the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Statistical assessment of a Doppler radar model of TKE dissipation rate for low Richardson numbers (weakly stratified or strongly sheared conditions)
Hubert Luce
Lakshmi Kantha
Hiroyuki Hashiguchi
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 εS = CS σ2 S 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 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 that 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 ≈ 0.0875 D or equivalently Lout ~ 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, εS = 0.64 σ2 S and εLout = 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 Lout, which would be qualitatively identical to that for neutral boundary layers.
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Hubert Luce et al.
Status: closed
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RC1: 'Comment on amt-2023-141', Anonymous Referee #1, 07 Aug 2023
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-141/amt-2023-141-RC1-supplement.pdf
- AC1: 'Reply on RC1', Hubert Luce, 08 Sep 2023
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RC2: 'Comment on amt-2023-141', Anonymous Referee #2, 08 Aug 2023
This paper presents a feasible method to estimate TKE dissipation rate (ε) based on a unit of WPR-LQ-7 in a sheared atmospheric boundary layer. The model is illustrated clearly with proper experimental settings. The authors point out the relevance of Lout and D, which is valuable in a real-world application. Although the condition (in a sheared environment) is a little bit strict, I think this work can be published after some minor revisions.
Specific comments:
- In Abstract, the definition of Loutshould be clearly pointed out.
- Line 30: half the Doppler spectral width mentioned here is not consistent with half width σ of the Doppler spectrum peak mentioned in Abstract, which may confuse readers without background.
- Line 42-46. The sentence starting from (2) The model... is too long. I suggest the authors use short sentences.
- In Table 1, the authors list many key parameters of the WPR-LQ-7. It would be better if they could include what parameters can be derived from WPR-LQ-7 measurement. In this section, I cannot find this critical information.
- Line 123. The authors need to explain why a KH layer can be visible with enhanced SNR signal or to provide a reference.
- In Figure 3, I suggest the authors mark the KH layer mentioned in Figure 2a with two dash lines or a grey zone.
- Line 304-307. This part should be mentioned in a Discussion. I suggest the authors discuss the strengths and shortages of the new mode compared with other studies in this paragraph and change the section title to Discussion.
Citation: https://doi.org/10.5194/amt-2023-141-RC2 - AC2: 'Reply on RC2', Hubert Luce, 08 Sep 2023
Status: closed
-
RC1: 'Comment on amt-2023-141', Anonymous Referee #1, 07 Aug 2023
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-141/amt-2023-141-RC1-supplement.pdf
- AC1: 'Reply on RC1', Hubert Luce, 08 Sep 2023
-
RC2: 'Comment on amt-2023-141', Anonymous Referee #2, 08 Aug 2023
This paper presents a feasible method to estimate TKE dissipation rate (ε) based on a unit of WPR-LQ-7 in a sheared atmospheric boundary layer. The model is illustrated clearly with proper experimental settings. The authors point out the relevance of Lout and D, which is valuable in a real-world application. Although the condition (in a sheared environment) is a little bit strict, I think this work can be published after some minor revisions.
Specific comments:
- In Abstract, the definition of Loutshould be clearly pointed out.
- Line 30: half the Doppler spectral width mentioned here is not consistent with half width σ of the Doppler spectrum peak mentioned in Abstract, which may confuse readers without background.
- Line 42-46. The sentence starting from (2) The model... is too long. I suggest the authors use short sentences.
- In Table 1, the authors list many key parameters of the WPR-LQ-7. It would be better if they could include what parameters can be derived from WPR-LQ-7 measurement. In this section, I cannot find this critical information.
- Line 123. The authors need to explain why a KH layer can be visible with enhanced SNR signal or to provide a reference.
- In Figure 3, I suggest the authors mark the KH layer mentioned in Figure 2a with two dash lines or a grey zone.
- Line 304-307. This part should be mentioned in a Discussion. I suggest the authors discuss the strengths and shortages of the new mode compared with other studies in this paragraph and change the section title to Discussion.
Citation: https://doi.org/10.5194/amt-2023-141-RC2 - AC2: 'Reply on RC2', Hubert Luce, 08 Sep 2023
Hubert Luce et al.
Hubert Luce et al.
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