In addition to the mechanisms by which sediment and runoff are captured, nutrients may be adsorbed onto vegetation, surface residues, or the soil surface (Barfield et al., 1998). For the sake of simplicity, nutrient reduction was considered to be a function of sediment or runoff reduction only. Only nitrogen and phosphorus were considered. All nutrient models were developed from measured VFS data; the current version of VFSMOD does not account for nutrients.

The sediment reduction model developed for SWAT+ was based on measured VFS data. A VFS removes sediment by reducing runoff velocity due to increased resistance of the vegetative media and enhanced infiltration in the VFS area (Barfield et al., 1998). Both result in a reduction in transport capacity and the deposition of sediment. Both the filtering and infiltration aspects are represented in the model. Similar to the runoff loading approach used earlier, sediment loading per unit VFS area was found to correlate with measured sediment reduction. Dosskey et al. (2002) hypothesized that sediment trapping efficiency decreases as the load per unit of buffer area increases. Sediment loading was calculated as the mass of sediment originating from the upslope area per unit of VFS area express as kg m$^{-2}$. The infiltration aspect was represented in the model by incorporating the runoff reduction as a percentage. Sixty-two experiments reported in the literature were used to develop this model.

$S_R(\%)=79.0-1.04 S_L+0.213R_R$ 6:5.1.2

where $S_R$ is the predicted sediment reduction (%); $S_L$ is sediment loading (kg/m$^2$); and $R_R$ is the runoff reduction (%). Sediment loading alone was correlated with sediment reduction ($R^2$ = 0.41) (Figure 6:5-2). The addition of runoff reduction allowed the regression model to explain most of the variability ($R^2$ = 0.64) in the measured data.

The model for total phosphorus was based on sediment reduction. Although total phosphorus is composed of both soluble and particulate forms, particulate forms represent the bulk of phosphorus lost from conventionally cultivated fields. The total phosphorus model was developed from 63 observations; more data than any other nutrient model. The intercept was not significant. Sediment reduction was able to explain 43% of the variability. The model was applied to all particulate forms of phosphorus in the SWAT+ VFS submodel. The model is given below:

$TP_R=0.90 S_R$ 6:5.1.5

where $TP_R$ is the total phosphorus reduction (%); and $S_R$ is the sediment reduction (%).

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:

6:5.1.1

where is the runoff reduction (%); is the runoff loading (mm); and is the saturated hydraulic conductivity (mm/hr). The regression was able to explain the majority of the variability (R = 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 = 0.84) when the range was limited.

The soluble phosphorus model was based on runoff reduction only. The observations censored from (Dillaha et al., 1989) for the nitrates were also censored for soluble phosphorus. The soluble phosphorus model has the weakest relationship of all the nutrient models (R = 0.27), yet both the slope and intercept were significant (p = 0.01).

6:5.1.6

where is the dissolved phosphorus reduction (%); and is the runoff reduction (%). Like nitrate, there is a significant reduction in soluble phosphorus (29.3%) with no corresponding runoff reduction. Experimental observations of soluble phosphorus reduction at low runoff reductions are highly variable. Dillaha et al. (1989) found reductions in soluble phosphorus ranging from 43% to -31% with near zero runoff reduction. The minimum reduction predicted by equation 6 could be the result of mechanisms similar to those cited for the removal of nitrates, or simply an artifact of experimental variability.

VFSs were implemented at the HRU level in SWAT+. Three additional model parameters were added as SWAT+ inputs: the drainage area to VFS area ratio (), the fraction of the field drained by the most heavily loaded 10% of the VFS (), and the fraction of the flow through the most heavily loaded 10% of the VFS which is fully channelized (), all are specified in the HRU (.hru) file. A two-segment VFS was used. Section one represents the bulk of the VFS area (90%) which receives the least flow. Section two is the remaining 10% of the buffer which receives between 25% and 75% of the field runoff (Figure 6:5-4).

The fraction of flow through section two which is channelized is not subject to the VFS model; all sediment and nutrient are conservatively delivered to the tributary channel. for sections one and two are calculated from using the following equations:

6:5.1.7

The nitrate nitrogen model was developed from 42 observations. Four observations from Dillaha et al. (1989) had negative runoff reduction values due to additional runoff generated in the VFS. Because the VFS SWAT+ sub model is not allowed to generate additional loads, these observations were censored. All nutrient models initially included both runoff and sediment reductions as independent variables, but the nitrate nitrogen model was the only model where both were significant (=0.05). Nitrate is soluble and should not be associated with sediments, yet they were statistically correlated in the measured data. It is likely that the relationship between nitrate and sediment is an artifact of cross- correlation between sediment and runoff reductions (as demonstrated by Equation (2)). The nitrate model was based only on runoff reduction; both the slope and the intercept were significant (p<0.01). The nitrate nitrogen model is given below:

6:5.1.4

where is the nitrate nitrogen reduction (%); and is the runoff reduction (%). Because both the slope and the intercept were significant, there is a minimum reduction of 39.4% in nitrate, even if there is no reduction in runoff due to the VFS. This outcome may be unexpected, but it is supported by the measured data. Dillaha et al. (1989) observed nitrate reductions of 52% and 32% with only 0% and 7% reductions in runoff volume. Lee et al. (2000) also found significant reductions in nitrate (61%) with low runoff reductions (7%). One possible explanation is that sufficient runoff can be generated in the VFS such that there is little net reduction in runoff, but significant infiltration may still occur. Another possibility is foliar uptake of nitrates by vegetation within the strip.

The total nitrogen model was based on sediment reduction only. Much of the nitrogen lost in runoff from agricultural fields travels with sediments. Harmel et al. (2006) found that approximately 75% of the nitrogen lost from conventional tilled fields was in particulate forms. They also found that dissolved nitrogen forms, such as nitrate, were more dominant in no-till treatments. The vast majority of VFS data derived from literature were designed to simulate higher erosion conditions where particulate forms would represent the majority of nitrogen losses.

The total nitrogen model was based on sediment reduction from 44 observations reported in the literature. Two trials were censored during the development of the model. These experiments from Magette et al. (1989) yielded significant increases in total nitrogen exiting the VFS. The authors attributed this phenomenon to flushing of fine particulates captured in the VFS from prior experimental trials. Both the slope and the intercept were significant (P < 0.01). The model is given below and shown in Figure 6:5-3.

6:5.1.3

where is the total nitrogen reduction (%); and is the sediment reduction (%). Although this model was developed from total nitrogen, which includes both soluble and particulate forms, it was applied only to particulate forms in the SWAT+ model.