A first order decay function is used to calculate changes in bacteria concentrations (Bowie et al., 1985).

$bact_{lprch,i}=bact_{lprch,i-1}*exp(-\mu_{lprch,die})$ 7:5.1.1

$bact_{prch,i}=bact_{prch,i-1}*exp(-\mu_{prch,die})$ 7:5.1.2

where $bact_{lprch,i}$ is the amount of less persistent bacteria present in the reach on day $i$ (#cfu/100mL), $bact_{lprch,i-1}$ is the amount of less persistent bacteria present in the reach on day $i-1$ (#cfu/100mL), $\mu_{lprch,die}$ is the rate constant for die-off of less persistent bacteria in streams (1/day), $bact_{prch,i}$ is the amount of persistent bacteria present in the reach on day $i$ (#cfu/100mL), $bact_{prch,i-1}$ is the amount of persistent bacteria present in the reach on day $i-1$ (#cfu/100mL), and $\mu_{prch,die}$ is the rate constant for die-off of persistent bacteria in streams (1/day).

The die-off rate constants are adjusted for temperature using the equations:​

$\mu_{lprch,die}=\mu_{lprch,die,20}*\theta_{bact}^{(T_{water}-20)}$ 7:5.1.3

$\mu_{prch,die}=\mu_{prch,die,20}*\theta_{bact}^{(T_{water}-20)}$ 7:5.1.4

where $\mu_{lprch,die}$, is the rate constant for die-off of less persistent bacteria in streams (1/day), $\mu_{prch,die}$ is the rate constant for die-off of persistent bacteria in streams (1/day), $\mu_{lprch,die,20}$is the rate constant for die-off of less persistent bacteria in streams at 20$\degree$C (1/day), $\mu_{prch,die,20}$ is the rate constant for die-off of persistent bacteria in streams at 20$\degree$C (1/day), $\theta_{bact}$ is the temperature adjustment factor for bacteria die-off/re-growth, and $T_{water}$ is the water temperature ($\degree$C).

Table 7:5-1: SWAT+ input variables that pertain to bacteria die-off in the stream.

In sediment channel routing, the maximum concentration of sediment that can be transported by the water, $conc_{sed,ch,mx}$, (ton/m$^3$ or kg/L) is compared to the concentration of sediment in the reach at the beginning of the time step, $conc_{sed,ch,i}$ (Neitsch et al., 2005).

If $conc_{sed,ch,i}$ < $conc_{sed,ch,mx}$, resuspension is the dominant process in the reach segment and the net amount of sediment reentrained is calculated:

$sed_{deg}=(conc_{sed,ch,mx}-conc_{sed,ch,i})*V_{ch}*K_{ch}*C_{ch}$ 7:5.2.1

where $sed_{deg}$ is the amount of sediment reentrained in the reach segment (metric tons), $conc_{sed,ch,mx}$ is the maximum concentration of sediment that can be transported by the water (ton sediment/m$^3$ H$_2$O or kg sediment/L H$_2$O), $conc_{sed,ch,i}$ is the initial sediment concentration in the reach (ton sediment/m$^3$ H$_2$O or kg sediment/L H$_2$O), $V_{ch}$ is the volume of water in the reach segment (m$^3$ H$_2$O), $K_{ch}$ is the channel erodibility factor (cm/hr/Pa), and $C_{ch}$ is the channel cover factor. When sediment resuspends, both bacteria in sediment solution and on sediment particles are released, and the net amount of bacteria released from streambed is calculated:

$bact_{deg}=sed_{deg} *conc_{bact,sed}$ 7:5.2.2

where $bact_{deg}$ is the amount of bacteria released from streambed in the reach segment (# cfu), $sed_{deg}$ is the amount of sediment reentrained in the reach segment (metric tons), and $conc_{bact,sed}$ is the concentration of bacteria in streambed in the reach segment (# cfu/ton sediment). Bacteria concentration in streambed is calculated by the empirical regression equation, logarithmic sine function of the days of year:

$log(conc_{bact,sed})=bsc_1*sin(bsc_2*\frac{day-bsc_3}{366}*\pi)+bsc_4$ 7:5.2.3

where $conc_{bact,sed}$ is the concentration of bacteria in streambed (# cfu/ton sediment), day is the days of year, and $bsc_1$ through $bsc_4$ are the regression coefficients in streambed bacteria concentration equation.

If $conc_{sed,ch,i}$ > $conc_{sed,ch,mx}$, deposition is the dominant process in the reach segment and the net amount of sediment deposited is calculated:

$sed_{dep}=(conc_{sed,ch,i}-conc_{sed,ch,mx})*V_{ch}$ 7:5.2.4

where $sed_{dep}$ is the amount of sediment deposited in the reach segment (metric tons), $conc_{sed,ch,i}$ is the initial sediment concentration in the reach (ton sediment/m$^3$ H$_2$O or kg sediment/L H$_2$O), $conc_{sed,ch,mx}$ is the maximum concentration of sediment that can be transported by the water (ton sediment/m$^3$ H$_2$O or kg sediment/L H$_2$O), and $V_{ch}$is the volume of water in the reach segment (m$^3$ H$_2$O). When suspended sediment deposits, bacteria on settling sediment particles are deposited, and the net amount of bacteria settled from stream water is calculated (Bai and Lung, 2005):

$bact_{dep}=bact_{ch,i}*\frac{K_p*sed_{dep}}{V_{ch}+K_p*(conc_{sed,ch,i}*V_{ch})}$ 7:5.2.5

where $bact_{dep}$ is the amount of bacteria settled from stream water in the reach segment (# cfu), $bact_{ch,i}$ is the amount of bacteria in the stream water in the reach segment at the beginning of the time period (# cfu), $K_p$ is the linear partitioning coefficient of bacteria between the suspended sediment and water (m$^3$ H$_2$O/ton sediment or L H$_2$O/kg sediment), $sed_{dep}$ is the amount of sediment deposited in the reach segment (metric tons), $V_{ch}$ is the volume of water in the reach segment (m$^3$ H$_2$O), and $conc_{sed,ch,i}$ is the initial sediment concentration in the reach (ton sediment/m$^3$ H$_2$O or kg sediment/L H$_2$O). The linear partitioning coefficient is calculated from the empirical regression equation (Pachepsky et al., 2006):

$K_p=10^{-1.6}*clay^{1.98}$ 7:5.2.6

where $K_p$ is the linear partitioning coefficient of bacteria onto the suspended sediment (m$^3$ H$_2$O/ton sediment or L H$_2$O/kg sediment) and $clay$ is the percentage of clay in suspended sediment in stream water in the reach segment (%). clay normally varies between 2 and 50%.

Once the amount of bacteria released and settled has been calculated, the final amount of sediment in the reach is determined:

$bact_{ch}=bact_{ch,i}+bact_{deg}-bact_{dep}$ 7:5.2.7

where $bact_{ch}$ is the amount of bacteria in the stream water in the reach segment (# cfu), $bact_{ch,i}$ is the amount of bacteria in the stream water in the reach segment at the beginning of the time period (# cfu), $bact_{deg}$ is the amount of bacteria released from streambed in the reach segment (# cfu), and $bact_{dep}$ is the amount of bacteria settled from stream water in the reach segment (# cfu).

The final bacteria concentration in the reach is calculated:

$conc_{bact,ch}=\frac{bact_{ch}}{V_{ch}}*10^{-4}$ 7:5.2.8

where $conc_{bact,ch}$ is the concentration of bacteria in the stream water in the reach segment (# cfu/100 mL), $bact_{ch}$ is the amount of bacteria in the stream water in the reach segment (# cfu), and $V_{ch}$ is the volume of water in the reach segment (m$^3$ H$_2$O).

SWAT+ calculates loading of pathogens and indicator bacteria for pathogens from land areas in the watershed. In the stream, bacteria die-off is the only process modeled.