Abstract
We tested models commonly used for estimating turbulence kinetic energy dissipation rates varepsilon from very high frequency stratosphere–troposphere radar data. These models relate the root-mean-square value sigma of radial velocity fluctuations assessed from radar Doppler spectra to varepsilon. 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 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}) directly obtained from relative wind speed spectra inferred from UAV measurements. Firstly, statistical analysis results revealed a very close relationship between enhancements of sigma and varepsilon_{U} for varepsilon_{U} ,{ gtrsim },10^{ - 5} ,{text{m}}^{2} ,{text{s}}^{ - 3}, indicating that both instruments detected the same turbulent events with varepsilon_{U} above this threshold. Secondly, varepsilon_{U} was found to be statistically proportional to sigma^{3}, whereas a sigma^{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 sigma^{3} dependence was found even after excluding convectively generated turbulence in the planetary boundary layer and below clouds. The best agreement between varepsilon_{U} and radar-derived varepsilon was obtained with the simple formulation based on dimensional analysis varepsilon = sigma^{3} /L_{c} where LC ≈ 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.
Highlights
Turbulence kinetic energy (TKE) dissipation rate ε is a fundamental parameter indicative of the strength of turbulence
The purpose of the present work is to show the results of comparisons between ε estimates made from middle and upper atmosphere (MU) radar data in the lower troposphere using existing formulations and direct in situ estimates of ε obtained from small unmanned aerial vehicles (UAVs) equipped with high-frequency sampling and fast-response Pitot sensors (Kantha et al 2017)
TKE dissipation rates ε were estimated from measurements made by high-frequency response Pitot sensors onboard UAVs and from MU radar Doppler spectra in the lower troposphere
Summary
Turbulence kinetic energy (TKE) dissipation rate ε is a fundamental parameter indicative of the strength of turbulence. Because ST radars can be used for detecting turbulence in the free atmosphere (above the atmospheric boundary layer), standard models are based on the assumption that turbulence results from shear flow instabilities in a stably stratified background (e.g., Fukao et al 1994; Kurosaki et al 1996; Nastrom and Eaton 1997). For such turbulence, the stable stratification limits the size of the largest turbulent eddies and damps vertical motions, leading to the definition of various outer scales of stratified turbulence (e.g., Weinstock 1978a, b, 1981). Indirect estimates of ε can be obtained from the estimates of refractive index structure constant Cn2 from radar echo power (e.g., Gage and Balsley 1978; Cohn 1995; Hocking and Mu 1997; Hocking 1999) but that is beyond the scope of the present work
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