Shape of the particulate beam attenuation spectrum and its inversion to obtain the shape of the particulate size distribution

The link between the spectral shape of the beam attenuation spectrum and th e shape of the particle size distribution (PSD) of oceanic particles is rev isited to evaluate the extent to which one can be predicted from the other. Assuming a hyperbolic (power-law) PSD, N(D) proportional to D-xi, past stu dies have found for an infinite distribution of nonabsorbing spheres with a constant index of refraction that the attenuation spectrum is hyperbolic a nd that the attenuation spectral slope gamma is related to the PSD slope xi by xi = gamma + 3. Here we add a correction to this model because of the f inite size of the biggest particle in the population. This inversion model is given by xi = gamma + 3 - 0.5 exp(-6 gamma). In most oceanic observation s xi > 3, and the deviation between these two models is negligible. To test the robustness of this inversion, we perturbed its assumptions by allowing for populations of particles that are nonspherical, or absorbing, or with an index of refraction that changes with wavelength. We found the model to provide a good fit for the range of parameters most often encountered in th e ocean. In addition, we found that the particulate attenuation spectrum, c (p)(lambda), is well described by a hyperbolic relation to the wavelength c (p) proportional to lambda (-lambda) throughout the range of the investigat ed parameters, even when the inversion model does not apply. This implies t hat knowledge of the particulate attenuation at two visible wavelengths cou ld provide, to a high degree of accuracy, the particulate attenuation at ot her wavelengths in the visible spectrum. (C) 2001 Optical Society of Americ a.