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<p>The WPR-LQ-7 is a UHF (1.3575 GHz) wind profiler radar used for routine measurements of the lower troposphere at Shigaraki MU Observatory (34.85<span class="inline-formula">^∘</span> N, 136.10<span class="inline-formula">^∘</span> 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 the rate of turbulence kinetic energy (TKE) dissipation <span class="inline-formula"><i>ε</i></span> from the Doppler spectral width in the altitude range <span class="inline-formula">∼</span> 0.7 to 4.0 km above sea level (a.s.l.). For this purpose, we compared LQ-7-derived <span class="inline-formula"><i>ε</i></span> using processed data available online (<span class="uri">http://www.rish.kyoto-u.ac.jp/radar-group/blr/shigaraki/data/</span>, last access: 24 July 2023) with direct estimates of <span class="inline-formula"><i>ε</i></span> (<span class="inline-formula"><i>ε</i>_U</span>) 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 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ε</mi><mrow><msub><mi>L</mi><mi mathvariant="normal">out</mi></msub></mrow></msub><mo>=</mo><msup><mi mathvariant="italic">σ</mi><mn mathvariant="normal">3</mn></msup><mo>/</mo><msub><mi>L</mi><mi mathvariant="normal">out</mi></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="72pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="7a1128f132436c8c0050e70c9183b504"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00001.svg" width="72pt" height="18pt" src="amt-16-3561-2023-ie00001.png"/></svg:svg></span></span>, with <span class="inline-formula"><i>L</i>_out∼70</span> m, provides the best statistical agreement with <span class="inline-formula"><i>ε</i>_U</span>. (2) The model <span class="inline-formula"><i>ε</i>_<i>N</i></span> predicting a <span class="inline-formula"><i>σ</i>²<i>N</i></span> law (<span class="inline-formula"><i>N</i></span> is Brunt–Vaïsälä frequency) for stably stratified conditions tends to overestimate for <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">U</mi></msub><mo>≲</mo><mn mathvariant="normal">5</mn><mo>×</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="67pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="c71df514ef701a448f4bcfbd6cb04ec0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00002.svg" width="67pt" height="16pt" src="amt-16-3561-2023-ie00002.png"/></svg:svg></span></span> m<span class="inline-formula">²</span> s<span class="inline-formula">⁻³</span> and to underestimate for <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M17" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ε</mi><mi mathvariant="normal">U</mi></msub><mo>≳</mo><mn mathvariant="normal">5</mn><mo>×</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="67pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="321efc2babd9a033f02fbcdec5aad131"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00003.svg" width="67pt" height="16pt" src="amt-16-3561-2023-ie00003.png"/></svg:svg></span></span> m<span class="inline-formula">²</span> s<span class="inline-formula">⁻³</span>. We also tested a model <span class="inline-formula"><i>ε</i>_S</span> predicting a <span class="inline-formula"><i>σ</i>²<i>S</i></span> law (<span class="inline-formula"><i>S</i></span> is the vertical shear of horizontal wind) supposed to be valid for low Richardson numbers (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M23" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi mathvariant="italic">Ri</mi><mo>=</mo><msup><mi>N</mi><mn mathvariant="normal">2</mn></msup><mo>/</mo><msup><mi>S</mi><mn mathvariant="normal">2</mn></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="58pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="ee7de1c324df542151a216fce384f543"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00004.svg" width="58pt" height="15pt" src="amt-16-3561-2023-ie00004.png"/></svg:svg></span></span>). From the case study of a turbulent layer produced by a Kelvin–Helmholtz (K–H) instability, we found that <span class="inline-formula"><i>ε</i>_S</span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M25" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ε</mi><mrow><msub><mi>L</mi><mi mathvariant="normal">out</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="22pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="5a94a7b1d3d2f0d6afddc7dfffa93555"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00005.svg" width="22pt" height="12pt" src="amt-16-3561-2023-ie00005.png"/></svg:svg></span></span> are both very consistent with <span class="inline-formula"><i>ε</i>_U</span>, while <span class="inline-formula"><i>ε</i>_<i>N</i></span> underestimates <span class="inline-formula"><i>ε</i>_U</span> in the core of the turbulent layer where <span class="inline-formula"><i>N</i></span> 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 length scale defined for weakly stratified turbulence. A statistical analysis showed that <span class="inline-formula"><i>ε</i>_S</span> also provides better statistical agreement with <span class="inline-formula"><i>ε</i>_U</span> and is much less biased than <span class="inline-formula"><i>ε</i>_<i>N</i></span>. Combining estimates of <span class="inline-formula"><i>N</i></span> and shear from DataHawk and radar data, respectively, a rough estimate of the Richardson number at a vertical resolution of 100 m (<span class="inline-formula"><i>Ri</i>₁₀₀</span>) was obtained. We performed a statistical analysis on the <span class="inline-formula"><i>Ri</i></span> dependence of the models. The main outcome is that <span class="inline-formula"><i>ε</i>_S</span> compares well with <span class="inline-formula"><i>ε</i>_U</span> for low <span class="inline-formula"><i>Ri</i>₁₀₀</span> (<span class="inline-formula"><i>Ri</i>₁₀₀≲1</span>), while <span class="inline-formula"><i>ε</i>_<i>N</i></span> fails. <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M41" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ε</mi><mrow><msub><mi>L</mi><mi mathvariant="normal">out</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="22pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="61a1527d62b2a9225ccb63e183aa88ed"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00006.svg" width="22pt" height="12pt" src="amt-16-3561-2023-ie00006.png"/></svg:svg></span></span> varies as <span class="inline-formula"><i>ε</i>_S</span> with <span class="inline-formula"><i>Ri</i>₁₀₀</span>, so that <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M44" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ε</mi><mrow><msub><mi>L</mi><mi mathvariant="normal">out</mi></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="22pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="0a018139dc2b55e0838b587acb7a037d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00007.svg" width="22pt" height="12pt" src="amt-16-3561-2023-ie00007.png"/></svg:svg></span></span> remains the best (and simplest) model in the absence of information on <span class="inline-formula"><i>Ri</i></span>. Also, <span class="inline-formula"><i>σ</i></span> appears to vary as <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M47" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">Ri</mi><mn mathvariant="normal">100</mn><mrow><mo>-</mo><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="32pt" height="20pt" class="svg-formula" dspmath="mathimg" md5hash="4d9573d69ef0e3c92d037780e17c326c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-16-3561-2023-ie00008.svg" width="32pt" height="20pt" src="amt-16-3561-2023-ie00008.png"/></svg:svg></span></span> when <span class="inline-formula"><i>Ri</i>₁₀₀≳0.4</span> and shows a degree of dependence on <span class="inline-formula"><i>S</i>₁₀₀</span> (vertical shear at a vertical resolution of 100 m) otherwise.</p>