Some Statistics of Temperature Structure Parameters in the Convective Boundary Layer Observed by Sodars

The characteristics of the temporal and height variations of the temperature structure parameter C_T2 in strongly convective situations derived from the sodar echo-signal intensity measurements were analyzed for the first 100 m. It was corroborated that the probability density function (pdf) of the logarithm of C_T2 in the lower convective boundary layer is markedly non-Gaussian, whereas turbulence theory predicts it to be normal. It was also corroborated that the sum of two weighted Gaussians, which characterize the statistics of C_T2 within convective plumes and in their environment and the probability of plume occurrence, well approximates the observed pdfs. It was shown that the height behaviour of the arithmetic mean of C_T2 (both total and within plumes) follows well a power law C_T2 (z) ~ z^{-q} with the exponent q close to the theoretically predicted value of 4/3. But for the geometrical means of C_T2 (both total and within the plumes), q is close to 1. The difference between arithmetically and geometrically averaged C_T2 profiles was analyzed. The vertical profiles of the standard deviation, skewness and kurtosis of {ln}C_T2 pdfs were analyzed to show their steady behaviour with height. The standard deviations of the logarithm of C_T2 within the plumes and between them are similar and are 1.5 times less than the total standard deviation. The estimate of the variability index F_T and its height behaviour were obtained, which can be useful to validate some theoretical and modelling predictions. The vertical profiles of the skewness and kurtosis show the negative asymmetry of pdfs and their flatness, respectively. The spectra of variations in {ln}C_T2 are shown to be satisfactorily fitted by the power law f^{-? } in the frequency range 0.02 and 0.2 Hz, with the average exponent ? 1.27 ± 0.22