VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL 1

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1 Vol. 51, No. 2 AMERICAN WATER RESOURCES ASSOCIATION April 2015 VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL 1 Jan Boll, Erin S. Brooks, Brian Crabtree, Shuhui Dun, and Tammo S. Steenhuis 2 ABSTRACT: In nondegraded watersheds of humid climates, subsurface flow patterns determine where the soil saturates and where surface runoff is occurring. Most models necessarily use infiltration-excess (i.e., Hortonian) runoff for predicting runoff and associated constituents because subsurface flow algorithms are not included in the model. In this article, we modify the Water Erosion Prediction Project (WEPP) model to simulate subsurface flow correctly and to predict the spatial and temporal location of saturation, the associated lateral flow and surface runoff, and the location where the water can re-infiltrate. The modified model, called WEPP-UI, correctly simulated the hillslope drainage data from the Coweeta Hydrologic Laboratory hillslope plot. We applied WEPP-UI to convex, concave, and S-shaped hillslope profiles, and found that multiple overland flow elements are needed to simulate distributed lateral flow and runoff well. Concave slopes had the greatest runoff, while convex slopes had the least. Our findings concur with observations in watersheds with saturation-excess overland flow that most surface runoff is generated on lower concave slopes, whereas on convex slopes runoff infiltrates before reaching the stream. Since the WEPP model is capable of simulating both saturation-excess and infiltration-excess runoff, we expect that this model will be a powerful tool in the future for managing water quality. (KEY TERMS: modeling; water quality; hillslope hydrology; subsurface lateral flow; saturation-excess overland flow.) Boll, Jan, Erin S. Brooks, Brian Crabtree, Shuhui Dun, and Tammo S. Steenhuis, Variable Source Area Hydrology Modeling with the Water Erosion Prediction Project Model. Journal of the American Water Resources Association () 51(2): DOI: / INTRODUCTION Over 82 million hectares in the United States (U.S.) have either restrictive soil layers or bedrock at shallow depths, with periodically perched water tables according to the USDA NRCS STATSGO soils database (Figure 1). These restrictive soil layers consist of illuvial, argillic, or fragipan soil horizons, and have a low hydraulic conductivity (McDaniel et al., 2008). In humid climates, saturation-excess runoff is dominant in landscapes with shallow restrictive soils (Dunne and Black, 1970; Dunne et al., 1975; Walter et al., 2000; McDaniel et al., 2008). Surface runoff occurs when the capacity to store water above the restrictive layer is exceeded. Since the soil water 1 Paper No P of the Journal of the American Water Resources Association (). Received September 16, 2013; accepted October 8, American Water Resources Association. Discussions are open until six months from print publication. 2 Director & Professor (Boll), Environmental Science and Water Resources Program, Research Assistant Professor (Brooks) and former Graduate Research Assistant (Crabtree), Department of Biological and Agricultural Engineering, University of Idaho, 875 Perimeter Drive MS 3006, Moscow, Idaho 83844; Post-doctoral Associate (Dun), Biological Systems Engineering, Washington State University, Pullman, Washington 99164; and Professor (Steenhuis), Department of Biological and Environmental Engineering, Cornell University, Ithaca, New York ( /Boll: jboll@uidaho.edu). 330

2 VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL FIGURE 1. United States of America Perched Water Table Map. Derived from the USDA NRCS STATSGO database. storage capacity varies throughout the landscape, the area contributing surface runoff increases during the storm. The terms partial-area or variable source area were coined for these types of hydrological processes by Hewlett and Hibbert (1967) and Dunne and Black (1970). Surface runoff predictions in many models ignore variable source area hydrological concepts and use the curve number approach (Merritt et al., 2003), where surface runoff depends on soil type, crop type, and antecedent moisture content. These models, therefore, represent infiltration-excess (or Hortonian) runoff mechanisms where the rainfall intensity exceeds the soil s infiltration capacity for runoff to occur (Horton, 1940; Walter et al., 2000). Runoff producing areas differ spatially between these runoff mechanisms. Since overland flow carries all sediments and most agricultural chemicals (except dissolved forms), it is, therefore, important to simulate the appropriate runoff processes in the landscape for proper placement of conservation practices to improve water quality (Ebel and Loague, 2006; Rode et al., 2010). Despite the widespread occurrence of shallow soils with restrictive layers, very few readily accessible erosion models include variable source area hydrology to correctly locate the areas with saturation-excess runoff and erosion. One model that can simulate interflow, and therefore runoff from saturated variable source areas, is the Water Erosion Prediction Project (WEPP) model (Flanagan and Nearing, 1995). At the same time, WEPP is a robust erosion model, and includes routines for pesticide transport (Saia et al., 2013). Thus, WEPP has been expanded to include water quality as well. Initially, before 2006, WEPP could only simulate infiltration-excess runoff but more recent versions of the WEPP model made operational the subsurface flow algorithm in Savabi et al. (1995) which was modified from original work by Sloan and Moore (1984) (see also Dun et al., 2009). There are various versions of WEPP. The original version without subsurface flow is WEPP (v.2006). Pieri et al. (2007) had adequate results simulating conditions in northern Italy using WEPP (v ) at the plot scale when aggregated to an annual time step. Subsurface lateral flow may have played a role but was not included in WEPP (v ). WEPP (v.2008) was the first release with a working subsurface flow component. Dun et al. (2009) applied WEPP (v ) to a small, forested watershed in Idaho, USA. They included an adjusted effective saturated 331

3 BOLL, BROOKS, CRABTREE, DUN, AND STEENHUIS hydraulic conductivity for forested soil with a restrictive bedrock layer, and, in addition, added an anisotropy factor to increase the lateral saturated hydraulic conductivity in the soil profile above bedrock. When using WEPP (v.2010), our initial tests overpredicted drainage when multiple overland flow elements (OFEs) were used for short hillslopes with steep slopes using a daily time step. OFEs are sections on the hillslope of homogeneous soil and cropping management. Given the importance of subsurface flow in the prediction of locations of variable source areas for surface runoff, the objectives of this article are to update the subsurface flow routines in WEPP (v.2010), to validate the subsurface flow routines using hillslope drainage data from the Coweeta Hydrologic Laboratory (Hewlett and Hibbert, 1963), and to compare the use of one OFE vs. multiple OFEs for different slope configurations. This WEPP version with the modified (sub) surface flow routines is called WEPP-UI (University of Idaho), and is available as part of the WEPP release. Validation of these modifications in either of these releases has not been previously reported. WEPP-UI is used as a tool for water quality planning and management in Brooks et al. (2015). WEPP MODEL Background on Hillslope Flow Processes One of the primary hydrologic processes driving the spatial variability of surface runoff in variable source area hydrology, especially in steep topography, is the convergence of subsurface lateral flow, also referred to as subsurface storm flow (Dunne and Black, 1970; Weiler et al., 2006). Once a perched water table has developed above a restrictive layer, large macropores and soil pipes in the saturated layer can rapidly conduct water downslope (Dohnal et al., 2012). Examples of rapid subsurface lateral flow in forested and agricultural landscapes can be found in Whipkey (1965), Brooks et al. (2004), and Weiler et al. (2006). Since subsurface lateral flow in perched systems is largely controlled by gravitational forces, the magnitude of saturated lateral flow is directly related to the land surface slope (Frankenberger et al., 1999; Wigmosta and Lettenmaier, 1999). The close linkage between topography and the spatial distribution of runoff led to the development of the topographic (or wetness) index which was the basis for predicting spatial variability of runoff in the TOP- MODEL (Beven and Kirkby, 1979). In TOPMODEL, subsurface flow is averaged across the watershed and can therefore only indicate the general location of the saturated areas. In WEPP, subsurface flow is spatially distributed along the hillslope, and, therefore, can more accurately simulate the spatially and temporally varying runoff source area at the hillslope scale. Moreover, WEPP has well developed, physically based soil erosion and deposition routines (Flanagan et al., 2007). Model Description The WEPP model simulates the water balance and predicts erosion at the hillslope scale and at the watershed scale. Users have the option to manually divide a hillslope into multiple OFEs. The WEPP model simulates water and erosion processes from agricultural and forest lands for soil and water conservation planning and assessment (Flanagan et al., 2007). The WEPP model was developed to serve as a replacement for empirically based erosion modeling technologies such as the Universal Soil Loss Equation. A detailed history of the development of WEPP was provided by Flanagan et al. (2007). Here, we focus on the hillslope version of WEPP. Physical processes in the WEPP model include: infiltration and runoff, soil detachment, transport, deposition, plant growth, senescence, and residue decomposition (Flanagan and Nearing, 1995). The model uses the Green and Ampt method to estimate infiltration of water into soil (Flanagan and Nearing, 1995). Subsurface lateral flow in Savabi et al. (1995) was taken from the kinematic-storage approach model of Sloan and Moore (1984), in which subsurface lateral flow occurs when a layer is saturated and the excess rainfall percolates vertically down as unsaturated flow. Differently from Sloan and Moore (1984), however, WEPP (v.2010) uses numerically defined soil layers (e.g., two 0.10 m near surface soil layers followed by multiple 0.20 m layers to the bottom of the soil profile), which generate subsurface lateral flow prior to development of a fully saturated layer (i.e., the perched water table) above the restrictive layer. Supplementary information S1 provides information on the subsurface flow equations in WEPP (v.2010). Re-infiltration of surface runoff is possible with the model based on relative rates of runoff and infiltration. Each hillslope in WEPP is represented as a rectangular unit with a length equal to the average flowpath length along a stream reach and an effective width calculated by dividing the total drainage area by the average flow-path length. All calculations within a hillslope are made on a per unit width basis, and, therefore, plan form topographic convergence (along the hillslope width) is not represented in WEPP. 332

4 VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL For subsurface lateral flow calculations, the profile curvature of a hillslope is ignored within a single planar OFE, and more OFEs allow for better representation of hydrologic and erosion processes. With multiple OFEs, the lateral flow from the upslope OFE is routed to the downslope neighboring OFE during a single time step. If the downslope OFE is saturated or becomes saturated during the time step, then saturation-excess runoff occurs. An example of an S-shaped hillslope is shown in Figure S2, representing a topographic profile represented by 1, 3, and 10 OFEs. The basic modeling time step in the current version of WEPP depends on the specific algorithm in the model. Runoff and sediment transport algorithms are simulated in the model on a daily time step, or on an event basis, snow hydrology is simulated on an hourly basis, and subsurface hydrology, crop growth, and residue decomposition algorithms are simulated using a daily time step. In this study, we evaluate the time step for the subsurface flow routine (see below). Input files needed for the WEPP model are the slope file, management file (crop information and tillage type), soil file (soil type and associated parameters), and climate file, which contains information to calculate evaporation and rainfall intensities. In addition, if local climate data are not available, WEPP has the CLIGEN weather generator program with weather data statistics for over 2,600 stations within the U.S. Detailed descriptions of these WEPP input files are provided in Data S2 and S3. Output from WEPP includes daily precipitation, snowmelt, overland flow, plant and soil evaporation, deep percolation, subsurface lateral flow, soil moisture content by OFE, as well as net erosion/deposition along the hillslope and delivered to the base of the hillslope. WEPP tracks particle sorting and breaks down delivered sediment into five particle/ aggregate size classes. Cropping, plant yield, and winter hydrology output files are provided. Model Modifications Modifications to the code of WEPP (v.2010) in this study were to improve subsurface lateral flow routines so that they closely match the original kinematicstorage approach in Sloan and Moore (1984). In addition, we reduced the time step in subsurface flow calculations to less than one day (see below). Modification 1 was to calculate the effective lateral saturated hydraulic conductivity for a soil layer that is partially saturated (i.e., where a perched water table resides) based on the percent of the soil layer that is saturated. Rather than using the unsaturated hydraulic conductivity power function based on the average moisture content of the soil layer (Equations S2a-S2b), a linear function is used in WEPP-UI to estimate the portion of the soil layer that is saturated (Equation 1). The fraction of the layer that is saturated multiplied by the saturated hydraulic conductivity (K s ) of the layer yields the effective lateral K s for the layer, K e, as follows: KeðÞ i ¼ K s,i! i fc,i for s,i i > fc,i fc,i where K s is lateral saturated hydraulic conductivity (m/s), h is the average moisture content, h fc is the field capacity moisture content, h s is the saturated moisture content, and subscript i indicates the individual soil layer (Stagnitti et al., 1992; Frankenberger et al., 1999). Equation (1) follows the main assumptions underlying the kinematic-storage model (Sloan and Moore, 1984) that (1) subsurface lateral flow only occurs as saturated flow and (2) unsaturated flow only occurs in the vertical direction due to steep gradients in hydraulic potential associated with drying and wetting fronts. The K e using Equations (S2a-S2b) is much smaller at the same average moisture content than the effective lateral K s using Equation (1), as illustrated in Figure S2. Modification 2 was to update the subsurface flow routine. Since WEPP does not track soil hydraulic potential gradients within a profile, a rule-based approach was implemented. In WEPP-UI water flow is assumed to be vertical if (1) the moisture content of the soil layer exceeds field capacity and (2) the lower subsequent soil layer has sufficient capacity to store or conduct the infiltrating water to the next layer. By definition, since vertical flow will normally be unsaturated (e.g., a wetting front following a rain storm), Equations (S2a and S2b) is used to determine the K e of the layer. This modification assures that a saturated layer, and, in turn, subsurface lateral flow, is generated first above a restrictive soil layer, typically at the base of the soil profile (e.g., an argillic or fragipan horizon, or bedrock), rather than in the near surface soil layers when the moisture content of the upper soil layers exceeds field capacity moisture content (see Beven and Germann, 1982; Frankenberger et al., 1999; Brooks et al., 2004). Modification 3 was to achieve a more realistic soil characterization. In addition to using pedotransfer functions for estimating bulk density, K s, field capacity, and wilting point from soil texture, WEPP-UI gives the user the option to specify these parameters for each soil layer. Users also can specify an anisotropy ratio for each soil layer rather than a single value for the entire soil profile and can provide a thickness of the lower boundary soil restrictive layer. ð1þ 333

5 BOLL, BROOKS, CRABTREE, DUN, AND STEENHUIS These modifications build on the original description of subsurface lateral flow by Savabi et al. (1995) and Dun et al. (2009). However, we found differences between the computer code and Savabi et al. (1995), indicating that modifications to the original WEPP model as described in Flanagan and Nearing (1995) were made between 1995 and For example, Equations S2a and S2b were not included in the original WEPP documentation. METHODS In the following sections, we describe a number of tests on the performance of WEPP-UI and WEPP (v.2010) to model the subsurface flow processes in particular and, in more general terms, if WEPP can be used as a tool to simulate variable source area hydrology. In the first test, we investigate what is the optimum time step for simulating subsurface flow. Once the optimum time step is established, we compare the subsurface outflow of WEPP (v.2010) and WEPP-UI with the well-known Coweeta experimental data. Finally, we test the modeling procedure of using a single vs. multiple OFEs for various hillslope configurations using WEPP-UI, and demonstrate the effect of concave, convex, and S-shaped hillslope profiles on the distribution of subsurface lateral flow and surface runoff source areas. Effect of Time Step on Lateral Flow We compared drainage rates from two initially saturated hillslopes using a time step of 1 min, 1 h, 6 h, 12 h, and 24 h for the subsurface flow calculations (i.e., subsurface lateral flow, percolation between soil layers, deep percolation, and evapotranspiration [ET]), one with a lateral K s of 0.28 m/day and the other with a lateral K s of 2.8 m/day. Both hillslopes were 5 m long and had a uniform 20% slope. These slope characteristics were chosen to demonstrate the sensitivity of the lateral flow response to a single, short OFE segment when water may travel beyond the length of a single OFE within the time step. Hillslope Validation WEPP (v.2010) and WEPP-UI models were applied to a uniform hillslope measuring 0.9 m m 9 15 m (3 ft 9 3ft9 45 ft) with a uniform slope of 40% (21.8 ) as per Hewlett and Hibbert (1963), also known as the Coweeta Experiment. A soil file was created containing TABLE 1. WEPP-UI Soil File Inputs for Coweeta Hillslope Drainage Experiment. Soil depth (mm) 914 % sand 60 % clay 22 % organic matter 3.5 % rock fragments 0 Bulk density (g/cm 3 ) 1.3 Anisotropy ratio 1 Field capacity 0.25 Wilting point* 0.05 Saturated hydraulic conductivity (mm/h) 168 Critical shear stress (N/m 2 )* 3.5 Rill erodibility (s/m)* Interrill erodibility (kg/s/m 4 )* Cation exchange capacity (meq/100 g soil)* 23.3 Albedo* 0.23 Restrictive layer saturated hydraulic 1.00e-99 conductivity (mm/h) * Estimated soil properties. the same soil properties used by Hewlett and Hibbert (1963) (Table 1). Some of these soil properties were also provided in Sloan and Moore (1984). A no-flux restrictive boundary layer was placed at the bottom of the soil profile at the depth of 914 mm to prevent percolation. In the WEPP-UI model, values for bulk density (1.3 g/cm 3 ), K s (168 mm/h), field capacity (0.25 cm 3 /cm 3 ), and an anisotropy ratio of 1.0 were fixed based on the soil characterization provided by Hewlett and Hibbert (1963). In the WEPP (v.2010) model, bulk density, K s, and field capacity were estimated with pedotransfer functions based on soil texture, so observed soil characteristics were not directly entered in runs with that model. In WEPP (v.2010), bulk density was 1.5 g/cm 3, K s was mm/ day, and field capacity moisture content was 0.26 cm 3 / cm 3. Since the initial water content in the Coweeta experiment was not at full saturation but at an equilibrium state where the soil profile at the bottom of the slope was saturated, and the profile at the top of the slope was at a state less than field capacity, the initial soil water content in the model was set by matching the initial simulated drainage rate with the initial drainage rate from the WEPP-UI model. This initial soil water content was determined to be 84% of saturation and was used as the starting point in both models. The input climate file was set up with a minimum and maximum temperature of 1 and 2 C, respectively. The dew point was set to 40 C to prevent condensation. Solar radiation and wind speed were set to 0 because the plot was covered with plastic. A grass management file was used to reflect the surface conditions of a repacked soil without tillage in the Coweeta experiment. Since the experimental plot was covered with plastic, plant growth and ET were prevented by eliminating solar radiation and lowering the maximum temperature to below the necessary lower limit for growth. To examine the effect of Modification 2 on subsurface lateral flow, we compared 334

6 VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL simulated drainage from an initially dry (i.e., wilting point moisture content) hillslope that was wetted at a constant rate of 2 mm/h. To directly evaluate the effects of Modification 2, soil hydraulic properties used in the WEPP-UI model were set equal to the properties predicted using the soil texture-based pedotransfer functions in WEPP (v.2010). To determine goodness of fit between observed and simulated data, the observed data were carefully determined from graphs in the original paper by Hewlett and Hibbert (1963), and equivalent time series to the WEPP simulated data were created by fitting a polynomial equation to these data (Coefficients of determination, R 2, of these fits were for both the discharge and cumulative discharge data series). We used the Nash-Sutcliff (N S ) and the R 2 as the statistics for goodness of fit of simulated to observed data. Evaluation of Hillslope Profiles Using Single vs. Multiple OFEs in WEPP-UI Since, by default, the WEPP (v.2010) model simulates subsurface hydrology using a single plane, we investigated the importance of using a single OFE and 10 OFEs for hydrologic simulations. Three hillslope profiles were considered: a concave slope, a convex slope, and an S-shaped slope. The average slope for each of these hillslopes was fixed at 15%. The topography for each slope configuration was created using the Slope Profile Editor in the WEPP windows interface (v ). The concave slope had a 30% slope at the upper point of the slope and a 0% slope at the hillslope outlet. The convex slope consisted of a 0% slope at the upper point and 30% at the outlet. The S-curve-shaped slope was made with a 0% slope at the upper and lower points and 30% slope midway (i.e., 75 m) through the slope. Figure S2 shows a comparison of the topography of the S-shaped slope used in this analysis as represented by 1, 3, and 10 OFEs. In all hillslope configuration simulations, a silt loam soil was underlain by a hydrologically restrictive soil layer (K s = 0.2 mm/day) at 0.5 m, with the following soil parameter values: bulk density = 1.5 g/cm 3 ; vertical K s = 17 mm/h; anisotropy ratio = 10; field capacity moisture content = 31%; wilting point moisture content = 16%; soil texture composition of 11% sand, 69% silt, and 20% clay. Each hillslope was assumed to be managed under reduced tillage, three-year winter-wheat, spring barley, pea crop rotation typical of the eastern edge of the Palouse region in Idaho. A 30-year climate file was used representative for Moscow, Idaho. This is a Mediterranean climate with cool wet winters and hot dry summers. The mean annual precipitation for the 30-year simulation was 674 mm. RESULTS AND DISCUSSION Effect of Time Step on Lateral Flow Simulated perched water depths are sensitive to the time step in the model. Reducing the time step in the computation of subsurface lateral flow, percolation between soil layers, deep percolation, and ET improves model performance for hillslopes having relatively rapid lateral subsurface drainage. Figure 2 shows the comparison of the WEPP simulation of perched water depth (cm) for a single OFE hillslope with lateral K s of 0.28 m/day (Figure 2a) and lateral K s of 2.8 m/day (Figure 2b), each using a time step of 1 min, 1 h, 6 h, 12 h, and 24 h. Figure 2a shows that a daily time step for a K s of 0.28 m/day simulates perched water depth equally well as smaller time steps. Figure 2b, however, shows that a daily time Perched Water Depth (cm) Perched Water Depth (cm) Time (days) Lateral K s = 0.28 m/day (a) Lateral K s = 2.8 m/day OFE Length = 5 m Slope = 20% Soil Depth = 20 cm Porosity = 43.6% Field Cap = 29% 1 min 1 hr 6 hr 12 hr 24 hr OFE Length = 5 m Slope = 20% Soil Depth = 20 cm Porosity = 43.6% Field Cap = 29% 1 min 1 hr 6 hr 12 hr 24 hr (b) Time (days) FIGURE 2. Comparison of WEPP Simulation of Water Depth (cm) for a Hillslope with (a) Lateral Saturated Hydraulic Conductivity of 0.28 m/day and (b) Lateral Saturated Hydraulic Conductivity of 2.8 m/day, Each Using a Time Step of 1 min, 1 h, 6 h, 12 h, and 24 h. 335

7 BOLL, BROOKS, CRABTREE, DUN, AND STEENHUIS step with a K s of 2.8 m/day underpredicts water depth compared to smaller time steps. The difference between a 1-h time step and 1-min time step is miniscule, justifying a 1-h time step. Only for an extreme short burst of rainfall, a shorter duration time step might be needed for the fine detail of a hydrograph. Effects of the time step on ET (data not shown) are directly related to the differences in soil moisture content. TABLE 2. Nash-Sutcliffe (N S ) and Coefficient of Determination (R 2 ) for Observed vs. Simulated Discharge and Cumulative Drainage Data Based on the Coweeta Experiment Using WEPP (v.2010) and WEPP-UI. WEPP (v.2010) WEPP-UI N S R 2 N S R 2 Discharge Cumulative drainage Hillslope Validation To our knowledge, verification of the WEPP model for the Coweeta experiment is the first hillslope validation of subsurface lateral flow. Prediction of hillslope drainage with the WEPP-UI model compared well to measured discharge data, whereas WEPP (v.2010) predictions were relatively poor compared to the measured data (see Figures 3a and 3b and Table 2). Nash-Sutcliffe values for discharge vs. time were for WEPP-UI and for WEPP (v.2010), and N S Discharge (liters day-1 m-1) 1000 (a) (b) Cumulative Drainage (liters) Observed WEPP-UI WEPP Time (days) Observed WEPP-UI WEPP Time (days) FIGURE 3. (a) Discharge (liters/day/meter) and (b) Cumulative Drainage (liters) for Hillslope Plot in the Coweeta Experiment. values for cumulative discharge vs. time were for WEPP-UI and 1.75 for WEPP (v.2010), respectively. Similarly, R 2 values for discharge vs. time were for WEPP-UI and for WEPP (v.2010), and R 2 values for cumulative discharge vs. time were for WEPP-UI and for WEPP (v.2010), respectively. Observed cumulative drainage was 1.26 m 3 with 76% draining during the first five days. WEPP-UI predicted 1.22 m 3 of drained water over 30 days with 90% occurring during the first five days. WEPP (v.2010) predicted 1.00 m 3 of drained water after more than 300 days with 36% occurring during the first five days. The pedotransfer routines in WEPP (v.2010) to estimate soil properties based on soil texture cause a large discrepancy in the initial phase of the drainage experiment where the total available soil water volume is clearly underestimated. Schaap and Leij (1998) demonstrated, using three large soil databases, that the uncertainty in predicting water retention points is about 4-10% by volume with pedotransfer functions based on texture and bulk density, whereas the uncertainty in K s was one-half to one order of magnitude. One of the primary challenges in pedotransfer functions is adequately representing soil structure (Lin et al., 1999; Pachepsky et al. 2006) especially with macropores (Schaap and Leij, 2000). Similar to Figure S3, the drainage curves simulated by the WEPP (v.2010) model are erratic and demonstrate clear threshold behavior as each individual soil layer drains (Figure 3a). The observed data indicate a decrease in the drainage rate with time after day eight which is not captured by WEPP-UI, because unsaturated lateral transport is not included. This is similar to all other published attempts to physically describe the discharge of this plot (Sloan and Moore, 1984; Steenhuis et al., 1999). By having an exponential lateral hydraulic conductivity function with moisture content, the WEPP (v.2010) model simulated a much longer drainage period. The slight overprediction in drainage rate after day seven by WEPP-UI had minimal effect on the cumulated drainage curve since by day eight roughly 85% of the water had drained from the hillslope (Figure 3b). 336

8 VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL FIGURE 4. Lateral Flow (mm/day) vs. Time (days) While Wetting Up the Coweeta Soil Profile Using WEPP (v.2010) and WEPP-UI. In a separate wetting simulation, where soil properties in both models were the same, the WEPP (v.2010) shows earlier onset of lateral subsurface flow and sudden irregular jumps in lateral flow as the hillslope wetted (Figure 4). In WEPP (v.2010), subsurface lateral flow was initiated after 42 days vs. 64 days in WEPP-UI. These effects are caused by lateral flow in the near-surface, numerically created soil layers in WEPP (v.2010), before the full soil profile reaches saturation. Without a physical change in soil properties with depth, the behavior of WEPP (v.2010) can only be due to the numerical layering in the model itself. Evaluation of Hillslope Profiles Using Single vs. Multiple OFEs in WEPP-UI Graphical output from WEPP-UI of average annual surface runoff depth and average number of days per year of surface runoff using 10 OFEs as compared to a single OFE are presented in Figure 5 for three slope configurations: concave slope, convex slope, and S-shaped slope. The average annual hydrologic response at the outlet for all three slope configurations for various approaches ranging from a single 150 m OFE to a hillslope broken down into 19, 8 m OFEs is summarized in Table 3. When using a single OFE, simulated total runoff, subsurface lateral flow, ET, number of days with surface runoff, and days with subsurface lateral flow are the same for all three hillslope configurations (see Figures 5a-5c, and Table 3). Using a single OFE to represent the shape of the topography forces the model to compute subsurface lateral flow using an FIGURE 5. Thirty-Year Average Runoff Depth (mm/yr), Average Lateral Flow Depth (mm/yr), and Number of Days of Runoff Simulated Along (a) a Concave Hillslope, (b) a Convex Hillslope, and (c) an S-Shaped Hillslope, Each Using 1 OFE vs. 10 OFEs. average slope of 15%. Use of an average slope eliminates slope changes, and, therefore, produces a uniform distribution of surface runoff and subsurface 337

9 BOLL, BROOKS, CRABTREE, DUN, AND STEENHUIS TABLE 3. WEPP-UI Simulation Results for Three Hillslope Configurations Using OFEs Ranging in Size from a Single, 150 m OFE Up to 19 OFEs of 7.9 m: Average Annual Runoff and Subsurface Lateral Flow Leaving the Hillslope, Average Annual Evapotranspiration (ET) for the Entire Hillslope, Number of Days with Runoff, and Days with Subsurface Lateral Flow. Slope Shape Number of OFEs OFE Length (m) Avg. Runoff (mm/yr) Avg. Subsurface Lateral Flow (mm/yr) Avg. ET (mm/yr) Days with Runoff Days with Subsurface Lateral Flow Concave Convex S-Curve lateral flow over the entire hillslope (Figures 5a-5c). In contrast, the hydrology of a hillslope is greatly controlled by the shape of a hillslope when using multiple OFEs. Simulation results using 10 OFEs and the effect of hillslope shape on the hydrology of each of the three hillslope configurations is discussed below. Concave Slope Configuration The concave hillslope generates more runoff for a longer period of time than the other two slope shapes (Table 3 and Figure 5a). Compared to the single OFE simulation, when using multiple OFEs the model accounts for the convergence of subsurface lateral flow in the downslope direction. On a concave slope, the hydraulic gradient decreases downslope. Thus, the amount of subsurface lateral flow entering a downslope OFE is always greater than the subsurface lateral flow leaving the OFE. By a simple OFE mass balance, this leads to increased storage in the downslope direction, and increased likelihood of surface runoff generated by saturation-excess processes in downslope OFEs. Using a single OFE for the entire slope, the WEPP-UI model predicts that, on average, the hillslope will generate surface runoff 5 days/yr providing a total depth of 48 mm/yr. In contrast, by representing the hillslope shape with 10 OFEs the WEPP-UI model predicts that the concave hillslope will generate surface runoff 82 days/yr providing a total depth of 141 mm/yr (Table 3). Another important distinction is that a single OFE implies that the surface runoff depth is uniform over the entire length of the slope. As seen in Figure 5a, both the depth of runoff and number of days of runoff per year is smaller than that predicted by the single OFE for the upper six OFEs (i.e., the upper 60% of the hillslope). In other words, the majority of the surface runoff is generated on the lower 40% of the hillslope, as expected for saturation-excess runoff generation (Figure 5a). On hillslopes where surface runoff generation is dominated by saturation-excess processes (i.e., variable source area hydrology), there tends to be an inverse relationship between the generation of lateral flow and surface runoff. Figure 5 shows the distribution of both lateral subsurface flow and surface runoff along the three slope configurations (lateral flow for a single OFE is not shown because it is constant along the slope; see Table 3). Notice that subsurface lateral flow is greatest and surface runoff is smallest at the top of the slope and with increasing distance downslope subsurface lateral flow decreases and surface runoff increases. By the end of the slope, the average annual surface runoff is greater than the average annual subsurface lateral flow (Figure 5a and Table 3). According to the simulation using a single OFE much more of the water leaves the concave hillslope as subsurface lateral flow (186 mm/yr), than as 338

10 VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL surface runoff (48 mm/yr). According to simulations using 10 OFEs the opposite is true with much more of the water leaving as runoff (141 mm/yr) than as subsurface lateral flow (49 mm/yr). Convex Slope Configuration In contrast to the concave slope, surface runoff in a convex-shaped slope is much less affected by downslope convergence of subsurface lateral flow, and, therefore, simulated surface runoff is much more uniform along the slope (Figure 5b). The hydraulic gradient increases with distance downslope resulting in better downslope drainage. There are much fewer runoff events on a convex slope as compared to a concave slope. On average, surface runoff only occurs 5 days/yr on a convex slope as opposed to 82 days/yr for a concave slope (Figures 5a and 5b). Runoff is greatest on the upper flat slopes at the top of a convex hillslope. This upper section of the hillslope has low lateral flow gradients and, therefore, soils remain at greater soil moisture content (Figure 5b). As the slope begins to increase, lateral flow gradients increase and surface runoff generated upslope reinfiltrates into the soil, illustrated with the decrease in surface runoff. The reduced drainage on the upper end of the convex slope translates into wetter soil, greater ET, and lower overall runoff when simulating the slope using 10 OFEs as opposed to using a single OFE. In comparison with the other two slopes, the relative amount of subsurface lateral flow and runoff using a single OFE vs. 10 OFEs is closest to the convex slope. S-Shaped Slope Configuration The S-shaped slope configuration shows the effects of the convex hillslope in the upper sections, and the effects of the concave hillslope in the lower sections (Figure 5c). Surface runoff increases downslope as the hydraulic gradient is reduced, and storage is exceeded, resulting in saturation-excess runoff at the bottom of the slope. The average amount of surface runoff (71 mm/yr) and subsurface lateral flow (111 mm/yr) leaving the hillslope falls between that of the concave and convex hillslope configuration (see Table 3). Comparison with the single OFE simulation shows that at the upper sections, surface runoff is less than the 10 OFEs simulation, but greater at the lower sections. OFE Length In general, OFE lengths can be greater for convex slopes than for concave slopes. Figure 6 shows that the FIGURE 6. Sensitivity of Average Annual Runoff and Subsurface Lateral Flow at the Outlet of the Concave and Convex Slopes to OFE Length. average annual runoff leaving the hillslope for a convex slope is relatively insensitive to the length of OFEs. A single 150 m OFE has 48-mm annual runoff, while 19 OFEs of 7.9 m result in 36 mm/yr (Table 3). In contrast, for a concave slope, the number of OFEs is significant. A single 150 m OFE has again 48 mm/yr, while 19 OFEs has 151 mm/yr (Table 3). The S-curve slope shows a similar sensitivity to OFE length as the concave slope, while other results of OFE length fall in between the two extremes of 150 and 7.9 m length (Table 3). Illustration of Hillslope Profile on Soil Erosion and Deposition Despite the simulated increase in surface runoff when using multiple OFEs vs. a single OFE for the concave and S-shaped slopes, WEPP-UI simulated lower overall sediment yield for multiple OFEs than for a single OFE for all hillslope configurations (Table 4). In general, the multiple OFE simulations result in increased subsurface lateral flow on steep sections of each slope, and increased surface runoff on flat sections of the slope. Figure 7 illustrates the distribution of cumulative sediment yield and net erosion for the S-curve shape. Although average annual runoff at the outlet of the S-curve hillslope is greater using multiple OFEs, along the slope the 10 OFEs simulation shows greater surface runoff than the single OFE simulation only on the last two OFEs (i.e., the bottom 30 m of the slope; Figure 5c). From Figure 7, WEPP simulated net deposition over the last 30 m rather than net soil detachment. When using only one OFE all runoff water simulated at the hillslope outlet is assumed to be generated uniformly 339

11 BOLL, BROOKS, CRABTREE, DUN, AND STEENHUIS TABLE 4. Simulated Average Annual Sediment Yield Delivered at the Hillslope Outlet for Three Hillslope Configurations Using One 150 m Overland Flow Element (OFE) vs. Ten 15 m OFEs. Slope Shape Number of OFEs OFE Length across the slope, which leads to more erosion generated on the steeper slope sections than with the multiple OFE simulations. The model results suggest that a little runoff on steeper slopes has much more erosive power than extended saturation and greater runoff volumes on flatter slopes. Zheng et al. (2000), however, showed that erodibility parameters and sediment delivery of fully saturated soils (during artesian drainage conditions, or saturation-excess runoff) may be different than for partially saturated soils (during free drainage conditions, or infiltration-excess runoff). For example, recent research indicates that soil erodibility in saturated, seepage zones in a landscape can be 5.6 times greater than soil under free drainage conditions (Nouwakpo and Huang, 2011). Therefore, simulation results on erosion and deposition with WEPP-UI will require further research. Implications to Water Quality Modeling and Watershed Management Avg. Sediment Yield (Tonnes/ha) Concave Convex S-Curve FIGURE 7. Thirty-Year Average Net Erosion and Sediment Yield along an S-Shaped Hillslope Using 1 OFE vs. 10 OFEs. Hillslope scale analyses shown here using the WEPP-UI model have widespread implications to hydrologic modeling approaches and watershed management. Hydrologic models are often used to evaluate and assess the effectiveness of management practices. The effectiveness of management practices is highly dependent upon the flow path that water takes to reach a stream and the location of sediment detachment, transport, and deposition on a slope. Any model that routes subsurface lateral flow from hillslopes or other hydrologic units using a single uniform plane will not be able to capture the effects of lateral convergence on the magnitude, spatial distribution, and persistence of runoff within a slope. In the case of a convergent hillslope, this may be a difference between a model estimating surface runoff to occur only 5 days/yr vs. 99 days/yr (see Table 3). Without lateral convergence, a toe slope section of a hillslope could be predicted to have incorrect amounts of dissolved and adsorbed chemicals in runoff water simply because of incorrect identification of source and flow path. Accurate spatial distribution of runoff at the hillslope scale is important, as erosion computations are dependent on the amount of runoff generated as well as the location of runoff on the hillslope. At the watershed scale, accurate computation of loads to streams from hillslopes is important for further computation of changes due to stream dynamics. Soils in areas with saturation-excess-generated runoff can have greatly increased erodibility (Rockwell, 2002). Erosion can increase by an order of magnitude at a seepage face due to the interaction of shear stress on pore water content (Rockwell, 2002). CONCLUSIONS Testing of the WEPP model revealed several shortcomings in the lateral flow routines, as well as errors associated with the quasi-steady state assumption when using multiple OFEs on a daily time step. A modified version of WEPP (WEPP-UI), applied to the Coweeta experiment by Hewlett and Hibbert (1963), showed that an updated lateral flow routine using an hourly time step compared very favorably with observed discharge and cumulative drainage volumes. The importance of using multiple OFEs was illustrated for three hillslope configurations emphasizing the ability to simulate flow convergence effects on complex hillslopes. Models which neglect subsurface lateral convergence by approximating the subsurface flow as a single plane likely will inaccurately predict the spatial distribution of surface runoff and the proportion of surface runoff and lateral flow leaving each hillslope, particularly in complex topography. 340

12 VARIABLE SOURCE AREA HYDROLOGY MODELING WITH THE WATER EROSION PREDICTION PROJECT MODEL Findings of this study show that the hydrological processes in WEPP-UI are more physically based than in WEPP (v.2010), especially when the proper time step is used and hillslope configurations are adequately configured using multiple OFEs. With these changes, the WEPP model now is a robust model for simulation of both saturation-excess variable source area hydrology and Hortonian overland flow. Further research is needed on the application of WEPP at the watershed scale, and to evaluate WEPP s erosion and deposition predictions. The improved subsurface routines in WEPP not only provide the opportunity to examine the importance of runoff generation processes on detachment and erosion in seepage zones but provide a much more complete understanding of the effects of soil properties, topography, climate, and management on the hydrologic flow paths that transport pollutants through a landscape. SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article: A description of subsurface flow equations in WEPP (v.2010), a description of WEPP input files, and a comparison of drainage response curves in WEPP (v.2010) and WEPP-UI. ACKNOWLEDGMENTS The authors thank Joan Wu from Washington State University in Pullman WA, Dennis Flanagan and Jim Frankenberger from the USDA Sedimentation Laboratory in Lafayette, IN, and William Elliot from the Rocky Mountain Research Station, USDA-Forest Service in Moscow, ID for assistance and advice related to modifications of the WEPP Fortran code. This study was funded through the USDA-NIFA Conservation Effects Assessment Program (grant ) and a USDA-Forest Service Round 7 Southern Nevada Public Land Management Act (2A11) grant through the Rocky Mountain Research Station (08-JV ). LITERATURE CITED Beven, K.J. and P. Germann, Macropores and Water Flow in Soils. Water Resources Research 18(5): Beven, K.J. and M.J. Kirkby, A Physically Based Variable Contributing Area Model of Basin Hydrology. Hydrological Sciences Bulletin 24: Brooks, E.S., J. Boll, and P.A. McDaniel, An Experiment to Determine the Lateral Saturated Hydraulic Conductivity. Water Resources Research 40:W04208, doi: /2003WR Brooks, E.S., S.M. Saia, J. Boll, L. Wetzel, Z.M. Easton, and T.S. Steenhuis, Assessing BMP Effectiveness and Guiding BMP Planning Using Process-Based Modeling. Journal of the American Water Resources Association 51(2): Dohnal, M., T. Vogel, M. Sanda, and V. Jelınkova, Uncertainty Analysis of a Dual-Continuum Model Used to Simulate Subsurface Hillslope Runoff Involving Oxygen-18 as Natural Tracer. Journal of Hydrology and Hydromechanics 60: Dun, S., J.Q. Wu, W.J. Elliot, P.R. Robichaud, D.C. Flanagan, J.R. Frankenberger, R.E. Brown, and A.C. Xu, Adapting the Water Erosion Prediction Project (WEPP) Model for Forest Applications. Journal of Hydrology 366(1-4): Dunne, T. and R. Black, An Experimental Investigation of Runoff Production in Permeable Soils. Water Resources Research 6: Dunne, T., T.R. Moore, and C.H. Taylor, Recognition and Prediction of Runoff-Producing Zones in Humid Regions. Hydrological Sciences Bulletin 20(3): Ebel, B.A. and K. Loague, Physics-Based Hydrologic- Response Simulation: Seeing Through the Fog of Equifinality. Hydrological Processes 20: Flanagan, D.C., J.E. Gilley, and T.G. Franti, Water Erosion Prediction Project (WEPP): Development History, Model Capabilities, and Future Enhancements. Transactions of the ASABE 50(5): Flanagan, D.C. and M.A. Nearing (Editors), USDA-Water Erosion Prediction Project Hillslope Profile and Watershed Model Documentation. NSERL Report No. 10, USDA-ARS National Soil Erosion Research Laboratory, West Lafayette, Indiana. Frankenberger, J.R., E.S. Brooks, M.T. Walter, M.F. Walter, and T.S. Steenhuis, A GIS-Based Variable Source Area Hydrology Model. Hydrological Processes 13: Hewlett, J.D. and A.R. Hibbert, Moisture and Energy Conditions within a Sloping Soil Mass During Drainage. Journal of Geophysical Research 68: Hewlett, J.D. and A.R. Hibbert, Factors Affecting the Response of Small Watersheds to Precipitation in Humid Areas. In: Forest Hydrology, W.E. Sopper and H.W. Lull (Editors). Pergamon Press, New York, pp Horton, R.E., An Approach Toward a Physical Interpretation of Infiltration Capacity. Soil Science Society Proceedings 5:C, Lin, H.S., K.J. McInnes, L.P. Wilding, and C.T. Hallmark, Effects of Soil Morphology on Hydraulic Properties II. Hydraulic Pedotransfer Functions. Soil Science Society of America Journal 63(4): McDaniel, P.A., M.P. Regan, E.S. Brooks, J. Boll, S. Barndt, A. Falena, S.K. Young, and J.E. Hammel, Linking Fragipans, Perched Water Tables, and Catchment-Scale Hydrological Processes. Catena 73: Merritt, W.S., R.A. Letcher, and A.J. Jakeman, A Review of Erosion and Sediment Transport Models. Environmental Modeling & Software 18: Nouwakpo, S.K. and C.H. Huang, Quantifying Intrinsic and Extrinsic Factors Affecting Soil Erodibility. In: Proceedings International Symposium on Erosion and Landscape Evolution, ISELE Paper No D.C. Flanagan, J.C. Ascough II, and J.L. Nieber (Editors). ASABE, St. Joseph, Michigan, doi: / Pachepsky, Y.A., W.J. Rawls, and H.S. Lin, Hydropedology and Pedotransfer Functions. Geoderma 131(3): Pieri, L., M. Bittelli, J.Q. Wu, S. Dun, D.C. Flanagan, P.R. Pisa, F. Ventura, and F. Salvatorelli, Using the Water Erosion Prediction Project (WEPP) Model to Simulate Field-Observed Runoff and Erosion in the Apennines Mountain Range, Italy. Journal of Hydrology 336: Rockwell, D.L., The Influence of Groundwater on Surface Flow Erosion Processes During a Rainstorm. Earth Surface Processes Landforms 27: