__Ocean Retrieval Algorithm__

The ocean inversion derives three parameters: the AOD at one wavelength (τ _{0.55}), the ‘reflectance weighting parameter’ (the over-ocean definition of Fine Weighting - η_{ 0.55}) at one wavelength, and the ‘effective radius’ (r_{e}), which is the ratio of the 3rd and 2nd moments of the aerosol size distribution. The effective radius is represented by choosing a single ‘fine’ (f ) and single ‘coarse’ (c) aerosol mode for combining with the η parameter. The inversion is based on the look-up table (LUT) of four fine modes and five coarse modes, described in the aerosol models section. Although the LUT is defined in terms of a single wavelength of optical thickness, the parameters of each of the single mode models define a unique spectral dependence for that model, which is applied to the retrieved value of τ _{0.55 }to determine optical thickness at other wavelengths.

The retrieval requires a single fine mode and a single coarse mode. The trick, however, is to determine which of the (4 x 5 =) twenty combinations of fine and coarse modes and their relative optical contributions that best mimics the MODIS-observed spectral reflectance. For each of the twenty combinations of one fine mode and one coarse mode, the inversion finds the pair of τ _{0.55} and η _{0.55 }that minimizes the ‘fitting error’ (ε) between the measured top of the atmosphere (TOA) reflectance and the modeled TOA reflectance. The inversion requires the reflectance at 0.86 µm to match exactly to the LUT, and then finds the best fit to the other wavelengths. The 0.87 µm channel was chosen to be the primary wavelength because it is expected to be less affected by variability in water leaving radiances than the shorter wavelengths, yet still exhibit a strong aerosol signal, even for aerosols dominated by the fine mode.

The twenty solutions are then sorted according to values of fitting error. The ‘best’ solution is the combination of modes with accompanying τ _{0.55} and η _{0.55 }that minimizes ε. The solution may not be unique. The ‘average’ solution is the average of all solutions with ε< 3% or if no solution has ε< 3%, then the average of the 3 best solutions. Once the solutions are found, then the chosen combination of modes is the de facto derived aerosol model and a variety of parameters can be inferred from the chosen size distribution including spectral optical depth, effective radius, spectral flux, mass concentration, etc.