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

Luce, Hubert; Kantha, Lakshmi; Hashiguchi, Hiroyuki

The potential ability of VHF or UHF Doppler radars to measure turbulence kinetic energy (TKE) dissipation rate inline-formulaε 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 inline-formulaε to half the Doppler spectral width inline-formulaσ, 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 (inline-formulaRi) numbers. Its simplest expression is inline-formulaεS=CSσ2S, where inline-formulaCS∼0.64 and inline-formula M7inlinescrollmathml S = | normal d bold-italic V / normal d z | 61pt14ptsvg-formulamathimg5d2fbd3b45a154c0fb90237a368fc707 amt-16-5091-2023-ie00001.svg61pt14ptamt-16-5091-2023-ie00001.png is the vertical shear of the horizontal wind inline-formulaV. 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 (34.85inline-formula N, 136.10inline-formula E) in Japan. For this purpose, we selected turbulence events associated with Kelvin–Helmholtz (KH) billows, because their formation necessarily requires inline-formulaRi<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 inline-formulaεS was first based on its consistency with an empirical model inline-formula M13inlinescrollmathml italic ε Lout = italic σ normal 3 / L out 73pt16ptsvg-formulamathimg3bb1253bc56ac9087659192e6b794dc6 amt-16-5091-2023-ie00002.svg73pt16ptamt-16-5091-2023-ie00002.png , where inline-formulaLout has the dimension of an outer scale of turbulence. It was found to compare well in a KH layer with direct estimates of inline-formulaε from in situ measurements for inline-formulaLout≈70 m. Some degree of equivalence between inline-formulaεS and inline-formulaεLout was confirmed by statistical analysis of 192 KH layers found in the height range 0.3–5.0 km indicating that inline-formula M19inlinescrollmathml L out L normal H / normal 0.64 74pt14ptsvg-formulamathimgab979a54b90d985dd60394fc824ad715 amt-16-5091-2023-ie00003.svg74pt14ptamt-16-5091-2023-ie00003.png , where inline-formula M20inlinescrollmathml L normal H = italic σ / S 48pt14ptsvg-formulamathimg278c4a6f2c45f049d05acd1e309295b1 amt-16-5091-2023-ie00004.svg48pt14ptamt-16-5091-2023-ie00004.png is the Hunt scale defined for neutral turbulence. The degree of equivalence is even significantly improved if inline-formulaLout is not treated as a constant but depends on the depth inline-formulaD of the layer. We found inline-formulaLout≈0.0875D or equivalently inline-formulaLH∼0.056D, which also means that inline-formulaσ is proportional to the apparent variation in the horizontal velocity (inline-formulaS×D) over the depth of the KH layer. Consequently, inline-formulaεS=0.64σ2S and inline-formula M28inlinescrollmathml italic ε Lout = italic σ normal 3 / normal 0.0875 D 97pt16ptsvg-formulamathimg0f09d63f60fea67e85f17e4a6a2ad851 amt-16-5091-2023-ie00005.svg97pt16ptamt-16-5091-2023-ie00005.png would express the same model for KH layers when inline-formulaRi remains low. For such a condition, we provide a physical interpretation of inline-formulaεLout, which would be qualitatively identical to that for neutral boundary layers.

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Luce, Hubert / Kantha, Lakshmi / Hashiguchi, Hiroyuki: Statistical assessment of a Doppler radar model of TKE dissipation rate for low Richardson numbers. 2023. Copernicus Publications.

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