WIP: LAI

[schymans]

This is a PR in progress to incorporate the feature of enabling dynamic leaf area index for trees and grasses, prepared by @rcnijzink. Initially, it is a copy of #67, but still needs to be tested and documented before merging.

Here is what @rcnijzink wrote in #67:

This branch had my latest edits for the LAI in the VOM (just before EGU 2022). I think it would be best to merge this into a branch on git@github.com:schymans/VOM.git, then you could start from there. I tried below to give an overview on what I did.

This branch includes a first attempt to separate PAR into PAR shade and PAR sunlit, based on the approach in Campbell & Norman. I followed the example on p260 (example 15.2). Specifically:

• estimate average PAR on shaded leaves (transpmode.f90, lines 1685 and 1713, first equation p261 Campbell & Norman):

                    par_shade_avg = (pardiff_h(th_) * ( 1.d0 - p_E ** ( -sqrt(i_alpha_abs) * kappa_d * lai_lt(ii) )   ) ) / &
                                    ( sqrt(i_alpha_abs) * kappa_d* lai_lt(ii)    ) 

• determine scattered PAR (transpmode.f90, lines 1689 and 1717)::

                    par_sct = 0.5* ( pardir_h(th_) * p_E ** (-sqrt(i_alpha_abs) * kappa_t * lai_lt(ii) )  -  &
                                    pardir_h(th_) * p_E ** (-kappa_t * lai_lt(ii) ) )

the above is the same as the calculation on p261 of Campbell & Norman, with scattered PAR as Qsc = 0.5 (Qbt - Qb), with Qbt the top beam radiation and Qb bottom beam radiation.

• Eventually, PARshade and PARsun are determined like this:

PARshade = (par_sct + par_shade_avg) * i_alpha_abs

PARsun = i_alpha_abs * (kappa_t * pardir_h(th_) + PARshade )

On p261 of Campbell & Norman, these are the equations for Qsh and Qsl.

[schymans]

@rcnijzink, could you provide the full reference to Campbell and Norman? Could you also add a link to the relevant repo on renkulab.io, where the current state of the branch can be tested?

[rcnijzink]

The full reference is:

Campbell, G. S. and Norman, J. M.: An introduction to environmental biophysics, 2nd ed., Springer, New York, 316 pp., 1998.

The repo on renkulab:
git@renkulab.io:remko.nijzink/vom-lai.git

with copies here:
git@git.list.lu:wave/vom_lai.git
git@renkulab.io:wave/vom_lai.git