Can the Lambert‐Beer law be applied to the diffuse attenuation coefficient of ocean water?

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Abstract
Radiative transfer theory is combined with a bio‐optical model of Case 1 waters and an optical model of the atmosphere to simulate the transport of radiation in the ocean‐atmosphere system. The results are treated as experimental data to study the downwelling irradiance attenuation coefficient. It is shown that the downwelling irradiance attenuation coefficient just beneath the surface and the mean downwelling irradiance attenuation coefficient from the surface to the depth where the irradiance falls to 10% of its value at the surface can be corrected for the geometric structure of the in‐water light field to yield quantities that are—to a high degree of accuracy— inherent optical properties. For Case 1 waters these geometry‐corrected attenuation coefficients are shown to satisfy the Lambert‐Beer law with a maximum error of 5–10% depending on wavelength. This near‐validity of the Lambert‐Beer law, when there are compelling reasons to believe that it should fail, is shown to result from three independent facts: the dependence of the diffuse attenuation coefficients on the geometric structure of the light field can be removed; pure seawater is a much better absorber than scatterer at optical frequencies; and the phase function for particles suspended in the ocean differs significantly from that of pure seawater. Finally, it is shown that extrapolation of the corrected diffuse attenuation coefficients to the limit c → cw yields quantities that are within 2% of the corresponding quantities that would be measured for an ocean consisting of pure seawater with the sun at zenith and the atmosphere removed.