2.7.1.2.6.3 Clear water atmospheric corrections (step 2.6.9)
The objective of the clear water atmosphere correction is to identify and subtract from the TOA reflectances (corrected for stratospheric aerosols, gaseous absorption and Sun glint), the contribution of the atmosphere, which consists of molecular (Rayleigh) and particulate (aerosol) scattering and extinction. The correction is performed in order to provide normalised waterleaving reflectances.
A secondary objective is to estimate aerosol products: type and optical thickness.
The principle of the clear water atmosphere correction is to identify aerosol models which, together with a tabulated model of the molecular scattering and assumptions on the surface reflectance, fit the observed glintcorrected reflectance in the infrared part of the spectrum (bands 705, 775, 865nm) and in a visible band (510nm).
The assumptions for Case 1 waters are that reflectance is null at all wavelengths beyond 700nm, and that reflectance at 510nm is nearly constant.
The output of the turbid water atmosphere correction (step 2.6.10, see section 7.3.4.2 above) provides as input estimates of the water reflectance at the bands used by the algorithm.
The algorithm provides one or two aerosol models and their properties in the visible and NIR wavelength domain, which allow to perform a correction of the atmosphere contribution and compute waterleaving reflectances.
The waterleaving reflectances output by the atmosphere corrections above water are normalised in order to remove dependency of the signal upon atmosphere conditions. The normalised waterleaving reflectance product r'_{w} is defined as follows:
where L_{w} is the waterleaving radiance and E_{d }(0^{+}) the downwelling irradiance.
The waterleaving reflectance is used by other substeps and provided to the Product formatting (step 2.10). This step is applied to all pixels where ACFAIL_F is FALSE.
2.7.1.2.6.3.1 Path reflectance estimate (step 2.6.9.1)
When starting the atmospheric correction, we dispose of the (measured) total glint corrected reflectance ROGC, and of rR(l) for each wavelength. When turbid case 2 water has been detected by a previous step, we also have an estimate of the marine reflectance at TOA, tr_{w}_C2.
Atmospheric corrections need an estimate of the contribution of the sky to the total reflectance, or path reflectance, at four wavelengths.
In Case 1 waters, the InfraRed (IR) contribution of water to the signal is neglected, so that we have, at 775 and 865nm:
r_{path} (l) = ROGC (l).
This is also performed at band 510nm, even though the water contribution is not negligible in the visible. That estimate will be useful in the MERIS aerosol model (see below).
In turbid Case 2 water, we subtract the water contribution so that
r_{path} (l) = ROGC (l)– tr_{w}_C2 (l)
2.7.1.2.6.3.2 MERIS aerosol model (step 2.6.9.2)
When starting the aerosol correction, we dispose on one hand of the path reflectance rpath at four wavelengths, and of the TOA reflectance ROGC(l) and Rayleigh reflectance rR(l) for each wavelength, and on the other hand of tabulated relationships linking the ratio r_{path} /r_{R} to the aerosol optical thickness ta(l), for N aerosol models.
The central problem is the selection, among a set of aerosol models, of the two models that most closely bracket the actual aerosol. The principle is to rely on the lookup tables, which should allow :
 To calculate the values of ta(865) from the rpath(865)/rR(865) ratio, for several aerosol models,
 To extrapolate ta from 865 to 775 nm, for each aerosol model,
 To obtain the (rpath(775) / rR(775)) ratios from ta(775), for each aerosol model. These ratios computed from aerosol model, will be noted z(l) in the following.
 To select a couple of aerosol models, by comparing the actual (rpath(775) / rR(775)) ratio, and the various z(775) ratios as obtained at the previous step.
 To estimate the z(l) ratio in the visible bands from the knowledge of the spectral behaviour of this couple of aerosol models.
The successive steps of such a correction scheme are as follows. For a given pixel, and thus for a given geometry (qs, qv, Df):
(1) The ratio rpath(l) / rR(l) is computed at 865 and 775 nm, rR(l) being taken in tabulated values (at these wavelengths, and for oceanic Case 1 waters, rpath = ROGC).
(2) A first set of N aerosol models is selected, which, in principle, is representative of clear oceanic atmospheres. For these N aerosol models, N ta(865) values are calculated from the (rpath(865) / rR(865)) ratio.
(3) N values of ta(775) are computed for the N aerosol models, from the knowledge of their spectral optical thicknesses (normalised by their values at 865 nm; tabulated values).
(4) N values of z (775) are computed from the N values of ta(775) for the N aerosol models, from the tabulated relationships between both quantities.
(5) The actual (rpath(775) / rR(775)) is then compared to the N individual values of z(775) obtained at step (4), and the 2 that most closely bracket the actual one indicate the two candidate aerosol models.
(6) 2 values of ta(l) are calculated for bands at 510 nm and 705 nm from the normalised spectral optical thicknesses of the 2 “bracketing” aerosol models. Step (2) is now inverted, to calculate two z(l) ratios from the two ta(l) at 510 nm and 705 nm.
(7) The following step lies on the assumption that the actual (rpath(l) / rR(l)) ratio falls between the two z(l) ratios calculated at step (6), proportionally, in the same manner as it does at 775 nm. rpath(l) is now estimated for bands at 510 nm and 705 nm.
(8) By making an assumption on the normalised waterleaving reflectance at 510 nm, the error in the atmospheric correction at 510 nm, Dr 510, can be assessed.
(9) A test is then made on this Dr510 value, if a number of conditions are met. If those conditions are not met, the correction is continued at step (10). Otherwise, depending on the test result, either the correction is continued at step (10), or it is carried out once more from step (2), by selecting however a different set of N’ aerosol models. In the latter situation, the correction is actually carried out for several aerosol databases, so that steps 28 are carried out several times; several couples of aerosol models are then selected (one at each time steps 28 are done), and the one which is retained at the end is the one that leads to the lowest Dr510.
(10) For every wavelength l of the visible domain, 2 values of ta are calculated from the knowledge of the spectral scattering coefficients of the 2 “bracketing” aerosol models.
(11) Step (2) is now inverted, to calculate two z(l) ratios from the two ta(l) for the visible bands, and then to obtain rpath(l) (see step 7).
2.7.1.2.6.3.3 Correction (step 2.6.9.3)
At then end of the MERIS model step, we now have an estimate of the path reflectance and aerosol optical parameters at all visible and NIR wavelengths where the atmospheric correction is required.
The waterleaving reflectance at the instrument level is then obtained as :
t_{u}(l).td(l).r’w(l) = ROGC(l)  rpath^{*}(l)
The following step consists in calculating the diffuse transmittance, downward td(l) and upward t_{u}(l), in order to retrieve the normalised waterleaving reflectance at surface level r’_{w}(l).
