Stocker2020 Eq.12

[kongdd]

Dear Stocker,

Following your 2020 "P-model v1.0: an optimality-based light use efficiency model for simulating ecosystem gross primary production", the deduced Eq. 12 different from yours.
Could you have a look please?

The following is the corresponding MATLAB code:

syms gamma c_i c_s C_i C_a A g_sw beta Gamma R_d Chi g_0 epsilon xi eta K D
% epsilo = 1.6

% K = 2 * Gamma
xi = sqrt( beta * (K + Gamma) / (epsilon * eta ))
Chi = Gamma/C_a + (1 - Gamma/C_a) / xi/(xi + sqrt(D))

C_i = simplify( Chi * C_a )

m = (C_i - Gamma) / (C_i + 2 * Gamma);
m = simplify(m)

[stineb]

Hi there. Thanks for your input. Did you check whether the solution Matlab spits out is equivalent with Eq. 12? It should be. You can test it numerically if you don't want to do the algebra...

[kongdd]

I think they are different.

But when replace C_i = ((xi * C_a) + Gamma * sqrt(D)) / (xi + sqrt(D)) (Eq 27 in Wang Han 2017), the equation becomes the same as the Eq. 12 in your article.