u r o p e a n Hydrological S y s t e m - - S y s t e m e H y d r o l o g i q u e E u r o p e e n ) ( A b b o t t et al. (1986), H Y D R O T E L (Fortin et al. 1986), and W A T F L O O D (Kouwen 1988). Spatial variability in basin characteristics in most distributed models is apresented at the August 20-24, 1990, International Symposium on Remote Sensing and Water Resources, held at Enschede, Netherlands. 1Prof., Dept. of Civ. Engrg., Univ. of Waterloo, Waterloo, Ontario, Canada, N2L 3G1. 2Asst. Prof., Dept. of Civ. Engrg., Univ. of Waterloo, Waterloo, Ontario, Canada, N2L 3G1. 3Res. Sci., Hydro. Sci. Res. Div., Nat. Hydro. Res. Ctr., Saskatoon, Saskatchewan, Canada 37N 3H5. 4Special Projects Engr., Connestoga Rovers and Associates, Waterloo, Ontario, Canada. 5proj. Engr., Paragon Engrg., Kitchener, Ontario, Canada. Note. Discussion open until October 1, 1993. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on October 21, 1991. This paper is part of the Journal of Water Resources Planning and Management, Vol. 119, No. 3, May/June, 1993. 9 ISSN 0733-9496/93/00030289/$1,00 + $.15 per page. Paper No. 2846. 289
J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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captured using small subbasin elements often called hydrologic response units (HRUs) (Leavesley and Stannard 1990) or representative elemental areas (REAs) (Wood et al. 1988). These are regions that have a locally uniform hydrologic response to meteorological stimuli. In fact, many distributed models can be considered an assembly of lumped models applied to a collection of HRUs. The number of HRUs required varies with basin characteristics. For example, in regions with fairly homogeneous land cover types, such as the Canadian prairies, the number may be small. In other areas where small-scale mixed agriculture is practiced, such as in southern Ontario, Canada, the number may be quite large. These problems may be overcome by geographic information systems (GIS) and new models. Grayman (1990) states that: "by the year 2000, the sophisticated GIS and greater availability of data will have spurred renewed development of models that can incorporate detailed spatial data." This paper addresses the need for new approaches to hydrologic modeling. The modeling technique described is designed to incorporate detailed spatial data while remaining computationally efficient. GIS systems or image processing techniques may be used to create all or part of the data base but traditional methods may also be used.
FIG. 1.
Landsat Image of Mixed Land Cover in Southern Ontario, Canada 290 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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The main difficulty in subdividing watersheds into areas having uniform hydrologic response is determining what constitutes a hydrologically homogeneous area. This is illustrated by the portion of a Landsat MSS image of an agricultural region in southern Ontario, Canada shown in Fig. 1. Each pixel in this figure represents the average reflection in the green visible band of a 79-m-by-79-m area. Variation in the spectral characteristics of the image indicates variation in the vegetative cover. This variation, in turn, can be related to underlying soil or topographic differences. The image in Fig. 1 shows that nearly every pair of adjacent pixels has different spectral characteristics. This leads to the speculation that separate pixel areas do not have the same hydrologic response. Different sensors may indicate variations at even smaller scales. Fig. 2 is an active microwave image of the same agricultural area. Here each pixel represents the radar backscatter from a 20-m-by-10-m area. Adjoining pixels are different even though they represent the same crop type. In Fig. 2, the differences are caused by differences in vegetation, soil moisture, and field roughness. In both figures the pixels are resampled to a 25-m-by-25-m grid. Some of the variations are a consequence of the imaging process but both suggest that the size of an H R U could be the size of one pixel and that
FIG. 2.
SAR Image of Uniform Land Cover in Southern Ontario, Canada 291 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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many HRUs are necessary to describe a basin. In fact, an H R U could be smaller than a pixel if the sensor has already performed some averaging. In practice, however, the number of HRUs that can be used is limited by data availability and computational constraints. For example, prediction of a hydrograph using a sparse rain gauge network is unlikely to improve by applying uncertain interpolated rainfall estimates to a collection of HRUs no matter how well defined they are. In fact, the forecast may degrade due to model errors arising from calibrations with limited data. The purpose of this paper is to present an alternate scheme, called the grouped response unit (GRU) approach, to represent the heterogeneity of a watershed. The method has its origins in a paper by Tao and Kouwen (1989) that showed that the urban runoff modeling practice of summing runoff contributions from distinctly different areas (pervious and impervious) within a watershed prior to routing (Viessman et al. 1989), could be applied to nonurban regions that have a larger number of distinct land covers. The method significantly reduced the calibration and validation errors in the modeling of rainfall-runoff events in southern Ontario (Tao and Kouwen 1989) and the concept has subsequently been used in other studies (Kouwen et al. 1990; Kite and Kouwen 1991; Duchon et al. 1992). This paper formally defines the G R U approach, describes its elements and discuses a model in which it is used. Calibration and validation results from a peak-flow forecasting study are presented. The results suggest the model parameters are uniquely related to land-cover classes, which makes the model parameters transferable to other watersheds in physiographically similar areas. HYDROLOGIC RESPONSEAND GROUPED RESPONSE UNIT
The grouped response unit is the computational uniL It consists of a subwatershed, called an element, that may have a range of land cover characteristics. Element size is limited to an area that is subject to uniform meteorological conditions or to a size where element travel times are small compared with either the overall basin travel time or the duration of meteorological events of interest. Runoff is modeled in an element by calculating runoff contributions from each hydrologically unique land cover separately and routing the results independently to the drainage system. Identical hydrologic parameters are used for the same land cover in all elements of the basin. The within-element routing parameters are also land cover-dependent but the topographic characteristics of each GRU are used with these parameters to determine the local routing of each land cover in each element. It is assumed that, unless there are major irregularities in the soil types, the topographic and land cover effects far outweigh the effects of variations of soil types. This assumption is supported by recent work by de Roo et al. (1992). Differences in soil types are largely coincident with differences in vegetative covers and topogaphy and their independent effects cannot be separately identified. With the exception of urban runoff models, the GRU approach is radically different from conventional modeling, where runoff generating subbasins or elements are considered to be hydrologically homogeneous. The size restrictions are such that a GRU may be considered to contain a scattered coUection of contiguous or noncontiguous runoff generating HRUs. Because the within GRU routing time is short, average H R U routing behavior within a G R U is sufficient for modeling purposes. Therefore the location of the HRUs within the GRU is not significant and only the percent 292 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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cover of classes of H R U s is necessary to characterize a grouped response unit. These data are readily available from resource satellites, land-use maps, or geographic information systems. The transition from a derived land use map to a G R U is demonstrated in Fig. 3. Fig. 3(a) shows an initial land-use map that identifies four distinct hydrological units distributed within the single GRU. In the example, nine pixels were classified as belonging to land-cover class A, 10 to class B, two to class C and four to class D. For example, these classes could be bare ground, forest, wetland, and grass-covered land. More classes are possible but the number of classes that can be included depends on the number of distinct spectral signatures that can be identified in the land-cover data. In
A B
B B
C
B A
A
B
B B A
A
B C
B B A A D D
A
D D A (a)
I
Streamflow routing
(b)
FIG. 3. Construction of Grouped Response Unit: (a) Land-Use Map Number of Pixels: A = 9, B = 10, C = 2, D = 4; (b) Fraction of GRU: A = 36%, B = 40%, C = 8%, D = 16%
293 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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the GRU method, it is assumed that all pixels in a computational element, the GRU, receive the same meteorological stimuli but that each class responds in its own characteristic way. For instance, high infiltration and low runoff in the forest pixels and the opposite in the bare areas. The watershed is divided into as many computational elements as are needed and these elements may be subjected to differing initial and meteorological conditions. To represent the land use hydrologically, the classified hydrological units (pixels) of Fig. 3(a) are grouped into the summary form of a GRU [Fig. 3(b)]. The hydrological processes for each group are modeled identically, the response weighted according to the group's percentage of the area occupied, the resulting outflow is summed and the total GRU outflow is routed through the stream network. The optimum area covered by a GRU varies with time scale and basin size. Sensitivity studies have shown that, for hourly event models, GRUs can have areas as large as 4% of basin area for large basins (>3,000 km 2) and as much as 100% for small basins (approximately 100 km 2) without degrading hydrograph simulation (Tao and Kouwen 1989). For daily continuous models of basins with areas of about 10,000 km 2, four or five GRUs appear to be sufficient (Kite and Kouwen 1991). In both studies, considerable insensitivity to GRU size was found to exist over a wide range of areas. A significant gain in using t h e GRU concept is that the shape of the element is not restricted. A basin subdivided into GRUs can be viewed as a collection of contiguous elements with shapes that can be selected to conveniently fit relevant data bases. For the examples in this paper, the GRUs are square elements adapted to rectangular coordinates associated with the remotely sensed imagery and the GIS used. In Kite and Kouwen (1991), the approach was applied to the Kootenay River, a mountain watershed in British Columbia, Canada using GRUs that correspond to gauged subcatchments. APPLICATIONOF GRUs IN WATFLOOD AND SIMPLE
WATFLOOD (Kouwen 1988) is a hydrologic data-base-management system that was designed to incorporate the GRU concept. The system is expressly designed for distributed modeling using remotely sensed data although it can be used with conventional meteorological and hydrometric data as well. The data base uses a Cartesian coordinate system usually aligned with the local UTM system. It can therefore easily accommodate georeferenced imagery and be connected to a GIS. It has a convenient graphical interface for data inspection and spreadsheetlike displays for data correction. SIMPLE is the hydrological simulation model within WATFLOOD and uses the GRU approach.
Modeling Details SIMPLE was initially designed for flood forecasting and therefore reflects the dominant short duration rainfall-runoff processes. Excluding river routing, the processes that are modeled occur primarily at or near the surface, and are thus most likely to benefit from a more detailed land-cover description. LANDSAT imagery is used to determine the percent cover of hydrologically significant classes (forest, crops, barren land, urban areas, and wetland) in each unit (Kouwen 1988). Before describing the watershed model in detail, it should be pointed out 294
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that the values of many parameters need to be determined for the equations used to describe the rainfall-runoff and routing processes. While some may be assigned standard well known values, others may be subject to great variations and uncertainty. Where possible, standard values are used, but those parameters that cannot be predicted are estimated using a pattern search-optimization technique. The modeling process begins with the addition of rainfall to the watershed. The various submodels are described next.
Interception Interception of precipitation by vegetation is calculated in SIMPLE using the equation given by Linsley et al. (1949)
V = (S, + CpEatn)(1 - e -kP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
where V = depth of interception from the beginning of the storm (mm); S~ = storage capacity per unit of projected area (mm); Ce = ratio of vegetal surface area to its projected area; E, = evaporation rate per unit per unit of surface area (mm/hr); tn = the duration of the rainfall (hr); k = a constant (l/mm); and P = the precipitation since the beginning of the storm (mm). In SIMPLE, Cp is assumed to be 100 and Ea at 0.00025 mm/hr. The values for Si are set for each month and each land use/cover class and tR is taken as the time from the beginning of rainfall. The values of S; range up to 9 mm for forests, 5 mm for lower vegetation and up to 3 mm for short vegetation.
Surface Storage The ASCE Manual of Engineering Practice No. 37 ("Design" 1969) for the design of sanitary and storm sewers gives upper limits of retention for various surface types. The values used in the model were within these limits except for forest litter: impervious urban areas 1.25 mm, pervious urban areas 2.0 mm, smooth cultivated land 2.0 mm, good pasture and low vegetation 3.0 mm, and forest litter 10.0 mm. Infiltration Due to the importance of the infiltration process in runoff calculations and also because infiltration capacity is such a highly variable quantity, this process requires a great deal of attention in any hydrologic model. The Philip formula (Philip 1954) is chosen as representing the important physical aspects of infiltration process. It also readily incorpor~ites the notion of surface detention:
dF --dt = K
[
((m - mo)(Pot + Dl))] 1+
F
(2) .......................
where F = total depth of infiltrated water (mm); t = time (s); K = saturated conductivity (mm/s); m = the average moisture content of the soil to the depth of the wetting front; mo = initial soil moisture content; Pot = capillary potential at the wetting front (ram); and D 1 = depth of water on the soil surface = detention storage (mm). Eq. (2) represents the physical process of infiltration in that the pressure gradient acting on the infiltrating water is used to determine the flow using Darcy's law. Because of the uncertainty of its effective value over the basin, K = an optimized parameter. The values of K range from 2 mm/hr for 295 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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forested areas to 0.3 mm/hr for bare or sparsely vegetated areas. These values are very low but this is because water tends to flow to low areas and infiltrate from ponds. The result is that when the value of K is expressed for the whole area, its effective value is greatly reduced because of large areas that do not contribute to infiltration except for short periods. Initially, the infiltration capacity is very high because of the shallow depth of the wetting front. The capillary potential causes a very large pressure gradient inducing high infiltration. However, as the wetting front descends, the pressure gradient is quickly reduced, thus reducing the potential infiltration rate. Using the information in Philip (1954) relating permeability to capillary potential, the following relationship provides the capillary potential: Pot = 250 log(K) + 100
.....................................
(3)
The potential head calculated by (3) compares very well with values reported by Rawls and Brakensiek (1983). Water depth on the soil surface is continually modified to reflect the net precipitation input, infiltration, and overland flow discharge. Interflow
Infiltrated water initially is what is commonly referred to as the upper zone storage (UZS). Water within this layer percolates downward or is exfiltrated to nearby water courses and called interflow. In the model, percolation downward is ignored because in most cases when dealing with single rainfall events, the path from the UZS to the stream via the ground water reservoir is too long in duration to contribute appreciably to streamflow during the event. Of course, exceptions do occur and must be recognized. Interflow is represented by a simple storage-discharge relation: QINT = REC • WAC
......................................
(4)
where Q I N T = interflow (m3/s); R E C = a coefficient (optimized); and W A C = water accumulation in the UZS region. R E C is a coefficient that cannot be predicted and is therefore estimated through optimization. Values of R E C are expressed as the depletion fraction per hour of the UZ storage and range from 0.001 to 0.005, i.e., from 0.1 to 0.5% of the water stored in the upper zone is drained off each hour. Overland Flow When the infiltration capacity is exceeded by the water supply, and the depression storage has been satisfied, water is discharged to the channeldrainage system. The relationship employed is based on the Manning formula and takes the form: 1
Qr : ~
(D1
-
Ds)l67Sl~
.................................
(5)
where Qr = channel inflow (m3/s); Ds = depression storage capacity (optimized); Sl = average overland slope; A = the area of the basin element (m2); and R3 = combined roughness and channel-length parameter (optimized). The R3 parameter lacks physical meaning in that it includes both roughness and drainage density effects. For a basic time step of one hour, values 296
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of R3 range from 1.0 for impervious surfaces in urban areas to approximately 100 for in forested areas. These values serve only to show the relative effects of storage roughness and drainage density. Because of its nature, R3 obviously can only be evaluated through optimization. In SIMPLE (1)-(5) are used separately for each land class in each computational element. Base Flow The base is determined from a measured hydrograph at the basin outlet. The base flow contributed by each basin subelement is found by prorating it to the total basin area. A recession constant is used to gradually diminish the base flow over the duration of the event being modeled. Values of this parameter range from 0.99 to 0.995 per hour. The model is not sensitive to this value because the events modeled are of relatively short duration and base flow is assumed not to change a great deal during the simulation. In addition, in the areas studied, base flow is insignificant compared to flood flows. Total Runoff The total inflow to the river system is found by adding the surface runoff contributions from the various land cover classes to the base flow. These flows are then added to the channel passing through the element. Routing Model The routing of water through the channel system is accomplished using a storage-routing technique. More sophisticated routing models are available but the application of such models does not appear to promise more accurate flood forecasts than the simple routing model. In fact, for large watersheds, differences between the routing methods may well be smaller than the noise in the data (Ponce 1990). When the hydrologic errors are also considered, the use of more sophisticated and necessarily more computationally intensive methods are not warranted for flood forecasting on rivers where dynamic effects can be ignored. In addition, simple routing can be based on a minimal amount of river cross-section and profile data. The method involves a straightforward application of the continuity equation: I 1 -]- 12
2
0 1 + 0 2 -- S2 -
2
At
51
................................
(6)
where/1,2 = inflow to the reach consisting of overland flow, interflow, base flow, and channel flow from all contributing upstream basin elements (m3/ s); O1,2 = outflow from reach (m3/s); $1,2 = storage in the reach (m3); and At = time step of the routing (s). The subscripts 1 and 2 indicate the quantities at the beginning and the end of the time step. The flow is related to the storage through the Manning formula:
0 = - ~ AX133S~ "s
..........................................
(7)
where O = flow (m3/s); R2 = channel roughness parameter (optimized); A X = channel cross-section area, which is related to storage by dividing the storage by the channel length (m2); and So = channel slope. A change in this relationship occurs when the flow exceeds the channel 297
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capacity and the flow spills into the flood plain. One requirement for running SIMPLE is a relation that gives the channel capacity at any point in the basin. This is accomplished by measuring the channel cross-section area at various points in the watershed and fitting a relation such that the channel cross-section area is given as a function of drainage area. This relation is used to determine if the flow exceeds the channel's capacity at any point at any time. Values of R2 range from 0.3 to 1.0 and the overbank roughness is set at double this value. CALIBRATIONAND VALIDATIONOF SIMPLE
SIMPLE can be classed as a simplified process-based model and therefore, the model parameters must be calibrated by trial and error or optimization for each land cover class. Because model parameters are associated with particular land-cover classes, calibration in nearby, and physiographically similar watersheds may be avoided, thus reducing the need for recalibration on other watersheds. HoweVer, calibration can never be totally eliminated and validation tests should always be conducted when the model is applied elsewhere. The number of land-cover classes defining the GRUs should not exceed the number of independent streamflow gauges times the number of independent periods of record used to calibrate the model. More importantly, the relative areal coverage of each land cover class must vary within subbasins defined by stream-gauge locations. If two land-cover classes have the same areal coverage in each su,bbasin, their parameters could be interchanged and the total runoff contributed by these two areas would remain unchanged. The Hooke and Jeeves (1961) pattern-search optimization method as programmed by Monro (1971) is used to determine the best-fit parameter values. The advantage of the pattern search technique is that it does not require the parameters to be independent, which is rarely the ease in hydrologic models. SIMPLE was calibrated for events on the Grand River watershed using LANDSAT land-cover data and adjusted radar rainfall data. The validation of SIMPLE was divided into validation in time and validation in both time and space. The validation with respect to time was carried out on the same watershed as the calibration but different events were used. With respect to time and space, the model was validated on different watersheds for different events. Fig. 4 is a map of southern Ontario showing the location of the study area and the Grand, Saugeen, and Humber rivers as well as four smaller basins referred to as the Eastern Metropolitan T o r o n t o area watersheds. Grand River Basin--Calibration and Validation in Time
The Grand River watershed is located in southern Ontario approximately midway between Lakes Ontario and Huron and drains southerly into Lake Erie. It has a total drainage area of 6,700 km 2 but SIMPLE was applied only to the 3,520 km 2 contributing area above Cambridge (Galt), Ontario. Between five and eight Streamflow gauges were used depending on the runoff event. SIMPLE is configured to model three events in tandem to allow optimization to be based on an additive error for all calibration events and all gauges. A total of 17 parameters were fitted using three events that occurred 298 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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45 ~
Lake Hur~ ~ ( L A
(~
~
[ ~, ~ J ) /'~ /
,_/ ] ~ -~JJ,'~---t/'J)'t
j ,/ ~ / /
"~-
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HumberR
j,,/I
Wotershe(i
GrandR.V'~'~) ~ ' j
FIG. 4.
/
East Metro Toronto Watersheds ~ I
=L~3t ke
o
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Map of Southern Ontario, Canada
Grand River 1000
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FIG. 5, Calculated versus Measured Peak Flows--Grand River (Kouwen et el. 1990)
between 1981 and 1983. The average calibration error for the peak flows at Cambridge for those events was 11%. SIMPLE then was run for eight additional data sets between 1954 and 1986 excluding those used for the calibration. Fig. 5 is a plot of the calculated peak flows versus the measured peak flows for these events. The average error for forecasting the peak flow at Cambridge (Galt) for
299 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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10 events is 22%. These errors compare favorably with average errors for an urban runoff model computed by Stall and Terstriep (1972) as reported by Viessman (1989). Urban models are inherently simpler to calibrate because of their sensitivity to the easily measured impervious area. Generally, the results are better for larger flows, with the exception of the May 1974 event when the calculated peak flow is greatly underestimated, This is due to the lack of rainfall measurements in the areas where the heaviest rainfall occurred. Fig. 5 also shows that there is generally more scatter for the validation points than for the calibration points. The model tends to overestimate the peak flow for low-intensity rainfall events.
Validation in Time and Space Simulations for the Saugeen, the Humber, and the Eastern Toronto Basins were carried out using Landsat land-cover distributions and parameters fitted to the Grand River data. The river roughness parameters were optimized for each of the watersheds because these parameters are not related to land-cover classes. Saugeen River Basin The Saugeen River is located northwest of the Grand River, drains westerly into Lake Huron and has a drainage area of 4,056 km 2. Seven stream flow gauges were used for comparison of the measured and computed flows. Compared to the Grand River, the Saugeen River watershed has more forest cover and more wetland. This provides an opportunity to test the GRU approach, that is, parameters are associated with land cover classes and not with the relative amounts of each land cover class. Fig. 6 plots the peak calculated flows versus the peak measured flows for the calibration runs on the Grand River (crosses) and the validation runs on the Saugeen River (boxes). The closeness of the Saugeen River points to the 45~ line shows that using the LANDSAT derived land-cover types for the Grand River to classify hydrologic response (i.e., classify model Saugeen River
1000
+ calibration 9 Grand River D validation - Saugeen River
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+ + D~o~3 D
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Calculated versus Measured Peak Flows--Saugeen River (Kouwen el al.
300 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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parameter values) results in very good predictions of peak flow in a similar geographic area. The average peak flow error at all stations for seven events is 22%. At the basin outlet (Port Elgin) the average error is 19%. For the Saugeen basin, the raingauge data is sparse, with only one rain gauge located in the watershed while three others were some distance away. This leads to poor rainfall data set for input to the model if only rain-gauge data is used as input. It has been shown that for this density of rain-gauge networks, radar can improve the flood flow forecast (Cooper 1988). Humber River Basin The Humber River watershed is located directly east of the upper (northern) tributaries of the Grand River. It drains an area of 570 km 2 and drains easterly into Lake Ontario. The lower part of the watershed is heavily urbanized by the suburbs and neighboring cities of metropolitan Toronto. The simulations for the Humber were also carried out using the rainfallrunoff parameters fitted to the Grand River rainfall-runoff data. Fig. 7 compares the calculated to the measured peak flows for the Humber River watershed. The average peak flow error at Weston is 32%. For smaller subbasins the errors were much larger and quiet erratic. This appears to be due to a very poor distribution of rain gauges in the Humber River basin as most of the gauges are concentrated in the lower part of the basin. River rainfall measurements are available for the area and may improve the peak flow estimates considerably. For all basins in this study, urban areas were classified as a single class. The impervious area was then estimated as a fraction of the urban area. To eliminate the possibility that the scatter in Fig. 7 was due to an inaccurate classification of the land cover classes in the Humber River watershed, the LANDSAT image was reanalyzed to explicitly classify impervious, grassed, and other land covers within the urban areas. The modeling results did not improve appreciably. Humber River
1000
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+ calibration - Grand River [] validation- H u m b e r River
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FIG. 7. (1990)
Calculated versus Measured Peak Flows--Humber River (Kouwen et al.
301 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
East Metro Watersheds
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FIG. 8. Calculated versus Measured Peak Flows--East Metro Toronto (Kouwen et al, 1990)
Eastern Metropolitan Toronto Watersheds The eastern metro Toronto basins have very small drainage areas. Four separate watersheds were modeled, namely, the Rouge River with 328 km 2, Duffin's Creek with 288 km 2, Lynde Creek with 112 km ~, and Oshawa Creek, which drains 122 kmL The four watersheds are adjacent and drain in a southeasterly direction into Lake Ontario. They are on the east side of metropolitan Toronto. The lower parts of the watersheds are urbanized. Fig. 8 is a plot of the computed peak flows versus the measured peak flows for the five events. The average error is 20% for the Rouge River and 41% for Duffin's Creek. These larger errors are consistent with the poor areal distribution of the rain-gauge locations. While there are a good number of stations in the area, many of the rain gauges were not in operation or were discontinued during the simulation times. Those gauges that could be used were too far apart to accurately reflect the spatial distribution of the rainfall on the small areas. Sensitivity Assessment As a check on the calibration of the model, parameter values were interchanged to determine the sensitivity of the model to those parameters. The depression storage, permeability, interflow, and overland flow roughness parameters were interchanged for forested and cropped lands on the Saugeen River watershed. Changing these parameters resulted in a 15% increase in the average error for calculated peak flows. This supports the validity to the optimization process and the G R U approach. As a second check of the calibration, cropped land was converted back to forested land. Fig. 9 shows how the peak flows could change due to this hypothetical reforestation of part of the watershed. The results indicate that the peak flows would drop 27%, with an maximum reduction of 65%. Comparison for Runoff Amounts In addition to comparison of the peak flows, the total storm runoff provides another modeling criteria. For flood control, the volume of flow is of 302
J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
Saugeen River
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FIG. 9. Sensitivity of SIMPLE to Changes in Vegetation
equal importance to the peak flow. In all cases, it appears more difficult to estimate the total runoff but in three cases out of four, the results improve for the more intense runoff-producing events. This is encouraging, especially for a flood-forecasting model. SUMMARY AND CONCLUSIONS
The grouping of hydrologic response units into GRUs is a practical way to manage the heterogeneity of basins for distributed hydrologic simulation and to provide a convenient procedure to connect hydrologic models to coordinate-based imagery and GIS data. The flexibility and ease of use of the G R U concept is demonstrated through its application to watersheds ranging in size from 125 km 2 to 4,000 km 2 and over a wide variety of hydrologic units (e.g., impervious, forested, agricultural, and wetlands). The GRU approach was tested using ground-based radar for rainfall estimates and LANDSAT data for land-cover estimation for flood forecasting. Because the modeling parameters are associated with particular land covers, it is shown that it is possible to calibrate the model on one watershed (Grand River) and then transfer the parameters to a neighboring watershed (Saugeen River), where it gives equally good flood forecasts. The results degrade as the parameters are applied to the watersheds located in a different physiographic area and further away from the calibration watershed (Humber and eastern metro watersheds, respectively). Very few published studies present calibration-validation results of the type presented in this paper. However, there are a few such results reported for urban storm water models (Viessman et al. 1989). The plots presented in this paper compare favorably with those shown in Viessman et al. (1989). ACKNOWLEDGMENTS
The writers would like to thank the Ontario Ministry of Natural Resources for sponsoring this study under the Flood Damage Reduction Program. The 303 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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development of W A T F L O O D has been supported by the University of Waterloo and the National Science and Engineering Research Council of Canada. Data has been provided by Environment Canada and the Grand River Conservation Authority. This support is gratefully acknowledged. The writers would also like to acknowledge the International Association of Hydrogeology and the Netherlands Society for Remote Sensing for permission to reproduce some of the figures in this paper as well as much of the text. APPENDIX I,
REFERENCES
Abbott, M. B., Bathurst, J. C., Cunge, J. A., O'Connell, P. E., and Rasmussen, J. (1986). "An introduction to the European hydrological system--Systeme hydrologique Europeen, 'SHE,' 1: History and philosophy of a physically-based, distributed modeling system." J. Hydrol., 87(1/2), 45-59. Cooper, T. E. (1988). "Measuring the enhancement weather radar provides a rain gauge network for streamflow forecasting," MaSc thesis, University of Waterloo, Ontario, Canada. de Roo, A. P. J., Hazelhoff, L., and Heuvelink, G. B. M. (1992). "Estimating the effects of spatial variability on infiltration of the output of a distributed runoff and soil erosion model using Monte Carlo methods." Hydrological Processes, 6, 127143. "Design and construction of sanitary and storm sewers." (1969). Manuals and Reports on Engineering Practice, No. 37, ASCE, New York, N.Y. Duchon, C. E., Salisbury, J. M., Williams, T. H. L., and Nicks, A. D. (1992). "An example of using Landsat and GOES data in a water budget model." Water Resour. Res., 28(2), 527-538. Fortin, J. P., Villeneuve, J. P., Guibot, A:, and Seguin, B. (1986). "Development of a modular hydrological forecasting model based on remotely sensed data, for interactive utilization on a microcomputer." Hydrologic applications of space technology, A. I. Johnson, ed., 307-319. Grayman, W. (1990). "GIS in water resources in the year 2000." Proc., 17th Annual Nat. Conf. of Water Resour. Planning and Mgmt. Div. of ASCE, ASCE, Apr., 111-114. Green, W. H., and Ampt, G. A. (1911). "Studies in soil physics, 1, the flow of air and water through soils." J. Agric. Sci., 4, 1-24. Hooke, R., and Jeeves, T. A. (1961). "'Direct search' solution of numerical and statistical problems." J. Assoc. Comput. Mach., 8(2), 212-229. Kite, G. W., and Kouwen, N. (1992). "A semi-distributed model for a mountain watershed." Water Resour. Res. Kouwen, N. (1988). "WATFLOOD: A micro-computer based flood forecasting system based on real-time weather radar." Can. Water Resour. J., 13(1), 62-77. Kouwen, N., and Garland, G. (1989). "Resolution considerations in using radar rainfall data for flood forecasting." Can. J. Cir. Engrg., 16,279-289. Kouwen, N., Soulis, E. D., Pietroniro, A., and Donald, J. (1990). "Flash flood forecasting with a rainfall-runoff model designed for remote sensing inputs and geographic information systems." Proc. Int. Syrup. on Remote Sensing in Water Resour., Aug., 805-814. Leavesley, G. H., and Stannard, L. G. (1990). "Application of remotely sensed data in a distributed-parameter watershed model." Proc. Workshop on Applications of Remote Sensing in Hydrol., Feb., 47-68. Link, L. E. (1983). "Compatibility of present hydrologic models with remotely sensed data." Proc., 17th Int. Syrup. on Remote Sensing of Envir. Linsley, R. K., Kohler, M. A., and Paulhus, J. L. H. (1949). Applied hydrology. McGraw-Hill, New York, N.Y., 689. Monro, J. C. (1971). Direct search optimization in mathematical modeling and a watershed application. Naef, F. (1981). "Can we model the rainfall-runoff process today?" Hydrol. Sci. Bul., 26(3). 304 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
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Philip, J. R. (1954). "An infiltration equation with physical significance." Soil Sci., 77(1), 153-157. Rawls, W. J., and Brakensiek, D. L. (1983). "A procedure to predict Green and Ampt infiltration parameters." Advances in Infiltration, Proc. Nat. Conf. on Advances in Infiltration, ASAE, Dec. 12-13, 102-112. Stall, J. B., and Terstriep, M. L. (1972). "Storm sewer design--An evaluation of the RRL method." EPA Technology Series EPA-R2-72-068, Oct. Tao, T., and Kouwen, N. (1989). "Remote sensing and fully distributed modeling for flood forecasting." J. Water Res. Plng. and Mgrnt., ASCE, 115(6), 809-823 Viessman, W., Lewis, G. L., and Knapp, J. W. (1989). Introduction to hydrology. Harper and Row, New York, N.Y. Wood, E. F., Sivapalan, M., Bevan, K., and Band, L. (1988). "Effects of spatial variability and scale with implications to hydrologic modeling." J. Hydrol., 102, 29-47. APPENDIX II.
NOTATION
The following symbols are used in this paper: A = area of basin element (m2); A X = channel cross-section area, which is related to storage by dividing storage by channel length (m2); Cp = ratio of vegetal surface area to its projected area; Ds = depression storage capacity (mm); Dt = time step of routing (s); D1 = average depth of water stored on element (mm); Ea = evaporation rate per unit per unit of surface area (mm/hr); F = total depth of infiltrated water (mm); I1,2 = channel inflow (m3/s); K = saturated conductivity (mm/sec); k = constant (1/mm); m = soil moisture content above wetting front; m0 = initial soil moisture content; O = flow (m3/s); 01,z = outflow from reach (m3/s); P = precipitation since beginning of storm; Pot = capillary potential (mm); Qr = channel inflow (m3/s); Q I N T = interflow (m3/s); R E C = coefficient (optimized); R2 = channel roughness parameter (optimized); R3 = combined roughness and channel length parameter (optimized); Si = storage capacity per unit of projected area (mm); So = chanel slope; Sl = average overland slope; $1,2 = storage in reach (m3); t = time in seconds (Philip formula); tR = duration of rainfall; V = depth of interception from beginning of storm (mm); and W A C = water accumulation in U Z S region (mm).
305 J. Water Resour. Plann. Manage., 1993, 119(3): 289-305
