issue with growth respiration calculation

[ckoven]

Last week, @JessicaNeedham and I were discussing growth respiration, and we noticed that the growth respiration calculation may not be doing exactly what is intended. the key line is here:

https://github.com/NGEET/fates/blob/main/biogeophys/FatesPlantRespPhotosynthMod.F90#L998-L999

The issue is the max(0._r8, gpp-mr) part. while it makes sense to not let growth respiration go negative at night, adding the zero floor to this means that, integrated over a whole day/night cycle, GR != grperc*(GPP-MR), it only equals that over the part of the day when GPP > MR. And this high frequency growth respiration gets integrated through the npp_tstep term over the day to result in the total carbon available to grow with. So as a result, I think we are likely overestimating the growth respiration and thus underestimating the NPP relative to what we intend for a given value of the grperc parameter. Unless the grperc parameter is only intended to be applied during the day, but I don't believe that is the case. So if the intention is that the grperc parameter is meant to be applied over both day and night, we should reformulate this expression (somehow, not sure exactly best how to, that can be a later part of the discussion).

[ckoven]

Just wanted to note that we discussed this on a call last week and decided that we really should be using the daily integrated difference between GPP and maintenance respiration as the basis for growth respiration. And so will change the code to do that. The expectation when we do so is two things will change:

1. growth respiration should decrease, for a given value of the grperc parameter. In principle, this doesn't really do anything but change the relationship between the (highly uncertain) parameter and the growth respiration itself.
2. more substantively, this may change the behavior of the model as trees tend towards carbon starvation. currently, there can still be growth respiration on a given day even under conditions where a plant has greater MR than GPP, and thus contribute to a more negative NPP and further deplete carbon stores. One of the intentions of the maintenance respiration throttling was to prevent carbon stores from ever reaching zero by reducing the maintenance respiration as carbon stores approach zero. I had thought that growth respiration couldn't reduce carbon stores, because it would only ever be nonzero on days when a plant was growing and thus in positive carbon balance; but that hasn't necessarily been true and thus growth respiration may be contributing to further depletion of carbon stores. So changing this may also impact carbon starvation mortality behavior in a more qualitative way.