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#### An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra

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##### Citation

Hasselmann, S., Bruning, C., Hasselmann, K., & Heimbach, P. (1996). An improved
algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra.* Journal
of Geophysical Research: Oceans,* *101*, 16615-16629. doi:10.1029/96JC00798.

Cite as: https://hdl.handle.net/21.11116/0000-0008-89EF-1

##### Abstract

An earlier algorithm for retrieving two-dimensional wave spectra from synthetic aperture radar (SAR) image spectra is improved by using a modified cost function and introducing an additional iteration loop in which the first-guess input spectrum is systematically updated. For this purpose a spectral partitioning scheme is applied in which the spectrum is decomposed into a finite number of distinct wave systems. At each iteration step, the individual wave systems of the partitioned nth-guess wave spectrum are adjusted to agree in mean energy, frequency, and direction with the corresponding mean values of the associated wave systems of the SAR-inverted wave spectrum. The algorithm retrieves smooth wave spectra, avoiding the discontinuities which tended to arise in the previous algorithm in the transition region near the azimuthal wavenumber cutoff of the SAR image spectrum. The azimuthal cutoff of the SAR spectrum is also reproduced more accurately. The greatest improvement of the new retrieval algorithm is obtained when the discrepancies between the initial first-guess wave spectrum and the observed SAR spectrum are large. In this case the additional updating loop for the input spectrum enables the retrieved spectrum to adjust such that the simulated SAR spectrum matches more closely the observed SAR spectrum. The overall correlation of a large set of simulated SAR spectra with the measured SAR spectra is found to be significantly higher than with the previous algorithm, indicating that the algorithm not only overcomes isolated shortcomings of the earlier algorithm but also yields retrieved wave spectra which are generally more consistent with the input SAR data. An additional practical advantage of the new algorithm is that it returns spectral partioning parameters which dan be used in SAR wave data assimilation schemes.