Sea ice plays a pivotal role in the Earth’s climate system and exhibits high sensitivity to shifts in temperature and atmospheric conditions. The precise and timely assessment of sea ice parameters is essential for comprehending and forecasting the climate changes. However, the vast volume of satellite data covering ice-covered regions is impractical to be subjectively assessed. Hence, the utilization of automated algorithms becomes mandatory to fully exploit the continuous data streams from satellites. In this paper, we propose a UNet transformer-based architecture, called UT-MHTA, to sea ice segmentation using SAR satellite imagery. Our UT-MHTA network replaces the conventional multi-head attention (MHA) block with a multi-head transposed attention (MHTA) which can capture long-range pixel interactions, while still remaining suitable for large images. Our method demonstrates superior performance compared to state-of-the-art methods, without drastically raising the computational complexity. In particular, UT-MHTA achieves a mean intersection over union (mIoU) of 68.76% on the AI4Arctic data set, with an inference time of 865ms for a 400 km2product.

Until recently, intensity modulations in synthetic aperture radar (SAR) altimetry waveform tails have been considered a nuisance for geophysical-parameter retrieval. These modulations are actually predictable and might be exploited using a spectral analysis of the waveform tails. After Altiparmaki et al. (2022), a more elaborated analysis is performed to improve the interpretation of these SAR altimeter spectra. A fast numerical model is developed to explain the modulation mechanisms in focused SAR altimetry waveform tails. Using numerical solutions, standard analytical closed-form solutions, are demonstrated to be invalid to retrieve ocean-wave-spectra retrievals from nadir altimeters. Although not valid, a closed-form derivation provides intuitive insights about the information contained in a SAR altimetry cross-spectrum. Under moderate environmental conditions (significant wave heights of ~2 m), a closed-form solution might still be useful to infer swell-wave spectra from swath-altimetry SAR spectra at incident angles of ~4°. Comparable to side-looking SAR ocean processing, the cross-spectral analysis for nadir signals reduces noise and might remove the 180-degree ambiguity of the wave direction. Since the synthetic aperture length of nadir altimeters is larger than sidelooking imaging SARs (e.g. Sentinel-1, RadarSat, Gaofen-3), sublook processing can be performed to compute multiple cross-spectra for the same scene. With a slightly changing observation geometry, the cross-spectra reveal slightly different parts of the ocean-wave spectrum. The resulting stack of cross-spectra can thus be used to improve the retrieval of ocean-wave parameters. Retrieved ocean-wave parameters shall then enhance the sampling of the global wave field, but also serve to advance more consistent sea-state-bias corrections.

Earth Explorer 10 mission Harmony will consist of two satellites that fly in formation with Sentinel-1. It will operate as a multistatic radar in which Sentinel-1 transmits signals and all three satellites receive signals from different lines-of-sight. To prepare for Harmony and other possible future bistatic missions, transforms are derived to map the ocean-wave spectrum into bistatic synthetic aperture radar (SAR) spectra. The SAR mapping follows the standard derivation using the multi-dimensional characteristic function, but with adjustments for the modulation transfer functions compared to the monostatic case. This paper focuses on the SAR modulations caused by velocity bunching as it is the dominant distortion mechanism. We argue that a multistatic system, such as Harmony, leads to an inversion that constrains the real aperture radar (RAR) response on a scene-by-scene basis. A benefit of having additional receivers for wave-spectra estimation is that the three lines-of-sight enables to capture a larger fraction of the wave spectrum. Improvements are especially expected in high wind speed conditions such as tropical cyclones, where large energetic surface motions strongly deteriorate the (azimuth) resolution of the SAR data. Enhanced directional wave spectral characteristics will further help to improve the interpretation of the new bistatic Harmony high-resolution scatter and Doppler combined directional measurements.

The Poseidon-4 radar altimeter on board the Sentinel-6 “Michael Freilich” (S6-MF) satellite offers unique opportunities to assess the impact of ocean surface motion on delay-Doppler altimetry (DDA). In this article, earlier “frozen-sea” studies of the instrument response to an isolated sea surface facet are extended to include the effect of surface motions in its delay-Doppler Map (DDM) signature. Integrating this elementary signature over the instrument field of view, an analytical DDA stacked echo waveform model is then derived. This waveform is validated against a well-established waveform model for the special case of a frozen sea. Model sensitivity to changes in surface significant wave height, vertical velocity standard deviation, and the geophysical Doppler vector$\mathbf {U_{\mathrm { GD}}}$projection along the satellite ground-track velocity are discussed. These developments provide theoretical and analytical means to jointly exploit the S6-MF conventional and delay-Doppler radar waveforms to improve estimates of Essential Climate Variables (sea level, sea state) and to retrieve and map two new observables (the along-track projection of the$\mathbf {U_{\mathrm { GD}}}$vector and the ocean waves vertical velocity standard deviation). These new variables, being sensitive to higher order spectral moments of the wave directional spectrum, may help to mitigate sea state range bias impacts on altimeter sea level measurements.

Observations of wind and ocean surface velocity vectors by along-track interferometry (ATI) with the synthetic aperture radar (SAR) are not only important for direct applications but also to increase understandings of ocean upper layer mixing, air–ocean interactions, and mapping submesoscale (1–10 km) structures. An experimental bidirectional (BiDi) ATI acquisition mode of TanDEM-X observes with two squinted beams separated by an angle of approximately 13.2° in azimuth on the ground. The baseline is very short, and the along-track interferometric phase (ATI phase) of the ocean surface in the line-of-sight direction of the beams can be interpreted as a total Doppler velocity. The 2-D Doppler velocity field will thus include wind-wave detected motions. In this article, Doppler velocity fields acquired from this experimental acquisition mode are presented. The sequential retrieval of wind vector and total surface current vectors (TSCV) is demonstrated on the BiDi TanDEM-X data. The retrieval algorithm builds on existing geophysical model functions (GMFs) of normalized radar cross section (NRCS) and Doppler velocity. XMOD2 and a GMF based on the Elfouhaily ocean wave spectrum coupled with a Kirchhoff approximation (EOWS&KA) are used. The retrieved wind fields are generally consistent with the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-5. While the ATI phase errors are small, the retrieved TSCV field looks promising. Acquisitions were located at sea over the tip of the Novaya Zemlya in Russia and over an area near Tromsø, Norway.

The surface wave investigation and monitoring (SWIM) aboard the China-France Oceanography Satellite (CFOSAT), a pioneer conically scanning wave spectrometer, was successfully launched on October 29, 2018. Its innovative configuration composed of one nadir and five rotating near-nadir beams is designed to simultaneously observe the directional wave spectrum at a global scale. In this study, we systematically implement the spectral analysis of the radar backscattering with the periodogram technique to obtain the fluctuation spectrum for each azimuth direction. The 2-D fluctuation spectrum of the three spectral beams ($\theta = 6^\circ $, 8°, and 10°) combines all the azimuth directions within one entire rotation of 360°. The case study demonstrates that the wave features (peak wavelength and direction) are roughly consistent between the estimated fluctuation spectrum and the collocated WaveWatch III wave slope spectrum. A marked up-to-downwave asymmetry of the fluctuation spectrum with larger spectral level in the upwave direction for all the three spectral beams is observed. A ratio is defined between the fluctuation spectrum within the [0°, 180°] sector relative to the [180°, 360°] sector. Statistics display that this ratio is greater than 1 when it denotes the up-to-downwave ratio and smaller than 1 for the down-to-upwave ratio. This observed spectrum asymmetry is linked to the asymmetric modulation from upwind to downwind. In addition, we employ such finding to help remove the 180° wave direction ambiguity from a practical point of view. Preliminary results of the direction ambiguity removal display a bias of 41.3°, 40.6°, and 36.7° for the beams. The 10° beam shows slightly better performance compared to the other two beams in terms of bias and standard deviation. This shall lay a strong basis for the operational implementation of such algorithm to resolve the direction ambiguity.

The "Sea surface KInematics Multiscale monitoring" (SKIM) concept is a satellite mission designed to measure the world ocean surface currents, ice drift and ocean waves at spatial scales of 40 km [1] . It has been recently selected by the European Space Agency (ESA) as a finalist of the Earth Explorer 9 (EE9) call of proposal alongside with the FORUM concept. The onboard sensor will be a coherent rotating Ka-band radar providing Doppler measurements at 6 and 12 degrees incidence. This configuration allows for measurement of the directional wave spectrum, which yields accurate corrections of the wave-induced bias in the current measurements. Near nadir Doppler Ka-band measurements over the ocean have shown sensibilities to sea surface kinematics [2] , [3] and the surfacic motions due to waves and current are the main geophysical contributors to the measured microwave Doppler shift. However, these measured velocities have complex relations to oceanic motion and theoretical as well as numerical inspections are necessary to fully understand the undelying physical interactions. The understanding of this relation is at the heart of the SKIM mission measurement concept whose main objective is to provide the best estimate of the underlying sea surface current. The purpose of this work is to show how the strongest contribution of the geophysical Doppler shift is due to waves motion (the so called wave bais) and how it can be estimated to finally extract the current contribution. A theroretical approach is presented and compared to experimental results obtained from airborne campain (not presented in this abstract). To complete this two approaches, results of complex numerical simulations, processed on the High Performance Computer of Ifremer, involving a maximum of physical phenomena (satellite, sensor and surface kinematics, complex ocean electromagnetic scattering, ...) as well as onboard processings (range migration, pulse-pair algorithm, ...) are presented to corroborate theoretical predictions and experimental results.

Micro-wave radar backscatter signal depends on incidence angle. Along an ocean surface wave profile, the incident angle (relative to the local normal) of the emitted electromagnetic wave is modified according to the ocean surface wave slope (tilt effect). Consequently, highly spatially resolved radar measurements are modulated by the surface wave profile. On this basic principle, range resolved rotative micro-wave radars are about to be mounted on satellites to measure the directional ocean wave spectrum from space trough a Modulation Transfer Function (MTF). Three years of collocated near-nadir Normalized Radar Cross Section (NRCS) measurement from the Global Precipitation Measurements (GPM) with Wave Watch III (WW3) wave model are used to estimate the relationship between the sea state and the tilt MTF. At the incidence 10° and in Ku-band, azimuth angle relative to the wind direction impact on tilt MTF, is one of results featured in this article.

Doppler radars at all incidence angles measure mean velocities and spreads that have complex relations to oceanic motions, with opportunities to measure winds, waves, and currents. Here, we extend previous theoretical models of backscatter and Doppler using a Kirchhoff approximation and the physical optics model. We show that in Ka-band, around 12° incidence, range-resolved measurements of Doppler and backscatter provide unambiguous estimations of the wave spectrum and surface current. This property is illustrated with numerical examples and airborne data from the Air Surface Water Ocean Topography instrument. The same measurement conditions can be exploited for global ocean mapping from the low Earth orbit sensor satellite configuration.

Radar scattering from ocean surfaces is investigated by 3-D numerical solution of Maxwell's equations [numerical Maxwell's model in 3-D (NMM3D)] using the ocean surface profiles stochastically generated from a 3-D Durden-Vesecky ocean spectrum. The surface integral equations (SIEs) are formulated for dielectric surfaces using Green's functions of the air and the ocean permittivities with the surface tangential electric and magnetic fields as the unknowns. In solving the SIEs using the method of moment, a fast matrix solver of the sparse matrix canonical grid is used in conjunction with Rao-Wilton-Glisson basis functions. The computation has been implemented on a high-performance parallel computing cluster for problems with up to six million surface unknowns. Unlike the two-scale model (TSM) approximation, NMM3D does not require division of the surface spectrum into large- and small-scale ocean waves. The results of backscattering simulations are compared to Aquarius satellite radar measurements for wind speeds of 5, 8, and 10 m/s and for incidence angles of 29°, 39°, and 46°. The results show that NMM3D ocean backscattering solutions at L-band are in good agreement with Aquarius satellite radar data for co-polarized VV, HH, and cross-polarized VH returns as well as for the VV/HH ratio. The azimuthal dependence of L-band backscatter is also assessed. Finally, NMM3D results are compared to TSM solutions and are shown to lie close to Aquarius data in observed VV/HH ratio, and their azimuthal dependencies.

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.

Global colocalized ocean surface measurements using the Global Precipitation Measurement near-nadir dual-frequency Ku- and Ka-band microwave measurements are analyzed and compared. Focusing on the Ka and Ku cross-sections fall-off with incidence angles, the contemporaneous measurements enable to more precisely document differing ocean scattering characteristics for both microwave frequencies. Sensitivity with wind speed and significant wave height is further reported using global comparisons with numerical estimates. As demonstrated, the bifrequency capability can provide direct means to efficiently separate short-scale wave contributions, between mean squared slope and curvature characteristics, and to further gain valuable insights concerning near-nadir instruments onboard future ocean satellite missions including the China-France Oceanography Satellite and the Surface Water Ocean Topography Mission.

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.

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.

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 .

This paper is the first in a series of two papers on the use of combined improved hydrodynamic and electromagnetic analytical models for the simulation of the ocean Doppler spectrum at microwave frequencies. Under a linear assumption for the sea surface, we derive statistical expression for the main Doppler characteristics according to asymptotic scattering models. We consider classical models such as the Kirchhoff approximation and the two-scale model, as well as the more recent weighted curvature approximation (WCA). We recover two salient features of Doppler signature in the microwave regime. First, the Doppler characteristics are very sensitive to polarization, with higher mean Doppler shift in horizontal polarization. This is correctly rendered by the WCA but not the classical models. Second, the first two moments of the Doppler spectrum exhibit a nontrivial dependence on incidence angle. Results compare favorably with rigorous numerical computations for 1-D surfaces published in the literature. The simplicity and accuracy of the analytical models provide a valuable tool for the Doppler analysis of 2-D sea surfaces.

This paper extends the results of a previous work by combining hydrodynamic and electromagnetic analytical models for the simulation of the ocean Doppler spectrum at microwave frequencies. We consider weakly nonlinear sea surfaces after the choppy wave model and incorporate them in classical and unified scattering models, namely, the Kirchhoff and weighted curvature approximations. We show that statistical expressions can be obtained for the Doppler spectrum in a way similar to the case of linear surfaces. As expected, the nonlinear nature of the sea surface dramatically impacts the Doppler spectrum at moderate to large incidence angles, with a shift of the central frequency and a broadening of the spectrum. Monte Carlo comparisons are performed with the Creamer model, which is frequently used to describe weakly nonlinear sea surfaces but does not enjoy a statistical formulation for the Doppler characteristics. The same qualitative behavior is found but some quantitative differences are found and discussed.

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.