As climate change continues to drive an increase in extreme weather events, the need for reliable predictions and observational data has never been more critical. Oceans, playing a vital role in regulating the Earth’s climate, are central to understanding these changes. Specifically, accurately modeling ocean wave dynamics, i.e., how waves are generated, evolve, and interact with oceanic processes such as currents, helps track ocean circulation and predict future variations. Thanks to Earth Observation satellites, continuous global observations have been available over the past few decades. Satellite altimeters, active sensors utilizing radar’s ranging capabilities, have emerged as pioneers in space oceanography. These instruments measure critical geophysical parameters such as sea surface height, significant wave height and near-surface wind speed along satellite tracks. Recognizing the immense value of these measurements for climate studies and operational activities, continuous technological innovations are essential for optimizing the performance and use of these instruments. One major breakthrough in satellite altimetrywas the incorporation of Synthetic Aperture Radar (SAR) technology in 2010, which enhanced spatial resolution from around 7 km, provided by Low-ResolutionMode sensors, to about 300m. In 2017, the fully-focused coherent processing of pulse echoes was implemented, a concept widely used in SAR imaging, enabling meter-scale resolution. This improvement led to significant benefits in near-coast applications, improving the quality of geophysical parameters by reducing signal contamination from surrounding land features. Additionally, for the first time, offnadir signals, previously considered a nuisance, were exploited to map narrow inland water bodies and detect sea-ice leads and floes. Recognizing this imaging potential led to investigating its capabilities over open oceans. Existing challenges in conventional, or unfocused, SAR altimetry relate to the accuracy of significant wave height estimates, especially when long waves, known as swells, dominate the sea surface. Swell waves, with wavelengths exceeding 150 meters, are often too long to be fully captured within the SAR altimeter’s footprint, leading to noisy, multi-peaked waveforms. Recognizing the interference of swell signals in SAR responses, combined with the high-resolution data provided by fully-focused processing, this dissertation first investigated the feasibility of transforming what was previously considered a nuisance into valuable information about the sea surface. To achieve this, the identification of swell-induced power variations in off-nadir altimeter’s signals, representing the so-called trailing edge of the returned echo, was first confirmed. These patterns were analyzed to compute a fully-focused modulation spectrumderived from altimetry. The modulation spectrumis a commonly used Level-2 product provided by satellites designed to measure the wave field, such as Sentinel-1 and CFOSAT, and allows for the estimation of swell characteristics, including wavelength, direction and wave height. The proposed method involved normalizing the signal intensity and re-projecting the range bins to cross-track ground locations, followed by spectral analysis akin to side-looking SAR systems. The analysis revealed that fully-focused altimetrymodulation spectra display power in all four quadrants due to the inherent 180-degree SAR ambiguity, plus two additional ambiguities caused by inseparable signals received from both sides of the radar footprint. The study also identified the main modulation mechanisms, using as reference numerical and analytical models. Range bunching was found to be a dominant mechanism alongside velocity bunching, with their relative strength highly dependent on the wave propagation angle. Fully-focused altimetry modulation spectra, derived from Cryosat-2, were evaluated through comparisons with buoy-derived directional wave spectra, showing good agreement. Furthermore, applying the proposed technique to Sentinel-6A data demonstrated that exploiting its full-beamfootprint, which is partially truncated onboard for data volume efficiency, improves swell retrieval. This is particularly true for waves propagating in or near the cross-track direction, due to its extended observational window and higher resolution compared to the operational truncated data. Yet, the development of a method to invert modulation-derived spectra to real ocean wave spectra is necessary to reliably use these instruments as a new source for providing operational global swell observations. The dissertation further explored the limitations of SAR altimeters in ocean wave imaging, focusing on resolution loss. This was addressed by estimating the azimuth cutoff wavelength, which serves as a proxy for the shortest detectable waves across different sea states and wave directions. The method used to estimate this parameter involved a SAR imaging technique applied in the spatial domain, minimizing residuals between the along-track autocorrelation function of fully-focused SAR radargrams, representing successive waveforms, and a fitted Gaussian function. Sentinel-6A data were then used to evaluate the method’s performance through comparisons with model-derived values globally. The analysis revealed that the method performs well under the majority of sea states but tends to underestimate values in extreme wind wave conditions. Furthermore, sensitivity to swell presence was observed, leading to pronounced over estimations, with the magnitude of these errors influenced by the swell direction. To mitigate these errors, an alternative approach was developed in the wave number domain. Results revealed an improvement in the correlation between azimuth cutoff estimates and model-derived values by 10%. Given the strong relationship between resolution loss and sea state conditions, the azimuth cutoff was further used to derive a new sea-state parameter: the variance of wave orbital velocities. Wave orbital velocity statistics offer valuable insights into wave climate by isolating wave components associated with developing seas. Comparisons between modeled and estimated wave orbital velocity variances showed similar sensitivities to swell presence and high sea states, suggesting further refinement of the proposed methods. Despite these challenges, the ability to extract these two additional parameters from the radar signal is valuable for identifying sensors capabilities and providing a new geophysical parameter for oceanographic studies. Lastly, the dissertation assessed the impact of wave-current interactions on wave products derived from both models and satellites, focusing on the Agulhas Current region, one of the most dynamic ocean environments. In situ wave measurements, collected during the One Ocean Expedition in 2023, in which the author participated, served as a reference for this study. The study first examined ocean current products. A clear underestimation of surface current velocities exceeding 0.5 m/s was found for both the Mercator operational model and the altimetry-derived Globcurrent product, with Mercator showing greater variability. Next, wave products, both with and without these ocean current products included in their modeling, were validated. The ECMWF reanalysis v5, known as ERA5, consistently underestimated wave heights above 2.5 m, whereas the MFWAM, which is the Global Ocean Wave Analysis and Forecast system from Meteo-France, showed good agreement with in situ data. This discrepancy was attributed to the lack of ocean current forcing in ERA5, underscoring the need for refinement in areas dominated by currents. Customized MFWAM simulations, including and excluding current data, further supported this finding. MFWAM forced with Globcurrent aligned most closely with drifter measurements, outperforming the operational product that uses Mercator currents. Comparisons between satellite altimeter observations and drifters also showed good agreement in significant wave height, with clear evidence of current-induced wave height variations along satellite tracks. Additionally, a multi-mission analysis of swellinduced modulation spectra from Sentinel-1, CFOSAT and SAR altimeters demonstrated alignment with in situ data and between them, highlighting the potential for synergistic use of these instruments in operational oceanography and climate studies. ... Read more

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. ... Read more

This study investigates the influence of ocean currents on wave modeling and satellite observations using in situ wave measurements from the One Ocean Expedition 2021–2023. In January 2023, six OpenMetBuoy drifters were deployed in the Agulhas Current region. Their high immersion ratio minimized wind effects, allowing them to follow the current and return to the Indian Ocean by the Agulhas retroflection, collecting data for about 2 months. Comparing surface current velocities from both the Mercator model and Globcurrent product with drifter data reveals underestimation for velocities over (Formula presented.) with Mercator showing greater variability. Significant wave height and Stokes drift parameters from MFWAM and ERA5 were also evaluated against drifters. Both models tend to overestimate Stokes drift more noticeable in ERA5, indicating sensitivity to wind seas. For significant wave height, both models agree well with drifter measurements with correlations of 0.90 for MFWAM and 0.83 for ERA5. However, ERA5's lack of surface current data combined with its coarse resolution (0.5 (Formula presented.)) lead to underestimation of wave heights exceeding 2.5 m. MFWAM products including and excluding currents exhibit root mean square errors of 0.39 and 0.45 m, respectively, when compared to drifter measurements. This confirms that neglecting currents introduces additional errors particularly in areas with sharp current gradients. Analyzing MFWAM wave spectra, including and excluding currents, reveals wave energy transfer attributed to wave-current interactions. The spatial extent of these interactions is captured by satellite altimeters, revealing wave modulations with considerable wave height variations when waves cross eddies and the current core. ... Read more

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. ... Read more

In this study, the full-focusing (FF) algorithm is reviewed with the objective of optimizing it for processing data from different types of surfaces probed in altimetry. In particular, this work aims to provide a set of optimal FF processing parameters for the Sentinel-6 Michael Freilich (S6-MF) mission. The S6-MF satellite carries an advanced radar altimeter offering a wide range of potential FF-based applications which are just beginning to be explored and require prior optimization of this processing. In S6-MF, the Synthetic Aperture Radar (SAR) altimeter acquisitions are known to be aliased in the along-track direction. Depending on the target, aliasing can be tolerated or may be a severe impairment to provide the level of performance expected from FF processing. Another key aspect to consider in this optimization study is the unprecedented resolution of the FF processing, which results in a higher posting rate than the standard SAR processing. This work investigates the relationship between posting rate and noise levels and provides recommendations for optimal algorithm configurations in various scenarios, including transponder, open ocean, and specular targets like sea-ice and inland water scenes. The Omega–Kappa (WK) algorithm, which has demonstrated superior CPU efficiency compared to the back-projection (BP) algorithm, is considered for this study. But, unlike BP, it operates in the Doppler frequency domain, necessitating further precise spectral and time domain settings. Based on the results of this work, real case studies using S6-MF acquisitions are presented. We first compare S6-MF FF radargrams with Sentinel-1 (S1) images to showcase the potential of optimally configured FF processing. For highly specular surfaces such as sea-ice, distinct techniques are employed for lead signature identification. S1 relies on image-based lineic reconstruction, while S6-MF utilizes phase coherency of focalized pulses for lead detection. The study also delves into two-dimensional wave spectra derived from the amplitude modulation of image/radargrams, with a focus on a coastal example. This case is especially intriguing, as it vividly illustrates different sea states characterized by varying spectral peak positions over time. ... Read more

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. ... Read more

The Fully-Focused SAR (FF-SAR) processing, introduced in Egido and Smith (2016) allows obtaining a maximum resolution of 0.5 m in the along-track direction. It provides significant benefits for inland water altimetry investigations allowing the successful investigation of very small rivers and canals (Kleinherenbrink, 2020) that are typically harder to be analysed by using unfocused Delay-Doppler SAR (DD-SAR) data (about 300 m resolution in the along-track direction).
In its development, two major limitations were associated with the FF-SAR processing: 1) the presence of evenly spaced high sidelobes in the Point Target Response (PTR) due to the closed-loop burst mode implemented in Sentinel-3 & Cryosat-2 altimeter payloads, used for initial FF-SAR investigations, and 2) the heavy computational burden with respect to the unfocused DD-SAR processing.
The first limitation can be overcome by designing the radar system differently adopting an open-loop transmission scheme as, for instance, the one implemented in the altimeter payload of the Sentinel-6 Michael Freilich mission, launched on 21 November 2020.
The second limitation has been addressed in research works following Egido and Smith (2016) indicating that an improvement in terms of computational burden can be achieved by adopting algorithms in the frequency domain (Guccione et al., 2018).
Being the role of FF-SAR for future inland water altimetry well understood, along with the possibility to see it implemented with reduced drawbacks during the Sentinel-6 Michael Freilich mission, a collaboration has started between the ESA GPOD Team, already hosting the successful SARvatore services portfolio for unfocused SAR & SARin altimetry, and Aresys.
Aresys has developed a generic FF-SAR prototype processor, that is able to process data acquisition from different instruments and exploiting the frequency-domain Omega-K algorithm (Guccione et al., 2018 & Scagliola et al., 2018). The Aresys's FFSAR prototype processor for CryoSat-2 allows users to process, on line and on demand, low-level CryoSat FBR products in SAR mode up to FF-SAR Level-1 products with self-customized options. Additionally a wide set of processing parameters is configurable, allowing as an example to select the along-track resolution or to obtain FFSAR multilooked waveforms at the desired posting rate.
The collaboration led to the creation of a new service for the processing of CryoSat Baseline D data in FF-SAR mode. Users will be able to select the following options: 1) range oversampling factor, 2) bandwidth factor (responsible for the along-track resolution value) and 3) multilook posting rate (1Hz-500Hz). Geophysical corrections and L2 estimates from both a threshold peak retracker and an ALES-like subwaveform retracker are part of the output package. In preliminary open ocean analyses, very good results on SSH noise have been obtained by the ALES-like subwaveform retracker.
In this presentation, the Aresys FF-SAR prototype processor is described and the outcome of some preliminary validation activities, performed by a group of altimetry researchers, is reported. The service is scheduled to open to all GPOD/SARvatore users in the first semester of 2021. Future evolutions should include the extension of the service to Sentinel-3 and Sentinel-6 data.
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Satellite altimetry has successfully been applied to derive water level time series over lakes and rivers for many years. In the last decade major advancement within the field have been achieved. The SAR altimetry era, initiated with the launch of CryoSat-2, has made it possible to measure much smaller targets more accurately. The standard 20 Hz radar altimetry products generally allow to study targets down to a few hundred meters in optimal conditions. However, recent advancement in the low-level data processing, the Fully-Focused SAR (FFSAR) technique, where the footprint in the along-track direction can be as small as a few meters, has made it possible to measure the water level of even smaller targets.

FFSAR processed data from CryoSat-2 in SAR mode is made freely available by ESA through a newly integrated service on the Grid Processing on Demand (G-POD) platform, within the SARvatore Family of custom processors, where the user can order data from an area and specify various parameters to be applied in the processing. The FFSAR processor has been developed within the ESA ESTEC Sentinel-6 Project and adapted to CryoSat-2 for verification and validation purposes.

Here we demonstrate the value of FFSAR and evaluate the FFSAR product obtained from the ESA G-POD service over different inland water targets. The evaluation and validation is done via in situ water level data, external processed FFSAR data, unfocused SAR data and laser altimetry data from ICESat-2.

More specific, we perform an evaluation over the narrow ( < 100 m) American Rivers: Red River, Little River, and Canadian River located in the Mississippi basin. Where we compare the water level based on different retracker e.g. ALES+ and threshold retrackers.
We make a joint water level time series by considering data from CryoSat-2 and ICESat-2 over a reach, and validate the results against in situ data. Preliminary results show that we can capture the main part of the water level signal.

Over the Elbe River, we compare the FFSAR based river water levels with results based on unfocused SAR processing and in situ gauges.

We extend our analysis with a case study conducted over the Lake IJssel which is located in The Netherlands and covers an area of approximately 1100 km2. We examine the performance of the G-POD processor by evaluating the FFSAR lake height estimates using externally processed FFSAR data that have been validated against in situ data.
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