Optimal LAI

[AlexisRenchon]

Optimal LAI (optimal_lai.jl), after Zhou et al., 2025

• New AbstractLAIModel (not AbstractAreaIndexModel which also gives RAI and SAI)

TODO:

• Compute Ao as LUE * PAR (FAPAR = 1, beta = 1) (from the pmodel - and store it in cache, and integrate it to daily and annual in Y)
• Read varying in space precip, growing season, growing season VPD, annual potential GPP.. see spatialvaryinginput
• In compute_L_max (equation 11 in paper), Ao is "potential GPP" (annual) = PAR * LUE (assumes fPAR = 1) - this is NOT observed annual GPP. LUE is from P model (equation 2 and 3). Kat question: if we modified LUE to account for moisture stress, do we need the second part of equation 11 (water limitation adjustment of fAPARmax).
  Note: for initialization, we will need to compute this Ao first and read it...
• m is the fraction of GPP allocated to LAI - shouldn't it be between 0 and 1? (or can it be more - say, using non-structural carbohydrates...)
• in equation 14, it is a bit unclear what the units of Ao are. the text mention "it is reasonable to model GPP on an hourly to daily basis" (whereas Ao was annual before). Figure 1 shows daily units for Ao (g C m−2day−1). But for equation 11, for example, Ao is also used, but this time is said in the text to be annual (molm−2 year−1). - It is confusing to use the same name throughout the text for variable with different units. In equation 20, Aosum is used for annual - which is great. but not in equation 11 (even if annual too)

TODO (call with Kat 11/5):

• Fix GPU error - could be because params are keywords arg, should be args (read with toml). test this on clima GPU as unit test.
• Make sure LAI initialization looks okay globally.

TO DO:

• currently updates via callback (akin to pmodel). We may want to update in Y instead. (let's discuss)
• This currently stores LAI in p.canopy.lai_model.LAI, which means there are two LAIs: the prescribed one p.canopy.biomass.area_index.leaf, and the modeled one. (this is intentional for now - so we can compare them). Maybe we want to do this differently. (and maybe we want to use biomass and not a new lai_model). let's discuss.
• Currently, optimal LAI is computed, but the LAI used for photosynthesis etc. is still the prescribed LAI.
• Daily GPP is actually local noon scaled to day (assuming 8 hours) - it would be better to use actual daily GPP
• To go global, how do we get, at all (lon, lat):
• annual precip
• annual gpp
• growing season mean VPD
• growing season length
• daily GPP

--> we could start by reading them and have them constant (except daily gpp), and later, store in Y starting year 2?

Ozark, with

Ao_annual = FT(100.0), # mol CO2 m-2 y-1, for an average forest
P_annual = FT(60000.0), # ~ 1000 mm precipitation per year,
D_growing = FT(1000.0), # mean VPD growing season (Pa) - also some average value,
GSL = FT(180.0), # days, growing season length