99 9 Spatially Distributed Watershed Model of Water and Materials Runoff Thomas E. Croley II and Chansheng He 9.1 INTRODUCTION Agricultural nonpoint source contamination of water resources by pesticides, fertil- izers, animal wastes, and soil erosion is a major problem in much of the Laurentian Great Lakes Basin, located between the United States and Canada. Point source con- taminations, such as combined sewerage overows (CSOs), also add wastes to water ows. Soil erosion and sedimentation reduce soil fertility and agricultural productiv- ity, decrease the service life of reservoirs and lakes, and increase ooding and costs for dredging harbors and treating wastewater. Improper management of fertilizers, pesticides, and animal and human wastes can cause increased levels of nitrogen, phosphorus, and toxic substances in both surface water and groundwater. Sediment, waste, pesticide, and nutrient loadings to surface and subsurface waters can result in oxygen depletion and eutrophication in receiving lakes, as well as secondary impacts such as harmful algal blooms and beach closings due to viral and bacterial and/or toxin delivery to affected sites. The U.S. Environmental Protection Agency (EPA) has identied contaminated sediments, urban runoff and storm sewers, and agri- culture as the primary sources of pollutants causing impairment of Great Lakes shoreline waters (USEPA 2002). Prediction of various ecological system variables or consequences (such as beach closings), as well as effective management of pollution at the watershed scale, require estimation of both point and nonpoint source material transport through a watershed by hydrological processes. However, currently there are no integrated ne-resolution spatially distributed, physically based watershed- scale hydrological/water quality models available to evaluate movement of materials (sediments, animal and human wastes, agricultural chemicals, nutrients, etc.) in both surface and subsurface waters in the Great Lakes watersheds. The Great Lakes Environmental Research Laboratory (GLERL) and Western Michigan University are developing an integrated, spatially distributed, physically- based hydrology and water quality model. It is a nonpoint source runoff and water quality model used to evaluate both agricultural nonpoint source loading from soil erosion, fertilizers, animal manure, and pesticides, and point source loadings at the watershed level. GLERL is augmenting an existing physically based distributed 64142.indb 99 11/12/07 9:59:05 AM © 2008 by Taylor & Francis Group, LLC 100 Wetland and Water Resource Modeling and Assessment surface/subsurface hydrology model (their Distributed Large Basin Runoff Model) by adding material transport capabilities to it. This will facilitate effective Great Lakes watershed management decision making, by allowing identication of critical risk areas and tracking of different sources of pollutants for implementation of water quality programs, and will augment ecological prediction efforts. This paper briey reviews distributed watershed models of water and agricultural materials runoff and identies their limitations, and then presents our resultant distributed model of water and material movement within a watershed. 9.2 AGRICULTURAL RUNOFF MODELS Estimating point and nonpoint source pollutions and CSOs is critical for planning and enforcement agencies in protection of surface water and groundwater quality. During the past four decades, a number of simulation models have been developed to aid in the understanding and management of surface runoff, sediment, nutrient leaching, and pollutant transport processes. The widely used water quality mod- els include ANSWERS (Areal Nonpoint Source Watershed Environment Simula- tion) (Beasley and Huggins 1980), CREAMS (Chemicals, Runoff, and Erosion from Agricultural Management Systems) (Knisel 1980), GLEAMS (Groundwater Load- ing Effects of Agricultural Management Systems) (Leonard et al. 1987), AGNPS (Agricultural Nonpoint Source Pollution Model) (Young et al. 1989), EPIC (Erosion Productivity Impact Calculator) (Sharpley and Williams 1990), and SWAT (Soil and Water Assessment Tool) (Arnold et al. 1998) to name a few. These models all use the SCS Curve Number method, an empirical formula for predicting runoff from daily rainfall. Although the Curve Number method has been widely used worldwide, it is an event-based (storm hydrograph) method not really suitable for continuous simula- tions. Researchers have expressed concern that it does not reproduce measured run- off from specic storm rainfall events because the time distribution is not considered (Kawkins 1978; Wischmeier and Smith 1978; Beven 2000; Garen and Moore 2005). Limitations of the Curve Number method also include (1) no explicit account of the effect of the antecedent moisture conditions in runoff computation, (2) difcul- ties in separating storm runoff from the total discharge hydrograph, and (3) runoff processes not considered by the empirical formula (Beven 2000; Garen and Moore 2005). Consequently, estimates of runoff and inltration derived from the Curve Number method may not well represent the actual. As sediment, nutrient, and pesti- cide loadings are directly related to inltration and runoff, use of the Curve Number method may also result in incorrect estimates of nonpoint source pollution rates. Due to the limitations of the Curve Number method, ANSWERS, CREAMS, GLEAMS, AGNPS, and SWAT were developed to assess impacts of different agri- cultural management practices, not to predict exact pesticide, nutrient, and sediment loading in a study area (Ghadiri and Rose 1992; Beven 2000; Garen and Moore 2005). In addition, most water quality models, such as CREAMS and GLEAMS, are eld-size models and cannot be used directly at the watershed scale. Applications of these models have been limited to eld-scale or small experimental watersheds. Some models, such as ANSWERS, CREAMS, EPIC, and AGNPS, also do not con- sider subsurface and groundwater processes. 64142.indb 100 11/12/07 9:59:05 AM © 2008 by Taylor & Francis Group, LLC Spatially Distributed Watershed Model of Water and Materials Runoff 101 Recently, several water quality models have been modied to take into consider- ation available multiple physical and agricultural databases. The USEPA designated two of the most widely used water quality models, SWAT and HSPF (Hydrologic Simulation Program in FORTRAN) (Bicknell et al. 1996), for simulation of hydrol- ogy and water quality nationwide. SWAT is a comprehensive watershed model and considers runoff production, percolation, evapotranspiration, snowmelt, channel and reservoir routing, lateral subsurface ow, groundwater ow, sediment yield, crop growth, nitrogen and phosphorous, and pesticides. But it uses the curve number method for estimating runoff, and therefore has the same limitations the curve num- ber method has in runoff simulation. The basic simulation unit in SWAT is the sub- watershed, instead of a ne-resolution grid network, thus limiting its incorporation of spatial variability in simulating hydrologic processes. Evolved from the Stanford Watershed Model (Crawford and Linsley 1966), HSPF is one of the most extensively used general hydrologic and water quality mod- els (Bicknell et al. 1996). Under the auspices of the USEPA, the rst version of the HSPF was completed in 1980. Since then, the model has gone through extensive revisions, corrections, renements, and validations in many areas, and is one of the three simulation models included in BASINS (Better Assessment Science Integrat- ing Point and Nonpoint Sources), the USEPA’s watershed modeling tools for support of water quality management programs throughout the country (Lahlou et al. 1998). HSPF utilizes time series meteorology data to simulate hydrological processes in both pervious and impervious land segments. The hydrological processes in the model include accumulation and melting of snow and ice, water budget, sediment transport, soil moisture, and temperature. The water quality modules of the model include concentration and transport of nitrogen, phosphorus, pesticides, and other pollutants. However, HSPF requires extensive input parameters such as wind speed, dew point temperature, potential evapotranspiration, and channel characteristics. Many of these parameters are not available in most watersheds, particularly large watersheds. In addition, HSPF is a semidistributed model since a basin is divided into lumped-parameter model applications to subbasins and land parcels to coarsely represent spatial variations of rainfall and land surface. Moreover, neither SWAT nor HSPF considers nonpoint sources from animal manure and CSOs and infectious diseases. Thus, there is an urgent need for the development of a spatially distributed, physically based watershed model that simulates both point and nonpoint source pol- lutions in the Great Lakes Basin. 9.3 DISTRIBUTED LARGE BASIN RUNOFF MODEL GLERL developed a large basin runoff model in the 1980s for estimating daily rainfall/runoff relationships on each of the 121 large watersheds surrounding the Laurentian Great Lakes (Croley 2002). It is physically based to provide good rep- resentations of hydrologic processes and to ensure that results are tractable and explainable. It is a lumped-parameter model of basin outow consisting of a cascade of moisture storages or “tanks,” each modeled as a linear reservoir, where tank out- ows are proportional to tank storage. We applied it to a 1-km 2 “cell” of a watershed and modied it to allow lateral ows between adjacent cells for moisture storage; see 64142.indb 101 11/12/07 9:59:06 AM © 2008 by Taylor & Francis Group, LLC 102 Wetland and Water Resource Modeling and Assessment Figure 9.1. By grouping cell applications appropriately, we built a spatially distrib- uted accounting of moisture in several layers (zones), the distributed large basin run- off model (DLBRM). Daily precipitation, air temperature, and insolation (the latter available from cloud cover and meteorological summaries as a function of location and time of the year) may be used to determine snowpack accumulations, snowmelt (degree-day computations), and supply, s, into the upper soil zone. Water ow, u, also enters from upstream cells’ upper soil zones. The total supply is divided into sur- Supply, s α g G (s+u) U C Snow Pack Melt, m Runoff Snow Rain Insolation Precipitation Temperature Evapotranspiration, β ℓ e p L Upstream, ℓ Downstream, α ℓ L Evapotranspiration, β u e p U Upstream, u Downstream, α u U Evapotranspiration, β g e p G Upstream, g Downstream, α w G Evaporation, β s e p S Upstream, h Downstream, α s S Surface Runoff Interflow Ground Water Percolation, α p U Deep Percolation, α d L Upper Soil Moisture, U Lower Soil Moisture, L Groundwater Moisture, G Surface Moisture, S α i L FIGURE 9.1 Model schematic for one cell. 64142.indb 102 11/12/07 9:59:06 AM © 2008 by Taylor & Francis Group, LLC Spatially Distributed Watershed Model of Water and Materials Runoff 103 face runoff, s u U C+ ( ) , and inltration to the upper soil zone, s u U C+ ( ) − ( ) 1 , in relation to the upper soil zone moisture content, U, and the fraction it represents of the upper soil zone capacity, C (variable area inltration). Percolation to the lower soil zone, a p U, evapotranspiration, b u e p U, and lateral ow to a downstream upper soil zone, a u U, are taken as outows from a linear reservoir (ow is proportional to storage). Likewise, water ow, ,, enters the lower soil zone from upstream cells’ lower soil zones. Interow from the lower soil zone to the surface, a i L, evapotrans- piration, b , e p L, deep percolation to the groundwater zone, a d L, and lateral ow to a downstream lower soil zone, a , L, are linearly proportional to the lower soil zone moisture content, L. Water ow, g, enters the groundwater zone from upstream cells’ groundwater zones. Groundwater ow, a g G, evapotranspiration from the ground- water zone, b g e p G, and lateral ow to a downstream groundwater zone, a w G, are linearly proportional to the groundwater zone moisture content, G. Finally, water ow, h, enters the surface zone from upstream cells’ surface zones. Evaporation from the surface storage, b s e p S, and lateral ow to a downstream surface zone, a s S, are linearly proportional to the surface zone moisture, S. Additionally, evaporation and evapotranspiration are dependent on potential evapotranspiration, e p , as determined independently from a heat balance over the watershed, appropriate for small areas. The alpha coefcients (a) represent linear reservoir proportionality factors and the beta coefcients (b) represent partial linear reservoir coefcients associated with d dt U s u s u U C U U e U p u u p = + − + ( ) − − −α α β (9.1) d dt L U L L L e L p i d p = − − − + −α α α α β , , , (9.2) d dt G L G G g e G d g w g p = − − + −α α α β (9.3) d dt S s u U C L G S h e S i g s s p = + ( ) + + − + −α α α β (9.4) Solution Consideration of equations (9.1)–(9.4) reveals multiple analytical solutions; while tractable, a simpler approach uses a numerical solution based on nite difference approximations of equations (9.1)–(9.4). Consider equation (9.1) approximated with nite differences, ∆ ∆ ∆U s u t s u C e U t p u u p ≅ + ( ) − + ( ) + + + α α β (9.5) 64142.indb 103 11/12/07 9:59:10 AM evapotranspiration. From Figure 9.1, © 2008 by Taylor & Francis Group, LLC 104 Wetland and Water Resource Modeling and Assessment where ΔU = change in upper soil zone moisture storage over time interval Δt, s , u , and e p = average supply, upstream inow, and potential evapotranspiration rates, respectively, over time interval Δt, and U = average upper soil zone moisture storage over time interval Δt. By taking ΔU = U – U 0 (where U 0 and U are beginning-of- and end-of-time-interval storages, respectively) and U U≅ , equation (9.5) becomes U U s u t s u C e t p u u p ≅ + + ( ) + + + + + 0 1 ∆ ∆α α β (9.6) Equation (9.6) is good for small Δt and as ∆t → 0 , equation (9.6) approaches the true solution (converges) to equation (9.1). Likewise, using similarly dened terms, equations (9.2)–(9.4) become L L U t e t p i d p ≅ + + ( ) + + + + ( ) 0 1 α α α α β ∆ ∆ (9.7) G G L g t e t d g w g p ≅ + + ( ) + + + ( ) 0 1 α α α β ∆ ∆ (9.8) S S s u C U L G h t e t i g s s p ≅ + + + + + + + ( ) 0 1 α α α β ∆ ∆ (9.9) As equations (9.6)–(9.9) are used over time interval Δt, end-of-time-interval values are computed from beginning-of-time-interval values (e.g., U from U 0 ). These end- of-time-interval values for one time interval become beginning-of-time-interval val- ues for the subsequent time interval. Each cell’s inow hydrographs must be known before its outow hydrograph can be modeled; therefore we arranged calculations in a ow network to assure this. It is determined automatically from a watershed map of cell ow directions. The ow network is implemented to minimize the number of pending hydrographs in computer storage and the time required for them to be in computer storage. We used the same network for surface, upper soil, lower soil, and groundwater storages. We implemented routing network computations as a recursive routine to compute out- ow, which calls itself to compute inows (which are upstream outows) (Croley and He 2005, 2006). 9.3.1 APPLICATION We have discretized 18 watersheds to date. The elevation map for the Kalamazoo tions taken from a 30-m digital elevation model (DEM) available from the United 64142.indb 104 11/12/07 9:59:15 AM River watershed in southwestern Michigan is shown in Figure 9.2. We used eleva- © 2008 by Taylor & Francis Group, LLC Spatially Distributed Watershed Model of Water and Materials Runoff 105 States Geological Survey (USGS). We also used USGS land cover characteristics and the U.S. Department of Agriculture State Soil Geographic Database to add land cover, upper and lower soil zone parameters (depth, actual water content, and perme- we used gradient search techniques to minimize root mean square error between modeled and actual basin outow by selecting the best spatial averages for each of the eleven parameters; the spatial variation of each parameter follows a selected watershed characteristic, as shown here and arrived at by experimentation. α α p i p i U f K ( ) = ( , %)80 (9.10) β β u i u i U f K ( ) = ( , %)80 (9.11) α α i i i i L f K ( ) = ( , %)80 (9.12) α α d i d i L f K ( ) = ( , %)80 (9.13) β β ( ) = i i L f K( , %)80 (9.14) α α g i g i L f K ( ) = ( , %)80 (9.15) α α η s i s i i f s ( ) = , %80 (9.16) α α u i u i U f K ( ) = ( , %)80 (9.17) α α ( ) = i i L f K( , %)80 (9.18) α α w i w i L f K ( ) = ( , %)80 (9.19) Saugatuck, Michigan, USA 86° 13´ W. Lon. 42° 40´ N. Lat. 612 km east-west 332 km north-south N 180.00 360.00 FIGURE 9.2 Kalamazoo watershed elevations (m). 64142.indb 105 11/12/07 9:59:20 AM ability), soil texture, and surface roughness; see Croley et al. (2005). In application, © 2008 by Taylor & Francis Group, LLC 106 Wetland and Water Resource Modeling and Assessment C C f C i i U ( ) = ( , %)80 (9.20) f x x n x i i j j n ( , ) % ε ε = − + = ∑ 1 1 100 1 1 (9.21) where α • ( ) i = linear reservoir coefcient for cell i, α • = spatial average value of the linear reservoir coefcient (from parameter calibration), β • ( ) i and β • are dened similarly for partial linear reservoir coefcients (used in evapotranspiration), C i ( ) and C are dened similarly for the upper soil zone capacity, K i U = upper and K i L = lower soil zone permeability in cell i, s i = slope of cell i, η i = Manning’s roughness coefcient for cell i, C i U = upper soil zone available water capacity, x i = data value for cell i, and n = number of cells in the watershed. Note two parameters not shown here, which govern the heat balance used for snow- melt and potential evapotranspiration, are taken as spatially constant over the water- shed. Also, the partial linear reservoir coefcients for the groundwater and surface zones are taken as zero, ignoring evapotranspiration from those two zones. Thus there are 13 parameters (of a possible 15) searched in the calibration. To speed up calibrations, we preprocessed all meteorology for all watershed cells and preloaded it into computer memory. The correlation between modeled and observed watershed outows was 0.88, the root mean square error was 0.19 mm/d (compare with a mean ow of 0.78 mm/d); the ratio of modeled to actual mean ow was 1.00, and the ratio of modeled to actual ow standard deviation was 0.87 (Croley and He 2006). We used the model to look at modeling alternatives, including alternative evapo- transpiration calculations, spatial parameter patterns, and solar insolation estimates. We also explored scaling effects in using lumped parameter model calibrations to calculate initial distributed model parameter values (Croley and He 2005; Croley et al. 2005). 9.3.2 TESTING As a test of equations (9.6)–(9.9), we used them for Δt = 1.5 minutes to approxi- mate the solution of equations (9.1)–(9.4) over about 17 years of daily values for the Maumee River watershed (Croley and He 2006) and found them identical (in all variables) through three signicant digits (all that were inspected) with the exact analytical solution. For Δt = 15 minutes, the solution was nearly identical with only an occasional difference of one in the third signicant digit. As the Mau- mee River watershed has a very “ashy” response to precipitation (very fast upper soil and surface storage zones) these comparisons are deemed signicant and the time intervals should be more than adequate for the slower response of lower soil and groundwater zones (the Maumee application has no lower soil or groundwater zones). 64142.indb 106 11/12/07 9:59:25 AM © 2008 by Taylor & Francis Group, LLC Spatially Distributed Watershed Model of Water and Materials Runoff 107 9.4 MATERIALS RUNOFF MODEL Consider now the addition of some material or pollutant dissolved in, or carried by, Figure 9.3. At any time, let the concentration of this conservative pollutant in the inow u be c u and in the supply s be c s . If these ows do not mix together, then the fraction U/C of each of these ows runs off directly (without even entering the upper soil zone) and the surface runoff of pollutant is sc uc U C s u + ( ) . If the concentra- tion in the upper soil zone moisture storage U is c U , then the percolating pollutant is a p Uc U and the lateral pollutant ow downstream to the next cell’s upper soil zone is a u Uc U . Taking pollutant movement with evaporation as zero, mass continuity (of the pollutant) gives: d dt Uc sc uc sc uc U C Uc Uc U s u s u p U u U ( ) = + − + ( ) − −α α (9.22) or d dt U s u s u U C U U c c c c c p c u c = + − + ( ) − −α α (9.23) where s c = sc s , u c = uc u , and U c = Uc U . s c U c L c G c S c α i L c α g G c α s S c α p U c α d L c h c u c α u U c α ℓ L c (s c +u c ) U C α w G c g c ℓ c FIGURE 9.3 Distributed “pollutant” ows schematic for a single cell. 64142.indb 107 11/12/07 9:59:27 AM the water ows in Figure 9.1, except that none is considered to be evaporated; see © 2008 by Taylor & Francis Group, LLC 108 Wetland and Water Resource Modeling and Assessment Likewise from Figure 9.3, mass continuity of the pollutant gives: d dt L U L L L c p c i c d c c c = − − − +α α α α (9.24) d dt G L G G g c d c g c w c c = − − +α α α (9.25) d dt S s u U C L G S h c c c i c g c s c c = + ( ) + + − +α α α (9.26) where L c , G c , and S c are the amounts of pollutant in the lower soil zone, the ground- water zone, and surface storage, respectively, and , c , g c , and h c are the upstream pollutant ows from the lower soil zone, the groundwater zone, and surface storage, respectively. Solution Similar to the numerical solution of equations (9.1)–(9.4) [(9.6)–(9.9)], the numerical solution for equations (9.23)–(9.26) becomes U U s u t s u U C t t c c c c c c p u ≅ + + ( ) − + ( ) + + ( ) 0 1 ∆ ∆ ∆α α (9.27) L L U t t c c p c c i d ≅ + + ( ) + + + ( ) 0 1 α α α α ∆ ∆ (9.28) G G L g t t c c d c c g w ≅ + + ( ) + + ( ) 0 1 α α α ∆ ∆ (9.29) S S s u C U L G h t t c c c c i c g c c s ≅ + + + + + + 0 1 α α α ∆ ∆ (9.30) where terms are dened for material ows in a manner similar to that for water ows. We used the same network for surface, upper soil, lower soil, and groundwater storage of pollutant as we used for water ows. 9.4.1 INITIAL AND BOUNDARY CONDITIONS Suppose a pollutant deposit P exists on top of the upper soil zone. Precipitation or snowmelt on top of this deposit will produce a supply s to the upper soil zone that 64142.indb 108 11/12/07 9:59:31 AM © 2008 by Taylor & Francis Group, LLC [...]... Water Resource Modeling and Assessment Lahlou, N., L Shoemaker, S Choudhury, R Elmer, A Hu, H Manguerra, and A Parker 199 8 BASINS V.2.0 user’s manual Washington, DC: U.S Environmental Protection Agency Office of Water, EPA-823-B -9 8-0 06 Leonard, R A. , W G Knisel, and D A Still 198 7 GLEAMS: Groundwater loading effects of agricultural management systems Transactions of ASAE 30:1403–1418 Sharpley, A N., and. .. Spatially Distributed Watershed Model of Water and Materials Runoff 111 employing a numerical solution instead of the analytical solution used in the original lumped-parameter water balance model, we are able to easily represent the mass balance of both water and an arbitrary conservative pollutant spatially throughout all storage zones in the watershed Model testing reveals that the numerical solution converges... over a two-month simulation, demonstrating that the model could be used to simulate real-world material movement in a watershed ACKNOwLEDGmENTs This is GLERL Contribution No 1375 REfERENCEs Arnold, G., R Srinavasan, R S Muttiah, and J R Williams 199 8 Large area hydrologic modeling and assessment Part I: Model development Journal of the American Water Resources Association 34: 73– 89 Beasley, D B., and. .. very coarse spatial discretizations of the watershed We adapted an existing lumped-parameter conceptual water balance model of watershed hydrology into a spatially distributed model of runoff It employs moisture storage in the upper and lower soil zones, in a groundwater zone, and on the surface, with lateral flows from all storages into similar storages in adjacent grid cells defined over the watershed. .. FiGURE 9. 4 Kalamazoo model lateral flows (cm/d) d istributed agricultural runoff models and learned that there are no integrated spatially distributed, physically based watershed- scale hydrological /water quality models available to evaluate movement of materials in both surface and subsurface waters Either the hydrology is limited to very simple empirical descriptions or the application is made to only... to the analytical solution for a 1-km2 grid on a watershed with a very fast response By assigning initial pollutant surface amounts and introducing a single parameter (pollutant concentration in water) , we can model its movement In a simple example on the Kalamazoo River watershed, in which a uniform layer of pollutant is assumed initially, we present the consecutive spatial distributions that occur... varying site moisture Journal of the Irrigation and Drainage Division 104: 3 89 398 Knisel, W G 198 0 CREAMS: A fieldscale model for chemical, runoff, and erosion from agricultural management systems, Conservation Report No 26 Washington, DC: U.S Department of Agriculture, Science and Education Administration © 2008 by Taylor & Francis Group, LLC 64142.indb 111 11/12/07 9: 59: 34 AM 112 Wetland and Water. .. watershed By applying the surface drainage network to all storage lateral flows, we can trace the movement of water throughout the watershed We further adapt the distributed model to incorporate the storage and movement of an arbitrary material, conservative in nature, and to trace its movement throughout the watershed By © 2008 by Taylor & Francis Group, LLC 64142.indb 110 11/12/07 9: 59: 34 AM Spatially Distributed... Journal of Hydrologic Engineering 10: 182– 191 Garen, D C., and D S Moore 2005 Curve number hydrology in water quality modeling: uses, abuses, and future directions Journal of the American Water Resources Association 41: 377–388 Ghadiri, H., and C W Rose 199 2, Modeling chemical transport in soils: Natural and applied contaminants Ann Arbor, MI: Lewis Publishers Kawkins, R H 197 8 Runoff curve number relationships... of day 1) and the increased surface water flow; the surface pollutant map shows extensive response The surface response then drops off as pollutant is only available in the USZ and GWZ However, on 15 January, the surface pollutant response increases with the flush of water through the USZ that occurs then (see third row in columns 3 and 4 in Figure 9. 4) 9. 6 SUmmaRY Prediction and management of watershed . lumped-parameter water balance model, we are able to easily represent the mass balance of both water and an arbitrary conservative pollutant spatially throughout all storage zones in the watershed. . the watershed. Note two parameters not shown here, which govern the heat balance used for snow- melt and potential evapotranspiration, are taken as spatially constant over the water- shed. Also,. evapotranspiration, and channel characteristics. Many of these parameters are not available in most watersheds, particularly large watersheds. In addition, HSPF is a semidistributed model since a