Addresses both fundamental and applied aspects of ocean waves including the use of wave observations made from satellites. More specifically it describes the WAM model, its scientific basis, its actual implementation, and its many applications. This model has been developed by an international group (the Wave Modelling group), and is based on a detailed physical description of air/sea interactions. It is widely used for wave forecasting for meteorological and oceanographic purposes. The three sections of the volume describe the basic statistical theory and the relevant physical processes; the numerical model and its global and regional applications; and satellite observations, their interpretation and use in data assimilation. Written by leading experts, it is a comprehensive guide and reference for researchers and advanced students in physical oceanography, meteorology, fluid dynamics, coastal engineering and physics.
A new, closed nonlinear integral transformation relation is derived describing the mapping of a two‐dimensional ocean wave spectrum into a synthetic aperture radar (SAR) image spectrum. The general integral relation is expanded in a power series with respect to orders of nonlinearity and velocity bunching. The individual terms of the series can be readily computed using fast Fourier transforms. The convergence of the series is rapid. The series expansion is also useful in identifying the different contributions to the net imaging process, consisting of the real aperture radar (RAR) cross‐section modulation, the nonlinear motion (velocity bunching) effects, and their various interaction products. The lowest term of the expansion with respect to nonlinearity order yields a simple quasi‐linear approximate mapping relation consisting of the standard linear SAR modulation expression multiplied by an additional nonlinear Gaussian azimuthal cutoff factor. The cutoff scale is given by the rms azimuthal (velocity bunching) displacement. The same cutoff factor applies to all terms of the power series expansion. The nonlinear mapping relation is inverted using a standard first‐guess wave spectrum as regularization term. This is needed to overcome the basic 180° mapping ambiguity and the loss of information beyond the azimuthal cutoff. The inversion is solved numerically using an iteration technique based on the successive application of the explicit solution for the quasi‐linear mapping approximation, with interposed corrections invoking the full nonlinear mapping expression. A straightforward application of this technique, however, generally yields unrealistic discontinuities of the best fit wave spectrum in the transition region separating the low azimuthal wave number domain, in which useful SAR information is available and the wave spectrum is modified, from the high azimuthal wave number region beyond the azimuthal cutoff, where the first‐guess wave spectrum is retained. This difficulty is overcome by applying a two‐step inversion procedure. In the first step the energy level of the wave spectrum is adjusted, and the wave number plane rotated and rescaled, without altering the shape of the spectrum. Using the resulting globally fitted spectrum as the new first‐guess input spectrum, the original inversion method is then applied without further constraints in a second step to obtain a final fine‐scale optimized spectrum. The forward mapping relation and inversion algorithms are illustrated for three Seasat cases representing different wave conditions corresponding to weakly, moderately, and strongly nonlinear imaging conditions.
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 can be used in SAR wave data assimilation schemes. whether the nonlinear distortions induced in the ima-Paper number 96JC00798. 0148-0227/96/96J0-00798509.00 ging process by the Doppler effects of the long-wave orbital velocities could be properly described. Nevertheless, the SAR imaging of ocean waves is now well understood (compare review by Hasselmann et al. [1985]), and the imaging theory has been successfully applied to compute SAR image spectra from wave spectra using Monte Carlo techniques [e.g. Briining et al., 1990] or, more recently, a closed spectral integral transform relation [Hasselmann and Hasselmann, 1991] (referred to in the following as HH), [Krogstad, 1992; Hasselmann et al., 1994a; Bao et al., 1994]. The forward mapping theory has been extensively verified against data from SEASAT, the Shuttle Imaging Radar-B (SIR-B) and the First European Remote Sensing satellite (ERS-1) 16,615
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