## Application

In the context of an operational application where the containment of computational expenses is a significant driver, it is essential to ensure that the inversion procedure is restricted to daily sequences showing a high level of temporal consistency that conforms to the physical expectations expressed by the Meteosat data simulator. These expectations are such that, for all Meteosat pixels, the intrinsic variations of the BRF data strings built from the accumulation of half-hourly measurements from sunrise to sunset for all Meteosat pixels can be fully explained by Equation 4. Based on the classical plane-parallel approach, this equation is only valid for stationary clear-sky systems and any BRF measurement corrupted by clouds and/or cloud shadows and/or rapid change in aerosol load and radiative properties must be excluded before entering the inversion procedure. In addition, artificial BRF changes in a daily data string may occur due to an inaccurate pointing of the same region during the daily sequence of BRF data accumulation. The latter is a particularly sensitive issue for those pixels close to sharp geophysical boundaries such as lake shores, rivers, coastlines and mountains. In other words, for every pixel, variations in the time series during the day due to undesired geophysical and instrumental effects should be rejected. A first level of screening is performed by setting a threshold value equal to 0.6 on the TOA BRF measurements in order to eliminate obviously cloudy conditions. A second level, yielding a finer screening of undesired conditions, is achieved by implementing a Data Consistency Procedure (DCP) to produce an angularly smooth but coherent TOA BRF series which accounts for hot spot conditions. This procedure checks the consistency of the pre-screened TOA BRF values by attempting to fit the data series against a generic parametric BRF model, namely the Modified version of the RPV (MRPV) model (Engelsen et al., 1996). The MRPV model permits to fit angularly consistent BRF data strings, including the effects due to hot spot conditions, in the case of daily "clear-sky" situations (Pinty et al., 2000b). This constitutes a novel approach to cloud screening conditions since it does not require any additional information from thermal bands, as is usually the case for cloud identification techniques. This novel approach is entirely based on the analysis of the angular coherence of the bi-directional shapes emulated by the daily accumulation of TOA BRF measurements.

The procedure compares the values of the standard deviation of the fit, cract, against a pre-defined threshold value, crDCp, which represents the maximum value of the standard deviation of the fit that is considered acceptable for successful interpretability. When the condition cract < crDcp is fulfilled, the procedure ends and the daily data time series is interpreted by the algorithm described in Section 2. Otherwise, the observed BRF value exhibiting the largest absolute departure with respect to the model prediction is eliminated and the series of observed BRF values is screened again. This iterative procedure is pursued until an acceptable fit is obtained, or the number of BRF data points remaining in the time series becomes too low to ensure a reliable retrieval of the geophysical parameters. In practice, the value of the following function is estimated:

where i?Msatfeat, 0 is the TOA BRF value measured at level zsat by Meteosat for the current slot i, Ryi(z<M, i', r0, km, bm) is the TOA BRF value simulated with the MRPV model for the same image i using the optimal parameter values retrieved as indicated above, and is the maximum acceptable standard deviation value to guarantee an appropriate smoothness and angular consistency between the reflectances in the various images of the same day for a given pixel. This smoothness condition is deemed verified when the Xdcp2 value is equal to or less than one.

In summary, the data consistency procedure guarantees the selection of samples of the Meteosat BRF fields (at the full pixel resolution, as well as for each and every pixel of the image) which can be interpreted at a pre-specified quality level given by the value of the obcp parameter controlling the cost function. It should be underscored that the procedure does produce valuable geophysical information concerning

1. the characterization of the fields required to estimate TOA albedos,

2. the identification of clouds and cloud-shadows every thirty minutes in the daily sequence, and

3. the detection of potential error sources due to the inaccuracy in the geo-

rectification process of the raw data.

For all practical purposes, the choice of the numerical values for the fxDCP and parameters results from the compromise between generating accurate products and retrieving the desired information over a maximum number of pixels. Too small a value for the parameter translates into the rejection of a high number of slots for all pixels. Although this would ensure that an angularly consistent string of BRF values is retained, a too small number of slots may not provide sufficient angular constraints on the inversion procedure which, in turn, may affect the reliability of the final products since too many acceptable solutions would be identified. In order to ensure that these constraints remain strong enough, it was decided to impose that a total of at least 9 solar angles would be required for performing the inversion. Although the parameter value should be as small as possible to limit the number of acceptable solutions, too small a value, corresponding to a high accuracy in the data fitting exercise, may not permit us to identify even a single solution. In the present application based on Meteosat-5 data, 0dcp> °"data and the minimum number of solar angles were set to 5%, 8% and 9, respectively, regardless of the pixel location and period of the year.

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