Bacteria Die-off/Re-growth

Chick’s Law first order decay equation is used to determine the quantity of bacteria removed from the system through die-off and added to the system by regrowth. The equation for die-off/re-growth was taken from Reddy et al. (1981) as modified by Crane and Moore (1986) and later by Moore et al. (1989). The equation was modified in SWAT+ to include a user-defined minimum daily loss. Die-off/re-growth is modeled for the two bacteria populations on foliage, in the surface soil solution and sorbed to surface soil particles. The equations used to calculate daily bacteria levels in the different pools are:

bactlpfol,i=bactlpfol,i−1∗exp(−μlpfol,net)−bactmin,lpbact_{lpfol,i}=bact_{lpfol,i-1}*exp(-\mu _{lpfol,net})-bact_{min,lp} 3:4.2.1

bactpfol,i=bactpfol,i−1∗exp(−μpfol,net)−bactmin,pbact_{pfol,i}=bact_{pfol,i-1}*exp(-\mu _{pfol,net})-bact_{min,p} 3:4.2.2

bactlpsol,i=bactlpsol,i−1∗exp(−μlpsol,net)−bactmin,lpbact_{lpsol,i}=bact_{lpsol,i-1}*exp(-\mu _{lpsol,net})-bact_{min,lp} 3:4.2.3

bactpsol,i=bactpsol,i−1∗exp(−μpsol,net)−bactmin,pbact_{psol,i}=bact_{psol,i-1}*exp(-\mu _{psol,net})-bact_{min,p} 3:4.2.4

bactlpsorb,i=bactlpsord,i−1∗exp(−μlpsorb,net)−bactmin,lpbact_{lpsorb,i}=bact_{lpsord,i-1}*exp(-\mu _{lpsorb,net})-bact_{min,lp} 3:4.2.5

bactpsorb,i=bactpsorb,i−1∗exp(−μpsorb,net)−bactmin,pbact_{psorb,i}=bact_{psorb,i-1}*exp(-\mu _{psorb,net})-bact_{min,p} 3:4.2.6

where bactlpfol,ibact_{lpfol,i} is the amount of less persistent bacteria present on foliage on day ii (#cfu/m2^2), bactlpfol,i−1bact_{lpfol,i-1} is the amount of less persistent bacteria present on foliage on day i−1i-1 (#cfu/m2^2), μlpfol,net\mu _{lpfol,net} is the overall rate constant for die-off/re-growth of less persistent bacteria on foliage (1/day), bactmin,lpbact_{min,lp} is the minimum daily loss of less persistent bacteria (#cfu/m2^2), bactpfol,ibact_{pfol,i} is the amount of persistent bacteria present on foliage on day ii (#cfu/m2^2), bactpfol,i−1bact_{pfol,i-1} is the amount of persistent bacteria present on foliage on day i−1i-1(#cfu/m2^2), μpfol,net\mu_{pfol,net} is the overall rate constant for die-off/re-growth of persistent bacteria on foliage (1/day), bactmin,pbact_{min,p} is the minimum daily loss of persistent bacteria (#cfu/m2^2), bactlpsol,ibact_{lpsol,i} is the amount of less persistent bacteria present in soil solution on day ii (#cfu/m2^2), bactlpsol,i−1bact_{lpsol,i-1} is the amount of less persistent bacteria present in soil solution on day i−1i-1 (#cfu/m2^2), μlpsol,net\mu_{lpsol,net} is the overall rate constant for die-off/re-growth of less persistent bacteria in soil solution (1/day), bactpsol,ibact_{psol,i} is the amount of persistent bacteria present in soil solution on day ii (#cfu/m2^2), bactpsol,i−1bact_{psol,i-1} is the amount of persistent bacteria present in soil solution on day i−1i-1(#cfu/m2^2), μpsol,net\mu_{psol,net} is the overall rate constant for die-off/re-growth of persistent bacteria in soil solution (1/day), bactlpsorb,ibact_{lpsorb,i} is the amount of less persistent bacteria sorbed to the soil on day ii (#cfu/m2^2), bactlpsorb,i−1bact_{lpsorb,i-1} is the amount of less persistent bacteria sorbed to the soil on day i−1i-1 (#cfu/m2^2), μlpsorb,net\mu _{lpsorb,net} is the overall rate constant for die-off/re-growth of less persistent bacteria sorbed to the soil (1/day), bactpsorb,ibact_{psorb,i} is the amount of persistent bacteria sorbed to the soil on day ii (#cfu/m2^2), bactpsorb,i−1bact_{psorb,i-1} is the amount of persistent bacteria sorbed to the soil on day i−1i-1 (#cfu/m2^2), and μpsorb,net\mu_{psorb,net} is the overall rate constant for die-off/re-growth of persistent bacteria sorbed to the soil (1/day).

The overall rate constants define the net change in bacterial population for the different pools modeled. The impact of temperature effects on bacteria die-off/re-growth were accounted for using equations proposed by Mancini (1978). The user defines the die-off and growth factors for the two bacterial populations in the different pools at 20°C. The overall rate constants at 20°C are then calculated:

μlpfol,net,20=μlpfol,die,20−μlpfol,grw,20\mu_{lpfol,net,20}=\mu_{lpfol,die,20}-\mu_{lpfol,grw,20} 3:4.2.7

μpfol,net,20=μpfol,die,20−μpfol,grw,20\mu_{pfol,net,20}=\mu_{pfol,die,20}-\mu_{pfol,grw,20} 3:4.2.8

μlpsol,net,20=μlpsol,die,20−μlpsol,grw,20\mu_{lpsol,net,20}=\mu_{lpsol,die,20}-\mu_{lpsol,grw,20} 3:4.2.9

μpsol,net,20=μpsol,die,20−μpsol,grw,20\mu_{psol,net,20}=\mu_{psol,die,20}-\mu_{psol,grw,20} 3:4.2.10

μlpsorb,net,20=μlpsorb,die,20−μlpsorb,grw,20\mu_{lpsorb,net,20}=\mu_{lpsorb,die,20}-\mu_{lpsorb,grw,20} 3:4.2.11

μpsorb,net,20=μpsorb,die,20−μpsorb,grw,20\mu_{psorb,net,20}=\mu_{psorb,die,20}-\mu_{psorb,grw,20} 3:4.2.12

where μlpfol,net,20\mu_{lpfol,net,20} is the overall rate constant for die-off/re-growth of less persistent bacteria on foliage at 20°C (1/day), μlpfol,die,20\mu_{lpfol,die,20} is the rate constant for die-off of less persistent bacteria on foliage at 20°C (1/day), μlpfol,grw,20\mu_{lpfol,grw,20} is the rate constant for re-growth of less persistent bacteria on foliage at 20°C (1/day), μpfol,net,20\mu_{pfol,net,20} is the overall rate constant for die-off/re-growth of persistent bacteria on foliage at 20°C (1/day), μpfol,die,20\mu_{pfol,die,20} is the rate constant for die-off of persistent bacteria on foliage at 20°C (1/day), μpfol,grw,20\mu_{pfol,grw,20} is the rate constant for re-growth of persistent bacteria on foliage at 20°C (1/day), μlpsol,net,20\mu_{lpsol,net,20} is the overall rate constant for die-off/re-growth of less persistent bacteria in soil solution at 20°C (1/day), μlpsol,die,20\mu_{lpsol,die,20} is the rate constant for die-off of less persistent bacteria in soil solution at 20°C (1/day), μlpsol,grw,20\mu_{lpsol,grw,20} is the rate constant for re-growth of less persistent bacteria in soil solution at 20°C (1/day), μpsol,net,20\mu_{psol,net,20} is the overall rate constant for die-off/re-growth of persistent bacteria in soil solution at 20°C (1/day), μpsol,die,20\mu_{psol,die,20} is the rate constant for die-off of persistent bacteria in soil solution at 20°C (1/day), μpsol,grw,20\mu_{psol,grw,20} is the rate constant for re-growth of persistent bacteria in soil solution at 20°C (1/day), μlpsorb,net,20\mu_{lpsorb,net,20} is the overall rate constant for die-off/re-growth of less persistent bacteria attached to soil particles at 20°C (1/day), μlpsorb,die,20\mu_{lpsorb,die,20} is the rate constant for die-off of less persistent bacteria attached to soil particles at 20°C (1/day), μlpsorb,grw,20\mu_{lpsorb,grw,20} is the rate constant for re-growth of less persistent bacteria attached to soil particles at 20°C (1/day), μpsorb,net,20\mu_{psorb,net,20} is the overall rate constant for die-off/re-growth of persistent bacteria attached to soil particles at 20°C (1/day), μpsorb,die,20\mu_{psorb,die,20} is the rate constant for die-off of persistent bacteria attached to soil particles at 20°C (1/day), and μpsorb,grw,20\mu_{psorb,grw,20} is the rate constant for re-growth of persistent bacteria attached to soil particles at 20°C (1/day).

The overall rate constants are adjusted for temperature using the equations:

μlpfol,net=μlpfol,net,20∗θbact(T‾av−20)\mu_{lpfol,net}=\mu_{lpfol,net,20}*\theta_{bact}^{(\overline T_{av}-20)} 3:4.2.13

μpfol,net=μpfol,net,20∗θbact(T‾av−20)\mu_{pfol,net}=\mu_{pfol,net,20}*\theta_{bact}^{(\overline T_{av}-20)} 3:4.2.14

μlpsol,net=μlpsol,net,20∗θbact(T‾av−20)\mu_{lpsol,net}=\mu_{lpsol,net,20}*\theta_{bact}^{(\overline T_{av}-20)} 3:4.2.15

μpsol,net=μpsol,net,20∗θbact(T‾av−20)\mu_{psol,net}=\mu_{psol,net,20}*\theta_{bact}^{(\overline T_{av}-20)} 3:4.2.16

μlpsorb,net=μlpsorb,net,20∗θbact(T‾av−20)\mu_{lpsorb,net}=\mu_{lpsorb,net,20}*\theta_{bact}^{(\overline T_{av}-20)} 3:4.2.17

μpsorb,net=μpsorb,net,20∗θbact(T‾av−20)\mu_{psorb,net}=\mu_{psorb,net,20}*\theta_{bact}^{(\overline T_{av}-20)} 3:4.2.18

where θbact\theta_{bact} is the temperature adjustment factor for bacteria die-off/re-growth, T‾av\overline T_{av} is the mean daily air temperature, and all other terms are as previously defined.

Table 3:4-2: SWAT+ input variables that pertain to bacteria die-off/re-growth.

Variable Name
Definition
Input File

WDPQ

μpsol,die,20\mu_{psol,die,20}: Die-off factor for persistent bacteria in soil solution at 20°C (1/day)

.bsn

WGPQ

μpsol,grw,20\mu_{psol,grw,20}: Growth factor for persistent bacteria in soil solution at 20°C (1/day)

.bsn

WDLPQ

μlpsol,die,20\mu_{lpsol,die,20}: Die-off factor for less persistent bacteria in soil solution at 20°C (1/day)

.bsn

WGLPQ

μlpsol,grw,20\mu_{lpsol,grw,20}: Growth factor for less persistent bacteria in soil solution at 20°C (1/day)

.bsn

WDPS

μpsorb,die,20\mu_{psorb,die,20}: Die-off factor for persistent bacteria adsorbed to soil particles at 20°C (1/day)

.bsn

WGPS

μpsorb,grw,20\mu_{psorb,grw,20}: Growth factor for persistent bacteria adsorbed to soil particles at 20°C (1/day)

.bsn

WDLPS

μlpsorb,die,20\mu_{lpsorb,die,20}: Die-off factor for less persistent bacteria adsorbed to soil particles at 20°C (1/day)

.bsn

WGLPS

μlpsorb,grw,20\mu_{lpsorb,grw,20}: Growth factor for less persistent bacteria adsorbed to soil particles at 20°C (1/day)

.bsn

WDPF

μpfol,die,20\mu_{pfol,die,20}: Die-off factor for persistent bacteria on foliage at 20°C (1/day)

.bsn

WGPF

μpfol,grw,20\mu_{pfol,grw,20}: Growth factor for persistent bacteria on foliage at 20°C (1/day)

.bsn

WDLPF

μlpfol,die,20\mu_{lpfol,die,20}: Die-off factor for less persistent bacteria on foliage at 20°C (1/day)

.bsn

WGLPF

μlpfol,grw,20\mu_{lpfol,grw,20}: Growth factor for less persistent bacteria on foliage at 20°C (1/day)

.bsn

THBACT

θbact\theta_{bact}: Temperature adjustment factor for bacteria die-off/growth

.bsn

BACTMINLP

bactmin,lpbact_{min,lp}: Minimum daily loss of less persistent bacteria (# cfu/m2^2)

.bsn

BACTMINP

bactmin,pbact_{min,p}: Minimum daily loss of persistent bacteria (# cfu/m2^2)

.bsn

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