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 easurements closer to the coast

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

International audienceThe 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

Including antenna mispointing in a semi-analytical model for delay/Doppler altimetry

International audienceDelay/Doppler altimetry aims at reducing the measurementnoise 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 delay/Doppler altimetry which considers some simplifications as the absence of mispointing antenna. This paper first proposes a new semi-analytical model for delay/Doppler altimetry. The proposed analytical expression for the flat surface impulse response considers antenna mispointing angles, a circular antenna pattern, no vertical speed effect and a uniform scattering. The two dimensional delay/Doppler map is 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 multi-look 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

ALES+: Adapting a homogenous ocean retracker for satellite altimetry to sea ice leads, coastal and inland waters

Water level from sea ice-covered oceans is particularly challenging to retrieve with satellite radar altimeters due to the different shapes assumed by the returned signal compared with the standard open ocean waveforms. Valid measurements are scarce in large areas of the Arctic and Antarctic Oceans, because sea level can only be estimated in the openings in the sea ice (leads and polynyas). Similar signal-related problems affect also measurements in coastal and inland waters. This study presents a fitting (also called retracking) strategy (ALES+) based on a subwaveform retracker that is able to adapt the fitting of the signal depending on the sea state and on the slope of its trailing edge. The algorithm modifies the existing Adaptive Leading Edge Subwaveform retracker originally designed for coastal waters, and is applied to Envisat and ERS-2 missions. The validation in a test area of the Arctic Ocean demonstrates that the presented strategy is more precise than the dedicated ocean and sea ice retrackers available in the mission products. It decreases the retracking open ocean noise by over 1 cm with respect to the standard ocean retracker and is more precise by over 1 cm with respect to the standard sea ice retracker used for fitting specular echoes. Compared to an existing open ocean altimetry dataset, the presented strategy increases the number of sea level retrievals in the sea ice-covered area and the correlation with a local tide gauge. Further tests against in-situ data show that also the quality of coastal retrievals increases compared to the standard ocean product in the last 6 km within the coast. ALES+ improves the sea level determination at high latitudes and is adapted to fit reflections from any water surface. If used in the open ocean and in the coastal zone, it improves the current official products based on ocean retrackers. First results in the inland waters show that the correlation between water heights from ALES+ and from in-situ measurement is always over 0.95

Coastal Altimetry: A Promising Technology for the Coastal Oceanography Community

Satellite altimetry has been one of the most important implements for physical oceanographers. The conventional altimeter is best performed over open ocean surface, yet there are many attempts to exploit the potential of altimetry in coastal zone in the last decade. To achieve a high performance for coastal altimetry is a multi-fold effort: the more sophisticated instrument concepts, the smarter onboard trackers, the more expert data editing criteria, the more specific retracking algorithms, the more advanced error correction methods, etc. In this chapter, each of the above aspects is described in detail, and some representative works in the altimetry community are reviewed. Particularly, the coastal altimetry offshore Hong Kong is addressed as a case study to demonstrate the potential of the new technology. In the conclusive session, some prospects for the coastal oceanography community are presented

Bayesian Estimation of Smooth Altimetric Parameters: Application to Conventional and Delay/Doppler Altimetry

International audienceThis paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non-identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters. This algorithm has a low computational cost that is suitable for real-time applications. The proposed Bayesian strategy and the corresponding estimation algorithm are evaluated using both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason-2 and CryoSat-2 waveforms shows an improvement in parameter estimation when compared to state-of-the-art estimation algorithms

Sensitivity of Altimeter Wave Height Assessment to Data Selection

Thispaperaddressestheissueofhowtheselectionofbuoysandthecalculationofaltimeter averages affect the metrics characterising the errors of altimetric wave height estimates. The use of a 51-point median reduces the sensitivity to occasional outliers, but the quality of this measure can be improved by demanding that there is a minimum number of valid measurements. This had a marked impact in both the open ocean and the coastal zone. It also affected the relative ordering of algorithms’ performances, as some fared poorly when a representative value was gleaned from a single waveform inversion, but had a much better ranking when a minimum of 20 values were used. Validation procedures could also be improved by choosing altimeter-buoy pairings that showed a good consistency. This paper demonstrated an innovative procedure using the median of the differentretrackersanalysed,whichcanbeeasilyextendedtootherdatavalidationexercises. Thisled to improved comparison statistics for all algorithms in the open ocean, with many showing errors less than 0.2 m, but there was only one strong change in the relative performance of the 11 Jason-3 retrackers. For Sentinel-3A, removing the inconsistent coastal buoys showed that all of the new algorithms had similar errors of just over 0.2 m. Thus, although improvements were found in the procedure usedforthe SeaState RoundRobinexercise, the relative rankingsforthe buoycalibrations are mostly unaffected

BALTIC+ Theme 3 Baltic+ SEAL (Sea Level) Product Handbook

This handbook is designed to support both novice and more advanced users. It is a reference guide for users of the ESA Baltic SEAL suite of products. It provides fundamental information on the theory underpinning the products, and the technical specifications of the data you can access. It also provides links to the more in-depth literature and information on the theory and technical aspects of the product you are using. Newcomers to satellite altimetry data can find basic information on altimetry, and how to interpret and understand the data files you have obtained. There are also helpful basic codes to display and explore your newly acquired data. For more expert users, the overview information is presented here, with more technical, and in-depth information available in the referenced literature

Development of an ENVISAT altimetry processor providing sea level continuity between open ocean and Arctic leads

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 process- ing 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 com- puted. In the frame of the ESA Sea Level Climate Change Initiative (CCI, 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 net- work 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 18Hz ENVISAT/RA-2 dat