The comparison between Tsallis Maxent distribution (dash dot), the empirical distribution (dash), and Mallat’s model (solid) at the three finest scales of the discrete wavelet transformation. The left panel is the coarsest scale, while the finest scale is at the right panel. The fitted parameters for the three scales are , and , respectively, from the left to the right.
The logarithms of the empirical density and Mallat’s model at different scales for a typical fBm having a Hurst exponent of . Four panels show the pdf analysis at the four finest scales in the DWT. The top-left panel is the coarsest scale while the bottom-right panel is the finest scale. The ’s at different scales are estimated from the data and are 1.7891, 1.9388, 1.9307, and 1.9242, respectively. Note that these pdfs are approximately normal.
The plots of the measured and modeled random variables at different scales in the wavelet domain for a typical flow variable . The left panel shows the coarsest scale while the right panel shows the finest scale. The same turbulence measurement time series are used as in Fig. 6.
Box plots of the shape coefficients in model across different stability regimes. The four rows correspond to , , , and , respectively, from the top to the bottom. The three finest scales of wavelet coefficients are used here. The results in the left panels are from the coarsest level of wavelet decomposition while the right panels refer to the finest level .
Box plots of the quasi-Hurst exponents for four flow variables , , , and from the top left to the bottom right, respectively.
The average logarithm pdfs associated with atmospheric stability conditions of the four flow variables at first three finest scales. The four rows are corresponding to measurement , , , and , respectively from the top to the bottom. Three finest scales of wavelet coefficients are used here. The results in the left panels are from the coarsest level of wavelet coefficients while the right panels refer to the finest level .
Mean and standard deviations of the six runs for unstable, stable, and neutral wind speeds.
Mean and standard deviations of the quasi-Hurst exponent ’s for the four flow variables. The numbers in the brackets are the statistics for the selected six runs for each stability regime described in the experimental setup and are reported here for reference.
Mean and standard deviation of ’s for all four flow variables and stability classes. Recall that for a Gaussian process.
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