Turbulence kinetic energy dissipation rate: assessment of radar models from comparisons between 1.3 GHz wind profiler radar (WPR) and DataHawk UAV measurements

Abstract

The WPR-LQ-7 is a UHF (1.3575 GHz) wind profiler radar used for routine measurements of the lower troposphere at Shigaraki MU Observatory (34.85∘ N, 136.10∘ E; Japan) at a vertical resolution of 100 m and a time resolution of 10 min. Following studies carried out with the 46.5 MHz middle and upper atmosphere (MU) radar (Luce et al., 2018), we tested models used to estimate the rate of turbulence kinetic energy (TKE) dissipation ε from the Doppler spectral width in the altitude range ∼ 0.7 to 4.0 km above sea level (a.s.l.). For this purpose, we compared LQ-7-derived ε using processed data available online (http://www.rish.kyoto-u.ac.jp/radar-group/blr/shigaraki/data/, last access: 24 July 2023) with direct estimates of ε (εU) from DataHawk UAVs. The statistical results reveal the same trends as reported by Luce et al. (2018) with the MU radar, namely (1) the simple formulation based on dimensional analysis εLout=σ3/Lout, with Lout∼70 m, provides the best statistical agreement with εU. (2) The model εN predicting a σ2N law (N is Brunt–Vaïsälä frequency) for stably stratified conditions tends to overestimate for εU≲5×10-4 m2 s−3 and to underestimate for εU≳5×10-4 m2 s−3. We also tested a model εS predicting a σ2S law (S is the vertical shear of horizontal wind) supposed to be valid for low Richardson numbers (Ri=N2/S2). From the case study of a turbulent layer produced by a Kelvin–Helmholtz (K–H) instability, we found that εS and εLout are both very consistent with εU, while εN underestimates εU in the core of the turbulent layer where N is minimum. We also applied the Thorpe method from data collected from a nearly simultaneous radiosonde and tested an alternative interpretation of the Thorpe length in terms of the Corrsin length scale defined for weakly stratified turbulence. A statistical analysis showed that εS also provides better statistical agreement with εU and is much less biased than εN. Combining estimates of N and shear from DataHawk and radar data, respectively, a rough estimate of the Richardson number at a vertical resolution of 100 m (Ri100) was obtained. We performed a statistical analysis on the Ri dependence of the models. The main outcome is that εS compares well with εU for low Ri100 (Ri100≲1), while εN fails. εLout varies as εS with Ri100, so that εLout remains the best (and simplest) model in the absence of information on Ri. Also, σ appears to vary as Ri100-1/2 when Ri100≳0.4 and shows a degree of dependence on S100 (vertical shear at a vertical resolution of 100 m) otherwise.