Is your feature request related to a problem? Please describe.
I currently integrate the litter model using the simplest possible method, i.e. I find the total decay of each pool by
$$D = k P\Delta t ,$$
where $k$ is the decay rate, $P$ is the pool size and $\Delta t$ is the time step. This approximation only works when $\Delta t$ is small relative to the rate at which the pool sizes are changing, which given we use a month time step as default is only true when the pools are close to equilibrium (or when the forest floor is basically frozen 🫠)
Describe the solution you'd like
I'm unsure what I was thinking with the above as the dynamics are simple enough that they can be integrated to obtain an analytical solution (which I even provided to @hrlai here). I think I should try and extend this analytical solution to also include litter input, which should stop the weird behaviour we are seeing
Describe alternatives you've considered
Alternatively, I could convert the whole litter model into rates, and integrate the model using scipy. The big problem with doing this is that this require animal consumption to be expressed as a rate rather than a total amount, which would introduce a new way for litter pools to reach negative mass. So, I don't think I should go down this route unless I can't obtain an analytic solution
Is your feature request related to a problem? Please describe.
I currently integrate the litter model using the simplest possible method, i.e. I find the total decay of each pool by
where$k$ is the decay rate, $P$ is the pool size and $\Delta t$ is the time step. This approximation only works when $\Delta t$ is small relative to the rate at which the pool sizes are changing, which given we use a month time step as default is only true when the pools are close to equilibrium (or when the forest floor is basically frozen 🫠)
Describe the solution you'd like
I'm unsure what I was thinking with the above as the dynamics are simple enough that they can be integrated to obtain an analytical solution (which I even provided to @hrlai here). I think I should try and extend this analytical solution to also include litter input, which should stop the weird behaviour we are seeing
Describe alternatives you've considered
Alternatively, I could convert the whole litter model into rates, and integrate the model using
scipy. The big problem with doing this is that this require animal consumption to be expressed as a rate rather than a total amount, which would introduce a new way for litter pools to reach negative mass. So, I don't think I should go down this route unless I can't obtain an analytic solution