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.

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.

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%.

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.

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.