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 $$\varepsilon$$ ε from very high frequency stratosphere–troposphere radar data. These models relate the root-mean-square value $$\sigma$$ σ of radial velocity fluctuations assessed from radar Doppler spectra to $$\varepsilon$$ 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 fast-response and low-noise Pitot tube sensors for turbulence measurements were operated in the immediate vicinity of the MU radar. Radar-derived dissipation rates $$\varepsilon$$ 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 ($$\varepsilon_{U}$$ εU ) directly obtained from relative wind speed spectra inferred from UAV measurements. Firstly, statistical analysis results revealed a very close relationship between enhancements of $$\sigma$$ σ and $$\varepsilon_{U}$$ εU for $$\varepsilon_{U} \,{ \gtrsim }\,10^{ - 5} \,{\text{m}}^{2} \,{\text{s}}^{ - 3}$$ εU≳10-5m2s-3 , indicating that both instruments detected the same turbulent events with $$\varepsilon_{U}$$ εU above this threshold. Secondly, $$\varepsilon_{U}$$ εU was found to be statistically proportional to $$\sigma^{3}$$ σ3 , whereas a $$\sigma^{2}$$ σ2 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 $$\sigma^{3}$$ σ3 dependence was found even after excluding convectively generated turbulence in the planetary boundary layer and below clouds. The best agreement between $$\varepsilon_{U}$$ εU and radar-derived $$\varepsilon$$ ε was obtained with the simple formulation based on dimensional analysis $$\varepsilon = \sigma^{3} /L_{c}$$ ε=σ3/Lc 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.