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.

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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%.

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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.

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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.

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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.

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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.

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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.

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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.

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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.@en

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.@en

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.

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Rising sea levels due to climate change can have severe consequences for coastal populations and ecosystems all around the world. Understanding and projecting sea-level rise is especially important for low-lying countries such as the Netherlands. It is of specific interest for vulnerable ecological and morphodynamic regions, such as the Wadden Sea UNESCO World Heritage region. Here we provide an overview of sea-level projections for the 21st century for the Wadden Sea region and a condensed review of the scientific data, understanding and uncertainties underpinning the projections. The sea-level projections are formulated in the framework of the geological history of the Wadden Sea region and are based on the regional sea-level projections published in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5). These IPCC AR5 projections are compared against updates derived from more recent literature and evaluated for the Wadden Sea region. The projections are further put into perspective by including interannual variability based on long-Term tide-gauge records from observing stations at Den Helder and Delfzijl. We consider three climate scenarios, following the Representative Concentration Pathways (RCPs), as defined in IPCC AR5: The RCP2.6 scenario assumes that greenhouse gas (GHG) emissions decline after 2020; the RCP4.5 scenario assumes that GHG emissions peak at 2040 and decline thereafter; and the RCP8.5 scenario represents a continued rise of GHG emissions throughout the 21st century. For RCP8.5, we also evaluate several scenarios from recent literature where the mass loss in Antarctica accelerates at rates exceeding those presented in IPCC AR5. For the Dutch Wadden Sea, the IPCC AR5-based projected sea-level rise is 0.07±0.06m for the RCP4.5 scenario for the period 2018-30 (uncertainties representing 5-95%), with the RCP2.6 and RCP8.5 scenarios projecting 0.01m less and more, respectively. The projected rates of sea-level change in 2030 range between 2.6mma^-1 for the 5th percentile of the RCP2.6 scenario to 9.1mma^-1 for the 95th percentile of the RCP8.5 scenario. For the period 2018-50, the differences between the scenarios increase, with projected changes of 0.16±0.12m for RCP2.6, 0.19±0.11m for RCP4.5 and 0.23±0.12m for RCP8.5. The accompanying rates of change range between 2.3 and 12.4mma^-1 in 2050. The differences between the scenarios amplify for the 2018-2100 period, with projected total changes of 0.41±0.25m for RCP2.6, 0.52±0.27m for RCP4.5 and 0.76±0.36m for RCP8.5. The projections for the RCP8.5 scenario are larger than the high-end projections presented in the 2008 Delta Commission Report (0.74m for 1990-2100) when the differences in time period are considered. The sea-level change rates range from 2.2 to 18.3mma^-1 for the year 2100. We also assess the effect of accelerated ice mass loss on the sea-level projections under the RCP8.5 scenario, as recent literature suggests that there may be a larger contribution from Antarctica than presented in IPCC AR5 (potentially exceeding 1m in 2100). Changes in episodic extreme events, such as storm surges, and periodic (tidal) contributions on (sub-)daily timescales, have not been included in these sea-level projections. However, the potential impacts of these processes on sea-level change rates have been assessed in the report.

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Satellite radar altimetry is often considered to be the most succesful spaceborne remote sensing technique ever. Satellite radar altimeters were designed for static geodetic and ocean dynamics applications. The goal of the geodetic mission phases, which have a dense ground-track spacing, is primarily to acquire information about the marine gravity field. This enables the estimation of mean dynamic topography (geographical sea surface height patterns due to ocean currents) and deep-ocean bathymetry. The primary goal of the oceanographic mission phases is to gain information about time-varying currents and ocean dynamics. TOPEX/Poseidon is the first altimetry mission to reveal sea surface height variations related to ocean dynamics as the El Niño Southern Oscillation (ENSO). During the mission it became clear that secular changes in sea level could also be monitored. Already in 1995, Nerem (1995) computed a Global Mean Sea Level (GMSL) time series from the TOPEX/Poseidon data. Currently, the GMSL record spans 26 years, in which TOPEX/Poseidon time series is extended with the Jason-1&2&3 observations. The estimated secular trend of GMSL over the altimetry era is approximately 3 mm yr−1. The succes of the TOPEX/Poseidon mission spawned the Argo project with the deployment of the first floats in the year 2000. One argued that Argo would support the future Jason missions in separating changes into the two components (density and mass) of sea level. The Argo project aims to estimate temperature and salinity over a depth of 2000 meter using floats, which enable the estimation of density or steric sea level changes. By subtracting the steric signal from the absolute sea level measured by Jason (steric-corrected altimetry), the second component of sea level changes, mass, is estimated. The launch of the Gravity Recovery And Climate Experiment (GRACE) satellites in 2002 made it possible to independently validate oceanic mass variations. If the sum of the mass and steric components equals total sea level within the uncertainties, the sea level is said to be closed. Besides these two oceanic components, ocean bottom deformation or Vertical Land Motion (VLM) also affects the sea level observed by altimeters. Over the open ocean VLM signals are generally small after a correction for Glacial Isostatic Adjustment (GIA), but near large mass variations they might become significant. Additionally, tide-gauge records are affected by VLM changes, because they are connected to land. Therefore they measure sea level relative to the sea floor, while the satellite altimeters observe the absolute variations. To bring tide gauges in the same reference frame as the altimeters, corrections for VLM have to be applied, which is usually done with nearby Global Navigation Satellite System (GNSS) data... @en

The mass and steric components of sea level changes have been separated in the Tropical Asian Seas (TAS) using a statistically optimal combination of Jason satellite altimetry, GRACE satellite gravimetry, and ocean reanalyses. Using observational uncertainties, statistically optimally weighted time series for both components have been obtained in four regions within the TAS over the period January 2005 to December 2012. The mass and steric sea level variability is regressed with the first two principal components (PC1&2) of Pacific equatorial wind stress and the Dipole Mode Index (DMI). Sea level in the South China Sea is not affected by any of the indices. Steric variability in the TAS is largest in the deep Banda and Celebes seas and is affected by both PCs and the DMI. Mass variability is largest on the continental shelves, which is primarily controlled by PC1. We argue that a water flux from the Western Tropical Pacific Ocean is the cause for mass variability in the TAS. The steric trends are about 2 mm yr⁻¹ larger than the mass trends in the TAS. A significant part of the mass trend can be explained by the aforementioned indices and the nodal cycle. Trends obtained from fingerprints of mass redistribution are statistically equal to mass trends after subtracting the nodal cycle and the indices. Ultimately, the effect of omitting the TAS in global sea level budgets is estimated to be 0.3 mm yr⁻¹.

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The recent growth and deepening of inland lakes in the Tibetan Plateau (TP) may be a salient indicator of the consequences of climate change. The seasonal dynamics of these lakes is poorly understood despite this being potentially crucial for disentangling contributions from glacier melt and precipitation, which are all sensitive to climate, to lake water budget. Using in situ observations, satellite altimetry and gravimetry data, we identified two patterns of lake level seasonality. In the central, northern, and northeastern TP, lake levels are characterized by considerable increases during warm seasons and decreases during cold seasons, which is consistent with regional mass changes related to monsoon precipitation and evaporation. In the northwestern TP, however, lake levels exhibit dramatic increases during both warm and cold seasons, which deviate from regional mass changes. This appears to be more connected with high spring snowfall and large summer glacier melt. The variable lake level response to different drivers indicates heterogeneous sensitivity to climate change between the northwestern TP and other regions.

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Geodetic measurements of vertical land motion and gravity change are incorporated into an a priori model of present-day glacial isostatic adjustment (GIA) in North America via least-squares adjustment. The result is an updated GIA model wherein the final predicted signal is informed by both observational data, and prior knowledge (or intuition) of GIA inferred from models. The data-driven method allows calculation of the uncertainties of predicted GIA fields, and thus offers a significant advantage over predictions from purely forward GIA models. In order to assess the influence each dataset has on the final GIA prediction, the vertical land motion and GRACE-measured gravity data are incorporated into the model first independently (i.e., one dataset only), then simultaneously. The relative weighting of the datasets and the prior input is iteratively determined by variance component estimation in order to achieve the most statistically appropriate fit to the data. The best-fit model is obtained when both datasets are inverted and gives respective RMS misfits to the GPS and GRACE data of 1.3 mm/yr and 0.8 mm/yr equivalent water layer change. Non-GIA signals (e.g., hydrology) are removed from the datasets prior to inversion. The post-fit residuals between the model predictions and the vertical motion and gravity datasets, however, suggest particular regions where significant non-GIA signals may still be present in the data, including unmodeled hydrological changes in the central Prairies west of Lake Winnipeg. Outside of these regions of misfit, the posterior uncertainty of the predicted model provides a measure of the formal uncertainty associated with the GIA process; results indicate that this quantity is sensitive to the uncertainty and spatial distribution of the input data as well as that of the prior model information. In the study area, the predicted uncertainty of the present-day GIA signal ranges from ∼0.2-1.2 mm/yr for rates of vertical land motion, and from ∼3-4 mm/yr of equivalent water layer change for gravity variations.

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Long-term trends and decadal variability of sea level in the North Sea and along the Norwegian coast have been studied over the period 1958–2014. We model the spatially nonuniform sea level and solid earth response to large-scale ice melt and terrestrial water storage changes. GPS observations, corrected for the solid earth deformation, are used to estimate vertical land motion. We find a
clear correlation between sea level in the North Sea and along the Norwegian coast and open ocean steric variability in the Bay of Biscay and west of Portugal, which is consistent with the presence of wind-driven coastally trapped waves. The observed nodal cycle is consistent with tidal equilibrium. We are able to explain the observed sea level trend over the period 1958–2014 well within the standard error of the sum of all contributing processes, as well as the large majority of the observed decadal sea level variability.@en