Optimizing Trade-Offs Between Coherent and Incoherent Averaging of SAR Altimeter Pulse Echoes from Ocean Surfaces
Smith, Walter¹; Scharroo, Remko^2
1NOAA Lab. for Satellite Altimetry, UNITED STATES; ²Altimetrics LLC, UNITED STATES

The presently operating CryoSat-2 has, and future Sentinel-3 and Jason-CS radar altimeters will have, a SAR mode that allows one to borrow Doppler beam sharpening techniques from synthetic aperture radar and apply these to a pulse-limited, nadir-looking altimeter. This allows the measurement footprint to be narrowed in the flight direction, if there is sufficient coherency among successive echoes to support the beam sharpening calculation. The spatial resolution of this calculation is usually characterized by assuming that reflecting targets are perfectly coherent, in which case the resolution depends only on pulse repetition frequency (PRF), orbital height, and the number of echoes sequentially obtained at high PRF (the number of echoes in a burst). For example, for CryoSat-2 it is said that the resolution is around 300 m.

In reality the radar echo from a random rough surface such as the sea does not remain perfectly coherent, and so the spatial resolution of the beam sharpening is limited; the resolvable patch on the sea surface is likely to be wider than 300 m along-track. This suggests the possibility that one may establish a trade-off between coherent processing of successive echoes, which aims to use correlated information to narrow the footprint, versus incoherent (power averaging) processing, which aims to use uncorrelated information to reduce the speckle noise in the received echo power. This is a particular manifestation of a general and familiar problem in geophysical inverse theory: a trade-off between the resolution of an estimator and the variance of the estimator.

We are using CryoSat-2 Level-1a full bit rate (FBR) radar echoes in SAR mode to investigate this trade-off empirically. At the same time, we are developing a theoretical model of the statistical expectation for the power and power variance in echo waveforms under various choices of the trade-off. We also are developing retrackers that allow retrieval of the range, significant wave height, and back-scatter parameters of the model. By combining these we aim to determine the optimal processing strategy for an ocean altimeter with a high-PRF SAR mode.