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Richard Wilson, Francis Dalaudier, and Francois Bertin


Small-scale turbulence in the free atmosphere is known to be intermittent in space and time. The turbulence fraction of the atmosphere is a key parameter in order to evaluate the transport properties of small-scale motions and to interpret clear-air radar measurements as well.

Mesosphere–stratosphere–troposphere (MST)/stratosphere–troposphere (ST) radars provide two independent methods for the estimation of energetic parameters of turbulence. First, the Doppler spectral width σ 2 is related to the dissipation rate of kinetic energy εk. Second, the radar reflectivity, or C 2 n, relates to the dissipation rate of available potential energy εp. However, these two measures yield estimates that differ with respect to an important point. The Doppler width measurements, and related εk, are reflectivity-weighted averages. On the other hand, the reflectivity estimate is a volume-averaged quantity. The values of εp depend on both the turbulence intensity and the turbulent fraction within the radar sampling volume.

Now, the two dissipation rates εp and εk are related quantities as shown by various measurements within stratified fluids (atmosphere, ocean, lakes, or laboratory). Therefore, by assuming a “canonical” value for the ratio of dissipation rates, an indirect method is proposed to infer the turbulent fraction from simultaneous radar measurements of reflectivity and Doppler broadening within a sampling volume. This method is checked by using very high resolution radar measurements (30 m and 51 s), obtained by the PROUST radar during a field campaign. The method is found to provide an unbiased estimation of the turbulent fraction, within a factor of 2 or less.

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Richard Wilson, Hubert Luce, Francis Dalaudier, and Jacques Lefrère


The Thorpe analysis is a recognized method used to identify and characterize turbulent regions within stably stratified fluids. By comparing an observed profile of potential temperature or potential density to a reference profile obtained by sorting the data, overturns resulting in statically unstable regions, mainly because of turbulent patches and Kelvin–Helmholtz billows, can be identified. However, measurement noise may induce artificial inversions of potential temperature or density, which can be very difficult to distinguish from real (physical) overturns.

A method for selecting real overturns is proposed. The method is based on the data range statistics; the range is defined as the difference between the maximum and the minimum of the values in a sample. A statistical hypothesis test on the range is derived and evaluated through Monte Carlo simulations. Basically, the test relies on a comparison of the range of a data sample with the range of a normally distributed population of the same size as the data sample. The power of the test, that is, the probability of detecting the existing overturns, is found to be an increasing function of both trend-to-noise ratio (tnr) and overturns size. A threshold for the detectable size of the overturns as a function of tnr is derived. For very low tnr data, the test is shown to be unreliable whatever the size of the overturns. In such a case, a procedure aimed to increase the tnr, mainly based on subsampling, is described.

The selection procedure is applied to atmospheric data collected during a balloon flight with low and high vertical resolutions. The fraction of the vertical profile selected as being unstable (turbulent) is 47% (27%) from the high (low) resolution dataset. Furthermore, relatively small tnr measurements are found to give rise to a poor estimation of the vertical extent of the overturns.

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