# Towards the Optimization of SAR Altimetry Processing Over the Open Ocean

**CoAuthors**

**Event: **2018 Ocean Surface Topography Science Team Meeting

**Session: **Instrument Processing: Measurement and Retracking

**Presentation type: **Type Oral

Synthetic aperture radar (SAR) altimetry is based on the coherent processing of nadir looking pulse altimeter echoes. The delay/Doppler (D/D) algorithm implemented for CryoSat-2 and Sentinel-3 data, [Raney, 1998], applies coherent processing to the 64 echoes within each burst (equivalent to 3.5 milliseconds of flight) through an along-track FFT, creating Doppler beams of about 300 meters in the along track direction that are later multilooked to improve the final speckle noise statistics.

In the case of fully focused synthetic aperture radar (FF-SAR) altimetry [Egido & Smith, 2017] the coherent integration time can be extended, potentially, up to the illumination time of a target on ground, leading to the theoretical limit in the along-track resolution, equal to L/2, where L is the antenna length. The footprint of a fully focused SAR altimeter measurement is an elongated strip on the surface, which is pulse-limited across-track and SAR focused along-track. On a random rough surface like the open ocean, the fully focused altimeter waveforms are a random realizations of speckle noise. These single looks are essentially uncorrelated between each other so they can be incoherently averaged to obtain a multi-looked waveform leading to significantly more speckle noise reduction than conventional and D/D (unfocused SAR) altimeters.

Thanks to this improved multilooking capability, it was shown in [Egido & Smith, 2017] that, the FF-SAR technique presents a consistent improvement of a factor of √2 with respect to D/D in the estimation of sea surface height (SSH) and significant wave height (SWH) throughout the whole span of SWH values considered in the analysis.

One might conclude that fully focused estimates are better than unfocused estimates, and one might suppose that the more coherent processing, the better. However, the exact trade-off between coherent and incoherent processing actually depends on the application. For those applications where resolution is a strong advantage, such as hydrology, coastal areas, and sea-ice measurements, extending the coherent integration to the maximum aperture time is probably the right choice.

In the case of the open ocean the situation is not so clear. Wind and waves cause the instantaneous sea surface to be displaced from its equilibrium position as a random field with a complicated and directional correlation spectrum. In addition, as the coherent processing time increases, the measured area on Earth’s surface grows increasingly narrow in the along-track direction but remains the same width in the across-track direction, and so the measurement might become increasingly sensitive to the direction of winds and waves. This sensitivity could be a virtue, if it can be exploited, or a major drawback, if it makes the sea state bias correction dependent on an independent knowledge of vector winds and waves, rather than the scalar estimates of their magnitude obtained from the altimeter itself, as in classical incoherent altimetry.

In this paper we concentrate on finding an optimum trade-off between coherent and incoherent integration in the SAR altimetry processing over the open ocean, with the objective of maximizing the final SNR and ultimately obtaining a better precision in the estimation of geophysical parameters. For this investigation we have used an optimized version of the algorithm presented in [Egido & Smith, 2017], which is based on a classical SAR back-projection algorithm. Despite of being more computationally intensive than others, this method provides an accurate phase correction of the echoes along the aperture and allow us great flexibility when analyzing different coherent vs. incoherent integration strategies.

[Raney, 1998] R. K. Raney, "The delay/Doppler radar altimeter," in IEEE Transactions on Geoscience and Remote Sensing, vol. 36, no. 5, pp. 1578-1588, Sep 1998.

[Egido & Smith, 2017], A. Egido and W. H. F. Smith, "Fully Focused SAR Altimetry: Theory and Applications," in IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 1, pp. 392-406, Jan. 2017.

In the case of fully focused synthetic aperture radar (FF-SAR) altimetry [Egido & Smith, 2017] the coherent integration time can be extended, potentially, up to the illumination time of a target on ground, leading to the theoretical limit in the along-track resolution, equal to L/2, where L is the antenna length. The footprint of a fully focused SAR altimeter measurement is an elongated strip on the surface, which is pulse-limited across-track and SAR focused along-track. On a random rough surface like the open ocean, the fully focused altimeter waveforms are a random realizations of speckle noise. These single looks are essentially uncorrelated between each other so they can be incoherently averaged to obtain a multi-looked waveform leading to significantly more speckle noise reduction than conventional and D/D (unfocused SAR) altimeters.

Thanks to this improved multilooking capability, it was shown in [Egido & Smith, 2017] that, the FF-SAR technique presents a consistent improvement of a factor of √2 with respect to D/D in the estimation of sea surface height (SSH) and significant wave height (SWH) throughout the whole span of SWH values considered in the analysis.

One might conclude that fully focused estimates are better than unfocused estimates, and one might suppose that the more coherent processing, the better. However, the exact trade-off between coherent and incoherent processing actually depends on the application. For those applications where resolution is a strong advantage, such as hydrology, coastal areas, and sea-ice measurements, extending the coherent integration to the maximum aperture time is probably the right choice.

In the case of the open ocean the situation is not so clear. Wind and waves cause the instantaneous sea surface to be displaced from its equilibrium position as a random field with a complicated and directional correlation spectrum. In addition, as the coherent processing time increases, the measured area on Earth’s surface grows increasingly narrow in the along-track direction but remains the same width in the across-track direction, and so the measurement might become increasingly sensitive to the direction of winds and waves. This sensitivity could be a virtue, if it can be exploited, or a major drawback, if it makes the sea state bias correction dependent on an independent knowledge of vector winds and waves, rather than the scalar estimates of their magnitude obtained from the altimeter itself, as in classical incoherent altimetry.

In this paper we concentrate on finding an optimum trade-off between coherent and incoherent integration in the SAR altimetry processing over the open ocean, with the objective of maximizing the final SNR and ultimately obtaining a better precision in the estimation of geophysical parameters. For this investigation we have used an optimized version of the algorithm presented in [Egido & Smith, 2017], which is based on a classical SAR back-projection algorithm. Despite of being more computationally intensive than others, this method provides an accurate phase correction of the echoes along the aperture and allow us great flexibility when analyzing different coherent vs. incoherent integration strategies.

[Raney, 1998] R. K. Raney, "The delay/Doppler radar altimeter," in IEEE Transactions on Geoscience and Remote Sensing, vol. 36, no. 5, pp. 1578-1588, Sep 1998.

[Egido & Smith, 2017], A. Egido and W. H. F. Smith, "Fully Focused SAR Altimetry: Theory and Applications," in IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 1, pp. 392-406, Jan. 2017.