###### Abstract
The sea-surface scattering model is based on the improved combined sea-surface model [8; 9] proposed by [PERSON] and [PERSON], which considers the modulation effect of large-scale wave on small-scale Bragg waves. The normalized scattering coefficient can be calculated by taking the modulated wave spectrum and the given radar parameters as the input of the scattering model [8; 16]  
\[\begin{split}\left\langle\sigma\right\rangle=\sigma^{(0)}+ \left\langle\sigma^{(2)}\right\rangle\\ =\left.\sigma\right|_{\mathbf{s}=0}+\iint\left(\left.\frac{\partial^ {2}\overset{\wedge\vee}{\sigma}}  
\[V_{dop}=\frac{\pi\cdot\langle f_{D\pm}\rangle_{\varrho}}{k_{e}\sin\theta} \tag{6}\]  
where \(k_{e}\) is the wave number of the electromagnetic waves, and \(\theta\) is the incident angle. Therefore, the radial horizontal sea-surface Doppler velocity along the ascending and descending satellite beam represented by \(V_{S}\) and \(V_{G}\) in Figure 2 is calculated successively by the above process. The radial velocity is actually the Doppler velocity that reflects the average motion state of scatterers in the sea-surface resolution unit. In the range of medium incident angles, the radial Doppler velocity \(u_{r}\) includes not only the current velocity but also the component of the sea-surface wave motion [17]. \[u_{r}=u_{c}+u_{o}+u_{b} \tag{7}\]  
where \(u_{c}\) is the current velocity, \(u_{o}\) is the large-scale wave orbital velocity, and \(u_{b}\) is the net Bragg wave phase velocity. At present, the related wave motion model is not perfect, and thus it is difficult to extract the current velocity component by directly calculating the accurate wave velocity [10]. The authors in [18] stated that when there is no current field, the sea-surface velocity obtained by using the SAR ocean imaging model comes from the wave motion. Therefore, in the second step, the input current field velocity is set to zero, combined with the same wind field, and through the calculation process similar to the radial velocity, the wave motion velocities in the ascending and descending beam direction are obtained, which are \(V_{S}^{\varpi}\) and \(V_{G}^{\varpi}\), respectively. Since the influence of large-scale waves is considered in the previously used wave spectrum and scattering model, the simulated wave velocities include the sum of the last two velocity components of Equation (7). By making a difference between the radial Doppler velocity and the wave velocity, the current velocity components \(V_{S}^{c}\) and \(V_{G}^{c}\) in the ascending and descending beam direction can be obtained:  
\[V_{S}^{c}=V_{S}-V_{S}^{\varpi} \tag{8}\]  
\[V_{G}^{c}=V_{G}-V_{G}^{\varpi} \tag{9}\]  
Then, combined with the trajectory crossing current measurement geometric model in Figure 1, the east-west velocity component \(V_{U}\) and north-south velocity component \(V_{V}\) of the sea-surface current can be calculated:  
Figure 2.0  
Figure 2.1  
Finally, the magnitude and direction of the current vector are, respectively, expressed as:  
Figure 2.2SAR data used in this paper is shown in Figure 2.3 This is the Mozambique strait between southeast Africa and Madagascar, where the sea surface is affected by the warm current of Mozambique, and the motion state is relatively stable. The red box indicates the stripmap SAR data range of ESA sentinel-1 satellite's ascending pass, the acquisition time is 8 October 2019, 15:35 UTC (orbit number: 018385), the black box indicates the stripmap SAR data range of China Gaofen-3 (GF-3) satellite's descending pass, and the acquisition time is 9 October 2019, 02:43 UTC (orbit number: 016651). Although these two SAR data were not acquired at the same time, the time interval is short, the current motion status is basically unchanged here, and these two SAR images overlap partially in this sea area, which meets the requirements of the trajectory-crossing method. Figure 4 shows the SAR amplitude image of Sentinel-1 satellite and the horizontal radial Doppler velocity image of its secondary product.