The two-dimensional frequency-based omega-K method is known to be a suitable algorithm for Fully-Focused SAR (FF-SAR) radar altimeter processors, as its computational efficiency is much higher than equivalent time-based alternatives without much performance degradation. In this paper we provide a closed-form description of a two-dimensional frequency domain omega-K algorithm specific for instruments such as Poseidon-4 onboard Sentinel-6. The processor is validated with real data from point targets and over open ocean. Applications such as ocean swell retrieval and lead detection are demonstrated, showing the potentiality of the processor for future operational global-scale products.

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 closure phase, which is a circular summation of the phases of the three multilooked interferograms, comprises a geophysical component and phase noise. In agricultural regions of southern Spain, encompassing both open crop fields and greenhouses, the closure phases constructed from Sentinel-1 acquisitions consistently exhibit positive signatures. The evolution of these observations appears to be related to the phenological stages of plants, as evidenced by crop calendars. Moreover, the signatures of closure phases stand out as a potential indicator of vegetation development under dense vegetation conditions when compared with coherence and normalized radar cross section (NRCS). Two existing models, one based on dielectric variation in the subsurface and another on volume scattering combined with perpendicular baselines, do not explain observed time series. Therefore, the presence of these positive closure phases implies the existence of supplementary factors contributing to closure phases associated with plant development. In this context, we explore two potential factors: variations in dielectric properties within crop canopies and the line-of-sight (LoS) motion of crops. These factors are considered to establish connections between temporal changes in vegetation parameters and observed closure phase signatures. Regarding the first factor, we characterize the crop canopies using the dielectric constant of an equivalent medium, thereby capturing changes in wave propagation within the canopies due to leaves and vertical stalks’ development throughout the crop growth stages. We then model their contributions to closure phases in a manner analogous to an existing soil moisture model. Using realistic vegetation parameters derived from in situ measurements, this forward model generates synthetic data comparable in magnitude to the observations. As for the second factor, we propose an additional contributing mechanism to closure phases—skewed motion in the radar LoS direction induced by plant growth. This motion model is mathematically verified under a small-motion approximation. Both the models offer valuable insights into the origins of geophysical closure phases.

Estimating sea surface height using cross-track interferometry requires high sensitivity because the ocean surface signal is in the order of 10 cm. Additionally, the interferometer requires a temporal delay of a few milliseconds to ensure coherency of the moving ocean surface. We show that a squinted line of sight, in combination with a Helix satellite formation allows optimizing the effective perpendicular and along-track baselines to satisfy these conditions. This paper presents a model to estimate the performance of a formation-flying cross-track interferometer with a squinted line of sight. The tenth Earth Explorer, Harmony, which features two bistatic SAR companions, and a theoretical system with one monostatic and one bistatic SAR are used as case studies. The standard deviation of the height estimate is 1 cm to 10 cm between 29° to 41° and increases to 30 cm at the far range (46°) at a wind speed of 5ms-1. The power spectral density of the elevation shows that spatial scales of 47km can be resolved. The performance improves at higher wind speeds due to higher backscattering. At a wind speed of 15ms-1, wavelengths of 27km to 11km can be resolved, depending on the elevation spectrum. The performance over a 250km swath enables the instantaneous estimation of the surface elevation at the submesoscales for the first time.

The paper investigates the polarimetry of bistatic Synthetic Aperture Radar (SAR) acquisitions over rough surfaces, with focus on the rotation of the scattered wave orientation at the companion antenna axes and on the optimal linear polarization in transmission. This latter is defined as the polarization achieving the maximum radar cross section and will be herewith recalled as principal polarization. The paper outlines a geometrical framework for the interpretation and the estimation of the principal polarizations. It is shown that the theoretical formulation provides a good agreement with the second-order analytical approach in [1]. The paper finally postulates that a bistatic illumination in the traditional$\mathrm{H}$and V linear modes can be considered equivalent to a compact$\psi$-pol, i.e. with the transmittion in a linear polarization rotated by$\psi$. For long baselines, such those as those envisioned by the ESA Harmony EE10 candidate, and for steep incidence angles, an equivalent$\pi/4$-pol might be possible for rough surfaces.

Ocean topography using SAR interferometry requires coherent observations of the sea surface. To observe the surface coherently, the along-track baseline between observations of the same scene must be kept to a minimum. Minimising the along-track baseline while maintaining a cross-track baseline that allows good sensitivity to relative surface height is difficult to achieve in satellite missions. This paper shows how a squinted line of sight allows single-pass cross-track interferometry with a wide swath over oceans. The Harmony candidate mission will have a formation that uses such an acquisition geometry to coherently observe the oceans.