# Nutrient Lag in  Surface Runoff and Lateral Flow

         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. Nutrients in the surface runoff and lateral flow are lagged as well.

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

$$NO3\_{surf}=(NO3'*{surf}+NO3*{surstor,i-1})\*(1-exp\[\frac{-surlag}{t\_{conc}}])$$                     4:2.5.1

$$NO3\_{lat}=(NO3'*{lat}+NO3*{latstor,i-1})\*(1-exp\[\frac{-1}{TT\_{lat}}])$$                                4:2.5.2

$$orgN\_{surf}=(orgN'*{surf}+orgN*{stor,i-1})\*(1-exp\[\frac{-surlag}{t\_{conc}}])$$                        4:2.5.3

$$P\_{surf}=(P'*{surf}+P*{stor,i-1})\*(1-exp\[\frac{-surlag}{t\_{conc}}])$$                                              4:2.5.4

$$sedP\_{surf}=(sedP'*{surf}+sedP*{stor,i-1})\*(1-exp\[\frac{-surlag}{t\_{conc}}])$$                            4:2.5.5

where $$NO3\_{surf}$$ is the amount of nitrate discharged to the main channel in surface runoff on a given day (kg N/ha),$$NO3'*{surf}$$ is the amount of surface runoff nitrate generated in the HRU on a given day (kg N/ha), $$NO3*{surstor,i-1}$$ is the surface runoff nitrate stored or lagged from the previous day (kg N/ha), $$NO3\_{lat}$$ is the amount of nitrate discharged to the main channel in lateral flow on a given day (kg N/ha), $$NO3'*{lat}$$ is the amount of lateral flow nitrate generated in the HRU on a given day (kg N/ha), $$NO3*{latstor,i-1}$$ is the lateral flow nitrate stored or lagged from the previous day (kg N/ha), $$orgN\_{surf}$$ is the amount of organic N discharged to the main channel in surface runoff on a given day (kg N/ha),$$orgN'*{surf}$$ is the organic N loading generated in the HRU on a given day (kg N/ha), $$orgN*{stor,i-1}$$ is the organic N stored or lagged from the previous day (kg N/ha), $$P\_{surf}$$ is the amount of solution P discharged to the main channel in surface runoff on a given day (kg P/ha), $$P'*{surf}$$ is the amount of solution P loading generated in the HRU on a given day (kg P/ha), $$P*{stor,i-1}$$ is the solution P loading stored or lagged from the previous day (kg P/ha), $$sedP\_{surf}$$ is the amount of sediment-attached P discharged to the main channel in surface runoff on a given day (kg P/ha), $$sedP'*{surf}$$ is the amount of sediment-attached P loading generated in the HRU on a given day (kg P/ha), $$sedP*{stor,i-1}$$ is the sediment-attached P stored or lagged from the previous day (kg P/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 4:2-5: SWAT+ input variables that pertain to nutrient lag calculations.

| Variable Name | Definition                                     | Input File |
| ------------- | ---------------------------------------------- | ---------- |
| SURLAG        | $$surlag$$: surface runoff lag coefficient     | .bsn       |
| LAT\_TTIME    | $$TT\_{lag}$$: Lateral flow travel time (days) | .hru       |