Retracking CryoSat-2 Ocean Waveforms for Optimal Gravity Field Recovery

Achieving improved accuracy of the global marine gravity field derived from satellite altimetry depends primarily on two factors - a dense spatial distribution of ground tracks and high range measurement precision. CryoSat-2 is the first altimeter in the past 15 years that offers advancements in both of these capabilities. Over the ocean, the altimeter is operated in two modes, which produce distinct returned signals - one is similar to the conventional pulse-limited waveform, while the new SAR waveform results from along-track focusing. In order to extract physical measurements of the ocean surface, we are developing the models and algorithms for estimating the arrival time of the leading edge of both waveform types, specifically to enhance gravity field recovery. For the conventional-mode data, we have modified our two-pass approach originally developed for retracking ERS-1 waveforms and demonstrate a factor of 1.4 improvement in range precision for CryoSat-2. We attribute this to its 2 times higher pulse repetition frequency. Waveform retracking models and methods for the SAR mode data are still in active development by the community. We are testing three approaches to SAR waveform retracking. The simplest SAR waveform model (Raney, 1998) assumes a boxcar beamform along the track for a perfectly flat ocean surface, which results in a functional form that has the return power rising as the square root of time. A complete analytic waveform model accounts for the effects of a rough surface. Therefore, the flat ocean surface response is convolved with a Gaussian wave height model. We have obtained a solution for the functional form for this first model as well as its derivatives with respect to the arrival time and rise time parameters. The second retracking approach assumes a Gaussian beamform along the track, and this leads to a modified Bessel function representation of the waveform. This particular analytic model for a flat ocean surface cannot be convolved exactly with a Gaussian wave height model, and thus we resort to using a series approximation and numerical integration in separate instances. The third approach utilizes a purely numerical integration via quadrature of both the flat ocean response and the Gaussian wave height model. Comparing the modeled power from these three approaches results in remarkably similar waveform shapes with less than 10% differences for the flat ocean case and smaller differences for a typical Gaussian wave height. The range precision of the SAR mode data is expected to be 2 times better than the conventional mode data. We will select the optimal retracking approach based on the analysis of the CryoSat-2 SAR waveforms, which involves evaluating the data through comparisons with EGM2008 as well as through the analysis of repeat tracks.