Frédéric Nouguier

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.

Sea Surface Microwave Scattering at Extreme Grazing Angle: Numerical Investigation of the Doppler Shift

We present a numerical investigation of horizontally polarized microwave scattering from 1-D sea surfaces at extreme grazing angles. Rigorous electromagnetic calculations are performed with a specific integral formalism dedicated to grazing angles. Sample sea surfaces are simulated using a classical Pierson-Moskowitz elevation spectrum together with weakly nonlinear hydrodynamic models, namely, the Creamer solution, the “choppy wave model,” and a recent improved version thereof. For this, the electromagnetic integral formalism is extended to surfaces with irregular sampling. For the different nonlinear surface models and assuming no large-scale current, we evidence a dramatic increase, followed by a saturation of the mean Doppler shift in the last few grazing degrees, with a limiting value depending quasi-linearly on the significant wave height. Our numerical investigations confirm that breaking events are not necessary to produce fast scatterers but tend to show that they are necessary to reproduce the elevated level of backscattered power. The results of this study also support the hypothesis that the blow-up of the mean Doppler shift at grazing angle is associated to an electromagnetic sharp edge effect on the large surface crests rather than geometrical shadowing of the troughs.

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.

Nonlinear Ocean Wave Reconstruction Algorithms Based on Simulated Spatiotemporal Data Acquired by a Flash LIDAR Camera

We report on the development of free surface reconstruction algorithms to predict ocean waves, based on spatial observations made with a high-frequency Flash light detection and ranging camera. We assume that the camera is mounted on a vessel, in a forward looking position, and is pointing at some distance ahead of its path yielding a sample of spatiotemporal wave elevation data. Because of the geometry, the density of measurement points gradually decreases (i.e., becomes sparse) with the distance to the camera. Free surface reconstruction algorithms were first developed and validated for linear 1-D and 2-D irregular surface models, whose amplitude coefficients are estimated on the basis of minimizing the mean square error of simulated surface elevations to measurements, over space and time (for a specified time initialization period). In the validation tests reported here, irregular ocean surfaces are generated on the basis of a directional Pierson-Moskowitz or Elfouhaily spectrum, and simulated LIDAR data sets are constructed by performing geometric intersections of laser rays with each generated surface. Once a nowcast of the ocean surface is estimated from the (simulated) LIDAR data, a forecast can be made of expected waves ahead of the vessel, for a time window that depends both on the initialization period and the resolved wavenumbers in the reconstruction. The process can then be repeated for another prediction window, and so forth. To reconstruct severe sea states, however, nonlinear effects must be included in the sea surface representation. This is done, here, by representing the ocean surface using the efficient Lagrangian choppy wave model .

Surface roughness changes by fine scale current gradients: Properties at multiple azimuth view angles

AbstractAt times, high-resolution images of sea surface roughness can provide stunning details of submesoscale upper-ocean dynamics. As interpreted, transformations of short-scale wind waves by horizontal current gradients are responsible for those spectacular observations. Those observations could prove particularly useful to validate numerical ocean models that reach increasingly high resolutions. Focusing on surface roughness at optical wavelengths, two steps have recently been performed in that direction. First, it was shown in a previous paper by Rascle et al. that surface roughness variations not only trace surface current divergence but also other characteristics of the current gradient tensor, mainly the strain in the wind direction. The wind direction with respect to the current gradient thus stands out as an important interpretative parameter. The second step is the purpose of the present paper, where the effect of the viewing direction is investigated. To this end, the authors discuss pairs of ...

Eddy-Current Modeling of a Continous Conductivity Profile Resulting From a Diffusion Process

This paper deals with the modelization of eddy-current measurements over combustion turbine blade coatings affected by depletion of aluminum. First, we model the response of an eddy-current coil over a layered metallic structure with a top over-aluminized coating by extending the analytical Uzal-Roses model for one hyperbolic tangent conductivity profile to a conductivity profile using two hyperbolic tangents for taking inward and outward depletion of aluminum inside the coating into account. Results obtained with this model are similar to those obtained with a numerical multilayer model but with a reduced computing time.

Onto a Skewness Approach to the Generalized Curvature Ocean Surface Scattering Model

The generalized curvature ocean surface scattering model [general curvature model (GCM)] is extended and revisited. Two key steps are addressed in this paper, namely, a necessary sea surface spectrum undressing procedure and the inclusion of a skewness phase-related component. Normalized radar cross-section (NRCS) simulations are generated at C-band for various wind conditions, polarizations, and incidence angles. Results are compared with CMOD5.n. Although the sea surface spectrum undressing procedure is a necessary step, the overall NRCS dynamic is notably affected only in low wind conditions (≤5 m/s). The inclusion of the skewness phase-related component makes the most impact to the NRCS dynamic where the upwind/downwind asymmetry is clearly detectable. A good agreement between the upwind/downwind asymmetry of the extended GCM and CMOD5.n is achieved for moderate winds (≈5–10 m/s) and moderate incidence angles (≈32°–40°). For low incidence angles (<26°), the GCM tends to overestimate the upwind/downwind asymmetry compared with CMOD5.n.

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

We 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.

Eddy-current {NDE} of combustion turbine blade coatings. Determination of conductivity profiles in the presence of a diffusion process

This paper deals with the estimation of conductivity profiles using Eddy- Current measurements over combustion turbine blade coatings affected by depletion of aluminium. First, we model the response of an Eddy-Current coil over a layered metallic structure with a top over-aluminized coating by extending the analytical Uzal-Roses model for one hyperbolic tangent conductivity profile to a conductivity profile using two hyperbolic tangents for taking inward and outward depletion of aluminum inside the coating into account. Results obtained with this model are similar to those obtained with a numerical multi-layer model with a reduced computing time.