## 2 Doppler Anomaly Extraction  
The DCA technique, described in [4], is based on the measurement of the Doppler shifts induced on the SAR image by the line-of-sight component of the sea surface velocity. In our case, the measurement of DCA has been carried out by using the method based on the estimation of the azimuth auto-correlation function proposed in [29]. In particular, to avoid any bias induced by possible filtering of spectral components in the application of the SAR transfer function at the stage of generation of the Single Look Complex products, the method is applied starting from the raw data. The block diagram that describes the overall processing chain is shown in Figure 1. More specifically, starting from raw data and after the SAR focusing operation, the corresponding Doppler Centroid frequency, referred to in the following as \(f_{DC}\), is estimated over small sliding patches: details on the patch sized choice are provided in Section 7. Subsequently, the DCA, referred to as \(f_{DCA}\), is extracted by subtracting the Doppler centroid induced by the antenna pointing and Earth rotation. The DCA and the radial velocity \(v_{r}\) of the backscattering cells are related by the following simple equation:  
\[f_{DCA}(x,r)=f_{DC}(x,r)-f_{DC0}(x,r)=\frac{2}{\lambda}v_{r}(x,r) \tag{1}\]  
where \(x\) and \(r\) are the azimuth and range, respectively and \(\lambda\) is the wavelength. The term \(f_{DC0}\) is the Doppler Centroid corresponding to a \"stationary\" scene, more precisely to a scene with all scatterers moving at the same velocity of the associate one with the Earth rotation. The radial component of the target velocity \(v_{r}\) is then evaluated by the Doppler Anomaly as follows:  
\[v_{r}=\frac{\lambda f_{DCA}}{2} \tag{2}\]  
Under the white Gaussian assumption for the signal and noise, it has been shown that the accuracy of such estimator is given by [30]  
\[\sigma_{f_{DC}}=0.3407\frac{PRF}{\sqrt{M}} \tag{3}\]  
where \(M\) is the number of independent samples used for the spectral estimation and \(PRF\) is the pulse repetition frequency of the illuminating sensor. It is important to underline that the \"background\" DC, \(f_{DC0}\) in its polynomial approximation form could be extracted directly from the ancillary information in the ENVISAT data. In our case, to account also for additional deviations of the beam that might be present in the acquisition, we preferred to  
Figure 1: Block diagram of the processing chain. perform an estimation directly from the data by a factorization this term in an azimuth \(f_{D\text{C0}\text{r}}(x)\) and a range \(f_{D\text{C0}\text{r}}(r)\) component:  
\[f_{D\text{C0}}(x,r)=f_{D\text{C0}\text{r}}(x)f_{D\text{C0}\text{r}}(r) \tag{4}\]  
Based on the observed experimental patterns for the ENVISAT sensor we modeled \(f_{D\text{C0}\text{r}}(x)\) as a sinusoidal contribution:  
\[f_{D\text{C0}x}(x)=a\sin(2\pi\xi_{0}x) \tag{5}\]  
whereas for \(f_{D\text{C0}\text{r}}(r)\) is expressed by the use of a polynomial form as follows:  
\[f_{D\text{C0}\text{r}}(r)=a_{0}+a_{1}r+a_{2}r^{2}+.....=\sum_{n=0}^{L}a_{n}r^{n} \tag{6}\]  
The azimuth component was modeled as in Equation (5) because such a behavior was observed in the entire scene processed in the experimental results discussed in Section 7 and takes place at a constant frequency of 31.72 Hz. This component, whose origin is assumed to be related to the sensor, likely due to a systematic oscillation of the carrier frequency, was compensated simply via a notch filtering. As for the range component in \(f_{D\text{C0}}\), being the scene located in a coastal region involving both land and sea, we used an approach based on separate estimation in two regions starting from the sea mask.