crt1d.solvers._solve_4s

Module Contents

Functions

solve_4s(*, psi, I_dr0_all, I_df0_all, lai, leaf_t, ...)

4-stream from Tian et al. (2007) (featuring Dickinson).
crt1d.solvers._solve_4s.solve_4s(*, psi, I_dr0_all, I_df0_all, lai, leaf_t, leaf_r, soil_r, K_b_fn, G_fn, mu_s=0.501)

4-stream from Tian et al. (2007) (featuring Dickinson).

Notes

All eq./p. references in the code are to Tian et al. 2007 ([TDZ07]) unless otherwise noted.

Note that the authors use \(I\) for radiance, and \(F\) for irradiance. To be consistent with the other model codes, I am using

  • I for irradiance

  • R for radiance

  • F for actinic flux

mu_s (\(\mu_s\)) is the cosine of the dividing angle for the two beams:

\[\mu_s = \cos(\theta_s)\]

\(\mu_s\) divides each hemisphere into two sectors: \([0, \mu_s]\) and \([\mu_s, 1]\) for the upward and \([-1, -\mu_s]\) and \([-\mu_s, 0]\) for the downward.

Potential values for the mu_s “hyperparameter”:

  • 0.501: value suggested by the authors (~ 60 deg., arccos(0.501)*180/pi = 59.93)

  • 0.33998, 0.86114: Gauss–Legendre quadrature points for n=4, ~ 70 deg., ~ 31 deg. Tian et al. (2007) and Li and Dobbie (1998) find (0.33998) the former to give more accurate results.