> For the complete documentation index, see [llms.txt](https://swatplus.gitbook.io/io-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://swatplus.gitbook.io/io-docs/theoretical-documentation/section-4-erosion/pesticide-transport/movement-of-soluble-pesticide.md).

# Movement of Soluble Pesticide

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.

| Variable Name | Definition                                                  | Input File |
| ------------- | ----------------------------------------------------------- | ---------- |
| SOL\_BD       | $$\rho\_b$$: Soil bulk density     (Mg m$$^{-3}$$)          | .sol       |
| WSOL          | $$pst\_{sol}$$: Solubility of the pesticide in water (mg/L) | pest.dat   |
| PERCOP        | $$\beta\_{pst}$$: Pesticide percolation coefficient         | .bsn       |