Attenuation of visible light by phytoplankton in a vertically structured ocean: solutions and applications

To find the solution to problems in applied marine optics, wedo not always need to compute the submarine irradiance at alldepths; in many cases, it is sufficient to know the averageattenuation of light for finite layers of arbitrary thickness.If multiple scattering can be neglected, the average attenuationof light in a finite layer of the water column depends onlyon the vertical distribution of the attenuating substances;in open-ocean waters, the most important of these is phytoplankton.It is shown how the average attenuation of monochromatic lightin an arbitrary layer can be determined when the vertical pigmentprofile takes one of two standardized forms: a shifted Gaussianor a triangle. The choice of efficient algorithms to computethe attenuation in a layer using these models is discussed.The extension to polychromatic light involves the selectionof a function to represent the spectral distribution of thespecific absorption coefficient for phytoplankton, as determinedby observation. Chebyshev polynomial representation is shownto be convenient for applications which require the calculationof a weighted wavelength integral. An efficient procedure forthe evaluation of these integrals, Gauss-Chebyshev quadrature,is presented and evaluated. The extension to the computationof bulk properties for discrete layers is straightforward.