Detection of Turbulence from Temperature, Pressure and Position Measurements Under Superpressure Balloons
Authors: Wilson Richard , Pitois Clara , Podglajen Aurélien , Hertzog Albert , Corcos Miléna , Plougonven Riwal 
Published: July 2022

Abstract. This article deals with the detection of small-scale turbulence from in-situ meteorological measurements performed under superpressure balloons (SPBs). These balloons allow long duration flights (several months) at a prerequisite height level. The dataset is gathered from the Strateole-2 probationary campaign during which eights SPBs flew in the tropical tropopause layer at around 19 and 20.5 km altitudes, from November 2019 to March 2020. Turbulence is not directly measured by the instrument set onboard the SPBs. Nonetheless, there is a potential to derive information about the occurrence of turbulence from the well-resolved in time measurements of pressure, temperature and position. It constitutes a challenge to extract that information from a measurement set that was not designed for quantifying turbulence, and the manuscript explains the methodology developed to overcome this difficulty. It is observed that SPBs oscillate quasi-periodically around their equilibrium positions. The oscillation periods, 220 s in the average, range from 130 to 500 s, close to, but noticeably smaller than, the Brunt-Väisälä period (∼ 300 s). The amplitude of these vertical motions is ∼ ±15 m, inducing large fluctuations in all quantities, whether measured (pressure, temperature, positions) of inferred (density, potential temperature). The relationships between the changes in these quantities and vertical displacements of the balloons are used to infer properties of the flow in which the SPBs drift. In case of active turbulence, the vertical stratification as well as the wind shear are likely to be reduced by mixing. Hence, the increments of potential temperature, δθ, and of the vertical displacements of the balloon, δzB, are expected to be uncorrelated since ∂θ / ∂z → 0. Also, the local Richardson number is expected to be less than ∼ 0.25. Several binary indexes (true of false) to describe the state of the flow, laminar or turbulent, are evaluated. They are based either on correlations between δθ and δzB, or on estimations of the local Richardson number. Correlation coefficients are computed and compared, by using different measures of δθ and δzB and by estimating either the Pearson or the Spearman coefficients. Turbulence indexes based on a null-correlation are built using a randomisation test to check whether these correlations are significantly non-positive. It is also shown than a linear regression between the increments of a quantity and the increments of vertical displacements allows to estimate the vertical gradient of this quantity. Least square fit and Theil-Sen fit are used to estimate time series of vertical gradients ∂T / ∂z, ∂u / ∂z, ∂v / ∂z. Related quantities such as the Brunt-Väisälä frequency, or the local Richardson number, Ri, are inferred, allowing to establish turbulence indexes from Ri. These different indexes, based on independent measurements and on various methods, correlations or linear regressions, are found to be consistent: they differ for less than 3 % of the cases. The flow is observed to be turbulent for about 5 % of the time, with strong inhomogeneities along the longitude.