Francois Boy

Parameter Estimation for Peaky Altimetric Waveforms

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.

A Semi-Analytical Model for Delay/Doppler Altimetry and Its Estimation Algorithm

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.

CryoSat-2 SAR-Mode Over Oceans: Processing Methods, Global Assessment, and Benefits

Inspired by the synthetic aperture radar (SAR) technique, a nadir radar altimeter concept called the “Delay/Doppler altimeter” or “SAR mode altimeter” provides better precision and resolution capabilities than conventional pulse-limited altimeters (i.e., low-resolution mode). This concept was initially carried on board the CryoSat-2 satellite, then used on Sentinel-3, initially for user requirements on ice or inland water monitoring. This paper addresses geophysical parameter retrieval from Delay/Doppler altimetry over ocean surfaces. For the inversion of geophysical parameters (sea surface height, significant wave height, and backscatter coefficient), we developed an inversion method based on the numerical computation of the radar power-return equation, including instrument design features, such as the range and azimuth impulse responses. To compare this technique with respect to conventional altimetry, we also generated reduced SAR (RDSAR) measurements from the same input data. Geophysical parameter retrieval from low- and high-resolution techniques was then performed for cross-comparison, demonstrating consistency for both techniques, but with a constant 3-cm bias. The proposed processing strategy was then validated using two years of CryoSat-2 data over oceans. The SAR mode provides significant benefits for the observation of small-scale signals (below 50 km) and performs as accurately as conventional altimetry for basin or global scales. The results demonstrate what is expected from the upcoming Sentinel-3 and Sentinel-6/Jason-CS missions.

Including Antenna Mispointing in a Semi-Analytical Model for Delay/Doppler Altimetry

Delay/Doppler altimetry (DDA) aims at reducing the measurement noise and increasing the along-track resolution in comparison with conventional pulse-limited altimetry. In a previous paper, we have proposed a semi-analytical model for DDA, which considers some simplifications as the absence of mispointing antenna. This paper first proposes a new analytical expression for the flat surface impulse response (FSIR), considering antenna mispointing angles, a circular antenna pattern, no vertical speed effect, and uniform scattering. The 2-D delay/Doppler map is then obtained by a numerical computation of the convolution between the proposed analytical function, the probability density function of the heights of the specular scatterers, and the time/frequency point target response of the radar. The approximations used to obtain the semi-analytical model are analyzed, and the associated errors are quantified by analytical bounds for these errors. The second contribution of this paper concerns the estimation of the parameters associated with the multilook semi-analytical model. Two estimation strategies based on the least squares procedure are proposed. The proposed model and algorithms are validated on both synthetic and real waveforms. The obtained results are very promising and show the accuracy of this generalized model with respect to the previous model assuming zero antenna mispointing.

Calibrating the SAR SSH of Sentinel-3A and CryoSat-2 over the Corsica Facilities

Initially developed to monitor the performance of TOPEX/Poseidon and to follow the Jason legacy satellite altimeters at Senetosa Cape, Corsica, this calibration/validation site has been extended to include a new location at Ajaccio. This addition enables the site to monitor Envisat and ERS missions, CryoSat-2 and, more recently, the SARAL/AltiKa mission and Sentinel-3A satellites. Sentinel-3A and CryoSat-2 carry altimeters that use a synthetic aperture radar (SAR) mode that is different to the conventional pulse-bandwidth limited altimeters often termed “low resolution mode” (LRM). The aim of this study is to characterize the sea surface height (SSH) bias of the new SAR altimeter instruments and to demonstrate the improvement of data quality close to the coast. Moreover, some passes of Sentinel-3A and CryoSat-2 overfly both Senetosa and Ajaccio with only a few seconds time difference, allowing us to evaluate the reliability and homogeneity of both ground sites in term of geodetic datum. The Sentinel-3A and CryoSat-2 SSH biases for the SAR mode are respectively +22 ± 7 mm and −73 ± 5 mm (for CryoSat-2 baseline C products). The results show that the stability of the SAR SSH bias time series is better than standard LRM altimetry. Moreover, compared to standard LRM data, for which the measurements closer than ~10 km from the coast were generally unusable, SAR mode altimeters provide measurements that are reliable at less than few hundred meters from the coast.

A generalized semi-analytical model for delay/Doppler altimetry

This paper introduces a new model for delay/Doppler altimetry, taking into account the effect of antenna mispointing. After defining the proposed model, the effect of the antenna mispointing on the altimetric waveform is analyzed as a function of along-track and across-track angles. Two least squares approaches are investigated for estimating the parameters associated with the proposed model. The first algorithm estimates four parameters including the across-track mispointing (which affects the echos shape). The second algorithm uses the mispointing angles provided by the star-trackers and estimates the three remaining parameters. The proposed model and algorithms are validated via simulations conducted on both synthetic and real data.