Abstract
Important characteristics of watershed processes can be extracted from hydrologic data using spectral methods. We extract quantitative information from precipitation, stream discharge, and groundwater head data from watersheds in northern-lower Michigan using Fourier Transform (FT) methods. By comparing the spectra of these data using similar units, we graphically illustrate the hydrologic processes that link precipitation to stream discharge and groundwater levels including evapotranspiration. We also demonstrate how unit hydrographs can be efficiently and non-parametrically derived using the FT in a manner that allows for a quantitative seasonal comparison of precipitation and the resulting stream discharge response. This analysis clearly illustrates the reduction in summer discharge levels due to canopy interception and evapotranspiration. We also develop a systematic application of the FT we call the Scaled-Windowed Fourier Transform (SWFT), which extracts time-varying spectral content using a similar approach to the wavelet transform. While computationally less efficient than the wavelet transform, the SWFT allows for embedded detrending and tapering. Application of this method clearly illustrates the non-stationarities of spectral content within the three chosen data types, leading to a greater understanding of discharge-generating processes.

Download

Kendall and Hyndman (2007)