Internal wave detection and wavelength estimation from ERS-1 SAR images via wavelet analysis

Oceanographers and remote sensing researchers have long recognised the potential of using satellite imagery for studying oceanic internal waves. If, as seems likely, the greytone patterns of these images can be confirmed to correspond to trough and crest patterns of internal waves, then a great deal can be learnt about internal waves from satellite data. The utility of wavelet analysis as a tool for internal wave detection and wavelength estimation is examined using both continuous and discrete versions of the wavelet transform. The theoretical background of each procedure is briefly described and applied using a specific “wavelet” for each case. The authors first present the construction of an appropriate wavelet basis, based on an oceanographic soliton internal wave analytical model, to detect and localise nonlinear wave signatures from SAR ocean image profiles. The structure of the arbitrary wavelet basis derived from the compactly supported orthonormal B-splines wavelets is studied so as to obtain more optimal discrete wavelet decompositions. Comparisons are made for wavelet decompositions based on several families of compactly supported wavelets. Finally, the continuous wavelet transform is applied to estimate energies and wavelengths within soliton peaks from the detected internal wave trains. The results from this study show that wavelet analysis is an excellent tool to detect internal waves against background noise, and to estimate, with a good degree of precision, soliton wavelengths from SAR ocean image profiles