The Total Surface Current Velocity (TSCV) - the horizontal vector quantity that advects seawater - is an Essential Climate Variable, with few observations available today. The TSCV can be derived from the phase speed of surface gravity waves, and the estimates of the phase speeds of different wavelengths could give a measure of the vertical shear. Here we combine 10-m resolution Level-1C of the Sentinel 2 Multispectral Instrument, acquired with time lags up to 1s, and numerical simulation of these images. Retrieving the near surface shear requires a specific attention to waves in opposing direction when estimating a single phase speed from the phase difference in an image pair. Opposing waves lead to errors in phase speeds that are most frequent for shorter wavelengths. We propose an alternative method using a least-square fit of the current speed and amplitudes of waves in opposing directions to the observed complex amplitudes of a sequence of 3 images. When applied to Sentinel 2, this method generally provides more moisy estimate of the current. A byproduct of this analysis is the “opposition spectrum” that is a key quantity in the sources of microseisms and microbaroms. For future possible sensors, the retrieval of TSCV and shear can benefit from increased time lags, resolution and exposure time of acquisition. These findings should allow new investigations of near-surface ocean processes including regions of freshwater influence or internal waves, using existing satellite missions such as Sentinel 2, and provide a basis for the design of future optical instruments.

2D-parametric model is used to simulate waves under Tropical Cyclones (TCs). Set of equations describing either wind waves development and swell evolution, is solved using method of characteristics. Wave-rays patterns provide efficient visualization on how wave trains develop and travel through TC varying wind field and leave storm area as swell. The superposition of wave-trains rays exhibits coherent spatial patterns of significant wave height, peak wavelength and direction, depending on TC characteristics, - maximal wind speed (um), radius (Rm), and translation velocity (V). Group velocity resonance leads to appearance of waves with abnormal energy between the TC right and front sectors, further outrunning as swell through the TC front sector. Yet, when TC translation velocity exceeds a threshold value, waves cannot reach group velocity resonance, and travelling backwards, form a wake of swell systems trailing the forward moving TC. 2D-parametric model solutions are parameterized using 2D self-similar universal functions. Comparisons between self-similar solutions and measurements, demonstrate excellent agreement to warrant their use for scientific and practical applications. Self-similar solutions provide immediate estimates of azimuthal-radial distributions of wave parameters under TCs, solely characterized by arbitrary sets of um, Rm and V conditions. Self-similar solutions clearly divide TCs between slow TCs fulfilling conditions Rm/Lcr>1, and fast TCs corresponding to Rm/Lcr <1, where Lcr is a critical fetch. The region around Rm/Lc = 1 corresponds to the group velocity resonance conditions, leading to the largest possible waves generated by a TC.

A fully consistent 2D parametric model of waves development under spatially and temporally varying winds is suggested. The 2D model is based on first-principle conservation equations, consistently constrained by self-similar fetch-laws. Derived coupled equations written in the characteristic form provide practical means to rapidly assess how the energy, frequency and direction of dominant surface waves are distributed under varying wind forcing. For young waves, non-linear interactions are essential to drive the peak frequency downshift, and the wind energy input and wave breaking dissipation are the governing sources of the wave energy evolution. With a prescribed wind wave growth rate, proportional to ustar/c squared, wave breaking dissipation becomes a power-function of the dominant wave slope. Under uniform wind conditions, this growth rate imposes solutions for peak frequency and energy development to follow fetch-laws, with exponents q=-1/4 p=3/4 correspondingly. This set of exponents recovers the Toba’s laws, and imposes the wave breaking exponent equal to 3. A smooth transition from wind driven seas to swell is obtained. Varying wind direction is the only source to drive spectral peak direction changes. This can lead to occurrence of focusing/defocusing wave groups and formation of areas where wave-rays merge and cross. Solutions predict significant (but finite) local enhancements of the energy. Further propagating, wave rays diverge, leading to wave attenuation away from the storm area