Determining the wave-slope statistics using IASI observations of the sea surface

Abstract

The sea-surface slope probability is an important physical parameter to describe the ocean surface and its interaction with the atmosphere. Its reference measurement dates back to the celebrated airborne experiment conducted by Cox and Munk (CM) in 1951 using sun glitter patterns. The obtained two-dimensional slope distribution function deviates slightly from the Gaussian distribution with pronounced up-to-crosswind and up-to-downwind asymmetries, a stronger peakedness and a slower decay at large values. It is classically parametrized by a Gram-Charlier representation with seven directional parameters describing the mean square slopes (MSSs) as well as the skewness and kurtosis coefficients for wind speeds up to 15 m/s. The MSSs are shown to follow a quasi-linear trend with wind speed, a result which has been confirmed by many subsequent airborne and spaceborne optical measurements and wave-tank experiments. The higher-order statistical coefficients have a non trivial dependence on wind speed as shown by the more recent results by Bréon and Henriot (2006); however, they are challenging to evaluate accurately and suffer from a larger uncertainty. We re-examine the sea-surface probability by using radiances collected from space by the Infrared Atmospheric Sounder Interferometer (IASI) when looking down at ocean surface during the day. This is achieved by using about 300 channels between 3.6 and 4.0 μm and a physically-based approach which properly takes the contribution of the reflected solar radiation into account. This unique data set covers 13 years of observations over the world ocean, resulting in about 150 millions IASI appropriate spectra and as many wave-slope probabilities. Based on these experimental wave-slopes we revisit and discuss CM results and methodology and their limitations. We propose an original and robust approach for accurate retrievals of the Gram-Charlier parameters. Our findings for the MSSs are fully compatible with those of CM but our lower uncertainties enable to point out departures from the linear wind-speed dependencies and a slight overestimation of the upwind MSS described by the linear fit of CM at moderate wind speed. Our skewness and kurtosis coefficients show clear influences of the wind speed, with a steady decrease of the former and the alongwind kurtosis coefficient being maximal at moderate wind speeds, features that CM could not point out due to the limitations of their measurements. We revisit the renormalization procedure employed by CM to obtain the complete variances from truncated pdfs and show that it imposes stringent conditions on the kurtosis coefficients that allow to determine them accurately. We also provide measurements of the shifted position of the most probable slope as well as a demonstration of a qualitative change of regime in the updown wind asymmetry of the wave-slope probability when the wind speed increases.