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

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 of continuous monitoring of turbulence in the atmospheric column above the radars. Several models have been proposed over past decades to relate ε to the half width σ of the Doppler spectrum peak, 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 ε_S = C_S σ² S where C_S ~ 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 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 ε_S was first based on its consistency with an empirical model ε_Lout= σ³ / L_out that was found to compare well in a KH layer with direct estimates of ε from in-situ measurements for L_out ≈ 70 m. Some degree of equivalence between ε_S and ε_Lout was confirmed by statistical analysis of 192 KH layers found in the height range [0.3–5.0] km indicating that L_out ≈ L_H  / 0.64 where L_H = σ / S is the Hunt scale defined for neutral turbulence. The degree of equivalence is even significantly improved if L_out is not treated as a constant but depends on the depth D of the layer. We found L_out ≈ 0.0875 D or equivalently L_out ~ 0.056 D which also means that σ is proportional to the apparent variation of the horizontal velocity (S × D) over the depth of the KH layer. Consequently, ε_S  = 0.64 σ² S and ε_Lout = σ³ / 0.0875 D would express the same model for KH layers when Ri remains small. For such a condition, we provide a physical interpretation of L_out, which would be qualitatively identical to that for neutral boundary layers.