Abstract. An improved composite surface model for the calculation of the normalized radar backscattering cross section (NRCS) of the ocean surface at moderate incidence angles is presented. The model is based on Bragg scattering theory. A Taylor expansion of the NRCS in the two-dimensional surface slope yields nonzero second-order terms which represent a first approximation for the effect of the geometric and hydrodynamic modulation of the Bragg scattering facets by all waves that are long compared to these facets. The corresponding expectation value of the NRCS varies with the wave height spectral density of all these waves, and it depends in a well-defined way on frequency, polarization, incidence angle, and azimuthal look direction of the radar. We show that measured NRCS values at frequencies ranging from 1 GHz (L band) through 34 GHz (Ka band) and wind speeds between 2 and 20 m/s can be well reproduced by the proposed model after some reasonable tuning of the input ocean wave spectrum. Also, polarization effects and upwind/downwind differences of the NRCS appear to be relatively well represented. The model can thus be considered as an advanced wind scatterometer model which is based on physical principles rather than on empirical relationships. The most promising field of application, however, will be the calculation of NRCS variations associated with local distortions of the wave spectrum by surface current gradients or wind effects.

[1] A wide variety of oceanic and atmospheric phenomena are often observed in and around the sunglint region on optical images of the sea surface. The appearance of these phenomena depends strongly on the viewing geometry with areas on the sea surface that are rougher (or smoother) than the background appearing as either brighter or darker than the background depending on their position relative to the specular point. To understand these sea surface signature variations, this paper introduces the concept of a critical sensor viewing angle, defined as the sensor zenith angle at which different sea surface roughness variances produce identical sunglint radiance. It is when the imaging geometry transitions through the critical angle that a surface feature goes through a brightness reversal. Knowledge of where this transition takes place is important for properly interpreting the characteristics of the sea surface signature of these phenomena. The theory behind the concept of the critical angle is presented and then applied to sunglint imagery acquired over the ocean from space by the Moderate Resolution Imaging Spectroradiometer onboard NASA's Aqua and Terra satellites.Citation: Jackson, C. R., and W. Alpers (2010), The role of the critical angle in brightness reversals on sunglint images of the sea surface,

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An improved three‐scale composite surface model for the modulation of the radar backscatter from the ocean surface by long ocean waves is presented. The model is based on Bragg scattering theory. In the conventional two‐scale model, only the geometric modulation of the radar backscatter and the hydrodynamic modulation of the short Bragg waves by the long waves is considered. In the three‐scale model, the impact of intermediate‐scale waves (wavelengths between the length of the Bragg waves and the length of the long waves which are resolved by the radar) is also taken into account, which leads to a modified theoretical ocean wave‐radar modulation transfer function (MTF). For the first time the proposed model includes not only geometric effects associated with the intermediate‐scale waves but also the additional hydrodynamic modulation of the Bragg waves. The resulting theoretical expression for the measured “hydrodynamic” MTF depends on the radar polarization as well as on the azimuthal (upwave / downwave or upwind / downwind) radar look direction. Especially for HH polarization, the predicted “hydrodynamic” MTF becomes significantly larger than expected from conventional theory. We compare model results with tower‐based scatterometer measurements at L, C, and X band (1.0, 5.3, and 10.0 GHz, respectively), which were obtained during the Synthetic Aperture Radar and X Band Ocean Nonlinearities‐Forschungsplattform Nordsee (SAXON‐FPN) experiment. The measured magnitudes and phases of the MTF are better reproduced by the proposed three‐scale model than by the conventional two‐scale model. However, the large measured “hydrodynamic” MTFs for high microwave frequencies (C and X band) are still underestimated. The agreement between model predictions and measurements can be improved if, for example, an additional variation of the wind stress over the long waves is assumed. The required wind stress modulation depends on the long‐wave slope and appears to be coupled to the hydrodynamic modulation of the surface roughness by a positive feedback mechanism.

USAGEPermission is granted to copy this article for use in teaching and research. Republication, systematic reproduction, or collective redistribution of any portion of this article by photocopy machine, reposting, or other means is permitted only with the approval of The Oceanography Society. Send all correspondence to: info@tos.org or The Oceanography Society, PO Box 1931, Rockville, MD 20849-1931 S p e c i a l i S S u e O N O c e a N R e m O t e S e N S i N g w i t h S y N t h e t i c a p e R t u R e R a d a R B y c h R i S t O p pROpeRtieS Of iNteRNal waVe SigNatuReS theory of SaR imagingIn order for nonlinear internal waves to appear on SAR imagery, the internal wave must interact with the ocean surface and modify it at roughness scales that interact with the observing radar signal. As manifested on SAR images, a nonlinear internal wave packet typically appears as an alternating pattern of quasi-periodic bright and dark bands against a gray background. These radar bands result from enhanced and reduced radar backscatter, with the bright bands representing a convergence (rough) zone and the dark bands representing a divergent (smooth) zone. The convergence and divergence zones are the result of variations in the subsurface currents associated with the internal waves interacting with ocean surface. The most common pattern is a bright band followed by a dark band representing a nonlinear internal wave of depression (Figure 1, packets 1-6). However, a number of factors can affect the characteristics of this signature pattern, including the environment at the ocean surface (wind speed, wind direction, presence of surface films) and the properties of the internal wave itself (mode, half-width, amplitude, and currents).Theoretical models describing the modulation of short-scale sea surface roughness by variable surface currents have been developed in the framework of weak hydrodynamic interaction theory (Alpers, 1985). When using this theory together with Bragg scattering theory, figure 1. a Seasat l-band synthetic aperture radar (SaR) image from the gulf of california acquired September 29, 1978, at 18:11 utc (Rev 1355. The image contains a variety of internal wave packet signatures, with the most prominent labeled 1-8. it shows many distinctive internal wave features: alternating bright/dark band signatures grouped into packets, packets from multiple tidal cycles present on a single image, and the nonlinear interaction between packets. The series of bright "dots" arrayed in a line across the image are the result of system calibration pulses (fu and holt, 1982 which relates spectral values of the ocean surface waves to the normalized radar cross section (NRCS), the relationship between NRCS and surface current gradient dUx dx can be written as:where σ denotes the total NRCS, σ 0 is the NRCS of the background,x is the coordinate in the look direction of the SAR antenna projected onto the horizontal plane, and A is a constant that depends on radar wavelength, incidence angle, and relaxation rate. The relaxa...

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The dynamics of the Rhine outflow plume in the proximity of the river mouth is investigated by using remote sensing data and numerical simulations. The remote sensing data consist of 41 synthetic aperture radar (SAR) images acquired by the First and Second European Remote Sensing satellites ERS-1 and ERS-2 over the outflow region of the river Rhine. Most of them show sea surface signatures of oceanic phenomena, for example, surface current and wind variations, ship wakes, and oil slicks. In particular, in 36 of these images pronounced frontal features are visible as narrow zones of mainly enhanced, sometimes enhanced/reduced radar backscatter that can be associated with the Rhine surface front. Within the area enclosed by the frontal line, large zones characterized by a lower radar backscatter than in the outer area are often visible. The analysis of the ERS SAR images suggests that the form and the location of the frontal features are mainly linked to the semidiurnal tidal phase in the outflow region, although their variability suggests also that they weakly depend on river discharge, residual currents, and neap-spring tidal cycle. In order to test this observational hypothesis, the results obtained from the analysis of the ERS SAR images are compared with the results obtained from the numerical simulation of the hydrodynamics of the Rhine outflow region carried out using a two-layer, frontal model, which is based on the nonlinear, hydrostatic shallow-water equations on an f plane. The model is forced by prescribing tidal and residual currents and river discharge at the open boundaries. Several simulations are performed by varying the values of these forcing parameters. The numerical results corroborate the observational conjecture: It is found that the form and the location of the simulated interface outcropping lines in the proximity of the river mouth are mainly determined by the semidiurnal tidal phase in the outflow region and that river discharge, residual currents, and neap-spring tidal cycle contribute only secondarily to their determination. Inserting the simulated surface velocity field into a simple radar-imaging model that relates the modulation of the backscattered radar power to the surface velocity convergence in radar look direction, narrow, elongated bands of enhanced radar backscatter emerge near the model frontal line while patches of low radar backscatter appear within the simulated Rhine plume area. The consistency of the model results with the results obtained from the analysis of the SAR images enables one to infer a mean spatial and temporal evolution of the Rhine outflow plume over a semidiurnal tidal cycle from the analysis of spaceborne SAR images acquired during different tidal cycles over the Rhine outflow area and suggests the possibility of using numerical modeling, in conjunction with the analysis of spaceborne measurements, for monitoring the oceanic variability in the Rhine outflow area.