Diffraction électromagnétique par la surface océanique : influence des nonlinéarités et de l'écume

The first part of this document introduces a simple model based on the resolution of the Lagrangian equations of motion termed “Choppy Wave Model”. It takes into account the hydrodynamic nonlinearities of the surface and makes possible to establish its complete statistical properties. The obtained results emphasize the nongaussian aspect of the ocean surface and the importance of the undressed spectrum. Some samples of nonlinear seas illustrate the hydrodynamic modulation of short waves by the long ones. In the second part, the impact of sea surface nonlinearities on the scattering process is quantified. The obtained results correct the bias due to the Gaussian assumption in meteo-oceanic parameters estimation. A new calculation method for the Kirchhoff integral based on fast radial convolutions is also introduced. Finally, the foam impact on the scattering process in micro-waves is estimated and is shown to become significant at strong winds and mainly in HH polarization.La première partie de ce document présente un modèle basé sur la résolution des équations Lagrangiennes du mouvement nommé “Choppy Wave Model”. Il permet de tenir compte des nonlinéarités hydrodynamiques de la surface et d’établir une description complète des grandeurs statistiques. Les résultats obtenus soulignent leur caractère non Gaussien et l’importance du spectre déshabillé. Des échantillons de surfaces nonlinéaires illustrent la modulation des petites vagues par les grandes. L’étude menée en seconde partie quantifie l’impact des nonlinéarités hydrodynamiques sur le phénomène de diffraction et permet de s’affranchir des erreurs dues à l’hypothèse Gaussienne dans l’estimation de paramètres météo-océaniques. Une nouvelle méthode de calcul de l’intégrale de Kirchhoff basée sur des convolutions radiales rapides est aussi introduite. Enfin, l’impact de l’écume en micro-ondes est détaillé et les principaux résultats montrent son importance à forts vents et notamment en polarisation HH

Measuring ocean surface velocities with the KuROS and KaRADOC airborne near-nadir Doppler radars: a multi-scale analysis in preparation of the SKIM mission, Submitted to Ocean SCience, July 2019

Surface currents are poorly known over most of the oceans. Satellite-borne Doppler Waves and Current Scatterom-eters (DWCS) can be used to fill this observation gap. The Sea surface KInematics Multiscale (SKIM) proposal, is the first satellite concept built on a DWCS design at near-nadir angles, and now one of the two candidates to become the 9th mission of the European Space Agency Earth Explorer program. As part of the detailed design and feasibility studies (phase A) funded by ESA, airborne measurements were carried out with both a Ku-Band and a Ka-Band Doppler radars looking at the sea surface at 5 near nadir-incidence in a real-aperture mode, i.e. in a geometry and mode similar to that of SKIM. The airborne radar KuROS was deployed to provide simultaneous measurements of the radar backscatter and Doppler velocity, in a side-looking configuration , with an horizontal resolution of about 5 to 10 m along the line of sight and integrated in the perpendicular direction over the real-aperture 3-dB footprint diameter (about 580 m). The KaRADOC system has a much narrower beam, with a circular footprint only 45 m in diameter. 10 The experiment took place in November 2018 off the French Atlantic coast, with sea states representative of the open ocean and a well known tide-dominated current regime. The data set is analyzed to explore the contribution of non-geophysical velocities to the measurement and how the geophysical part of the measured velocity combines wave-resolved and wave-averaged scales. We find that the measured Doppler velocity contains a characteristic wave phase speed, called here C 0 that is analogous to the Bragg phase speed of coastal High Frequency radars that use a grazing measurement geometry, with little 15 variations ∆ C associated to changes in sea state. The Ka-band measurements at an incidence of 12 • are 10% lower than the theoretical estimate C 0 2.4 m/s for typical oceanic conditions defined by a wind speed of 7 m/s and a significant wave height of 2 m. For Ku-band the measured data is 1 https://doi. 30% lower than the theoretical estimate 2.8 m/s. ∆ C is of the order of 0.2 m/s for a 1 m change in wave height, and cannot be confused with a 1 m/s change in tidal current. The actual measurement of the current velocity from an aircraft at 4 to 18 • incidence angle is, however, made difficult by uncertainties on the measurement geometry, which are much reduced in satellite measurements

Measuring currents, ice drift, and waves from space: the Sea Surface KInematics Multiscale monitoring (SKIM) concept

We propose a new satellite mission that uses a near-nadir Ka-band Doppler radar to measure surface currents, ice drift and ocean waves at spatial scales of 40?km and more, with snapshots at least every day for latitudes 75 to 82, and every few days otherwise. The use of incidence angles at 6 and 12 degrees allows a measurement of the directional wave spectrum which yields accurate corrections of the wave-induced bias in the current measurements. The instrument principle, algorithm for current velocity and mission performance are presented here. The proposed instrument can reveal features on tropical ocean and marginal ice zone dynamics that are inaccessible to other measurement systems, as well as a global monitoring of the ocean mesoscale that surpasses the capability of today?s nadir altimeters. Measuring ocean wave properties facilitates many applications, from wave-current interactions and air-sea fluxes to the transport and convergence of marine plastic debris and assessment of marine and coastal hazards

SKIM, a candidate satellite mission exploring global ocean currents and waves

The Sea surface KInematics Multiscale monitoring (SKIM) satellite mission is designed to explore ocean surface current and waves. This includes tropical currents, notably the poorly known patterns of divergence and their impact on the ocean heat budget, and monitoring of the emerging Arctic up to 82.5°N. SKIM will also make unprecedented direct measurements of strong currents, from boundary currents to the Antarctic circumpolar current, and their interaction with ocean waves with expected impacts on air-sea fluxes and extreme waves. For the first time, SKIM will directly measure the ocean surface current vector from space. The main instrument on SKIM is a Ka-band conically scanning, multi-beam Doppler radar altimeter/wave scatterometer that includes a state-of-the-art nadir beam comparable to the Poseidon-4 instrument on Sentinel 6. The well proven Doppler pulse-pair technique will give a surface drift velocity representative of the top meter of the ocean, after subtracting a large wave-induced contribution. Horizontal velocity components will be obtained with an accuracy better than 7 cm/s for horizontal wavelengths larger than 80 km and time resolutions larger than 15 days, with a mean revisit time of 4 days for of 99% of the global oceans. This will provide unique and innovative measurements that will further our understanding of the transports in the upper ocean layer, permanently distributing heat, carbon, plankton, and plastics. SKIM will also benefit from co-located measurements of water vapor, rain rate, sea ice concentration, and wind vectors provided by the European operational satellite MetOp-SG(B), allowing many joint analyses. SKIM is one of the two candidate satellite missions under development for ESA Earth Explorer 9. The other candidate is the Far infrared Radiation Understanding and Monitoring (FORUM). The final selection will be announced by September 2019, for a launch in the coming decade

Analytical techniques for the Doppler signature of sea surfaces in the microwave regime-II : nonlinear surfaces

International audienc

Analytical prediction of the polarized Doppler spectrum from nonlinear ocean surface at microwave frequency

International audienceWe present the use of combined hydrodynamic and electromagnetic analytical models for the simulation of the polarized ocean Doppler spectrum at microwave frequencies. We consider linear and weakly nonlinear sea surfaces after the Choppy Wave Model and incorporate them in the Weighted Curvature Approximation surface scattering method. Statistical expressions are derived, for the Doppler spectrum as well as for its central frequency and width. Results compare favorably with rigorous numerical computations for one-dimensional surfaces published in the literature. The simplicity of the analytical models provide a valuable tool for the Doppler analysis of two-dimensional sea-surfaces

Second-order Lagrangian description of tri-dimensional gravity wave interactions

We revisit and supplement the description of gravity waves based on perturbation expansions in Lagrangian coordinates. A general analytical framework is developed to derive a second-order Lagrangian solution to the motion of arbitrary surface gravity wave fields in a compact and vectorial form. The result is shown to be consistent with the classical second-order Eulerian expansion by Longuet-Higgins (J. Fluid Mech., vol. 17, 1963, pp. 459-480) and is used to improve the original derivation by Pierson (1961 Models of random seas based on the Lagrangian equations of motion. Tech. Rep. New York University) for long-crested waves. As demonstrated, the Lagrangian perturbation expansion captures nonlinearities to a higher degree than does the corresponding Eulerian expansion of the same order. At the second order, it can account for complex nonlinear phenomena such as wave-front deformation that we can relate to the initial stage of horseshoe-pattern formation and the Benjamin-Feir modulational instability to shed new light on the origins of these mechanisms

Scattering From Nonlinear Gravity Waves: The "Choppy Wave" Model

To progress in the understanding of the impact of nonlinear wave profiles in scattering from sea surfaces, a nonlinear model for infinite-depth gravity waves is considered. This model, termed as the "Choppy Wave" Model (CWM), is based on horizontal deformation of a linear reference random surface. It is numerically efficient and enjoys explicit second-order statistics for height and slope, which makes it well adapted to a large family of scattering models. We incorporate the CWM into a Kirchhoff or small-slope approximation and derive statistical expressions for the corresponding incoherent cross section. We insist on the importance of "undressing" the wavenumber spectrum to generate a nonlinear surface with a prescribed spectrum. Interestingly, the inclusion of nonlinearities is found to be practically compensated by the spectral undressing process; an effect which might be specific to the CWM and needs to be investigated in the framework of fully nonlinear models. Accordingly, the difference between the respective normalized radar cross section is rather small. The most noticeable changes are faster azimuthal variations and a slight increase of the radar returns at nadir. A statistical analysis of sea clutter in the framework of a two-scale model is also performed at large but nongrazing incidence. It shows a pronounced polarization dependence of the distribution of large backscattered amplitudes, the tail being much larger in horizontal polarization and for small resolution cell. Surface nonlinearities are shown to increase the tail of the amplitude distribution, as expected. Less obviously, their relative impact is found lesser in horizontal polarization. This raises the question of the actual contribution of nonlinearities in radar sea spikes at nongrazing angles

The GO4 Model in Near-Nadir Microwave Scattering From the Sea Surface

We introduce a practical and accurate model, referred to as "GO4," to describe near-nadir microwave scattering from the sea surface, and at the same time, we address the issue of the filtered mean square slope (mss) conventionally used in the geometrical optics model. GO4 is a simple correction of this last model, taking into account the diffraction correction induced by the rough surface through what we call an effective mean square curvature (msc). We evaluate the effective msc as a function of the surface wavenumber spectrum and the radar frequency and show that GO4 reaches the same accuracy as the physical optics model in a wide range of incidence and frequency bands with the sole knowledge of the mss and msc parameters. The key point is that the mss entering in GO4 is not the filtered but the total slope. We provide estimation of the effective msc on the basis of classical sea spectrum models. We also evaluate the effective msc from near-nadir satellite data in various bands and show that it is consistent with model predictions. Non-Gaussian effects are discussed and shown to be incorporated in the effective msc. We give some applications of the method, namely, the estimation of the total sea surface mss and the recalibration of relative radar cross sections

Sun glint Imagery of Landsat 8 for ocean surface waves

Local changes in specular reflections of visible sunlight on the ocean surfaces can be captured effectively by satellite sensors operating in the visible range of the electromagnetic spectrum. This causes the sun-glint imagery to closely resemble the oceanic images obtained using Synthetic Aperture Radar (SAR) further allowing the identification of the various fine scale structures and patterns of the ocean. Moreover, at relevant spatial resolutions, cloud-free conditions as well as optimum relative positions of the sensor, sun and the wave front it is possible to image ocean waves, wave transformations and refraction patterns using Satellite Sun-glint imagery (SSGI). In the present study, Landsat OLI imagery captured along the coast of Brest, France is used to derive ocean wave characteristics such as wavelength, direction, amplitude and then mapped to better understand the process of wave transformation. The 2D fast Fourier transform technique has been used on Band 5 (NIR, 0.851 - 0.879 mu m) to derive the wavelength of swell waves in near-shore regions as well as to analyze the wavelength change. Furthermore, owing to the detector configuration of Landsat 8 OLI there is a small time lag between the channel acquisitions. This effectively helps to infer the space-time characteristics of the surface waves using the cross channel correlation between Band 5 and Band 6 subsequently enabling removal of the directional ambiguity associated with the wave spectra obtained from the analysis. The main purpose of this study is to demonstrate the importance of SSGI in deriving relevant coastal information which can be further utilized for bathymetry, surface current and wave motion determinations