In large subbasins with a time of concentration greater than 1 day, only a portion of the surface runoff and lateral flow will reach the main channel on the day it is generated. SWAT+ incorporates a storage feature to lag a portion of the surface runoff and lateral flow release to the main channel. Pesticides in the surface runoff and lateral flow are lagged as well.

Once the pesticide load in surface runoff and lateral flow is determined, the amount of pesticide released to the main channel is calculated:

$pst_{surf}=(pst'_{surf}+pst_{surstor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:3.4.1

$pst_{lat}=(pst'_{lat}+pst_{latstor,i-1})*(1-exp[\frac{-1}{TT_{lat}}])$ 4:3.4.2

$pst_{sed}=(pst'_{sed}+pst_{sedstor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:3.4.3

where $pst_{surf}$ is the amount of soluble pesticide discharged to the main channel in surface runoff on a given day (kg $pst$/ha), $pst'_{surf}$ is the amount of surface runoff soluble pesticide generated in HRU on a given day (kg $pst$/ha), $pst_{surstor,i-1}$ is the surface runoff soluble pesticide stored or lagged from the previous day (kg $pst$/ha), $pst_{lat}$ is the amount of soluble pesticide discharged to the main channel in lateral flow on a given day (kg $pst$/ha),$pst'_{lat}$ is the amount of lateral flow soluble pesticide generated in HRU on a given day (kg $pst$/ha), $pst_{latstor,i-1}$ is the lateral flow pesticide stored or lagged from the previous day (kg $pst$/ha), $pst_{sed}$ is the amount of sorbed pesticide discharged to the main channel in surface runoff on a given day (kg $pst$/ha), $pst'_{sed}$ is the sorbed pesticide loading generated in HRU on a given day (kg $pst$/ha), $pst_{sedstor,i-1}$ is the sorbed pesticide stored or lagged from the previous day (kg $pst$/ha), $surlag$ is the surface runoff lag coefficient, $t_{conc}$ is the time of concentration for the HRU (hrs) and $TT_{lag}$ is the lateral flow travel time (days).

Table 4:3-4: SWAT+ input variables that pertain to pesticide lag calculations.

Pesticide attached to soil particles may be transported by surface runoff to the main channel. This phase of pesticide is associated with the sediment loading from the HRU and changes in sediment loading will impact the loading of sorbed pesticide. The amount of pesticide transported with sediment to the stream is calculated with a loading function developed by McElroy et al. (1976) and modified by Williams and Hann (1978).

$pst_{sed}=0.001*C_{solidphase}*\frac{sed}{area_{hru}}*\varepsilon_{pst:sed}$ 4:3.3.1

where $pst_{sed}$ is the amount of sorbed pesticide transported to the main channel in surface runoff (kg $pst$/ha), $C_{solidphase}$ is the concentration of pesticide on sediment in the top 10 mm (g $pst$/ metric ton soil), sed is the sediment yield on a given day (metric tons), $area_{hru}$ is the HRU area (ha), and $\varepsilon_{pst:sed}$ is the pesticide enrichment ratio.

The total amount of pesticide in the soil layer is the sum of the adsorbed and dissolved phases:

$pst_{s,ly}=0.01*(C_{solution}*SAT_{ly}+C_{solidphase}*\rho_b*depth_{ly})$ 4:3.3.2

where $pst_{s,ly}$ is the amount of pesticide in the soil layer (kg $pst$/ha), $C_{solution}$ is the pesticide concentration in solution (mg/L or g/ton), $SAT_{ly}$ is the amount of water in the soil layer at saturation (mm H$_2$O), $C_{solidphase}$ is the concentration of the pesticide sorbed to the solid phase (mg/kg or g/ton), $\rho_b$ is the bulk density of the soil layer (Mg/m$^3$), and $depth_{ly}$ is the depth of the soil layer (mm). Rearranging equation 4:3.1.1 to solve for $C_{solution}$ and substituting into equation 4:3.3.2 yields:

$pst_{s,ly}=0.01*(\frac{C_{solidphase}}{K_p}*SAT_{ly}+C_{solidphase}*\rho_b*depth_{ly})$ 4:3.3.3

which rearranges to

$C_{solidphase}=\frac{100*K_p*pst_{s,ly}}{(SAT_{ly}+K_p*\rho_b*depth_{ly})}$ 4:3.3.4

where $C_{solidphase}$ is the concentration of the pesticide sorbed to the solid phase (mg/kg or g/ton), $K_p$ is the soil adsorption coefficient ((mg/kg)/(mg/L) or $m^3$/ton) $pst_{s,ly}$ is the amount of pesticide in the soil layer (kg $pst$/ha), $SAT_{ly}$ is the amount of water in the soil layer at saturation (mm H$_2$O), $\rho_b$ is the bulk density of the soil layer (Mg/m$^3$), and $depth_{ly}$ is the depth of the soil layer (mm).

The transport of pesticide from land areas into streams and water bodies is a result of soil weathering and erosion processes. Excessive loading of pesticides in streams and water bodies can produce toxic conditions that harm aquatic life and render the water unfit for human consumption. This chapter reviews the algorithms governing movement of soluble and sorbed forms of pesticide from land areas to the stream network. Pesticide transport algorithms in SWAT+ were taken from EPIC (Williams, 1995).

Pesticide in the soluble phase may be transported with surface runoff, lateral flow or percolation. The change in the amount of pesticide contained in a soil layer due to transport in solution with flow is a function of time, concentration and amount of flow:

$\frac{dpst_{s,ly}}{dt}=0.01*C_{solution}*w_{mobile}$ 4:3.2.1

where $pst_{s,ly}$ is the amount of pesticide in the soil layer (kg pst/ha), $C_{solution}$ is the pesticide concentration in solution (mg/L or g/ton), and $w_{mobile}$ is the amount of mobile water on a given day (mm H$_2$O). The amount of mobile water in the layer is the amount of water lost by surface runoff, lateral flow or percolation:

$w_{mobile}=Q_{surf}+Q_{lat,surf}+w_{perc,surf}$ for top 10 mm 4:3.2.2

$w_{mobile}=Q_{lat,ly}+w_{perc,ly}$ for lower soil layers 4:3.2.3

where $w_{mobile}$ is the amount of mobile water in the layer (mm H$_2$O), $Q_{surf}$ is the surface runoff generated on a given day (mm H$_2$O), $Q_{lat,ly}$ is the water discharged from the layer by lateral flow (mm H$_2$O), and $w_{perc,ly}$ is the amount of water percolating to the underlying soil layer on a given day (mm H$_2$O).

The total amount of pesticide in the soil layer is the sum of the adsorbed and dissolved phases:

$pst_{s,ly}=0.01*(C_{solution}*SAT_{ly}+C_{solidphase}*\rho_b*depth_{ly})$ 4:3.2.4

where $pst_{s,ly}$ is the amount of pesticide in the soil layer (kg pst/ha), $C_{solution}$ is the pesticide concentration in solution (mg/L or g/ton), $SAT_{ly}$ is the amount of water in the soil layer at saturation (mm H$_2$O), $C_{solidphase}$ is the concentration of the pesticide sorbed to the solid phase (mg/kg or g/ton), $\rho_b$ is the bulk density of the soil layer (Mg/m$^3$), and $depth_{ly}$ is the depth of the soil layer (mm). Rearranging equation 4:3.1.1 to solve for $C_{solidphase}$ and substituting into equation 4:3.2.4 yields:

$pst_{s,ly}=0.01*(C_{solution}*SAT_{ly}+C_{solution}*K_p*\rho_b*depth_{ly})$ 4:3.2.5

which rearranges to

$C_{solution}=\frac{pst_{s,ly}}{0.01*(SAT_{ly}+K_p*\rho_b*depth_{ly})}$ 4:3.2.6

Combining equation 4:3.2.6 with equation 4:3.2.1 yields

$\frac{dpst_{s,ly}}{dt}=\frac{pst_{s,ly}*w_{mobile}}{(SAT_{ly}+K_p*\rho_b*depth_{ly})}$ 4:3.2.7

Integration of equation 4:3.2.7 gives

$pst_{s,ly,t}=pst_{s,ly,o}*exp[\frac{-w_{mobile}}{(SAT_{ly}+K_p*\rho_b*depth_{ly})}]$ 4:3.2.8

where $pst_{s,ly,t}$ is the amount of pesticide in the soil layer at time t (kg $pst$t/ha), $pst_{s,ly,o}$ is the initial amount of pesticide in the soil layer (kg $pst$/ha), $w_{mobile}$ is the amount of mobile water in the layer (mm H$_2$O), $SAT_{ly}$ is the amount of water in the soil layer at saturation (mm H$_2$O), $K_p$ is the soil adsorption coefficient ((mg/kg)/(mg/L)), $\rho_b$ is the bulk density of the soil layer (Mg/m$^3$), and $depth_{ly}$ is the depth of the soil layer (mm).

To obtain the amount of pesticide removed in solution with the flow, the final amount of pesticide is subtracted from the initial amount of pesticide:

$pst_{flow}=pst_{s,ly,o}*(1-exp[\frac{-w_{mobile}}{(SAT_{ly}+K_p*\rho_b*depth_{ly})}])$ 4:3.2.9

where $pst_{flow}$ is the amount of pesticide removed in the flow (kg pst/ha) and all other terms were previously defined.

For the top 10 mm that interacts with surface runoff, the pesticide concentration in the mobile water is calculated:

$conc_{pst,flow}=min{[pst_{flow}/[w_{perc,surf}+\beta_{pst}(Q_{surf}+Q_{lat,surf})]], pst_{sol}/100}.$ 4:3.2.10

while for lower layers

$conc_{pst,flow}=min[{[pst_{flow}/w_{mobile}],}pst_{sol}/100.]$ 4:3.2.11

where $conc_{pst,flow}$ is the concentration of pesticide in the mobile water (kg $pst$/ha-mm H$_2$O), $pst_{flow}$ is the amount of pesticide removed in the flow (kg $pst$/ha), $\beta_{pst}$ is the pesticide percolation coefficient, $Q_{surf}$ is the surface runoff generated on a given day (mm H$_2$O), $Q_{lat,ly}$ is the water discharged from the layer by lateral flow (mm H$_2$O), $w_{perc,ly}$ is the amount of water percolating to the underlying soil layer on a given day (mm H$_2$O), $w_{mobile}$ is the amount of mobile water in the layer (mm H$_2$O), and $pst_{sol}$ is the solubility of the pesticide in water (mg/L).

Pesticide moved to the underlying layer by percolation is calculated:

$pst_{perc,ly}=conc_{pst,flow}*w_{perc,ly}$ 4:3.2.12

where $pst_{perc,ly}$ is the pesticide moved to the underlying layer by percolation (kg $pst$/ha), $conc_{pst,flow}$ is the concentration of pesticide in the mobile water for the layer (kg $pst$/mm H$_2$O), and $w_{perc,ly}$ is the amount of water percolating to the underlying soil layer on a given day (mm H$_2$O).

Pesticide removed in lateral flow is calculated:

$pst_{lat,surf}=\beta_{pst}*conc_{pst,flow}*Q_{lat,surf}$ for top 10 mm 4:3.2.13

$pst_{lat,ly}=conc_{pst,flow}*Q_{lat,ly}$ for lower layers 4:3.2.14

where $pst_{lat,ly}$ is the pesticide removed in lateral flow from a layer (kg $pst$/ha), $\beta_{pst}$ is the pesticide percolation coefficient, $conc_{pst,flow}$ is the concentration of pesticide in the mobile water for the layer (kg $pst$/mm H$_2$O), and $Q_{lat,ly}$ is the water discharged from the layer by lateral flow (mm H$_2$O). The pesticide percolation coefficient allows the user to set the concentration of pesticide in runoff and lateral flow from the top 10 mm to a fraction of the concentration in percolate.

Pesticide removed in surface runoff is calculated:

$pst_{surf}=\beta_{pst}*conc_{pst,flow}*Q_{surf}$ 4:3.2.15

where $pst_{surf}$ is the pesticide removed in surface runoff (kg $pst$/ha), $\beta_{pst}$ is the pesticide percolation coefficient, $conc_{pst,flow}$ is the concentration of pesticide in the mobile water for the top 10 mm of soil (kg $pst$/mm H$_2$O), and $Q_{surf}$ is the surface runoff generated on a given day (mm H$_2$O).

Table 4:3-2: SWAT+ input variables that pertain to pesticide transport in solution.

As surface runoff flows over the soil surface, part of the water’s energy is used to pick up and transport soil particles. The smaller particles weigh less and are more easily transported than coarser particles. When the particle size distribution of the transported sediment is compared to that of the soil surface layer, the sediment load to the main channel has a greater proportion of clay sized particles. In other words, the sediment load is enriched in clay particles. The sorbed phase of pesticide in the soil is attached primarily to colloidal (clay) particles, so the sediment load will also contain a greater proportion or concentration of pesticide than that found in the soil surface layer.

The enrichment ratio is defined as the ratio of the concentration of sorbed pesticide transported with the sediment to the concentration in the soil surface layer. SWAT+ will calculate an enrichment ratio for each storm event, or allow the user to define a particular enrichment ratio for sorbed pesticide that is used for all storms during the simulation. To calculate the enrichment ratio, SWAT+ uses a relationship described by Menzel (1980) in which the enrichment ratio is logarithmically related to sediment concentration. The equation used to calculate the pesticide enrichment ratio, $\varepsilon_{pst:sed}$, for each storm event is:

$\varepsilon_{pst:sed}=0.78*(conc_{sed,surq})^{-0.2468}$ 4:3.3.5

where $conc_{sed,surq}$ is the concentration of sediment in surface runoff (Mg sed/m$^3$ H$_2$O). The concentration of sediment in surface runoff is calculated:

$conc_{sed,surq}=\frac{sed}{10*area_{hru}*Q_{surf}}$ 4:3.3.6

where $sed$ is the sediment yield on a given day (metric tons), $area_{hru}$ is the HRU area (ha), and $Q_{surf}$ is the amount of surface runoff on a given day (mm H$_2$O).

Table 4:3-3: SWAT+ input variables that pertain to sorbed pesticide loading.

Pesticide in the soil environment can be transported in solution or attached to sediment. The partitioning of a pesticide between the solution and soil phases is defined by the soil adsorption coefficient for the pesticide. The soil adsorption coefficient is the ratio of the pesticide concentration in the soil or solid phase to the pesticide concentration in the solution or liquid phase:

$K_p=\frac{C_{solidphase}}{C_{solution}}$ 4:3.1.1

where $K_p$ is the soil adsorption coefficient ((mg/kg)/(mg/L) or m$^3$/ton), $C_{solidphase}$ is the concentration of the pesticide sorbed to the solid phase (mg chemical/kg solid material or g/ton), and $C_{solution}$ is the concentration of the pesticide in solution (mg chemical/L solution or g/ton). The definition of the soil adsorption coefficient in equation 4:3.1.1 assumes that the pesticide sorption process is linear with concentration and instantaneously reversible.

Because the partitioning of pesticide is dependent upon the amount of organic material in the soil, the soil adsorption coefficient input to the model is normalized for soil organic carbon content. The relationship between the soil adsorption coefficient and the soil adsorption coefficient normalized for soil organic carbon content is:

$K_p=K_{oc}*\frac{orgC}{100}$ 4:3.1.2

where $K_p$ is the soil adsorption coefficient ((mg/kg)/(mg/L)), $K_{oc}$ is the soil adsorption coefficient normalized for soil organic carbon content ((mg/kg)/(mg/L) or m$^3$/ton), and $orgC$ is the percent organic carbon present in the soil.

Table 4:3-1: SWAT+ input variables that pertain to pesticide phase partitioning.