Statistical assessment of a Doppler radar model of TKE dissipation rate for low Richardson numbers

Abstract

Abstract. The potential ability of VHF or UHF Doppler radars to measure turbulence kinetic energy (TKE) dissipation rate ε in the atmosphere is a major asset of these instruments because of the possibility to continuously monitor turbulence in the atmospheric column above the radars. Several models have been proposed over the past decades to relate ε to half the Doppler spectral width σ, corrected for non-turbulent contributions, but their relevance remains unclear. Recently, Luce et al. (2023) tested the performance of a new model expected to be valid for weakly stratified or strongly sheared conditions, i.e., for low Richardson (Ri) numbers. Its simplest expression is εS=CSσ2S, where CS∼0.64 and S=|dV/dz| is the vertical shear of the horizontal wind V. We assessed the relevance of this model with a UHF (1.357 GHz) wind profiler called WPR LQ-7, which is routinely operated at the Shigaraki Middle and Upper Atmosphere (MU) observatory (34.85∘ N, 136.10∘ E) in Japan. For this purpose, we selected turbulence events associated with Kelvin–Helmholtz (KH) billows, because their formation necessarily requires Ri<0.25 somewhere in the flow, a condition a priori favorable to the application of the model. Eleven years of WPR LQ-7 data were used for this objective. The assessment of εS was first based on its consistency with an empirical model εLout=σ3/Lout, where Lout has the dimension of an outer scale of turbulence. It was found to compare well in a KH layer with direct estimates of ε from in situ measurements for Lout≈70 m. Some degree of equivalence between εS and εLout was confirmed by statistical analysis of 192 KH layers found in the height range 0.3–5.0 km indicating that Lout≈LH/0.64, where LH=σ/S is the Hunt scale defined for neutral turbulence. The degree of equivalence is even significantly improved if Lout is not treated as a constant but depends on the depth D of the layer. We found Lout≈0.0875D or equivalently LH∼0.056D, which also means that σ is proportional to the apparent variation in the horizontal velocity (S×D) over the depth of the KH layer. Consequently, εS=0.64σ2S and εLout=σ3/0.0875D would express the same model for KH layers when Ri remains low. For such a condition, we provide a physical interpretation of εLout, which would be qualitatively identical to that for neutral boundary layers.