**Two and Three Parameter Waveform Retracking of Cryosat-2 and Jason-1 LRM Waveforms For Gravity Field Estimation**
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Jain, Maulik; Andersen, Ole Baltazar; Stenseng, Lars; Dall, Joergen
National Space Institute / DTU Space, DENMARK
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This presentation deals with physical retracking of Low Resolution Mode (LRM) waveforms from Cryosat-2 and Jason-1. The aim of the retracking is to generate accurate sea surface heights which are further used to develop the gravity field. This is possible because the gravity field is a derivative of the along track sea surface height anomaly. In the process of physical retracking the LRM echo power waveform is fitted to a three/two parameter model. This model fitting employs the use of Levenberg-Marquardt least squares algorithm. The fitting is based on an error function and the three parameters making the function are the maximum amplitude of the waveform, the rise time of the leading edge and the epoch location. The epoch location is very critical as it is the parameter which is used to obtain precise sea surface height.

The physical retracking algorithm starts with the extraction of the leading edge of the waveform using start/stop thresholds based on the standard deviation of power difference in consecutive/alternate bins. The extracted leading edge is subjected to a linear fit thereby providing the starting values of the 3 parameter fit. Once the three parameter fit is done, the fitted values of maximum amplitude and the rise time are smoothed along the track. This is based on the justification that the rise time (associated with Significant Wave Height) varies smoothly along the track. These smoothed values form the starting points of the next two parameter fit where only the epoch and the maximum amplitude are obtained. The fitted epochs are used to construct sea surface heights. Large part of the Jason-1 waveform is clearly more noisy than the Cryosat-2 LRM waveform and testing of smoothing/down weighting the Jason-1 was performed to create a more stable parameter fitting of the waveform.

The mean sea surface is removed and various corrections are applied on the sea surface height. The residual thus obtained is the sea surface height anomaly. The standard deviation of the sea surface height anomaly is a test for the quality of retracking algorithm as a lower value indicates better retracking. Once the retracking algorithm is successful the sea surface height anomaly's along slope derivation can be used to generate the gravity field.