The vertical attenuation of irradiance as a function of the optical properties of the water

Average vertical attenuation coefficients, K(av), for irradiance calculated by linear regression of ln E(z) on z through the euphotic zone or from two irradiance values in a certain depth interval, are useful but somewhat arbitrary procedures for estimating these important apparent optical properties of the ocean. A more fundamental approach is to calculate an irradiance-weighted coefficient, K(av), integrated over the whole water column, in which for each increment of depth, the corresponding irradiance value is used to weight the estimate of the irradiance coefficient in accordance with K(av) 5 # K(z)E(z) dz/# E(z) dz. Attenuation coefficients calculated in this way exhibit ` ` 0 0 some interesting relationships both to certain other properties of the light field and to the inherent optical properties of the water. In particular, I find that for all types of irradiance K(av) 5 E(0)/# E(z) dz, where E(0) is the value 0 of irradiance just below the water surface. For net downward irradiance, KE(av) 5 a/ c and KE(av) ø (a/ o)[1 m̄ m̄ 1 (b/a)(1 2 s)], where c is the integral average cosine for the water column, o is the average cosine of the m̄ m̄ m̄ incoming flux just below the water surface, a is the absorption coefficient, b is the scattering coefficient, and s is m̄ the average cosine (asymmetry factor) of the scattering phase function. For scalar irradiance, Ko(av) 5 a/ (0), m̄ where (0) is the average cosine of the light field just below the water surface. The extent to which these and m̄ conventionally calculated attenuation coefficients reproduce the depth variation of irradiance is explored using Monte Carlo modeling. The value of the vertical attenuation coefficient for irradiance, averaged over some depth interval of interest—typically the euphotic zone—is the most frequently measured and useful of the set of apparent optical properties (AOP) of the ocean. There are, however, several different versions of, and correspondingly different ways of measuring, this attenuation coefficient, and it is not always clear which is the most appropriate one to use. I consider here some of these possibilities and, in particular, examine the relationship between irradiance attenuation coefficients and certain other properties of the light field, as well as the inherent optical properties (IOP) of the aquatic medium.