Bacteria Decay

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.