# Bacteria Decay

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

       $$bact\_{lpres,i}=bact\_{lpre s,i-1}\*exp(\mu \_{lpres,die})$$                  8:5.1.1

        $$bact\_{pres,i}=bact\_{pres,i-1}\*exp(\mu \_{pres,die})$$                    8:5.1.2

where $$bact\_{lpres,i}$$ is the amount of less persistent bacteria present in the reservoir on day $$i$$ (#cfu/100mL), $$bact\_{lpres,i-1}$$ is the amount of less persistent bacteria present in the reservoir on day $$i-1$$ (#cfu/100mL), $$\mu\_{lpres,die}$$ is the rate constant for die-off of less persistent bacteria in water bodies (1/day), $$bact\_{pres,i}$$ is the amount of persistent bacteria present in the reservoir on day $$i$$ (#cfu/100mL), $$bact\_{pres,i-1}$$ is the amount of persistent bacteria present in the reservoir on day $$i-1$$ (#cfu/100mL), and $$\mu\_{pres,die}$$*,* is the rate constant for die-off of persistent bacteria in water bodies (1/day).

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

           $$\mu\_{lpres,die} =\mu\_{lpres,die,20} \* \theta *{bact}^{(T*{water}-20)}$$                       8:5.1.3

           $$\mu\_{pres,die} =\mu\_{pres,die,20} \* \theta *{bact}^{(T*{water}-20)}$$                                       8:5.1.4

where $$\mu\_{lpres,die}$$*,* is the rate constant for die-off of less persistent bacteria in water bodies (1/day), $$\mu\_{pres,die}$$ is the rate constant for die-off of persistent bacteria in water bodies (1/day), $$\mu\_{lpres,die,20}$$ is the rate constant for die-off of less persistent bacteria in water bodies at 20$$\degree$$C (1/day), $$\mu\_{pres,die,20}$$ is the rate constant for die-off of persistent bacteria in water bodies 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 8:5-1: SWAT+ input variables that pertain to bacteria die-off in the water bodies.

| Variable Name | Definition                                                                                                     | Input File |
| ------------- | -------------------------------------------------------------------------------------------------------------- | ---------- |
| WDPRES        | $$\mu\_{pres,die,20}$$: Die-off factor for persistent bacteria in water bodies at 20$$\degree$$C (1/day)       | .bsn       |
| WDLPRES       | $$\mu\_{lpres,die,20}$$: Die-off factor for less persistent bacteria in water bodies at 20$$\degree$$C (1/day) | .bsn       |
| THBACT        | $$\theta \_{bact}$$: Temperature adjustment factor for bacteria die-off/growth                                 | .bsn       |


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