Advances in the understanding and modelling of surface currents have revealed the importance of internal waves, mesoscale and submesoscale features. Indeed all these features should have a large influence on wind waves and in particular on wave heights. Still, the quantitative impact of currents on waves is not well known due to the complexity of the random wave fields and currents that are found in the ocean, and the lack of observations of both currents and waves at scales shorter than 150km. Here we compare novel satellite altimetry data and state of the art phase‐averaged numerical wave models forced both by wind and currents. Currents used are taken from the oceanic model CROCO, run at high resolution. The influence of current field resolution is investigated by applying Gaussian filters of different width to that same high resolution current field. We find that a numerical wave model that uses currents with resolutions of ∼30km or less and a directional resolution of 7.5°, can provide accurate representations of the significant wave height gradients found in the Agulhas current. Using smoother current fields such as derived from altimeters measurements alone, coarse directional spectral resolution or larger directional spread of the wave model, generally underestimates gradients and extreme wave heights. Hence, satellite altimetry provides high resolution wave height with a gradient magnitude that is highly sensitive to underlying surface current gradients, at resolutions that may not be resolved by today's altimeters measurements. This is demonstrated here for relatively steady currents averaged over 3 years.

Plain Language Summary

Mariners have learned to be wary of severe sea states, especially in strong currents like the Agulhas that flows along the South African coast, where wave heights in the current can be several meters taller than in the surrounding waters. Mariners have also learned to spot currents by watching the water ahead of them. Here we use satellite measurements of wave heights and a numerical wave model to understand the parameters that control the spatial variation of wave heights across currents. We particularly question the necessary current magnitude and gradient that are required to explain observed wave height gradients. Modeled gradients fade for smooth surface currents like surface currents estimated from satellite measurements of sea level or typical global ocean circulation models. Also, numerical experiments have shown that when incident waves have a narrow range of directions, wave height gradients are sharper. A good wave model should thus resolve both the current features, with a spatial resolution better than 30 km, and the range of wave directions, typically using 48 directions or more. Such a good model can then be used to evaluate the quality of modeled ocean currents by matching the modeled strength of wave height gradients with measurements.