The method is based on a comparison between POLDER measurements and Lookup tables (LUT) built for a set of aerosol models (size distribution, refractive index, optical thickness) for the POLDER observations.

Reference :** Herman M., Deuzé J.L., Marchand A., Roger B., Lallart P., 2005**

Aerosol remote sensing from POLDER/ADEOS over the ocean: Improved retrieval using a nonspherical particle model

Journal of Geophysical Research, Vol 110, N° D10S02, doi: 10.1029/2004JD0044798.

The inversion scheme mainly uses the normalized radiances in the 865 nm channel, where the ocean color reflectance is zero, and in the 670 nm channel with a constant water reflectance 0.001. The polarized Stokes parameters at 865 and 670 nm are also used to help to derive the best aerosol model.

The present algorithm uses bimodal aerosol model, which mix a mode of small particles (S) and a mode of large particles (L) with respective optical thickness _{S} and _{L}, at 865 nm. A mode of small particles (S) consists in a lognormal size distribution of spherical particles with a refractive index m_{S}. A mode of large particles (L) consists in a mixing of a lognormal spherical particles of refractive index m_{L}, with non-spherical particles, according to respective optical thickness at 865 nm _{L-S} and _{L-NS} (_{L} = _{L-S} + _{L-NS}). The model of non-spherical particles is the mean model given in **Volten et al. (2001)**.

Given a small and a large mode of particles with optical thickness = _{S} + _{L}, the corresponding radiance L () is calculated according to the approximation of **Wang and Gordon (1994)** by

L() = (_{S}/) L(S, ) + (_{L}/) L(L, )

where L(S, ) is the radiance of the small mode and L(L, ) the radiance of the large mode both calculated for the optical thickness of the mixture. c = _{S}/ is the concentration of the small mode in term of optical thickness.

A similar equation can be written for the normalized Stokes parameters Q and U. LUT of the radiances (865, 670 and 565 nm channels) and of the Stokes parameters Q and U (865 nm, 670 nm and blue channels) are built for different small modes, large modes of spherical particles and a non-spherical one, for 11 aerosol optical thickness from = 0 (molecular case) to = 2.6 (extreme turbid atmosphere). We consider 21 solar angles (3° to 77°), 20 viewing angles (3° to 73°) and 37 relative azimuth angles from 0° to 180°(step of 5°). Computations are performed with a rough ocean surface (Cox and Munk, 1954) and a wind speed 5m/s. The foam contribution is calculated according to the Koepke’s model (1984) and a constant value 0.22 of the foam reflectance.

When the aerosol content is low, we only consider a fixed aerosol model for which the aerosol optical thickness is deduced. In other cases, we apply the general following algorithm.

Let L^{averaged}_{865} and L^{averaged}_{670} stand for the averaged measured normalized radiances L_{865} and L_{565} on the view directions out of the glitter. Given a couple of a small and a large mode, in a first step c_{865} and _{865} are adjusted, by the way of the previous equation, in order to retrieve L^{averaged}_{865} and L^{averaged}_{670}. In a second step, given c_{865} and _{865}, the directional Stokes parameters L, Q and U are interpolated in the LUT in the 865 and 670 nm channels. Then the difference (r.m.s.) between these simulations and the measurements are computed for each couple of modes: the minimum value (best fit) gives the aerosol model (modes and c_{865} concentration) and the corresponding optical thickness _{865}.

Note that the large modes are combinations between spherical large particles and non-spherical particles; the mixture concentrations _{L-S}/_{L} vary from 0 to 1 by step 0.25.

The set of the refractive indices and modal radii of the small and large spherical particles used for depends on the viewing conditions.