Surface currents and significant wave height gradients: matching numerical models and high-resolution altimeter wave heights in the Agulhas current region

Abstract

Surface gravity waves generated by wind (hereinafter waves) interact with surface currents at all scales due to a wide range of processes (Phillips, 1977). Except for very short fetch near the coast or for the shortest wave components, the growth of waves in the presence of winds is only significant over large scales, so that the local gradients in the dominant wave properties are generally dominated by current gradients (Phillips, 1984). In the ocean, it appears that refraction, which focuses wave energy in current jets that flow in the wave direction, is probably the dominant source of variations of wave heights at scales 50-200 km with a minimal effect of wind gradients (Ardhuin et al., 2017). For currents speeds much weaker than the waves phase speed, it is the rotational part of the current that is expected to explain the variations in wave direc-Abstract Advances in the understanding and modeling 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 wavefields 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 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 Coastal and Regional Ocean COmmunity, 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 ∼30 km 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 SummaryMariners 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 ...

Focusing and defocusing of tropical cyclone generated waves by ocean current refraction

“…Recent observational and modeling studies have highlighted the importance of wavecurrent interactions in determining the sea state. In particular, these studies suggest that at oceanic meso-and submesoscales the spatial gradients in the significant wave height field arise from focusing and defocusing of wave action due to refraction by ocean currents (Ardhuin et al, 2017;Villas Bôas et al, 2020;Marechal & Ardhuin, 2021). To better understand the impact of currents on tropical-cyclone generated waves, here we used a regional wave model to show that including mesoscale currents in a tropical cyclone simulation leads to alternating regions of high and low H s starting near the eyewall and extending to the northeast all the way to 100 m isobath.…”

“…Waves are affected by ocean currents via wavecurrent interactions, which modify their amplitude, wavelength, and direction. Recent numerical modeling studies have shown that the spatial variability of significant wave height H s (the average of the highest one-third of the wave heights) at scales between 10 and 100 km is governed by the gradients in ocean currents (Ardhuin et al, 2017;Romero et al, 2020;Villas Bôas et al, 2020;Marechal & Ardhuin, 2021). Despite the limited spatial sampling of present satellite altimeters, novel signal processing techniques have provided observational evidence that supports these numerical results (Quilfen et al, 2018;Quilfen & Chapron, 2019).…”

Accuracy of numerical wave model results: Application to the Atlantic coasts of Europe

“…At global scale, the use of ocean surface currents can improve the accuracy of the simulated sea states (Echevarria et al, 2021;Alday et al, 2021), although a full effect generally requires relatively high spatial resolution that is generally not achievable by observations and thus models are usually not constrained at the necessary scale (Marechal and Ardhuin, 2020). Adding surface currents in the simulations can have effects on wave generation due to changes on the relative wind, it can modify the advection of waves or induce refraction in regions with large current gradients.…”

A global wave parameter database for geophysical applications. Part 3: Improved forcing and spectral resolution

“…We note that at the Equator and a few other places of interest, the 15-m depth drift is often in the opposite direction of the surface drift. Most importantly, finer spatial resolution is needed, typically down to 30 km, to represent most of the refraction effects (Ardhuin et al, 2017a;Marechal and Ardhuin, 2020). As a result, surface current estimates are often taken from numerical models, or, which is the case of the CMEMS Globcurrent product used here, derived from combined obser- 2016) with rms velocity computed over 30-day long trajectories and attributed to the center of that trajectory and white ocean pixels corresponding to 1 by 1 degree squares in which no data was available, (b) as given by the CMEMS GLORYS reanalysis, (c) as given by the CMEMS-Globcurrent product based on altimeter sea level anomalies, mean dynamic topography inferred from satellite gravimeters and ocean drifters, and "Ekman currents" estimated from ECMWF wind analyses.…”

“…However, to converge to the true solution of the wave action equation, increasing only the spatial resolution is not enough, and a finer spectral resolution is also needed, in particular for parameters sensitive to numerical diffusion like the directional spread (Ardhuin and Herbers, 2005). Although we know that current effects on wave heights would be better resolved with 48 directions instead of only 24 (Ardhuin et al, 2017b;Marechal and Ardhuin, 2020), we have stuck to 24 directions only because of the much lower CPU cost, and because differences in wave heights when using 24 or 36 directions were fairly limited. Compared to the costly increase of directional resolution, we found a higher benefit in terms of H s accuracy in increasing the spectral range with…”