Turbulence Kinetic Energy dissipation rate: Assessment of radar models from comparisons between 1.3 GHz WPR and DataHawk UAV measurements

Abstract

Abstract. The WPR-LQ-7 is a UHF (1.3575 GHz) wind profiler radar used for routine measurements of the lower troposphere at Shigaraki Middle and Upper (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 turbulence kinetic energy (TKE) dissipation rates ε from the Doppler spectral width in the altitude range ~0.7 to 4.0 km ASL. For this purpose, we compared LQ-7-derived ε by using processed data available on line (http://www.rish.kyoto-u.ac.jp/radar-group/blr/shigaraki/data/) 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 σ2 N 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 σ2 S 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 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 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's (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 with S100 otherwise.

Statistical assessment of a Doppler radar model of TKE dissipation rate for low Richardson numbers (weakly stratified or strongly sheared conditions)

“…If the measurements are made with a zenith-pointing beam as is the case in the present paper, 𝜎 2 is expected to be an estimate of the variance 〈𝑤 ′2 〉 of the vertical component of wind fluctuations produced by turbulence. Luce et al (2023) (hereafter L2023) tested three radar models relating 𝜎 2 to 𝜀 using data collected by a UHF wind profiler called WPR-LQ-7 (Imai et al, 2007), and routinely operated at Shigaraki MU Observatory (34.85°N, 136.10°E) in Japan. The models require determination of the nondimensional gradient Richardson number 𝑅𝑖 = 𝑁 2 𝑆 2 ⁄ , where 𝑆 = |𝑑𝑉 ⃗ 𝑑𝑧 ⁄ | (𝑠 −1 ) is the vertical shear of the horizontal wind, and 𝑁 (𝑟𝑎𝑑𝑠 −1 ) defined by 𝑁 2 = (𝑔 𝜃 ⁄ ) 𝑑𝜃 𝑑𝑧 ⁄ , where 𝜃 is the potential temperature and 𝑔 is gravitational acceleration, is the Brünt-Vaïsälä or buoyancy frequency.…”