The reader is forewarned of an unavoidable duplication of terminology in the optical and geophysical aspects of this paper. Some confusion may result if this duplication is not borne in mind. Here, the terms "frequency" and "wavenumber" refer to the geophysical distribution of irradiance in the sea, not to the wave-mechanical properties of light.
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In this paper, the terms "spectrum" and "spectra" are not optical terms, but refer to a time-series analysis of a random fluctuation.
z is taken positive upwards with z = 0 at the mean water surface.
Boldface letters will denote two-dimensional (horizontal) vector quantities. (h, ν) will denote a three-dimensional vector quantity with horizontal projection h and vertical component ν.
This calculation assumes that the mean irradiance field is entirely the result of direct sun rays. The observations of Dera and Olszewski suggest that this assumption is only crudely satisfied. The value of the resulting attenuation coefficient is probably more representative of a downwelling-irradiance attenuation coefficient than it is of a beam-attenuation coefficient.
As evidenced in the coordinate transformation (3) in Sec. III.
The expansion parameter is essentially the rms surface-wave slope.
The variables ξ and η here have a meaning different from their previous meaning.