New WAI adaptation for PAI calculation option from Fang et al.

[drnimbusrain]

@angehung5 This is the adaption of the WAI contribution using alpha (woody-to-total area ratio) for the PAI calculation option, PAI = LAI (1 - alpha), which is vegetation type dependent now.

This is based on Figure 1 of Fang et al., 2019: https://doi.org/10.1029/2018RG000608

[angehung5]

@drnimbusrain Are you using the Eq. 12 from Fang et al. 2019? If yes, how about the omega and gamma terms? Also should it be PAI = LAI / (1-alpha)? Otherwise, PAI would be less than LAI.

[drnimbusrain]

@drnimbusrain Are you using the Eq. 12 from Fang et al. 2019? If yes, how about the omega and gamma terms? Also should it be PAI = LAI / (1-alpha)? Otherwise, PAI would be less than LAI.

Actually, I that is what I am using PAI = LAI/(1-alpha): https://github.com/noaa-oar-arl/canopy-app/pull/100/files#diff-784b83d59c46a5575c78286c41ec9665e53c5edad0c9a4bc4e97e4abdb6cb743R62

[angehung5]

@drnimbusrain Are you using the Eq. 12 from Fang et al. 2019? If yes, how about the omega and gamma terms? Also should it be PAI = LAI / (1-alpha)? Otherwise, PAI would be less than LAI.

Actually, I that is what I am using PAI = LAI/(1-alpha): https://github.com/noaa-oar-arl/canopy-app/pull/100/files#diff-784b83d59c46a5575c78286c41ec9665e53c5edad0c9a4bc4e97e4abdb6cb743R62

How about the clumping index (omega term)? The paper says "ΩE is the element clumping index, which quantifies the effect of foliage clumping at scales larger than shoots". Should it be included in the calculation?
Yeah I think we can ignore gamma (needle‐to‐shoot area ratio) since we are working on grown trees.

[drnimbusrain]

@angehung5 Ah, yes, there are some other details here with gamma_eff (needle-to-shoot ratio, i.e., effect of clumping within the shoot) and omega_eff (clumping index effect beyond the shoot).
However we have observed total omega, clumping index (within and beyond the shoot) which is defined by (see Eq. 16 here https://academic.oup.com/treephys/article/29/8/1069/1670149_

Omega = Omega_eff/gamma_eff ; Omega)_eff is the clumping beyond the shoot only, where the gamma_eff is the effect of clumping within the shoot.

So combining this with Zhang et al. PAI_eff = LAI/(1-alpha) * Omega_eff/gamma_eff, we have a final equation for PAI total (not effective)

PAI = LAI/(1-alpha) * Omega.
So I do need to revise this for explanation and to include the effects of total clumping index here to get PAI.

[drnimbusrain]

@angehung5 OK, updated.

[angehung5]

@drnimbusrain Thanks Patrick! Just reviewed.