Intercomparison of two-dimensional wave spectra obtained from microwave instruments, buoys and WAModel simulations during the surface wave dynamics experiment

An intercomparison is made of two dimensional wave spectra obtained from buoys and various remote sensing microwave systems and predicted by the WAModel during the Surface Wave Dynamics Experiment (SWADE). The overall agreement between the measurements and the model is satifactory, but some differences in detail require further investigation. The buoy data yield reliable mean spectral parameters, but the maximum likelihood retrieval algorithm tends to produce directional distributions that are broader than those of other instruments. Various microwave instruments (ROWS, RESSAC, SRA) show good promise for the determination of 2d-wave spectra, but exhibit individual shortcomings (calibration uncertainties, directional ambiguity, impact of aircraft motion) that need to be further studied. The SAR system yields reliable retrievals with respect to the general spectral distribution, but suffers in this experiment from an undetermined calibration factor. Deviations between the WAModel and instrumental data could be largely attributed to wind field errors, but the model also exhibits deficiencies in the development of short-fetch wave systems and in the wave spectral response to rapidly turning wind fields. 1 Intro duct ion The Surface Wave Dynamics Experiment (SWADE) was carried out off the East Coast of the United States near Cape Hatteras during a six months period starting 1 October 1990 (Weller et al). The basic goal was to gain a better understanding of the dynamics of the evolution of the two-dimensional wave spectrum and the effect of waves on the fluxes of momentum, heat, and moisture at the air-sea interface. An improved understanding of these processes would be valuable for the development of wave, ocean and atmosphere models as well as more sophisticated coupled models incorporating a detailed representation of the interface dynamics. The experiment deployed a large number of wave buoys as well as a spatially dense array of buoy wind measurements. This enabled high quality wind fields to be produced for the entire experiment (Cardone et al, 1995). It can therefore be expected that in future attempts to derive improved source terms for the WAModel (WAMDI, 1988) from the measured wind and wave data (for example, by using an adjoint of the WAMode1, Hersbach, 1996), the traditional uncertainties in the wind field will no longer dominate the error budget. During three intensive measuring periods (IOP-1, 20-31 October, 1990; IOP-2, 13-25 January 1991; and IOP-3, 25 February 9 March 1991) the in situ measurements of winds and waves by buoys were augmented by measurements from ships and (during IOP-3) aircraft. The SWADE measurements have been described extensively in Caruso et al (1993), Caruso et al (1994), Jackson (1996) and other reports; details need not be repeated here. The most extensive set of observations, including measurements of two dimensional wave spectra with four different airborne microwave systems, were obtained during IOP-3. The data were taken under a variety of meteorological conditions. The present study was carried out as preparation for a more comprehensive analysis 3 of these data for the evaluation of wave models. Before such an analysis can be undertaken, a detailed intercomparison of the wave spectra derived from the different measuring systems needs to be carried out. This is the objective of this paper. Figure 1 shows the set of flight tracks for IOP-3, together with the locations of the wave buoys. The number of collocations which can be used for the intercomparison study is quite high. The data can also be used to test the SAR retrieval algorithm (Hasselmann and Hasselmann,1991, Hasselmann, et al, 1996) and to evaluate the WAModel (WAMDIG, 1988, Komen et al, 1994), which was run in a triple-nested version for all SWADE-IOP periods. Section 2 reviews briefly the measurement systems. A more detailed description of the instruments and their analysis procedures can be found in Parson and Walsh (1989), Hauser et al (1992), Vachon et al (1994), Jackson (1996) and Jackson and Jensen (1995). All data except the SAR and SRA spectra were preprocessed to remove the directional ambiguity, using additional directional information from the WAModel. The procedure is described in Section 3. A short review of the WAModel is given in Section 4. Statistical intercomparisons of integral wave parameters, both of the complete wave spectrum and of the separate windsea and swell constituents, are presented in Section 5. In the concluding Section 6 we summarize our results and assess the potential of the different measurement systems for data assimilation and inverse modeling applications. The complete set of 2d-wave spectra measured by all microwave systems, together with the buoy and collocated WAM spectra, are shown in the appendices. 2 Wave measurement systems 2.1 Buoys Four Wavescan buoys (Discus North, East, Central and CERC, see fig. 1.) provided directional wave spectra continuously for the entire SWADE period. The 3m diameter heave-pitch-roll discus buoys measure the vertical acceleration, two gin bal angles and the orientation of the buoy relative to north. From these measurements one can recover the vertical displacement and the two components of the surface slope, whose spectra and cross spectra yield the one dimensional frequency spectrum of wave height and four components (the first two pairs of harmonics) of the Fourier expansion of the directional spreading function. Various methods have been proposed for reconstructing the full 2d-wave spectrum from this information. Straightforward truncation of the Fourier expansion of the spreading function after the first two harmonics normally yields negative lobes and is therefore not suitable. The side condition of a positive spectrum can be satisfied either by fitting a directional model with free parameters to the data or, more generally, by some inverse modelling (variational or maximum likelihood/ entropy) method. In the latter approaches, a particular solution is selected from the infinite ensemble of possible spectra that satisfy the data and positivity constraints by requiring that the solution should minimize some positive-definite cost function that expresses an additional desirable property, such as proximity to a preferred spec4 trum, or smoothness. The methods normally also permit a relaxation of the data constraints through a suitable adjustment of the cost function weights. For the analysis of the SWADE buoy data, the maximum likelihood method of Drennan et al (1995) was applied. In general, the buoy data yielded broader directional distributions than the other instruments (see instrument intercomparisons discussed in Section 5.4). However, this could well be due to the maximum likelihood analysis we applied, since the directional distribution is underdetermined by the four Fourier components provided by a heave-pitch-roll buoy, enabling a variety of distributions to be fitted to the data. Accordingly, we carried out a detailed sensitivity test for three typical spectra to assess the permissible degree of freedom in fitting the directional distribution to the buoy data. For this analysis, the general variational method of Long and Hasselmann (Long and Hasselmann, 1979, Long, 1980, Lawson and Long, 1983) was found to be convenient, as it readily provides an upper and lower bound on the directional spread. The Long-Hasselmann method selects the directional distribution that is consistent with the data and at the same time closest to a preferred directional distribution. We considered two limiting cases: an isotropic preferred distribution, and a highly peaked preferred distribution The propagation direction of the peak in the latter case was defined as 00(f) = tan'1(< sin(0) >, < cos(0) >), where < . . . > denotes the energy-weighted average over the directional distribution at a given frequency f . Thus, the two limiting cases yield the broadest and narrowest possible directional distributions, respectively, that are consistent with the data. Fig.2 clearly shows the limitation of buoy measurements for the retrieval of two dimensional wave spectra. The solutions are far from unique for both simple and complex wave spectra. The spectra computed with an isotropic preferred directional distribution typically show only one or two wave systems with a relatively broad spread, while the preferred narrow distribution yields several peaks with a narrow net directional spread. The maximum-likelihood retrieval is smoother and more coherent than either of the limiting Long-Hasselmann distributions (as to be expected, as it is not forced towards either of the rather unnatural limits). However, it tends to agree more strongly with the Long-Hasselmann solution for a preferred isotropic distribution indicating that the maximum-likelihood retrieval may indeed be brassed towards broader distributions. But the principal conclusion is that the true directional distribution simply cannot be reliably determined from buoy data alone. 2.2 SRA The Scanning Radar Altimeter (SRA) (Walsh et al, 1985) measures the 2d-wave spectrum by scanning a narrow radar beam across the aircraft ground track. It measures the slant range at 64 evenly spaced points across the swath at a spatial resolution of 8m (at 640m altitude). The slant ranges are converted to surface elevation after correcting for aircraft motions, which are measured simultaneously with accelerometers. The data of the 520m swath over an along-track distance of 506km are then transformed into 2d elevation wavenumber spectra by a two dimensional Fast Fourier Transform (FFT), and subsequently into a frequency-directional