Simulation of the wave-current interaction effect on the SAR-derived radial velocity

Synthetic aperture radar (SAR) offers the possibility to observe the sea surface current with very high spatial resolution thanks to techniques such as Doppler centroid analysis and Along-Track Interferometry. These observations are relevant in coastal areas and shelf seas. SAR has been routinely providing valuable information on sea surface winds and waves for decades. However, the Doppler signature of the surface (aka Wind-wave Artefact Surface Velocity - WASV) is strongly affected by the waves and needs to be corrected accurately. In this study, we assess how strongly and how far convergent and divergent current fields impact the wave fields, hence the WASV. This is a numerical study, combining a numerical wave model (Simulating WAves Nearshore - SWAN) with a semi-empirical wave Doppler electromagnetic simulator (Yurovsky et al., 2019 - KaDOP).

In this study, the simulation of the effect of the wave-current interaction on the significant wave height is carried out using the SWAN model. Simulations are carried out for two different wind speeds 5 m/s and 10 m/s to represent different wave height regimes and two current profiles, convergent and divergent. The domain grid is one dimensional from x=0 to x=200 km with a spacing of 1 km. The depth is set to a constant value of 1000 m. The direction of propagation of the waves is perpendicular to the current front. Two scenarios are simulated waves propagating along the current and waves propagating against the current. The wind is set uniform over the whole fetch. The Doppler model KaDOP is used to estimate wave Doppler velocity (U_D). This model takes as inputs the incidence angle, wind speed, relative wind direction, significant wave height (H_s) and peak radial frequency (Ω_p) for wind sea and swell. The latter two quantities are affected by the wave-current interaction which affects the estimated wave Doppler. 

In summary, a combination of two different front widths (1 km and 3 km) and two wind speeds (5 m/s and 10 m/s) resulted in eight simulations. First,  it is shown that the spectral density increases (decreases) due to the convergent (divergent) current. The modulation is more important at the intermediate waves between the peak and around 0.6 Hz while it is negligible at the lowest and highest frequencies. As expected, the variation magnitude of H_s and U_D increases with increasing magnitude of the current divergence and wind speed. It is also noted that the convergent current, when the waves propagate in a direction opposing the current, yields larger variations ∆Hs and ∆U_D. Only in cases when the current front is 1 km wide, i.e. the divergence ≈ 0.19 10⁻³, ∆U_D exceeds 0.1 m/s, but this limit is only exceeded locally (over a few pixels).