Traditionally, nadir-looking satellite radar altimeters provide water levels of rivers only at intersections with the satellite's ground track, called virtual stations. These observations have limited spatial coverage because such cross-overs are sparse, depending on the altimeter's orbit. In this work, we introduce the novel concept of Polygon-Informed Cross-Track Altimetry (PICTA), enabling accurate estimation of water levels at cross-track distances — for as long as the target's signal is recorded in the altimeter's range window. Using fully-focused SAR data from the Sentinel-6 altimetry mission, we demonstrate how the new approach can provide detailed river water level profiles over a ground swath of about 14 km cross-track width and with an along-track resolution as fine as 10 m. On the one hand, this marks a drastic improvement in the number of available measurements when compared to the virtual station approach, on the other hand, for the first time, water surface slopes and level variations along the river, caused by rapids, dams, and sluices, can be directly observed using a nadir radar altimeter. The validation over two river segments in France reveals biases as low as ±4 cm and random errors on the order of 3–8 cm at 30 m along-track resolution. The new PICTA concept can potentially be generalized to other targets, such as lakes or even coastlines.

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 an SAR altimetry cross-spectrum. Under moderate environmental conditions (significant wave heights (SWHs) 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° 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.

This study presents the first azimuth cutoff analysis in Synthetic Aperture Radar (SAR) altimetry, aiming to assess its applicability in characterizing sea-state dynamics. In SAR imaging, the azimuth cutoff serves as a proxy for the shortest waves, in terms of wavelength, that can be detected by the satellite under certain wind and wave conditions. The magnitude of this parameter is closely related to the wave orbital velocity variance, a key parameter for characterizing wind-wave systems. We exploit wave modulations exhibited in the tail of fully-focused SAR waveforms and extract the azimuth cutoff from the radar signal through the analysis of its along-track autocorrelation function. We showcase the capability of Sentinel-6A in deriving these two parameters based on analyses in the spatial and wavenumber domains, accompanied by a discussion of the limitations. We use Level-1A high-resolution Sentinel-6A data from one repeat cycle (10 days) globally to verify our findings against wave modeled data. In the spatial domain analysis, the estimation of azimuth cutoff involves fitting a Gaussian function to the along-track autocorrelation function. Results reveal pronounced dependencies on wind speed and significant wave height, factors primarily determining the magnitude of the velocity variance. In extreme sea states, the parameters are underestimated by the altimeter, while in relatively calm sea states and in the presence of swells, a substantial overestimation trend is observed. We introduce an alternative approach to extract the azimuth cutoff by identifying the fall-off wavenumber in the wavenumber domain. Results indicate effective mitigation of swell-induced errors, with some additional sensitivity to extreme sea states compared to the spatial domain approach.

Traditionally, nadir-looking satellite radar altimeters provide water surface elevations of rivers only at intersections with the satellite’s ground track, called virtual stations. These observations have limited spatial coverage because such cross-overs are sparse, depending on the altimeter's orbit. In this work, we introduce the novel concept of Polygon-Informed Cross-Track Altimetry (PICTA), enabling precise measurement of water surface elevations at cross-track distances---for as long as the target's signal is recorded in the altimeter's range window. Using fully-focused SAR data from the Sentinel-6 altimetry mission, we demonstrate how the new approach can provide detailed river elevation profiles over a ground swath of about 14 km cross-track width and with an along-track resolution as fine as 10 m. On the one hand, this marks a drastic improvement in the number of available measurements when compared to the virtual station approach, on the other hand, for the first time, water surface slopes and level variations along the river, caused by rapids, dams, and sluices, can be directly observed using a nadir radar altimeter. The validation over two river segments in France reveals biases as low as [[EQUATION]]4 cm and random errors on the order of 3 to 8 cm at 30 m along-track resolution. The new PICTA concept can potentially be generalized to other targets, such as lakes or even coastlines.

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 multidimensional characteristic function, but with adjustments for the modulation transfer functions compared to the monostatic case. This article 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 enable 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.

The 2-D 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 article, we provide a closed-form description of a 2-D 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 the 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.

Earlier work has empirically demonstrated some advantages of an increased posting rate of Synthetic Aperture Radar (SAR) altimeters beyond the expected ground resolution of about 320 m in Delay-Doppler (unfocused SAR, UFSAR) processing, corresponding to ∼20 Hz sampling. Higher posting rates of 40–80 Hz were shown to prevent spectral aliasing of the signal, enable to measure swell wave related signal distortions and may lead to a reduced root mean square error of 1 Hz estimates of Sea Surface Heights (SSH), radar cross section (sigma0) and Significant Wave Heights (SWH) from current SAR altimeters. These improvements were explained by the narrow noise autocovariance function of the waveform signal's power speckle noise in along-track direction on one hand, and frequency doubling by power detection (squaring of the signal) on the other. It has not been explained, however, why the power speckle noise decorrelates faster than anticipated by the predicted Doppler resolution, and whether this decorrelation depends on the altimeter and processing configuration. Also, it has not been shown explicitly that the estimates of SSH, SWH and sigma0 decorrelate in the same way. Describing the noise autocovariance function – or equivalently the noise power spectral density via the Wiener-Kintchin theorem – is necessary on two counts: Knowing the noise autocovariance allows to apply optimal filtering strategies that maximize precision on one hand, while the noise power spectral density predicts the frequencies contained in the noise (and signals), which in turn determines the required sampling frequency according to the Nyquist theorem. Using a newly derived analytic noise autocovariance model for UFSAR-processed altimeter data, we show that the swift signal decorrelation is mainly due to the observation geometry. Furthermore, our results demonstrate that the noise autocovariance functions of power speckle, SSH, SWH and sigma0 estimates in along-track direction are different and depend on the sea state. On top of that, the noise autocovariance functions are strongly dependent on the number of Doppler beams used for multilooking, the used retracker, and the processing choices such as antenna gain pattern compensation and windowing within the UFSAR processing (Level-1b). We validated our noise autocovariance model with segments of 42 Sentinel-3B overpasses. Our findings are in accordance to all earlier work, but indicate that the reported precision improvements with respect to 20 Hz may have been too optimistic and that the SSH, SWH and sigma0 generally decorrelate slower than the power speckle noise. We found that the required posting rate is always higher or equal to 40 Hz. Our results will potentially enable improved spectral analysis and optimal filtering of any UFSAR altimetry data. More importantly, our results can be used to trade off different aspects for determining an optimal posting rate in UFSAR altimeter processing in different sea states and with changing processing parameters, which is necessary in view of strict precision requirements of existing and future SAR altimetry missions.

Two air-sea interaction quantification methods are employed on synthetic aperture radar (SAR) scenes containing atmospheric-turbulence signatures. Quantification performance is assessed on Obukhov length L, an atmospheric surface-layer stability metric. The first method correlates spectral energy at specific turbulence-spectrum wavelengths directly to L. Improved results are obtained from the second method, which relies on a machine-learning algorithm trained on a wider array of SAR-derived parameters. When applied on scenes containing convective signatures, the second method is able to predict approximately 80% of observed variance with respect to validation. Estimated wind speed provides the bulk of predictive power while parameters related to the kilometer-scale distribution of spectral energy contribute to a significant reduction in prediction errors, enabling the methodology to be applied on a scene-by-scene basis. Differences between these physically based estimates and parameterized numerical models may guide the latter's improvement.

We demonstrate in this work how we can take advantage of known unfocused SAR (UF-SAR) retracking methods (e.g. the physical SAMOSA model) for retracking of fully-focused SAR (FF-SAR) waveforms. Our insights are an important step towards consistent observations of sea surface height, significant wave height and backscatter coefficient (wind speed) with both UF-SAR and FF-SAR. This is of particular interest for SAR altimetry in the coastal zone, since coastal clutter may be filtered out more efficiently in the high-resolution FF-SAR waveform data, which has the potential to improve data quality. We implemented a multi-mission FF-SAR altimetry processor for Sentinel-3 (S3) and Sentinel-6 Michael Freilich (S6), using a back-projection algorithm, and analysed ocean waveform statistics compared to multilooked UF-SAR. We find for Sentinel-3 that the averaged power waveforms of UF-SAR and FF-SAR over ocean are virtually identical, while for Sentinel-6 the FF-SAR power waveforms better resemble the UF-SAR zero-Doppler beam. We can explain and model the similarities and differences in the data via theoretical considerations of the waveform integrals. These findings suggest to use the existing UF-SAR SAMOSA model for retracking S3 FF-SAR waveforms but the SAMOSA zero-Doppler beam model for S6 FF-SAR waveforms, instead. Testing the outlined approach over short track segments, we obtain range biases between UF-SAR and FF-SAR lower than 2 mm and significant wave height biases lower than 5 cm.

Estimating the three geophysical variables significant wave height (SWH), sea surface height, and wind speed from satellite altimetry continues to be challenging in the coastal zone because the received radar echoes exhibit significant interference from strongly reflective targets such as sandbanks, sheltered bays, ships etc. Fully focused SAR (FF-SAR) processing exhibits a theoretical along-track resolution of up to less than half a metre. This suggests that the application of FF-SAR altimetry might give potential gains over unfocused SAR (UF-SAR) altimetry to resolve and mitigate small-scale interferers in the along-track direction to improve the accuracy and precision of the geophysical estimates. The objective of this study is to assess the applicability of FF-SAR-processed Sentinel-6 Michael Freilich (S6-MF) coastal altimetry data to obtain SWH estimates as close as possible to the coast. We have developed a multi-mission FF-SAR processor and applied the coastal retracking algorithm CORALv2 to estimate SWH. We assess different FF-SAR and UF-SAR processing configurations, as well as the baseline Level-2 product from EUMETSAT, by comparison with the coastal, high-resolution SWAN-Kuststrook wave model from the Deltares RWsOS North Sea operational forecasting system. This includes the evaluation of the correlation, the median offset, and the percentage of cycles with high correlation as a function of distance to the nearest coastline. Moreover, we analyse the number of valid records and the L2 noise of the records. The case study comprises five coastal crossings of S6-MF that are located along the Dutch coast and the German coast along the East Frisian Islands in the North Sea. We observe that accurate and precise SWH records can be estimated in the nearshore zone within 1–3 km from the coast using satellite SAR altimetry. We find that the FF-SAR-processed dataset with a Level-1b posting rate of 140 Hz shows the greatest similarity with the wave model. We achieve a correlation of ∼0.8 at 80% of valid records and a gain in precision of up to 29% of FF-SAR vs UF-SAR for 1–3 km from the coast. FF-SAR shows, for all cycles, a high correlation of greater than or equal to 0.8 for 1–3 km from the coast. We estimate the decay of SWH from offshore at 30 km to up to 1 km from the coast to amount to 26.4% ± 3.1%.

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

Wind-generated waves strongly interact with sea ice and impact air-sea exchanges, operations at sea, and marine life. Unfortunately, the dissipation of wave energy is not well quantified and its possible effect on upper ocean mixing and ice drift is still mysterious. As the Arctic is opening up and wave energy increases, the limited amount of in situ observations is a clear limitation to our scientific understanding. Both radar and optical remote sensing has revealed the frequent presence of waves in ice, and could be used more systematically to investigate wave-ice interactions. Here we show that, in cloud-free conditions, Sentinel-2 images exhibit brightness modulations in ice-covered water, consistent with the presence of waves measured a few hours later by the ICESat-2 laser altimeter. We show that a full-focus SAR processing of Sentinel-3 radar altimeter data also reveals the presence and wavelengths of waves in sea ice, within minutes of Sentinel-2 imagery. The SWIM instrument on CFOSAT is another source of quantitative evidence for the direction and wavelengths of waves in ice, when ice conditions are spatially homogeneous. In the presence of sea ice, a quantitative wave height measurement method is not yet available for all-weather near-nadir radar instruments such as altimeters and SWIM. However, their systematic colocation with optical instruments on Sentinel-2 and ICESat-2, which are less frequently able to observe waves in sea ice, may provide the empirical transfer functions needed to interpret and calibrate the radar data, greatly expanding the available data on wave-ice interactions.

This article shows the first spectral analysis of fully-focused Synthetic Aperture Radar (FFSAR) altimetry data with the objective of studying backscatter modulations caused by swells. Swell waves distort the backscatter in altimetry radargrams by means of velocity and range bunching. These swell signatures are visible in the tail of the waveform. By locally normalizing the backscatter and projecting the waveforms on an along-/cross-track grid, satellite altimetry can be exploited to retrieve swell information. The analysis of FFSAR spectra is supported by buoy-derived swell-wave spectra of the National Oceanic and Atmospheric Administration network. Using cases with varying wave characteristics, we discuss the altimetry-derived spectra and relate them to what is known from side-looking SAR imaging systems. Besides having a vast amount of additional data for swell-wave analysis, altimeter data can also help us to better understand the side-looking SAR spectra.

This article describes the observation techniques and suggests processing methods to estimate dynamical sea-ice parameters from data of the Earth Explorer 10 candidate Harmony. The two Harmony satellites will fly in a reconfigurable formation with Sentinel-1D. Both will be equipped with a multi-angle thermal infrared sensor and a passive radar receiver, which receives the reflected Sentinel-1D signals using two antennas. During the lifetime of the mission, two different formations will be flown. In the stereo formation, the Harmony satellites will fly approximately 300km in front and behind Sentinel-1, which allows for the estimation of instantaneous sea-ice drift vectors. We demonstrate that the addition of instantaneous sea-ice drift estimates on top of the daily integrated values from feature tracking have benefits in terms of interpretation, sampling and resolution. The wide-swath instantaneous drift observations of Harmony also help to put high-temporal-resolution instantaneous buoy observations into a spatial context. Additionally, it allows for the extraction of deformation parameters, such as shear and divergence. As a result, Harmony's data will help to improve sea-ice statistics and parametrizations to constrain sea-ice models. In the cross-track interferometry (XTI) mode, Harmony's satellites will fly in close formation with an XTI baseline to be able to estimate surface elevations. This will allow for improved estimates of sea-ice volume and also enables the retrieval of full, two-dimensional swell-wave spectra in sea-ice-covered regions without any gaps. In stereo formation, the line-of-sight diversity allows the inference of swell properties in both directions using traditional velocity bunching approaches. In XTI mode, Harmony's phase differences are only sensitive to the ground-range direction swell. To fully recover two-dimensional swell-wave spectra, a synergy between XTI height spectra and intensity spectra is required. If selected, the Harmony mission will be launched in 2028.

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 H and V linear modes can be considered equivalent to a compact φ-pol, i.e. with the transmittion in a linear polarization rotated by φ. For long baselines, such those as those envisioned by the ESA Harmony EE10 candidate, and for steep incidence angles, an equivalent π/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.

This paper applies the Fully-Focussed SAR (FF-SAR) algorithm to CryoSat-2 full-bit-rate data to measure water levels of lakes and canals in the Netherlands, and validates these measurements by comparing them to heights measured by gauges. Over Lake IJssel, a medium-sized lake, the FF-SAR height is biased about 6 cm below the gauge height, and a similar bias is found at six sites where CryoSat-2 crosses rivers and canals. The precision of the FF-SAR measurements depends on the extent of multi-looking (incoherent averaging along-track) applied. Over Lake IJssel the precision varies from 4 to 11 cm, decreasing as multi-looking increases. The precision of FF-SAR with 100 m of multi-looking is equivalent to that of the standard delay/Doppler processing, which has an along-track resolution of about 300 m. The width and orientation of rivers and canals limits the maximum available multi-looking. After removing the 6 cm bias, FF-SAR heights of rivers and canals have an accuracy between 2 cm and several decimeters, primarily depending on the presence of other water bodies lying within the cross-track measurement footprint, as these contaminate the waveform. We demonstrate that FF-SAR processing is able to resolve and measure small ditches only a few meters in width. The visibility of these signals depends on the angle at which CryoSat-2 crosses the ditch and on whether or not the ditch remains straight within CryoSat-2’s field of view. In the best-case scenario, straight ditches at nearly 90° to the CryoSat-2 ground track, the ditch signal has high enough signal-to-noise to allow sub-decimeter accuracy of FF-SAR height measurement.

We investigated the sensitivity of fully focused SAR (FF-SAR) processing of Cryosat-2 altimeter data to Earth rotation. Earth’s rotation causes scatterers at varying cross-track locations to have a different relative velocity with respect to the satellite. This second-order effect of Earth rotation on the phase is currently not corrected for in FF-SAR processing of altimetry data. The difference is largest near the poles, where the satellite flies parallel to the equator. Not correcting for the second-order effect yields a parabolic shape in the counter-rotated phase, which increases with the cross-track distance. Its effect is, however, limited by the time-in-view of the scatterer, which is shorter at the edge of the altimeter footprint, and therefore destructive interference will not occur when using Cryosat-2 data. For Cryosat-2, the only expected effect is a reduction in power and along-track resolution in the waveform tail and in the grating lobes. If the FF-SAR processor focuses on one point, and there is a bright scatterer at another, then there is a residual parabolic phase, whose sign and shape depend on the cross-track distance and whether the signal is left or right of the chosen focal point. In theory, if the viewed scene only has few bright coherent scatterers, then it might be possible to determine the cross-track position of each. In practice, however, natural targets are rarely coherent over the integration time.

We investigated the sensitivity of Fully-Focussed SAR (FF-SAR) processing of CryoSat-2 altimeter data to Earth rotation and exploit it to decontaminate waveforms in coastal zones. Earth's rotation causes scatterers at varying cross-track locations to have a different relative velocity with respect to the satellite. This second-order effect of Earth rotation on the phase is currently not corrected for in FF-SAR processing of altimetry data. The difference is largest near the poles, where the satellite flies parallel to the equator. We show when not correcting for this second-order effect it yields a parabolic shape in the counter rotated phase, which increases with the cross-track distance. If the FF-SAR processor focusses on one point, and there is a bright scatterer at another, then there is a residual parabolic phase, whose sign and shape depend on the cross-track distance and on whether the signal is left or right of the chosen focal point. In theory, if the viewed scene only has few bright coherent scatterers, then it might be possible to determine the cross-track position of each. In practice though, natural targets are rarely coherent over the integration time. The incoherent property of natural targets can, however, also be exploited to decontaminate waveforms in coastal tracks from land signals, by differencing two radargrams computed with two different focal points. If the cross-track distance between the focal points is set correctly, the speckle signal from the ocean becomes quasi-independent, while the land signal is similar in both radargrams and can subsequently be removed.