Satellite radar altimetry has been used for over 30 years to measure Sea Surface Height (SSH) variations to build records of Essential Climate Variables like the Mean Sea Level (MSL) for a robust assessment of climate change. A key step of the data processing towards this goal is the retracking, that is, the statistical analysis of the radar waveforms to estimate the geophysical parameters. For a robust and optimal estimation, retracking algorithms should account for a reliable waveform model, the time-varying instrumental Point Target Response (PTR), and an accurate description of the waveform noise. However, this is not the case for the operational retracking solutions implemented in the ground segments, which specifically make use of an unweighted estimator, therefore not accounting for the waveform speckle noise. In this paper we present a novel computationally efficient retracking solution for Ku-band Low Resolution Mode (LRM) data that accounts for both, the in-flight PTR and a realistic waveform noise through a weighted estimator defined to be statistically equivalent to a Maximum Likelihood estimator.We consider two waveform models: the Adaptive model and the numerical Brown model, for a consistent comparison with operational retracking solutions. We focus on the current reference mission, Sentinel-6 MF, for which an accurate noise characterization is crucial to account for the pulse-to-pulse correlations resulting from the higher Pulse Repetition Frequency (PRF) compared to conventional configurations. We demonstrate that the novel retracking solution is optimal, providing with parameter uncertainties compatible with the Cramer-Rao bounds of minimum variance, and unbiased, while a bias up to 1 cm in the epoch estimation and sub-optimality for all parameters is found for the unweighted solutions. We validated the algorithm on realistic simulations and applied it to one cycle of Sentinel-6MF LR 20 Hz data, demonstrating significant improvements in the precision of estimated parameter: ∼60% for Significant Wave Height (SWH), ∼12% for the epoch, and ∼50% for σ0compared to current operational solutions. We report for the first time geophysical parameter uncertainties consistently computed at 20 Hz as output of the retracker. We also introduce an innovative Bayesian approach for analyzing waveform data to complement current solutions, providing with a robust method for the estimation of the parameter uncertainties and correlations. Finally, we perform a comprehensive analysis of parameter correlations, on simulations and data, compared to theoretical expectation based on Fisher matrix analysis, demonstrating the importance of optimality for a correct estimation. Specifically, we show that the unweighted, suboptimal retracking solution significantly underestimates the epoch-SWH correlation, by a factor of ∼1.5 in the correlation coefficients, compared to the optimal solution and theoretical expectations. This could significantly impact the estimation of corrections such as Sea State Bias (SSB) and High-Frequency Adjustment (HFA), warranting further assessment. Overall, optimal retracking solutions should be considered to derive robust long-term sea level records for climate research using past, current, and future altimetry missions.

Lake ice thickness (LIT), a thematic product of Lakes as an Essential Climate Variable (ECV), is sensitive to changes in air temperature and on-ice snow mass. Here, a novel and efficient analytic method (retracking approach) is presented for the estimation of LIT from Ku-band (13.6 GHz) radar altimetry data. The new retracker, referred to as LRM_LIT, is based on the physical modeling of the conventional radar echoes (also called Low Resolution Mode or LRM) over ice-covered lakes that show a characteristic step-like feature in their leading edge attributed to the reflection of radar waves at the snow-ice and ice-water interfaces. The method is applied to Jason-2 and Jason-3 data acquired over Great Slave Lake, Canada, over three ice seasons (2013-2016). As expected, the agreement between the Jason-2 and Jason-3 LIT estimates over their overlapping period (2016 ice season) is excellent with a mean bias error of 0.013 m and root mean square error (RMSE) of 0.024 m. LIT estimates from LRM_LIT are in good agreement with simulations from a thermodynamic lake ice model and in situ measurements with RMSE values of the order of few centimeters for the three winter seasons. The retracker also provides a robust way to assess the accuracy of LIT estimates which is in the order of 0.10 m when the ice cover is well established and prior to melt onset. In addition, LRM_LIT captures the seasonal transitions during the freeze-up and breakup periods and ice growth over different winter seasons, making it a promising method for monitoring inter-annual variability and trends in LIT from past and current conventional radar altimetry missions.

The Snow Microwave Radiative Transfer (SMRT) model was initially developed to explore the sensitivity of microwave scattering to snow microstructure for active and passive remote sensing applications. Here, we discuss the modular design of SMRT that has enabled its rapid extension by the community. SMRT can now represent a layered medium consisting of snow, land ice, lake ice and/or sea ice overlying a substrate of soil, water or parameterized by reflectivity. A time-dependent radiative transfer solution method has also been added to allow for low resolution mode altimetry applications. We illustrate the use of SMRT to simulate brightness temperature for snow on lake ice, backscatter for snow on soil and altimeter waveforms for snow on sea ice.

The purpose of this paper is to accompany the release of the Jason-3 GDR-F products delivered as part of the GDR-F reprocessing campaign and to explain its main benefits for the users of altimetry products. This reprocessing campaign has a twofold objective: improve the quality of the products and share common standards with Sentinel-6/Jason-CS. Illustrations of the different benefits for the users of altimetry products are provided.

The accuracy of sea surface parameters retrieved from altimeter missions is predominantly governed by the choice of the so-called “retracking” algorithm, i.e., the model and inversion method implemented to obtain the surface parameters from the backscattered waveform. For continuity reasons, the choice of space agencies is usually to apply the same retracker from one satellite mission to the other to ensure long-time homogeneous series. In this article, taking the opportunity of a new configuration of the nadir pointing measurements onboard the recently launched China France Oceanography Satellite (CFOSAT) with the Surface Waves Investigation and Monitoring (SWIM) instrument (Hauseret al.,2020), the retracking method was upgraded, by implementing a novel algorithm, called “Adaptive” retracker. It combines the improvements brought by Poissonet al.,(2018) for the estimation of surface parameters from peaked waveforms over sea ice, improvements in the way the instrumental characteristics are considered in the model (mispointing, point target response) and a more accurate consideration of speckle statistics. In this article, we first show from simulations carried out in the instrumental configuration of SWIM that the Adaptive algorithm has better accuracy and performance than the classical MLE4 algorithm. Then, the geophysical parameters obtained with real data from SWIM are analyzed with comparisons to reference data sets (model and products from altimeters). We show that this new algorithm has several benefits with respect to the classical MLE4 method: no need of lookup tables to correct biases, significant noise reduction on all geophysical variables especially the significant wave height, and performance of inversion over a large set of echo shapes, resulting from standard oceanic scenes as well as highly specular conditions such as over bloom or sea ice.

The detection of sea ice leads is a prerequisite for the estimation of ice freeboard and thickness from altimeter data. The classification of altimeter waveforms is generally performed using statistical parameters on the echo power or machine learning approaches directly on the waveforms. The validation and optimization of such algorithms can be carried out using a set of reference cases provided by Earth Observation images. In this paper, we first developed a new lead detector based on Sentinel-1 (S-1) synthetic aperture radar (SAR) images. A robust and consistent methodology for the joint assessment of Altimeter and SAR leads detector is then provided. We propose to fully account for the 2-D geometric problem when comparing the 1-D altimeter track and 2-D SAR image. The surface of the lead intersecting the altimeter footprint and its distance to nadir are considered here. Based on collocated Sentinel-3 (S-3) altimeter data and S-1 images, the performance of our S-3 lead detector is fully assessed. A new parameterization is found resulting in a better tradeoff between good detection and false alarm rate. A similar analysis is performed using AltiKa altimeter data, showing enhanced performance for S-3 altimeter data acquired in Delay-Doppler mode with reduced off-nadir returns.

Over the Arctic regions, current conventional altimetry products suffer from a lack of coverage or from degraded performance due to the inadequacy of the standard processing applied in the ground segments. This paper presents a set of dedicated algorithms able to process consistently returns from open ocean and from sea-ice leads in the Arctic Ocean (detection of water surfaces and derivation of water levels using returns from these surfaces). This processing extends the area over which a precise sea level can be computed. In the frame of the European Space Agency Sea Level Climate Change Initiative (http://cci.esa.int), we have first developed a new surface identification method combining two complementary solutions, one using a multiple-criteria approach (in particular the backscattering coefficient and the peakiness coefficient of the waveforms) and one based on a supervised neural network approach. Then, a new physical model has been developed (modified from the Brown model to include anisotropy in the scattering from calm protected water surfaces) and has been implemented in a maximum likelihood estimation retracker. This allows us to process both sea-ice lead waveforms (characterized by their peaky shapes) and ocean waveforms (more diffuse returns), guaranteeing, by construction, continuity between open ocean and ice-covered regions. This new processing has been used to produce maps of Arctic sea level anomaly from 18-Hz ENVIronment SATellite/RA-2 data.

The concept of delay/Doppler (DD) altimetry (DDA) has been under study since the mid-1990s, aiming at reducing the measurement noise and increasing the along-track resolution in comparison with the conventional pulse-limited altimetry. This paper introduces a new model for the mean backscattered power waveform acquired by a radar altimeter operating in synthetic aperture radar mode, as well as an associated least squares (LS) estimation algorithm. As in conventional altimetry (CA), the mean power can be expressed as the convolution of three terms: the flat surface impulse response (FSIR), the probability density function of the heights of the specular scatterers, and the time/frequency point target response of the radar. An important contribution of this paper is to derive an analytical formula for the FSIR associated with DDA. This analytical formula is obtained for a circular antenna pattern, no mispointing, no vertical speed effect, and a uniform scattering. The double convolution defining the mean echo power can then be computed numerically, resulting in a 2-D semi-analytical model called the DD map (DDM). This DDM depends on three altimetric parameters: the epoch, the sea surface wave height, and the amplitude. A multi-look model is obtained by summing all the reflected echoes from the same along-track surface location of interest after applying appropriate delay compensation (range migration) to align the DDM on the same reference. The second contribution of this paper concerns the estimation of the parameters associated with the multi-look semi-analytical model. An LS approach is investigated by means of the Levenberg-Marquardt algorithm. Simulations conducted on simulated altimetric waveforms allow the performance of the proposed estimation algorithm to be appreciated. The analysis of Cryosat-2 waveforms shows an improvement in parameter estimation when compared to the CA.

Much attention has been recently devoted to the analysis of coastal altimetric waveforms. When approaching the coast, altimetric waveforms are sometimes corrupted by peaks caused by high reflective areas inside the illuminated land surfaces or by the modification of the sea state close to the shoreline. This paper introduces a new parametric model for these peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and an asymmetric Gaussian peak. The asymmetric Gaussian peak is parameterized by a location, an amplitude, a width, and an asymmetry coefficient. A maximum-likelihood estimator is studied to estimate the Brown plus peak model parameters. The Cramér-Rao lower bounds of the model parameters are then derived providing minimum variances for any unbiased estimator, i.e., a reference in terms of estimation error. The performance of the proposed model and the resulting estimation strategy are evaluated via many simulations conducted on synthetic and real data. Results obtained in this paper show that the proposed model can be used to retrack efficiently standard oceanic Brown echoes as well as coastal echoes corrupted by symmetric or asymmetric Gaussian peaks. Thus, the Brown with Gaussian peak model is useful for analyzing altimetric measurements closer to the coast.

Coastal altimetric waveforms may be corrupted by peaks. A simple parametric model was recently introduced to model peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and a Gaussian peak. This model has provided interesting results for symmetric peaks affecting altimetric signals. However, it is not appropriate for altimetric signals corrupted by asymmetric peaks. This paper introduces a Brown with asymmetric Gaussian peak model for altimetric waveforms. The parameters of this model are estimated by a maximum likelihood estimator. The performance of the proposed model and the resulting estimation strategy is evaluated via simulations con ducted on synthetic and real data.

This paper addresses the problem of classifying altimetric signals according to their shapes. The proposed classifier is divided into three steps. A one-class support vector machine method is first used to isolate the large amount of Brown-like echoes from others signals which are considered as outliers. The second step extracts pertinent features from the the remaining echoes (which cannot be well described by the Brown model). These features are projected onto discriminant axes using linear discriminant analysis. The final step classifies the projected feature vectors using a standard Bayesian classifier. The proposed three step classification strategy is evaluated on supervised real altimetric echoes.

This paper studies a Bayesian algorithm for estimating the parameters associated to Brown's model. The joint posterior distribution of the unknown parameter vector (amplitude, epoch and significant wave height) associated with this model is derived. This posterior is too complex to obtain closed form expressions of the minimum mean square error and the maximumaposterioriestimators. We propose to sample according to this distribution using an hybrid Metropolis within Gibbs algorithm. The simulated samples are then used to estimate the unknown parameters of Brown's model. The proposed strategy provides better estimations than the standard maximum likelihood estimator at the price of an increased computational cost.

The Jason-1 satellite was launched on 7 December 2001 with the primary objective of continuing the high accuracy time series of altimetric measurements that began with the TOPEX/Poseidon mission in 1992. To achieve this goal and to improve the quality of the data, many studies have been performed to well characterize the observed signal, to refine the modelisation of this signal and to optimize the algorithms used for the estimation of the altimetric parameters. Among these studies, we have analysed the role of the skewness coefficient in the signal modelisation. We show in this paper, the impact of the skewness coefficient in the ocean parameters determination. In the Jason processing chain, the estimations of the range, power, significant waveheight and mispointing angle of the satellite are obtained thanks to an algorithm called « retracking ». These estimations are performed by making the measured waveform coincide with a return power model according to an unweighted Least Square Estimator derived from a Maximum Likelihood Estimator (Dumont (4) and Rodriguez (8)). The analytic ocean return model is the one, first given by Brown (2), refined by Hayne (5) and completed by Amarouche (1). In this model, a fixed skewness coefficient is included and for the first three years of Jason-1 mission, the skewness coefficient has been taken equal to 0. However, it is known that the skewness coefficient, representing the third order moment of the ocean wave heights distribution, is certainly not equal to 0. The aim of this work is to determine the optimized solution to take into account the skewness coefficient in the Jason retracking procedure. Several techniques to estimate the skewness coefficient have been investigated including retracking of the waveforms with four unknowns (range, backscatter coefficient, significant waveheight and skewness coefficient). The main results of this work are presented in this paper. The final aim of this study is of course to track eventual remaining biases on the ocean altimetric estimations. -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Poseidon 2 is the dual frequency, solid state radar altimeter embarked on the CNES/NASA oceanographic satellite JASON 1. This paper gives a brief sum up of the instrument design and some preliminary in flight performances.

Proposes a modified Fourier transform for the inversion of the visibility function acquired by an unidimensional interferometer observing the surface of the Earth from a low orbit. The inversion of the visibility function by the mean of the usual Fourier transform provides a profile of geometrically distorted brightness temperatures. A modified Fourier transform which takes into account the geometrical considerations of the problem and which avoids making geometrical corrections is described. The authors study the behaviour of this new transform when the input signal is corrupted with white noise. A convolution product associated with this modified Fourier transform is also defined.>