Cox Munk

Implements the Cox Munk BRDF. This BRDF is based on the work of Cox and Munk who analyzed the surface of water as a function of wind using aerial photographs in the 1950s. Their work includes dependence on wind direction and a Gram-Charlier correction to the Gaussian distribution of water facet orientations, but this BRDF neglects these corrections and assumes a symmetric distribution. This BRDF depends on two parameters, wind speed and the index of refraction of water.

This is one of eight BRDF kernels listed by Spurr in his 2002 paper.

Equation A.18 from Spurr is implemented with the following changes:

• cos(phi) is replaced with -cos(phi)

• the reflectance is divided by pi

Example

import sasktranif.sasktranif as skif
import math

brdf = skif.ISKBrdf('COX_MUNK')
mjd            = 52393.3792987115;
location       = [0.0, 0.0, 25000.0, mjd];
[ok,brdfvalue] = brdf.BRDF( 600.0, location, 0.6, 0.7, -0.8)

Properties

BRDFParameters

COX_MUNK.BRDFParameters(array param)

A 2 element array containing the wind speed and water refractive index required for the Cox Munk distribution

n	Setting
parameters[0]	wind speed
parameters[1]	water refractive index

References

Cox C, Munk W. “The measurement of the roughness of the sea surface from photographs of the Sun glitter”. J Opt Soc Ann 1954; 44:838–50.

Robert J. D. Spurr, “A new approach to the retrieval of surface properties from earthshine measurements”, Journal of Quantitative Spectroscopy & Radiative Transfer, vol. 83, pp. 15-46, Oct. 9, 2002. doi:10.1016/S0022-4073(02)00283-2 url: http://www.sciencedirect.com/science/article/pii/S0022407302002832