Advances in the understanding and modelling of surface currents have
revealed the importance of mesoscale and submesoscale features. These
features should have a large influence on wind waves, and in particular
wave heights are expected to be modified by refraction. 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 150 km. Here we combine novel satellite altimetry data with
phase-averaged numerical wave models forced by wind and surface currents
fields, taken from the oceanic model CROCO, run at 2.5km resolution. The
influence of the spatial resolution of the current field is investigated
using smoothed versions of the same current field. We find that a
numerical wave model forced with surface currents with resolutions of 30
km or less and a directional resolution of 7.5 degrees or less, can
provide accurate representations of the significant wave height
gradients found in the Agulhas current. Using smoother current fields,
such as derived from satellite measurements of dynamic height, generally
underestimates wave height gradients. Hence, satellite altimetry
provides high resolution wave height with a gradient magnitude that is a
constraint on surface current gradients, at resolutions that may not be
resolved by today's combination of mean dynamic topography and
altimeter-derived anomalies. Beyond a demonstration for relatively
steady currents, this may apply to time-varying currents if enough wave
measurements are available.