Abstract. The kinetic energy dissipation rate is one of the key intrinsic fluid flow parameters in environmental fluid dynamics. In an indirect method the kinetic energy dissipation rate is estimated from the Batchelor spectrum. Because the Batchelor spectrum has a significant difference between the highest and lowest spectral values, the spectral bias in the periodogram causes the lower spectral values at higher frequencies to increase. Consequently, the accuracy in fitting the Batchelor spectrum is affected. In this study, the multitaper spectral estimation method is compared to conventional methods in estimating the synthetic temperature gradient spectra. It is shown in the results that the multitaper spectra have less bias than the Hamming window smoothed spectra and the periodogram in estimating the synthetic temperature gradient spectra. The results of fitting the Batchelor spectrum based on four error functions are compared. When the theoretical noise spectrum is available and delineated at the intersection of the estimated spectrum, the fitting results of the kinetic energy dissipation rate corresponding to the four error functions do not have significant differences. However, when the noise spectrum is unknown and part of the Batchelor spectrum overlaps the region where the noise spectrum dominates, the weighted chi-square distributed error function has the best fitting results.

[1] The so-called indirect method of estimating the kinetic energy dissipation rate, a key parameter in environmental 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.

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