Satellite based shelf sea climate assessment system

Abstract

To assess the wave climate in offshore regions, a new algorithm has been developed to retrieve spectral wave information from SAR wave mode spectra. By combining the ERS SAR observation with the collocated wind measurement by the scatterometer, the new scheme does not require a first guess wave spectrum. This enhances the applicability of the SAR wave mode product significantly, as the SAR observations can be interpreted independently from a numerical wave model.

The new method is based on the nonlinear forward mapping relations derived by Hasselmann and Hasselmann (1991). The wind vector derived from the coinciding scatterometer observation is used to estimate the wind sea contribution to the wave spectrum. The stage of development of the wind sea is found by optimizing a cost function, which is a measure of the difference between a simulated and the observed SAR spectrum. The swell spectrum is subsequently found from the residual SAR spectrum by exploiting the fact that the mapping of these waves is linear.

The results of this scheme are compared with those of Hasselmann et al (1996). Major differences are found in cases when the signal to noise ratio in the observed SAR spectrum is in the order of unity, and in the treatment of long swell waves with lengths between 750 and 1000 m.

Keywords: SAR wave mode, multisensor algorithms, wave spectra, wind and wave climate, coastal regions

Introduction

As the vessels and platforms used for offshore operations are sensitive to particular wave lengths, the wave climate information should be spectral. The only spaceborne sensor that can provide spectral wave information is the SAR. To be able to derive wave spectra from observed SAR spectra the known relation between ocean wave spectra and their SAR image needs to be inverted. To date, all inversion methods require a priori knowledge about the sea state in the form of a first guess wave spectrum. Using these methods, the interpretation of all SAR spectra recorded by the ERS satellites would require running a wave model for almost six years for all regions of interest. This is a time consuming, and hence costly, operation.

In this paper a new SAR inversion method is presented that does not require a first guess wave spectrum. Instead, it uses a collocated wind vector obtained from the scatterometer measurement made simultaneously with the SAR wave mode observation. This wind vector is combined with the SAR spectrum to estimate the local wind sea. The swell is subsequently estimated from the residual SAR spectrum exploiting the fact that the mapping of these waves is linear.

Together with the wind and wave information from the different scatterometers and altimeters that have been operational in the past decade, the spectral wave information obtained from the SAR spectra will be stored in a database. An on-line service will be set up that will enable industry users to assess the offshore climate according to their specific needs.

The retrieval method

The alternative method described here does not require a first guess wave spectrum. Instead, the wind velocity from the scatterometer is used to retrieve wave information from ERS SAR wave mode observations. The retrieval of a full wave spectrum is done in two steps. In the first, the scatterometer wind vector is combined with the observed SAR spectrum to estimate the local wind sea. In the second step the swell is estimated from the residual in the observed SAR spectrum.

The reason that this two step approach works is that the presence of swell does not affect the mapping of the wind sea part of the spectrum. Hence the wind sea contribution to the SAR image spectrum can be worked out without knowledge of the height, length and direction of the swell. The scatterometer wind vector is used to determine whether or not the wind sea is resolved by the SAR, and if it is, which peak in the SAR spectrum should be attributed to it. The stage of development of the wind sea is estimated by minimizing the difference between the calculated SAR image of the wind sea and the observed SAR spectrum. The functional form of the cost function that expresses the difference between two SAR spectra is derived from the statistical properties of the Fourier components that make up such a spectrum.

In the formalism of Hasselmann and Hasselmann (1991) their are two ways in which waves of a given length, say swell waves, can influence the SAR mapping of waves from a different part of the spectrum, say wind waves. The first is via their contribution to the mean square vertical velocity of the ocean surface. This vertical velocity variance is responsible for a degradation of the resolution of the SAR in the azimuth direction. This smearing effect affects in particular the mapping of the relatively short wind waves. It turns out that in the overwhelming majority of cases the contribution of the swell to the vertical velocity variance can be neglected compared to wind sea contribution. Hence the swell waves do not influence the mapping of wind waves via the velocity variance.

As the mapping from ocean wave spectrum to SAR image spectrum is nonlinear, in principle the swell peaks can be mapped on any part of the SAR image spectrum. However, it can be shown that the mapping of the swell waves is, in general, linear. Given the vertical velocity variance, the slant range and the platform velocity, the extend of the domain in the ocean wave spectrum that is mapped linearly can be estimated. For low windspeeds, giving rise to few wind waves, this domain may include all waves resolved by the ERS SAR (i.e. those with lengths between 100 and 1000 m). For high wind speeds, when the longest wind sea waves may be resolved by the SAR, only waves longer than a few honderd meters may be mapped linearly. It should be noted that the method described here is not able to resolve the 180 degrees ambiguity which is present in the observed SAR image. For the present purpose, i.e. to assess wave climates in offshore regions, this is little of a problem, as the swell can be safely assumed to originate from the open sea. In future versions the ambiguity may be eliminated by considering the cross spectra between different looks of the radar.

After the wind sea part of the spectrum is retrieved from the SAR image, the fact that the mapping of the swell waves is linear is exploited again. This time it is used to invert the SAR mapping, which becomes a trivial operation in case of a linear mapping. As a final test the SAR mapping of the combined wind sea plus swell system is calculated and compared with the observed SAR spectrum. In the majority of cases the difference between the two is of the same order as the noise.

Comparison with results from Hasselmann et al (1996)

Figure 1: Comparison of wave spectra retrieved with the method of Hasselmann et al (1996) (left column) and with the new method (right). In the top row the SAR spectra are shown, with the observed SAR spectrum in the middle. The wave spectra retrieved with both models are shown on the bottom row.

In this example there is a 7 to 10 m/s (from the scatterometer and the ECMWF model, respectively) wind blowing in the azimuth direction. The wind sea associated with this wind vector can not be resolved by the SAR. Taking into account that in the wave spectrum of ARGOSS all retrieved swell systems are shown twice (to reflect the unresolved ambiguity), this example clearly illustrates the tendency of the Hasselmann et al scheme to retrieve wave spectra which consist of more wave systems than the ARGOSS scheme does. Future validation of both methods against buoy spectra will have to show which method is more realistic.

Conclusions

References

Hasselmann, K. and S. Hasselmann, 1991:

On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion. Journal of Geophysical Research, 96, pp. 10,713-10,729.

Hasselmann, S., C. Brüning, K. Hasselmann and P. Heimbach:

An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture image spectra. Journal of Geophysical Research, 101, pp. 16,615-16,629.

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry