## 5 The Data Analysis Procedure  
The former sections addressed the separate description of the different elements considered in this study to investigate the possibility of exploiting the Doppler information derived from the SAR data to achieve products that can provide an indication about the sea currents. As previously noticed, the sea surface current directly extracted from the SAR data can be heavily impacted by meteorological factors, mainly the wind. The procedure used in this work for the data analysis is depicted in Figure 4: it involves the joint processing of SAR acquisitions and the integration with the external information about the wind achieved by the external atmospheric model. Figure 4 highlights that SAR data are exploited following two main streams based on the use of the intensity and of the complex (amplitude and phase) information for the (spectral) Doppler analysis. As for the latter, the DCA is generated according to the procedure described in Section 2 and summarized in Figure 1 starting from the complex information associated with the raw data. The choice to start from the Level-0 product is, as already pointed out in Section 2, related to the need for avoiding any possible bias introduced at the data focusing stage for the generation of Level-1 products supplied by the data provider. The latter may in fact incorporate filtering for image enhancement based on ad hoc trade-off of the resolution and the sidelobes suppression. The achieved DCA, one converted to surface current (point 6 left output), is then stored for the subsequent comparison with the response associated with to meteorological factors carried at the final stage of the processing. Figure 3: Plots relevant to the Doppler Geophysical Mapping Function describing the Doppler Centroid Anomaly (DCA) in Equations (18)–(22) as a function of the wind speed and direction. (**A**) modulus of the DCA (\(f_{W\_DCA}\)) as a function of wind speed, for 23\({}^{\circ}\) of incidence angle and for VV polarization: upwind condition in green, downwind condition in red dashed. (**B**) DCA (\(f_{W\_DCA}\) ) as a function of the wind direction, same incidence angle polarization as in the left image, for three different wind speed values: 7 m/s (blue line), 5 m/s (green line), 2 m/s (red line). The estimation of the Doppler component induced by the meteorological factors follows the right side flow in Figure 4 and is composed of two sequential steps. In the first step, the wind information provided by the weather forecast model is enriched via the assimilation, based on the Bayesian strategy described in Section 3, of the High Resolution SAR intensity. A High-Resolution wind map is thus also produced (level 3). The second step exploits the Doppler GMF described in Section 4 to derive the wind related Doppler information from the wind intensity and direction achieved after from both the original wind data by the model and the HR wind results after integration with the intensity SAR data. The retrieved wind Doppler components are converted to surface current, see level 6 at middle and right, according to Equation (2). At this stage, a final subtraction between the DCA derived surface current and the one derived by the wind information could be implemented to extract the residual radial surface current component. As long as wind data derived from the weather forecast are given with a high confidence level, the output produced by the procedure shown in Figure 4 should therefore contain only the information relevant to the current associated with the ocean current and possible effects of the sea state. This subtraction is, however, not included because of the aim of this work was to evaluate the influence of the wind on the surface currents derived from the Doppler analysis. The above described procedure was adopted in the experimental section for the data analysis of the case studies.