The enrichment ratio is defined as the ratio of the concentration of bacteria transported with the sediment to the concentration of bacteria attached to soil partivles in the soil surface layer. SWAT+ calculates an enrichment ratio for each storm event which is used for the bacteria loading calculations. 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 bacteria enrichment ratio, $\varepsilon_{bact:sed}$, for each storm event is:

$\varepsilon_{bact:sed}=0.78*(conc_{sed,surq})^{-0.2468}$ 4:4.2.5

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:

$conc_{sed,surq}=\frac{sed}{10*area_{hru}*Q_{surf}}$ 4:4.2.6

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 4:4-2: SWAT+ input variables that pertain to loading of bacteria attached to sediment.

Due to the low mobility of bacteria in soil solution, surface runoff will only partially interact with the bacteria present in the soil solution. The amount of bacteria transported in surface runoff is:

$bact_{lp,surf}=\frac{bact_{lpsol}*Q_{surf}}{\rho_b*depth_{surf}*k_{bact,surf}}$ 4:4.1.1

$bact_{p,surf}=\frac{bact_{psol}*Q_{surf}}{\rho_b*depth_{surf}*k_{bact,surf}}$ 4:4.1.2

where $bact_{lp,surf}$is the amount of less persistent bacteria lost in surface runoff(#cfu/m$^2$), $bact_{p,surf}$ is the amount of persistent bacteria lost in surface runoff (#cfu/m$^2$), $bact_{lpsol}$ is the amount of less persistent bacteria present in soil solution (#cfu/m$^2$), $bact_{psol}$ is the amount of persistent bacteria present in soil solution (#cfu/m$^2$), $Q,_{surf}$ is the amount of surface runoff on a given day (mm H$_2$O), $\rho_b$ is the bulk density of the top 10 mm(Mg/m$^3$) (assumed to be equivalent to bulk density of first soil layer), $depth_{surf}$ is the depth of the “surface” layer (10 mm), and $k_{bact,surf}$ is the bacteria soil partitioning coefficient (m$^3$/Mg). The bacteria soil partitioning coefficient is the ratio of the bacteria concentration in the surface 10 mm soil solution to the concentration of bacteria in surface runoff.

Table 4:4-1: SWAT+ input variables that pertain to bacteria in surface runoff.

Bacteria attached to soil particles may be transported by surface runoff to the main channel. This bacteria is associated with the sediment loading from the HRU and changes in sediment loading will be reflected in the loading of this form of bacteria. The amount of bacteria 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) for nutrients.

$bact_{lp,sed}=0.0001*conc_{sedlpbact}*\frac{sed}{area_{hru}}*\varepsilon_{bact:sed}$ 4:4.2.1

$bact_{p,sed}=0.0001*conc_{sedpbact}*\frac{sed}{area_{hru}}*\varepsilon_{bact:sed}$ 4:4.2.2

where $bact_{lp,sed}$ is the amount of less persistent bacteria transported with sediment in surface runoff (#cfu/m$^2$), $bact_{p,sed}$ is the amount of persistent bacteria transported with sediment in surface runoff (#cfu/m$^2$), $conc_{sedlpbact}$ is the concentration of less persistent bacteria attached to sediment in the top 10 mm (# cfu/ metric ton soil), $conc_{sedpbact}$ is the concentration of persistent bacteria attached to sediment in the top 10 mm (# cfu/ metric ton soil), $sed$ is the sediment yield on a given day (metric tons), $area_{hru}$ is the HRU area (ha), and $\varepsilon_{bact:sed}$ is the bacteria enrichment ratio.

The concentration of bacteria attached to sediment in the soil surface layer is calculated:

$conc_{sedlpbact}=1000*\frac{bact_{lp,sorb}}{\rho_b*depth_{surf}}$ 4:4.2.3

$conc_{sedpbact}=1000*\frac{bact_{p,sorb}}{\rho_b*depth_{surf}}$ 4:4.2.4

where $bact_{lpsorb}$ is the amount of less persistent bacteria sorbed to the soil (#cfu/m$^2$), $bact_{psorb}$ is the amount of persistent bacteria sorbed to the soil (#cfu/m$^2$), $\rho_b$ is the bulk density of the first soil layer (Mg/m$^3$), and $depth_{surf}$ is the depth of the soil surface layer (10 mm).

The transport of pathogenic bacteria from land areas into streams and water bodies is a matter of concern in some watersheds. Excessive loading of bacteria into streams and water bodies could potentially contaminate drinking water and cause outbreaks of infection among the human population using the water. This chapter reviews the algorithms governing movement of bacteria from land areas to the stream network.

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

Once the bacteria load in surface runoff is determined, the amount of bacteria released to the main channel is calculated:

$bact_{lp,surf}=(bact'_{lp,surf}+bact_{lp,surstor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:4.3.1

$bact_{p,surf}=(bact'_{p,surf}+bact_{p,surstor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:4.3.2

$bact_{lp,sed}=(bact'_{lp,sed}+bact_{lp,sedstor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:4.3.3

$bact_{p,sed}=(bact'_{p,sed}+bact_{p,sedstor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:4.3.4

where $bact_{lp,surf}$ is the amount of less persistent bacteria discharged to the main channel in surface runoff on a given day (#cfu/m$^2$),$bact'_{lp,surf}$ is the amount of surface runoff less persistent bacteria generated in the HRU on a given day (#cfu/m$^2$), $bact_{lp,surstor,i-1}$ is the surface runoff less persistent bacteria stored or lagged from the previous day (#cfu/m$^2$), $bact_{p,surf}$ is the amount of persistent bacteria discharged to the main channel in surface runoff on a given day (#cfu/m2), $bact'_{p,surf}$ is the amount of surface runoff persistent bacteria generated in the HRU on a given day (#cfu/m$^2$), $bact_{p,surstor,i-1}$ is the surface runoff persistent bacteria stored or lagged from the previous day (#cfu/m$^2$), $bact_{lp,sed}$ is the amount of sediment-attached less persistent bacteria discharged to the main channel in surface runoff on a given day (#cfu/m$^2$),$bact'_{lp,sed}$ is the amount of sediment-attached less persistent bacteria generated in the HRU on a given day (#cfu/m$^2$), $bact_{lp,sedstor,i-1}$ is the sediment-attached less persistent bacteria stored or lagged from the previous day (#cfu/m$^2$), $bact_{p,sed}$ is the amount of sediment-attached persistent bacteria discharged to the main channel in surface runoff on a given day (#cfu/m$^2$), $bact'_{p,sed}$ is the amount of sediment-attached persistent bacteria generated in the HRU on a given day (#cfu/m$^2$), $bact_{p,sedstor,i-1}$ is the sediment-attached persistent bacteria stored or lagged from the previous day (#cfu/m$^2$), $surlag$ is the surface runoff lag coefficient, and $t_{conc}$ is the time of concentration for the HRU (hrs).

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