Abstract

The calculation of the true absorption coefficient of daylight in natural waters is discussed. It is shown that the vertical absorption coefficient K defined by K = −1/I(dI/dz), where I is the intensity of light and s the vertical depth, is related to the true absorption coefficient k, defined by k = −1/I(dI/dr), where r is the path length in the direction of the light, by the expression:

K=k02π1aJ(ϑ,φ)ekzxxdxdφ02π1aJ(ϑ,φ)ekzxx2dxdφ,
where J′(ϑ, φ) is the intensity per unit solid angle per unit area just below the surface, ϑ and φ are the angles of refraction and azimuth respectively, x is defined by x = sec ϑ, and a is a number which depends upon the total amount of light reflected at the surface and the index of refraction. The integrals are evaluated for the special case that J′(ϑ, φ) is a constant, corresponding to the conditions prevailing on a perfectly cloudy day, and it is found that near the surface K must be increased around 20 percent of its measured value to give k.

© 1938 Optical Society of America

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