## Literature Review:

Comparison of Common Watershed Models for Rainfall, Runoff Sediment Transport, and Contaminant Transport and F ate

Prepared By:

HydroQual, Inc. 1200 MacArthur Boulevard Mahwah, New Jersey 07436 United States

November 2010

### ACKNOWLEDGEMENTS

This report was prepared by Mark Velleux, Masatsugu (Masa) Takamatsu, and Lihong (Lucy) Yang. Portions of this report were derived f rom earlier works completed at Colorado State University. The ongoing support of D r. Pierre Julien (Colorado State University) is gratefully acknowledged.

### LITERATURE REVIEW

TREX is a spatially distributed, physically-based m odel to simulate hydrology, sediment transport, and chemical transport and fate at the w atershed scale (Velleux et al. 2008). It

has been used to simulate runoff and sediment trans port in mountain watersheds as well as extreme floods (Velleux et al. 2006; England et al. 2007). Brief overviews of watershed model frameworks are presented to give a context to the research that lead to TREX development and how TREX can be used to simula te a wide range of watershed

conditions.

WATERSHED MODEL FRAMEWORKS A range of watershed modeling methods and framework s exist. Methods include unit hydrograph/lumped parameter, advanced lumped parame ter/semi-distributed, and fully distributed, physically based approaches. 1 Singh (1995) presents descriptions of numerous watershed models. Each approach has charac teristic strengths and limitations and there are tradeoffs between the spatial and tem poral detail used to represent physical processes and model performance. Although methods u sed differ, all model frameworks reviewed have the ability to simulate runoff. Some frameworks can simulate soil erosion.

A few frameworks can also simulate stream sediment transport (erosion and deposition) processes. A small number of frameworks have specia lized capabilities such as the ability to simulate chemical transport.

TR-55, HEC-1, and HEC-HMS Unit hydrograph/lumped parameter models such as TR- 55 (USDA, 1986; USDA 2009), HEC-1 (USACE, 1998), and HEC-HMS (USACE, 2010) simu late watershed runoff. However, physical processes that generate runoff ar e represented in a simplified manner. For example, runoff is calculated using an empirica l curve number approach rather than

1 Absolute distinctions between approaches are somew hat subjective. For example, lumped parameter models that can treat a watershed as a number of su b-basins can be considered equivalent to semidistributed models while fully distributed models w ith limited spatial variation of parameters can approach the performance of lumped parameter models

.physically-based equations that use conservation of mass principles to relate precipitation

and infiltration rates to resultant runoff. In the case of TR-55, the maximum watershed

area that can be simulated is limited to a maximum of 65 km 2 (6,500 hectares; 25 mi 2 ). In addition, these simple frameworks do not permit the extent of model parameter variation that is needed to account for the wide range of lan dscape and soil property variations that occur in complex watersheds. Importantly, these fra meworks cannot simulate soil erosion and stream sediment transport.

1.1.1 HSPF HSPF (Hydrologic Simulation Program–Fortran) (Johan son et al. 1980; Donigian et al. 1984; Bicknell et al. 1997; Bicknell et al. 2001) h as its origins in the Stanford Watershed Model (Crawford and Linsley, 1966) and can be class ified as an advanced lumped parameter or semi-distributed model. Among its proc esses and state variables, HSPF simulates interception, infiltration, soil moisture , surface runoff, interflow, base flow, snowpack depth and water content, snowmelt, evapotr anspiration, groundwater recharge, dissolved oxygen (DO) and biochemical oxygen demand (BOD), temperature, pesticides, fecal coliform bacteria, sediment detachment and tr ansport, sediment routing by particle size, channel routing, reservoir routing, constitue nt routing, pH, nitrogen and phosphorus compounds, and plankton. Hydrologic processes are r epresented as flows and storages. Routing is performed using a modified form of the k inematic wave equation. Generally, flow is a one-dimensional outflow from storage, exp ressed as a function of the present storage amount and the physical characteristics of the subsystem. Although the overall model is physically based, many of the flows and st orages are represented in a simplified or conceptual manner. This requires use of calibrat ed parameters but has the advantage of avoiding the need to explicitly specify all physica l dimensions and characteristics of the flow system.

HSPF has been used for a wide variety of spatial sc ales from the Chesapeake Bay watershed (160,000 km 2 ) to small (a few acres) experimental plots near Wa tkinsville, Georgia. The model is best used for continuous simu lation of hydrology and water quality in watersheds. To simulate chemical transpo rt, HSPF incorporates the watershedscale NonPoint Source (NPS) (Donigian and Crawford, 1976a) Agricultural RunoffManagement (ARM) (Donigian and Crawford, 1976b; Don igian et al. 1977), and

Sediment and Radionuclides Transport (SERATRA) (Oni shi and Wise, 1979) models into a framework that includes fate and transport i n one dimensional stream channels. HSPF simulates three sediment types (sand, silt, an d clay) in addition to a single organic chemical and transformation products of that chemic al. However, it does not simulate metals. HSPF (Version 11.0) source code is publicly available.

KINEROS KINEROS (Kinetic Runoff and Erosion) (Woolhiser et al. 1990) is a semi-distributed, physically based, event-oriented model that simulat es rainfall, interception, infiltration,

surface runoff and erosion. A rainfall record is us ed to describe the spatial and temporal

distribution of rainfall to simulate runoff for a c atchment. A watershed is represented by a (cascading) series of planes and channels (open cha nnels or pipes). The kinematic wave approximation and the Manning equation are used for one-dimensional flow routing. Infiltration is determined using the Smith-Parlange (1978) equation. KINEROS does not include groundwater flow processes other than infil tration and overland flow is Hortonian. Erosion overland is represented by splas h and hydraulic rate components and a transport capacity relation of the form summarize d by Julien and Simons (1985), such as tractive force (Meyer and Wischmeier, 1969), uni t stream power (Yang, 1973), Ackers and White (1973), and Engelund and Hansen (1967). E rosion in channels is similar with the exception that splash erosion is neglected and lateral inflow is not. Deposition is computed from particle fall velocity for the partic le concentration in excess of the concentration computed from the transport capacity equation. Sediment transport is represented for a single effective grain size (d 50 ) that can vary by element in the model domain. KINEROS (Version 2) source code is publicly available.

SWAT SWAT (Soil and Water Assessment Tool) (Neistch et a l. 2002) is an advanced lumped/semi-distributed, physically based, continuo us simulation model that simulates rainfall, infiltration, flow routing through basin streams and reservoirs (including lateral flow, groundwater flow, and transmission losses), a nd sediment and chemical transport through ponds, reservoirs, and streams. Simulated w atersheds can be divided into sub-basins or hydrologic response units. SWAT was devel oped to predict the impact of land

management practices on water, sediment and agricul tural chemical yields in large complex watersheds with varying soils, land use and management conditions over long periods of time. Major components model include wea ther, hydrology, erosion, soil temperature, crop growth, nutrients, pesticides, su bsurface flow, and agricultural management. Instream chemical transport in SWAT is based on algorithms adapted from the QUAL2E (Brown and Barnwell, 1987) stream water quality model and includes firstorder decay relationships for algae, dissolved oxyg en (DO), carbonaceous biochemical oxygen demand (CBOD), as well as nitrogen and phosp horus compounds. However, it does not simulate metals. Bian et al. (1996) linked SWAT with the Arc/Info geographic information system (GIS).

Soil profiles can be divided into ten layers. Infil tration is computed as precipitation minus runoff (SCS curve number approach) or using the Gre en and Ampt (1911) relationship. Infiltration moves into the soil profile and is rou ted through the soil layers. A storage routing coefficient is used to compute flow through each layer, with flow occurring when a layer exceeds field capacity. When water percolat es past the bottom layer of the soil profile, it enters the shallow aquifer zone (Arnold et al. 1993). Channel transmission losses and pond/reservoir seepage replenish the sha llow aquifer layer, which can interact directly with the stream. Flow to the deep aquifer system is lost and cannot return (Arnold et al. 1993). An irrigation algorithm allow s water transfers from any reach or reservoir to any other in the watershed. Based on s urface runoff calculated using the SCS runoff equation, excess surface runoff not lost to other pathways is delivered to the

channel network and is routed downstream. Sediment erosion for stream transport is determined with the Modified Universal Soil Loss Eq uation (MUSLE) (Williams, 1975). For sediment routing, deposition is based on fall v elocities for various sediment sizes. Channel degradation rates are determined using the Bagnold (1977) stream power equation. Sediment size is estimated from the prima ry particle size distribution (Foster et al. 1980) for soils the described in the STATSGO da tabase (USDA, 1991). Stream power is also used in the sediment routing routine to cal culate re-entrainment of loose and deposited material in the system until all of the m aterial has been removed. SWAT is a continuous time (long-term yield) model and is not designed to simulate detailed, single-event flood routing (Neistch et al. 2002). SWAT (Ve rsion 2000) source code is publicly

available.

SHETRAN and MIKE SHE SHETRAN (Ewen et al. 2000; Ewen et al. 2002) has it s origins in the Système Hydrologique Europèen (SHE) (Abbott et al. 1986a,b) and is a fully-distributed, physically-based model. Among its processes and sta te variables are interception, infiltration, surface runoff, groundwater flow in s aturated and unsaturated zones including aquifers, snowpack and snowmelt, evapotra nspiration, channel transmission losses, sediment erosion and deposition for multipl e particle classes, and chemical transport and fate including advection, dispersion, erosion, deposition, partitioning, and decay. For surface waters, flow routing is performe d using the diffusive wave approximation and is two-dimensional overland and o ne-dimensional in channels. For the subsurface, flow is variably saturated and three-di mensional.

SHETRAN can be applied to a wide variety of spatial scales from large (2,500 km 2 ) contiguous river basins with multiple sub-basins, t o single or partial watersheds, to individual hillslopes and catchments (0.94 km 2 ) (Bathurst et al. 2004). However, most applications summarized in the literature are for s mall catchment areas (<2 km 2 ). Sediment transport processes in SHETRAN are derived from those in the earlier SHESED framework (Wicks and Bathurst, 1996). Overla nd erosion is computed based on raindrop impact and hydraulic erosion rates simi lar to the approach used in KINEROS. Channel erosion is computed using the Acke rs and White (1973), Engelund and Hansen (1967), and Day (1980) (a modification t o the Ackers and White approach) methods. Unfortunately, SHETRAN model source code i s not publicly available.

MIKE SHE is a commercial software package that is l icensed and distributed by DHI (2007). It is based on the SHE family of watershed model frameworks. In concept, MIKE SHE allows simulation of the full suite of hydrolog ic processes in a spatially-distributed, physically-based modeling system. The basic framewo rk includes MIKE SHE WM (Water Movement). Additional add-on modules are ava ilable to simulate soil erosion and water quality, including: SE (soil erosion), AD (ad vection and dispersion of solutes), GC (geochemical processes), and CN (crop growth and ni trogen processes in the root zone).Because it is commercial software, MIKE SHE has a v ery high initial purchase price

(approximately $13,000 to $22,000 USD) with additio nal annual licensing fees. Add-on modules increase initial purchase and annual licens ing costs.

SMDR SMDR (Soil Moisture Distribution and Routing) is a spatially-distributed, physicallybased model designed to simulate the location and s patiotemporal evolution of variable source areas that generate saturation excess runoff (SER) (Cornell, 2003). SER occurs when the topmost soil layer becomes saturated and w ater cannot infiltrate. This process is believed to be an important flow-generating process in humid, well-vegetated regions that have steep to moderate slope terrains with shallow, high infiltration capacity soils. SMDR uses daily precipitation as input and includes snow melt and evapotranspiration as model processes. Drainage (vertical) in soil layers is ca lculated using the 1-D Richards equation in which hydraulic conductivity varies as a functio n of water content and where capillary effects are neglected. Subsurface (lateral) flow in soil layers is calculated using Darcy’s Law in which transmissivity varies over time as a f unction of water saturation in each soil layer. However, surface runoff routing is not physi cally based; overland flow is assumed

to move from each cell where runoff occurs to the w atershed outlet in a single time step (Cornell, 2003; Veith et al. 2003). This overland f low routing approach neglects physical processes such as depression storage, the possibili ty of infiltration along the runoff flow path, and overland flow resistance (Veith et al. 20 03).

CASC2D CASC2D (including CASC2D-SED) (Julien and Saghafian , 1991; Julien et al. 1995; Johnson et al. 2000; Ogden and Julien, 2002; Rojas, 2002; Julien and Rojas, 2002) is a fully distributed, physically based, event-oriented model that simulates rainfall, interception, infiltration, overland flow, channel flow, as well as sediment erosion and deposition. For surface waters, flow routing is per formed using the diffusive wave approximation and is two-dimensional overland and o ne-dimensional in channels. CASC2D does not include groundwater flow processes other than infiltration and overland flow is Hortonian. However, it can be dire ctly coupled with GIS-based site characterization data obtained from remote sensing sources.CASC2D has been applied at a wide variety of spatia l scales from large river basins

(12,000 km 2 ) to moderate watersheds (560 km 2 ) (Molnár and Julien, 2000) to small watersheds (20-30 km 2 ) (Rojas, 2002). Overland erosion is computed using a modified form of the Kilinc-Richardson (1973) method (Johnso n et al. 2000). Channel erosion is computed using the Engelund and Hansen (1967) metho d. Up to three solids classes can be simulated (Rojas, 2002). Chemical transport and fate is not simulated. CASC2 D source code is publicly available.

GSSHA GSSHA (Gridded Surface/Subsurface Hydrologic Analys is) is a spatially-distributed, physically-based hydrologic model (Downer and Ogden , 2004). It is derived from CASC2D. GHSSA simulates stream flow generated by bo th infiltration-excess (rainfallexcess) and saturation-excess mechanisms, as well a s exfiltration and groundwater discharge to streams. To represent these additional flow-generating mechanisms, GHSSA includes hydrologic processes beyond those found in CASC2D. A 1-D (vertical) headbased form of Richards Equation (Richards, 1931) is used to represent downward water movement through the vadose (unsaturated) zone and a 2-D (lateral) free surface (unconfined) groundwater model to represent water m ovement in the saturated zone. This

allows the rise and fall of the water table to be s imulated and coupled to infiltration at the land surface. Groundwater exfiltration and discharg e to streams are calculated using Darcy’s Law. Sediment transport capabilities implem ented in GSSHA are essentially the same as those in CASC2D (Downer and Ogden, 2008). A nutrient submodel to permit simulation of nitrogen, phosphorus, and carbon cycl ing also exists (Johnson and Gerald, 2006). However, source code for GSSHA is not public ly available.

TREX TREX (Two-dimensional Runoff, Erosion, and Export) is a spatially-distributed, physically-based model that can be used to simulate precipitation, overland runoff, channel flow, soil erosion, stream sediment transpo rt and chemical transport and fate at the watershed scale (Velleux et al. 2008; England e t al. 2007; Velleux et al. 2006; Velleux, 2005). TREX combines surface hydrology and sediment transport features from the CASC2D watershed model (Johnson et al. 2000; Ro jas, 2002; Julien and Rojas, 2002)with chemical transport features from the WASP/IPX series of water quality models

(Ambrose et al. 1993; Velleux et al. 2001).

Hydrologic processes simulated are: (1) rainfall an d snowfall (precipitation), interception, snowmelt, and surface storage; (2) infiltration and transmission loss; and (3) overland and channel flow. Model state variables are water depth in the overland plane and stream channels. Precipitation can be uniform or distribut ed in both time and space and can also be specified using several grid-based formats to fa cilitate radar precipitation data use. When spatially distributed precipitation is simulat ed, areal estimates are interpolated from point gage data using an inverse distance weig hting approach. Interception and surface storage are simulated as equivalent depths. Infiltration and transmission loss rates are simulated using the Green and Ampt (1911) relat ionship. Overland flow is twodimensional and simulated using the diffusive wave approximation. Channel flow is onedimensional and is also simulated using the diffusi ve wave approximation.

Sediment transport processes simulated are: (1) adv ection-diffusion; (2) erosion and deposition; and (3) bed elevation adjustment. All p rocesses are simulated in the overland plane and stream channels. Model state variables ar e solid concentrations in overland runoff, soil, stream flow, and stream bed sediment. Any number of particle size classes

can be simulated.

Chemical transport and fate processes simulated are : (1) chemical partitioning and phase distribution; (2) advection-diffusion; (3) erosion and deposition; (4) infiltration and transmission loss; and (5) mass transfer and transf ormation (chemical reactions). Model

state variables are chemical concentrations in over land runoff, soil, stream flow, and stream bed sediment. Any number of chemicals can be simulated.

In floodplain areas, water and transported constitu ents are transferred between the overland plane and channel network based on the dif ference in water surface elevations. Floodplain transfers are bi-directional. Water and transported sediments and chemicals move into stream channels by overland flow and can return to the overland plane when water levels in the stream exceed bank heights. Sim ilarly, materials can be moved from

the sediment bed and can be delivered to the land s urface by floodwaters.TREX source code, a user manual, reference material , and example files are freely

available and can be downloaded from the following URL:

http://www.engr.colostate.edu/~pierre/ce_old/Project s/TREX%20Web%20Pages/TREXHome.html

### REFERENCES

Abbott, M.B., Bathurst, J.C., Cunge, J.A., O’Connel l, P.E., and Rasmussen, J. 1986a. An introduction to the European Hydrological System—Sy stème Hydrologique Europèen, SHE. 1: History and philosophy of a physi cally-based, distributed modelling system. Journal of Hydrology, 87(1-2):45- 59. Abbott, M.B., Bathurst, J.C., Cunge, J.A., O’Connel l, P.E., and Rasmussen, J. 1986b. An introduction to the European Hydrological System—Sy stème Hydrologique Europèen, SHE. 2: Structure of a physically-based, distributed modelling system. Journal of Hydrology, 87(1-2):61-77. Ackers, P., and White, W.R. 1973. Sediment transpor t: new approach and analysis. Journal of the Hydraulics Division, American Societ y of Civil Engineers, 99(HY11):2041-2060. Ambrose, R.B., Martin, J.L. and Wool, T.A. 1993. WA SP5, A hydrodynamic and water quality model — Model theory, user’s manual, and pr ogrammer’s guide. U.S. Environmental Protection Agency, Office of Research and Development, Environmental Research Laboratory, Athens, Georgia. Arnold, J.G., Allen, P.M., and Bernhardt, G.. 1993. A comprehensive surface groundwater flow model. Journal of Hydrology, 142(1 -4):47-69. Bagnold, R.A. 1977. Bedload transport by natural ri vers. Water Resources Research 13(2):303-311. Bathurst, J.C., Ewen, J., Parkin G., O’Connell, P.E ., and Cooper, J.D. 2004. Validation of catchment models for predicting land-use and climat e change impacts: 3. Blind validation for internal and outlet responses. Journ al of Hydrology, 287(1-4):74-94. Bian, L., Sun, H., Blodgett, C.F., Egbert, S.L., Li , W., Ran, L., and Koussis, A.D. 1996. An integrated interface system to couple the SWAT m odel and ARC/INFO. Proceedings of the Third International Conference o n Integrating GIS and Environmental Modeling, Santa Fe, New Mexico. Janua ry 21-25, 1996. Bicknell, B.R., Imhoff, J.C., Kittle, J.L., Jr., Do nigian, A.S., Jr., and Johanson, R.C. 1997. Hydrological Simulation Program—Fortran: User ’s manual for version 11. U.S. Environmental Protection Agency, National Expo sure Research Laboratory, Athens, Georgia. EPA/600/R-97/080. 755 p. Bicknell, B.R., Imhoff, J. C., Kittle, J.L., Jr., J obes, T.H., and Donigian, A.S., Jr. 2001. Hydrological Simulation Program—Fortran: User’s man ual for version 12. U.S. Environmental Protection Agency, National Exposure Research Laboratory, Athens, Georgia. 873 p. Brown, L.C. and Barnwell, T.O. 1987. The enhanced s tream water quality models QUAL2E and QUAL2E-UNCAS: documentation and user man ual. U.S.Environmental Protection Agency, Environmental Rese arch Laboratory, Athens,

Georgia. EPA/600/3-87/007. 189 p. Cornell. 2003. SMDR, The Soil Distribution And Rout ing Model: Documentation Version 2.0. Soil and Water Laboratory, Biological and Environmental Engineering Department, Cornell University, Ithaca, New York. 9 6 p. Crawford, N.H., and Linsley, R.K.. 1966. Digital Si mulation in Hydrology: Stanford Watershed Model IV. Department of Civil Engineering , Stanford University, Stanford, California. Technical Report 39. 210 p. ( Dated: July, 1966.) Day, T.J. 1980. A study of the transport of graded sediments. Hydraulics Research Station, Wallingford, UK. Report IT 190.

DHI. 2007. MIKE SHE–Volume 1: User Guide. DHI Water and Environment, Hørsholm, Denmark. 396 p. Donigian, A.S., Jr., and Crawford, N.H. 1976a. Mode ling Pesticides and Nutrients on Agricultural Lands, Environmental Research Laborato ry, Athens, Georgia. EPA 600/2-7-76-043. 317 p. Donigian, A.S., Jr., and Crawford, N.H 1976b. Model ing Nonpoint Pollution From the Land Surface, Environmental Research Laboratory, At hens, Georgia. EPA 600/3-76- 083. 280p. Donigian, A.S, Jr., Beyerlein, D.C., Davis, H.H., J r., and Crawford, N.H. 1977. Agricultural Runoff Management (ARM) Model Version II: Refinement and Testing, Environmental Research Laboratory, Athens, Georgia. EPA 600/3-77-098. 294 p. Donigian, A.S., Jr., Imhoff, J.C., Bicknell, Brian, Kittle, J.L., Jr. 1984. Application guide for Hydrological Simulation Program—Fortran (HSPF). U.S. Environmental Protection Agency, Environmental Research Laborator y, Athens, Georgia. EPA600/3-84-065. 177 p. Downer, C.W., and Ogden, F.L. 2004. GSSHA: model to simulate diverse stream flow producing processes. Journal of Hydrologic Engineer ing, 9(3):161-174. Engelund, F., and Hansen, E. 1967. A monograph on s ediment transport in alluvial streams. Teknisk Vorlag, Copenhagen, Denmark. 62 p. England, J., Velleux, M., and Julien, P. 2007. Two- dimensional simulations of extreme floods on a large watershed. Journal of Hydrology, 347(1):229-241. Ewen, J., Parkin, G., and O’Connell, P.E. 2000. SHE TRAN: distributed river basin flow and transport modeling system. Journal of Hydrologi c Engineering, 5(3):250-258. Ewen, J., Bathurst, J.C., Parkin, G., O'Connell, E. , Birkinshaw, S., Adams, R., Hiley, R., Kilsby, C., and Burton, A. 2002. SHETRAN: physicall y-based distributed river basin modeling system. In: Mathematical Modeling of Small Watershed Hydrology, V.P. Singh, D.K. Frevert and S.P. Meyer, eds. Water Reso urces Publications, Englewood, Colorado. pp. 43-68. Foster, G.R., Lane, L.J., Nowlin, J.D., Laflen, J.M ., and Young, R.A. 1980. “A model to estimate sediment from field sized areas.” In: CREA MS: a field scale model forchemicals, runoff and erosion from agricultural man agement systems, W. G. Knisel,

ed. U.S. Department of Agriculture, Washington, D.C . Conservation Report Number 26. pp. 36-64. Green, W.H., and Ampt, G.A. 1911. Studies on soil p hysics, 1: the flow of air and water through soils. Journal of Agricultural Sciences 4(1 ):11-24. Johanson, R.C., Imhoff, J.D., and Davis, H.H., Jr. 1980. Users manual for hydrological simulation program—Fortran (HSPF). Environmental Re search Laboratory, Athens, Georgia. EPA-600/9-80-015. Johnson, B.E., Julien, P.Y., Molnar, D.K., and Wats on, C.C. 2000. The two-dimensional upland erosion model CASC2D-SED. Journal of the Ame rican Water Resources Association, 36(1):31-42. Julien, P.Y. and Saghafian, B. 1991. CASC2D User’s Manual - A Two Dimensional Watershed Rainfall-Runoff Model. Department of Civi l Engineering, Colorado State University, Fort Collins, Colorado. Report CER90-91 PYJ-BS-12. 66 p. Julien, P.Y. and Rojas, R. 2002. Upland erosion mod eling with CASC2D-SED. International Journal of Sediment Research, 17(4):2 65-274. Julien, P.Y., and Simons, D.B. 1985. Sediment trans port capacity of overland flow. Transactions of the American Society of Agricultura l Engineers, 28(3):755-762. Kilinc, M.Y., and Richardson, E.V. 1973. Mechanics of soil erosion from overland flow generated by simulated rainfall. Hydrology Papers, Number 63. Colorado State University, Fort Collins, Colorado. Meyer, L.D., and Weischmeier, W.H. 1969. Mathematic al simulation of the process of soil erosion by water. Transactions of the American Society of Agricultural Engineers, 12(6):754-762. Molnár, D.K. and Julien, P.Y. 2000. Grid size effec ts on surface runoff modeling. Journal of Hydrologic Engineering, 5(1):8-16. Neitsch, S.L., Arnold, J.G., Kiniry, J.R., Williams , J.R., and King, K.W. 2002. Soil and Water Assessment Tool Theoretical Documentation, Ve rsion 2000. U.S. Department of Agriculture, Agricultural Research Service, Temp le Texas. 506 p. Ogden, F.L. and Julien, P.Y. 2002. CASC2D: A Two-Di mensional, Physically-Based, Hortonian Hydrologic Model. In: Mathematical Models of Small Watershed Hydrology and Applications, Singh, V.P. and Frevert , D., eds., Water Resources Publications, Littleton, Colorado. pp. 69-112. Pellicciotti, F., Brock, B., Strasser, U., Burlando , P., Funk, M., and Corripio, J. 2005. An enhanced temperature-index glacier melt model inclu ding the shortwave radiation balance: development and testing for Haut Glacier d ’Arolla, Switzerland. Journal of Glaciology, 51(175):573-587. Rojas, R. 2002. GIS-based Upland Erosion Modeling, Geovisualization and Grid Size Effects on Erosion Simulations with CASC2D-SED. Ph. D. dissertation, Department of Civil Engineering, Colorado State University, Fo rt Collins, Colorado.Singh, V.P. 1995. Computer Models of Watershed Hydr ology. Water Resources

Publications, Highlands Ranch, Colorado. 1144 p. Smith, R.E., and Parlange, J.-Y. 1978. A parameter efficient hydrologic infiltrations model. Water Resources Research, 14(3):533-538. USACE. 1998. Hydrologic Modeling System HEC-HMS Use r’s Manual. U.S. Army Corps of Engineers, Hydraulic Engineering Center, D avis, CA. (Report: CPD-74A, August, 2010.) 316 p. USDA. 1986. Urban Hydrology for Small Watersheds: T echnical Release 55 (TR-55). U.S. Department of Agriculture, Natural Resources C onservation Service, Conservation Engineering Division, Washington, D.C. (210-VI-TR-55, Second Ed., June 1986) USDA. 1991. State soil geographic (STATSGO) data ba se: data use information. U.S. Department of Agriculture, National Resources Conse rvation Service, National Soil Survey Center, Washington, D.C. Miscellaneous Publi cation Number 1492. 110 p. (Revised: July 1994) USDA. 2009. Small Watershed Hydrology: WinTR-55 use r guide. U.S. Department of Agriculture, Natural Resources Conservation Service , Conservation Engineering Division, Washington, D.C. 142 p. (January 2009) Veith, T.L., Srinivasan, M.S., and Gburek, W.J. 200 3. Process representation in watershed-scale hydrologic models: an evaluation in an experimental watershed. Proceedings of the First Interagency Conference on Research in the Watersheds. U.S. Department of Agriculture, Agricultural Research Se rvice, Benson, Arizona, October 27-30, 2003. Velleux, M., Westenbroek, S., Ruppel, J., Settles, M., and Endicott, D. 2001. A User’s Guide to IPX, the In-Place Pollutant Export Water Q uality Modeling Framework, Version 2.7.4. U.S. Environmental Protection Agency , Office of Research and Development, National Health and Environmental Effe cts Research Laboratory, MidContinent Ecology Division, Large Lakes Research St ation, Grosse Ile, Michigan. 179 pp. EPA/600/R-01/079. Velleux, M., Julien, P., Rojas-Sanchez, R., Clement s, W., and England, J. 2006. Simulation of metals transport and toxicity at a mi ne-impacted watershed: California Gulch, Colorado. Environmental Science and Technolo gy, 40(22):6996-7004. Velleux, M., England, J., and Julien, P. 2008. TREX : spatially distributed model to assess watershed contaminant transport and fate. Sc ience of the Total Environment, 404(1):113-128. Wicks, J.M., and Bathurst, J.C. 1996. SHESED: a phy sically based, distributed erosion and sediment yield component for the SHE hydrologic al modeling system. Journal of Hydrology, 175(1-4):213-238. Williams, J.R. 1975. Sediment routing for agricultu ral watersheds. Water Resources Bulletin, 11(5):965-974.Woolhiser, D.A., Smith, R.E., and Goodrich, D.C. 19 90. KINEROS, A Kinematic

Runoff and Erosion Model: Documentation and User Ma nual. U.S. Department of Agriculture, Agriculture Research Service. ARS-77 ( March, 1990). Yang, C.T. 1973. Incipient motion and sediment tran sport. Journal of the Hydraulics Division, American Society of Civil Engineers, 99(H Y10):1679-1704.