Empirical Model Development

To evaluate the effectiveness of VFSs under ideal conditions, a model was developed from a combination of measured data derived from literature and Vegetative Filter Strip MODel (VFSMOD) (Muñoz-Carpena, 1999) simulations. VFSMOD was selected for this application over other VFS-related models due to its process-based nature, abundant documentation, and ease of use. The algorithms used in VFSMOD are complex, requiring iterative solutions and significant computational resources. A watershed scale model, which may simulate many hundreds of VFS daily for decades, requires a less computationally intensive solution. VFSMOD was, therefore, not a candidate for incorporation into SWAT+.

VFSMOD model and its companion program, UH, were used to generate a database of 1650 VFS simulations. The UH utility uses the curve number approach (USDA-SCS, 1972), unit hydrograph and the Modified Universal Soil Loss Equation (MUSLE) (Williams, 1975) to generate synthetic sediment and runoff loads from a source area upslope of the VFS (Muñoz-Carpena and Parsons, 2005). This simulation database contained 3 h rainfall events ranging from 10 mm to 100 mm, on a cultivated field with a curve number of 85 and a C factor of 0.1. Field dimensions were fixed at 100 m by 10 m with a 10 m wide VFS at the downslope end. Width of the VFS ranged from 1 m to 20 m yielding drainage area to VFS area ratios from 5 to 100. Slopes of 2%, 5% and 10% were simulated on 11 soil textural classes. This database was generated via software, which provided input parameters to both UH and VFSMOD then executed each program in turn. This database and a variety of other VFSMOD simulations were used to evaluate the sensitivity of various parameters and correlations between model inputs and predictions.

An empirical model for runoff reduction by VFSs was developed based on VFSMOD simulations. The model was derived from runoff loading and saturated hydraulic conductivity using the statistical package Minitab 15 (Minitab-Inc., 2006). Saturated hydraulic conductivity is available in SWAT+, and runoff loading can be calculated from HRU-predicted runoff volume and drainage area to VFS area ratio (DAFSratio). Both independent variables were transformed to improve the regression. The final form is given below:

$R_R=75.8-10.8(ln(R_L)+25.9 ln(K_{SAT})$ 6:5.1.1

where $R_R$ is the runoff reduction (%); $R_L$ is the runoff loading (mm); and $K_{SAT}$ is the saturated hydraulic conductivity (mm/hr). The regression was able to explain the majority of the variability (R$^2$ = 0.76; n = 1,650) in the simulated runoff reduction. The resulting model (Figure 6:5-1) produced runoff reduction efficiencies from -30% to 160%. Reductions greater than 100% are not possible; these were an artifact of the regression model. VFSs in SWAT+ were not allowed to generate additional runoff or pollutants; the model was limited to a range of 0% to 100%. The comparison between the empirical model and VFSMOD simulations improved (R$^2$ = 0.84) when the range was limited.

Figure 6:5-1. Empirical runoff reduction model compared to the VFSMOD dataset from which it is derived. As regressed (top) and limited from 0% to 100% (bottom). The limited form of the empirical model was implemented in SWAT+. The Nash Sutcliff Efficiency (NSE), the number of sample used in the regression (n) are also given.