Turbulence kinetic energy dissipation rates estimated from concurrent UAV and MU radar measurements

Abstract

We tested models commonly used for estimating turbulence kinetic energy dissipation rates ε from very high frequency stratosphere-troposphere radar data. These models relate the root-mean-square value σ of radial velocity fluctuations assessed from radar Doppler spectra to ε. For this purpose, we used data collected from the middle and upper atmosphere (MU) radar during the Shigaraki unmanned aerial vehicle (UAV)-radar experiment campaigns carried out at the Shigaraki MU Observatory, Japan, in June 2016 and 2017. On these occasions, UAVs equipped with fastresponse and low-noise Pitot tube sensors for turbulence measurements were operated in the immediate vicinity of the MU radar. Radar-derived dissipation rates ε estimated from the various models at a range resolution of 150 m from the altitude of 1.345 km up to the altitude of ~ 4.0 km, a (half width half power) beam aperture of 1.32° and a time resolution of 24.6 s, were compared to dissipation rates (ε U) directly obtained from relative wind speed spectra inferred from UAV measurements. Firstly, statistical analysis results revealed a very close relationship between enhancements of σ and ε U for ε U 10 −5 m 2 s −3 , indicating that both instruments detected the same turbulent events with ε U above this threshold. Secondly, ε U was found to be statistically proportional to σ 3 , whereas a σ 2 dependence is expected when the size of the largest turbulent eddies is smaller than the longitudinal and transverse dimensions of the radar sampling volume. The σ 3 dependence was found even after excluding convectively generated turbulence in the planetary boundary layer and below clouds. The best agreement between ε U and radar-derived ε was obtained with the simple formulation based on dimensional analysis ε = σ 3 /L c where L C ≈ 50-70 m. This empirical expression constitutes a simple way to estimate dissipation rates in the lower troposphere from MU radar data whatever the sources of turbulence be, in clear air or cloudy conditions, consistent with UAV estimates.

On the estimation of vertical air velocity and detection of atmospheric turbulence from the ascent rate of balloon soundings

“…It is thus well adapted for the present purpose, i.e., the identification of turbulent layers when the balloons were flying. Values of ε can be calculated from UAV data using two methods described by Luce et al (2019). A direct estimate is obtained from onedimensional (1D) spectra of streamwise wind fluctuation measurements.…”

“…The TKE dissipation rate can also be estimated from MU radar data using the variance σ 2 of Doppler spectrum peaks produced by turbulence. It is based on an empirical model proposed by Luce et al (2018) and validated from comparisons with UAV-derived ε. The expression of the model is ε (MU) = σ 3 /L out where L out ∼ 60 m. In the present work, an estimate of ε (MU) at a given altitude z is obtained from an average of the values of σ 2 over a centered-in-time 2 min window (about 30 values since radar profiles were obtained every ∼ 4 s) around the time that the altitude z was reached by the radiosonde (see also Fig.…”

“…The white vertical lines are due to radar stops. See, e.g., Luce et al (2018) for more details about these figures. Labels refer to the location of turbulent layers.…”

“…In fact, the free stratified atmosphere usually reveals a "sheet and layer" structure (e.g., Fritts et al, 2003) consisting of more or less deep layers of turbulence (a few hundred meters) separated by quieter and generally statically stable regions. In such conditions, turbulence intensity, often quantified by turbulence kinetic energy dissipation rates, can vary over several orders of magnitude with height and can reach levels similar to those met in the convective atmospheric boundary layers (e.g., Luce et al, 2019).…”

Mitigating ground effect on mini quadcopters with model reference adaptive control

“…The averaged generalisation error, quantified by RMSE, of our mathematical model over the entire data set is 12.8%. It is worth pointing out that turbulence is an intrinsic part of the atmospheric boundary layer (the lowest 100 to 3000 m of the atmosphere) (Stull, 2012;Luce, Kantha, Hashiguchi, Lawrence, Doddi, 2018). Therefore, a 12.8% error is satisfactory considering the random nature of turbulences, which is a significant confounding factor in any outdoor flight mission.…”