Segmentation of temperature microstructure

The so-called indirect method of estimating the kinetic energy dissipation rate, a key parameter in environment fluid mechanics, involves fitting the observed spectrum to the theoretical Batchelor spectrum. This requires the statistically nonstationary temperature gradient profiles to be split onto statistically stationary segments. This comparative study of segmentation algorithms uses synthetic temperature gradient series and the temperature gradient profiles that are measured in an inland lake. The results of segmentation based on autoregressive (AR) models and wavelet analysis are compared. The bias in estimating the Batchelor spectrum from nonstationary segments, which have changes in the spectral shape or the spectral magnitude, is demonstrated. The estimated spectra of the resulting stationary segments should be stationary in both the shape and the magnitude of the spectra. A modified AR-based test and a proposed wavelet-based test are sensitive to changes in both the spectral shape and the spectral magnitude. An empirical segmentation technique sensitive to changes in the spectral shape only is not recommended for use.