Reformulation of nitrogen fixation: dependent on plant N uptake and availability of Nmin

[dlebauer]

Replace N fixation as f(NPP) with N fixation = f(N demand, N availability).

• Fixed N goes directly to plant
• Add parameters nFixFracMax and nFixHalfSatMinN
• unify N-cycle params table.
• Docs only; no code changes.

Any further modifications, other than reversion to N_fix = a * NPP, should be proposed as a separate pull request.

Highlights (from rendered model-structure.md):

[Alomir]

Seems like this would be great in the params doc

[Alomir]

Looks good! Might want to put the parameter estimate into the params doc, but that can be here in this PR or elsewhere

[dlebauer]

@Alomir RE:

Might want to put the parameter estimate into the params doc, but that can be here in this PR or elsewhere

I changed the formulation since that note, so didn't carry over this particular value, but drafted a document for priors and default values in #194 so that next time there would be a place to take notes.

[Alomir]

Looks good. I'll be able to take a better look when it's published, but let's get this in.

[infotroph]

Thanks for working this up.

Approving to keep the process moving, but I'm staking my prediction that this approach will need to be modified to include an explicit carbon cost of N fixation.

In a Slack discussion @dlebauer says that's handled implicitly by fixed C:N ratios making autotrophic respiration scale with N supply (when N is limiting), but I still don't see it -- my reading is the equations here will impose the same cost per unit N whether it comes from fixation or not. One or the other of us will get a told-you-so eventually 😉

[dlebauer]

@infotroph You’re right that this formulation dosn't include an explicit carbon cost of fixation; the cost is implicit through higher N demand for legumes (via plant C:N) and because fixation can only supply a fraction of demand up to a maximum.

There are other ways to represent N fixation, and we can consider those if validation and uncertainty analysis suggest that this formulation is insufficient, focusing on the CA cropland use case.

If you have a specific functional form and validation datasets in mind, please write those in a separate issue and / or PR.

[mdietze]

If we want to add a C cost of N fixation, there are existing schemes out there we can borrow, e.g. https://doi.org/10.1029/2022MS003204. And I agree with Chris that the cost of fixation goes above and beyond the more general cost of N uptake, though I feel like many models don't explicitly model the latter, but just lump it into the more general concept of growth respiration.

[dlebauer]

cost of fixation goes above and beyond the more general cost of N uptake ... just lump it into the more general concept of growth respiration.

I worked through a few ways of representing this and didn't come up with a suitable solution, not that one doesn't exist.

The ELM-FUN approach is interesting and it is great to see mechanistic representation of N and P limitation in ESMs. Notably, N limitation is relatively less important in croplands, and the paper suggests that the proposed representation is already more realistic than most ESMs.