RIVER LONG PROFILE ANALYSIS WITH THE CONTINUOUS WAVELET TRANSFORM

The use of the continuous wavelet transform (CWT) for the analysis of river long profiles is proposed. The CWT is an alternative to the continuous Fourier transform (CFT), which is well-suited to the study of signals (i.e. a spatial data series) containing spatially localized features or an evolving spectral content. Fourier transforms are commonly used to analyze long profile data. In particular, CFT based power spectral analysis (PSA) is a method used to estimate the dominant wavelengths in detrended long profiles. The dominant wavelengths are taken to be evidence of the periodicity of the morphological structure under study. These structures include riffle-pool and step-pool sequences.

However, Fourier analysis provides the global spectral content of a signal making it difficult to detect either localized features or spectral evolution. As such, PSA may provide an incomplete or misleading picture of the spectral content of a long profile. The CWT overcomes these deficiencies. An illustrated comparison of the results from a PSA of a number of test profiles, with the corresponding results obtained via the CWT, will be presented. This comparison highlights some of the important differences between CFT and the CWT. The results from a Fourier and a wavelet analysis of a long profile exhibiting step-pool morphology are also presented. The wavelet analysis reveals that a number of wavelengths, detected by PSA, correspond to spatially localized structures and that the spectral content of the profile residuals is not consistent along the reach.