# 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.

| Variable Name | Definition                                                                                                | Input File |
| ------------- | --------------------------------------------------------------------------------------------------------- | ---------- |
| WDPRCH        | $$\mu\_{prch,die,20}$$: Die-off factor for persistent bacteria in streams at 20$$\degree$$C (1/day)       | .bsn       |
| WDLPRCH       | $$\mu\_{lprch,die,20}$$: Die-off factor for less persistent bacteria in streams at 20$$\degree$$C (1/day) | .bsn       |
| THBACT        | $$\theta\_{bact}$$: Temperature adjustment factor for bacteria die-off/growth                             | .bsn       |


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