## 2 Materials and Methods
### Methods  
The Doppler shifts (\(f_{dc}\)) measured by SAR consist of both non-geophysical and geophysical components. The non-geophysical contributions include variations in the satellite attitude and orbit (\(f_{att}\)), scalloping effects (\(f_{sca}\)), antenna electronic mispointing (\(f_{ec}\)), and residual errors (\(\Delta f\)). The geophysical contributions arise from the ocean surface currents (\(f_{osc}\)) and sea state effects (\(f_{ss}\)). Accordingly, the total observed Doppler shift can be expressed as  
\[f_{dc}=f_{att}+f_{sca}+f_{ec}+f_{osc}+f_{ss}+\Delta f \tag{1}\]  
To accurately retrieve the radial OSC velocities, several correction procedures are applied to the observed Doppler shifts:  
1. **Correction of satellite attitude and orbit variations (\(f_{att}\))**: These contributions are corrected using information provided in the Sentinel-1 Level-2 OCN product. 2. **Correction of scalloping effects (\(f_{sca}\))**: A linear fitting method is employed to mitigate the Doppler distortions caused by scalloping. Notably, since 23 June 2020, the Sentinel-1 Instrument Processing Facility (IPF) has implemented internal corrections for Doppler scalloping [40]. 3. **Correction of antenna electronic mispointing (\(f_{\mathit{elec}}\)) and residual biases (\(\Delta f\))**: The doppler shift measurements over land are used as references to correct for the \(f_{\mathit{elec}}\) and \(\Delta f\) over the ocean. 4. **Removal of sea state effects (\(f_{\mathit{ss}}\))**: The geophysical Doppler contributions arising from wind waves and swell (\(f_{\mathit{ss}}\)) are estimated and removed using the DPDop model. The DPDop model expresses the Doppler velocity (\(V_{D}\)) as the sum of the OSC velocity, the contributions from Bragg waves and breaking wave motions, and the effects of tilt and hydrodynamic modulation. \[V_{D}=u_{s}+(1-P_{NP})c_{B}+P_{NP}c_{NP}+c^{T}+P_{NP}c_{wb}^{H}\] (2) Here, \(u_{s}\) denotes the radial OSC velocity, and \(P_{NP}\) represents the ratio of the non-polarized backscatter (\(\sigma_{np}\)) to the total radar backscatter (\(\sigma_{0}^{PP}\)). The terms \(c_{B}\) and \(c_{NP}\) correspond to the velocities of the Bragg waves and breaking waves, respectively, while \(c^{T}\) and \(c_{wb}^{H}\) account for the contributions of the tilt and hydrodynamic modulation to the \(V_{D}\). The formulas for each term are given as follows: \[c_{B}=c_{br}\frac{A_{br}(\varphi)-A_{br}(\varphi+\pi)}{A_{br}(\varphi)+A_{br}( \varphi+\pi)}\] (3) \[c_{np}=\varepsilon_{wb}\overline{c}_{wb}\frac{A_{np}(\varphi)-A_{np}(\varphi+ \pi)}{A_{np}(\varphi)+A_{np}(\varphi+\pi)}\] (4) \[c^{T}=-cot\theta M_{f}^{t}cos(\varphi_{R}-\varphi_{m})C_{m}k_{m}^{2}E\] (5) \[c_{wb}^{H}=[cos(\varphi_{R}-\varphi_{m})M_{\mathrm{lwb}}^{h}(\varphi_{m},k_ {m})+cot\theta M_{\mathrm{zwb}}^{h}(\varphi_{m},k_{m})]C_{m}k_{m}^{2}E\] (6)  
In these equations, \(c_{br}\) denotes the phase speed of the Bragg waves, and \(A_{br}\) represents the directional distribution of the Bragg wave spectrum. The variable \(\varphi\) is the angular offset between the radar look direction (\(\varphi_{R}\)) and the wind direction. The parameter \(\varepsilon_{wb}\) is the wave-breaking tuning coefficient, while \(\overline{c}_{wb}\) represents the average speed of the breaking waves, and \(A_{np}\) characterizes the angular distribution of the breaking facets. The radar incidence angle is denoted by \(\theta\). \(M_{f}^{t}\) and \(M_{\mathrm{wb}}^{h}\) are transfer functions describing the effects of the tilt and hydrodynamic modulation, respectively. \(\varphi_{m}\) is the mean wave direction, \(C_{m}\) is the phase velocity corresponding to the mean wave number (\(k_{m}\)), and \(E\) is the total wave energy. Detailed formulations for these parameters can be found in references [28; 29]. The sum of the last four terms on the right-hand side of Equation (2) corresponds to the sea state-induced Doppler velocity, denoted as \(U_{\mathit{ss}}\).