Modelling Concentration I'm currently doing a research project that involves modelling E. Coli growth in a wetland. 
The data I've been given is the E. Coli mass concentration ($mgC/L$) at various times throughout the two years it was sampled. The wetland receives influent from the local sewers and that influent contains a fairly constant concentration of E. Coli over the sampling period. The wetland has an outflow volume that is equal to the inflow volume plus the precipitation it receives.
My problem is this: If I am modelling the concentration of the E. Coli, how does this concentration change with the added precipitation (and increased outflow rate)? 
Is the added precipitation irrelevant if the outflow of the wetland will increase to compensate? Or will there be dilution of the outflow E. Coli concentration?
I feel like this shouldn't be as difficult to understand as it is, but I'm having a lot of trouble.  
 A: If you write two mass conservation equations (one for the volume of water in the wetland and the other for the mass of E. Coli) you get a qualitative model that can shed some light on your problem, but such models are as good as the underlying assumptions and some calibration, validation may be needed.  
If you denote by $V$ the volume of water in the wetland and $S$ the associated surface then 
$$\frac {dV} {dt}=i+r \times S-o \approx 0 \space $$ 
where $i$, $r$ and $o$ are the inflow, rain rate and outflow and
$$\frac {dM} {dt}=i\times c-\frac{M}{V}\times o $$
where $M$ is the mass of E. Coli in the wetland and $c$ is the concentration of E. Coli in the incoming flow. This is based on the assumption that $M$ is uniformly mixed into $V$.
If $r=0$, then $i=o$ and $dM/dt=0$ when the steady state is reached. If $r>0$ then $o>i$ and assuming that rain starts after the steady state is reached, i.e. $M/V=c$, then $dM/dt<0$ in the equation above.
So qualitatively, the concentration should decrease by dilution of the outflow, but in real life this depends on how effective and fast the mixing processes are.
