A fast convolution based waveform model for conventional and unfocused SAR altimetry

In this paper we derive a closed-form solution to generate a backscatter power representation for both unfocused synthetic aperture radar altimetry and conventional altimetry signals in the frequency/slow-time domain. This new approach involves fast convolutions and leads to a fast numerical computational model which uses very few approximations. The transform back to the range-time/doppler frequency domain is then made numerically. Two retrackers based on this Signal Model Involving Numerical Convolution (SINC) are constructed for conventional and synthetic aperture radar altimetry and are named SINC2 and SINCS respectively. Output from retracking are the epoch t(0) with respect to the tracking reference point, the significant wave height and the backscattering cross section at normal incidence sigma(0). Main benefits of the SINC model are its flexibility, the possibility to use the real point target response (PTR) or more complex representations of the height probability density function of scattering sea surface elements (PDF), and its fast computation speed to retrack the waveforms. The retrackers are applied to CryoSat-2 reduced SAR (RDSAR) and unfocused SAR waveforms. The RDSAR SINC2 retracker is only ten percent slower than the commonly used MLE3 retracker, which is a minor slowdown compared to the benefits of the SINC model. The SAR processing including the SINCS retracking procedure is three times slower than the RDSAR processing including retracking with SINC2. Model and algorithms are validated on both synthetic data generated by Monte-Carlo simulations and on real datasets. SAR SAMOSA+ results accessible through the ESA G-POD SARvatore service serve as a reference. Cross-validation shows higher agreement between SAR SAMOSA+ and SAR SINCS sea level anomaly and lower agreement between SAR SAMOSA+ and RDSAR SINC2, with accuracy of -0.1 cm for SAR SINCS and 1.7 cm for RDSAR SINC2. Instead, the accuracy of significant wave height, 4.9 cm and 3.9 cm for SAR and RDSAR and of backscatter coefficient, 0.16 and 0.12 dB in SAR and RDSAR, are comparable. Cross-validation results shows for sea level anomaly and significant wave height a higher precision of SAR SINCS and a lower precision of RDSAR SINC2, with precision of 0.92 cm and 6.6 cm for SAR SINCS and 1.96 cm and 12.6 cm for RDSAR SINC2 in sea level anomaly and significant wave height respectively. Instead, the precision of the backscatter coefficient is higher in RDSAR SINC2 than in SAR SINCS, and is 0.014 and 0.016 dB. In summary the new open ocean retrackers are a viable alternative recommended for both reduced and unfocused SAR processing in open ocean. (C) 2017 COSPAR. Published by Elsevier Ltd. All rights reserved.