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Some Statistics of the Temperature Structure Parameter in the Convective Boundary Layer Observed by Sodar

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Abstract

The characteristics of the temporal and height variations of the temperature structure parameter \(C_\mathrm{T}^{2}\) 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 \(C_\mathrm{T}^{2}\) 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 \(C_\mathrm{T}^{2}\) 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 \( C_\mathrm{T}^{2}\) (both total and within plumes) follows well a power law \(C_\mathrm{T}^{2} (z) \sim z^{-q}\) with the exponent \(q\) close to the theoretically predicted value of 4/3. But for the geometrical means of \(C_\mathrm{T}^{2}\) (both total and within the plumes), \(q\) is close to 1. The difference between arithmetically and geometrically averaged \(C_\mathrm{T}^{2}\) profiles was analyzed. The vertical profiles of the standard deviation, skewness and kurtosis of \(\hbox {ln}C_\mathrm{T}^{2}\) pdfs were analyzed to show their steady behaviour with height. The standard deviations of the logarithm of \(C_\mathrm{T}^{2}\) 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 \(F_\mathrm{T}\) 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 \(\hbox {ln}C_\mathrm{T}^{2}\) are shown to be satisfactorily fitted by the power law \(f^{-\gamma } \) in the frequency range 0.02 and 0.2 Hz, with the average exponent \(\approx \)1.27 \(\pm \) 0.22.

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Acknowledgments

The authors are thankful to Mr. A. Conidi for his assistance in experimental works, to Prof. M. Kallistratova for her help in the bibliography search, to Dr. A. Kumar for his help in editing the manuscript, and to anonymous reviewers.

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  1. Institute of Atmospheric Sciences and Climate CNR, Via del Fosso del, Cavaliere 100, Rome , 00133, Italy

    Igor Petenko, Giangiuseppe Mastrantonio, Angelo Viola, Stefania Argentini & Ilaria Pietroni

  2. A.M. Obukhov Institute of Atmospheric Physics RAS, Pyzhevskiy, 3, Moscow , 119017, Russia

    Igor Petenko

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  1. Igor Petenko
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Correspondence to Igor Petenko.

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Petenko, I., Mastrantonio, G., Viola, A. et al. Some Statistics of the Temperature Structure Parameter in the Convective Boundary Layer Observed by Sodar. Boundary-Layer Meteorol 150, 215–233 (2014). https://doi.org/10.1007/s10546-013-9867-1

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