Revisiting the Cox and Munk wave-slope statistics using IASI observations of the sea surface

We use radiances collected from space by the Infrared Atmospheric Sounder Interferometer (IASI) when looking down at ocean surfaces during the day to remotely determine the probability distribution of wave slopes. This is achieved by using about 300 channels between 3.6 and 4.0μm and a physically-based approach which properly takes the contribution of the reflected solar radiation into account. Based on about 150 millions observations, the same number of wave-slope probabilities are retrieved for wind speeds (at 10 m) up to 15 m/s. We revisit and discuss the methodology proposed by Cox and Munk (CM) to derive their celebrated wave-slope probability distribution function (pdf) from photographs of the sun glitter. We propose an original and robust approach for accurate retrievals of the 7 parameters appearing in the Gram–Charlier representation of the pdf. Our results for the mean square slopes (MSSs) are fully compatible with those of CM, and with the more recent results by Bréon and Henriot, 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, with wind-dependent values specific to the local sea state. 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. [Display omitted] •Probabilities of wind-driven wave-slopes from mid-infrared IASI radiances.•Wind-dependent wave-slope probability distribution from about 150 106 observations.•An original method for the derivation of wave-slope statistical parameters.•Qualitative change in wave-slope asymmetry as wind increases.•Refining Cox and Munk parameterization.