Turbulence kinetic energy dissipation rate estimated from a WindCube Doppler lidar and the LQ7 1.3 GHz radar wind profiler in the convective boundary layer
<p>From 21 August to 15 September 2022, a WindCube v2 infrared coherent Doppler lidar (DL) supplied by EKO Instruments Co. (Japan) was deployed at the Shigaraki MU Observatory (Japan) near the LQ7 UHF (1.357 GHz) wind profiler in routine operation. Horizontal and vertical velocity measurements...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2025-03-01
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| Series: | Atmospheric Measurement Techniques |
| Online Access: | https://amt.copernicus.org/articles/18/1193/2025/amt-18-1193-2025.pdf |
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| Summary: | <p>From 21 August to 15 September 2022, a WindCube v2 infrared coherent Doppler lidar (DL) supplied by EKO Instruments Co. (Japan) was deployed at the Shigaraki MU Observatory (Japan) near the LQ7 UHF (1.357 GHz) wind profiler in routine operation. Horizontal and vertical velocity measurements from the DL were reliably obtained in the [40–300] m height range with vertical and temporal resolutions of 20 m and 4 s, respectively. The LQ7 wind measurements are collected with range and temporal resolutions of 100 m and 59 s, respectively, and 10 min average profiles are calculated after data quality control. Reliable LQ7 Doppler data are collected from a height of 400 m. Despite the lack of overlap in the height range, we compared the turbulence kinetic energy (TKE) dissipation rate <span class="inline-formula"><i>ε</i></span> in the daytime planetary boundary layer estimated by the two instruments. A method based on the calculation of the one-dimensional transverse line spectrum of the vertical velocity <span class="inline-formula"><i>W</i></span> from mean <span class="inline-formula"><i>W</i></span> time series (TS method) was applied to DL (<span class="inline-formula"><i>ε</i><sub>DL</sub></span>). The same method was also applied to 1 min LQ7 data (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M5" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">TS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="ba0d959b1a5ed6400f248d9394c0e9c8"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00001.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00001.png"/></svg:svg></span></span>) to assess its performance with respect to DL despite the poorer time resolution. A more standard method based on the Doppler spectral width (DS) was also applied to LQ7 (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">DS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="4bf1fb14080f3abb0591b77b462d2528"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00002.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00002.png"/></svg:svg></span></span>) from the 10 min average profiles. We tested recently proposed models of the form <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi mathvariant="italic">ε</mi><mo>=</mo><msup><mi mathvariant="italic">σ</mi><mn mathvariant="normal">3</mn></msup><mo>/</mo><mi>L</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="d1a454f1c5a50ebac918e85abcbffae6"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00003.svg" width="46pt" height="15pt" src="amt-18-1193-2025-ie00003.png"/></svg:svg></span></span>, where <span class="inline-formula"><i>σ</i></span> is half the spectral width corrected for non-turbulent effects, and <span class="inline-formula"><i>L</i></span> is assumed to be a constant or a fraction of the depth <span class="inline-formula"><i>D</i></span> of the convective boundary layer (CBL). The main results are the following: (1) For the deepest CBLs (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>max</mo><mo>(</mo><mi>D</mi><mo>)</mo><mo>></mo><mo>∼</mo><mn mathvariant="normal">1.0</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="74pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="f35d4d5bf3eba68013ccd5499722234f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00004.svg" width="74pt" height="12pt" src="amt-18-1193-2025-ie00004.png"/></svg:svg></span></span> km) that develop under high atmospheric pressure, the time–height cross-sections of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M12" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">DS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="6303a479bec3aa3a297c0a2fc9023517"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00005.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00005.png"/></svg:svg></span></span> and <span class="inline-formula"><i>ε</i><sub>DL</sub></span> show very consistent patterns and do not show any substantial gaps in the transition region of 300–400 m when <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">DS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="99944765097f316553f0903a76c724e9"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00006.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00006.png"/></svg:svg></span></span> is evaluated with <span class="inline-formula"><i>L</i>∼70</span> m, which is found to be about one-tenth of the average of the CBL depth (<span class="inline-formula"><i>L</i>∼0.1<i>D</i></span>). (2) Hourly mean <span class="inline-formula"><i>ε</i><sub>DL</sub></span> averaged over the [100–300] m height range is on average about twice the hourly mean <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M18" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">TS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="06acdaa63b127355fee38a93502522c4"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00007.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00007.png"/></svg:svg></span></span> averaged over the [400–500] m height range when <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M19" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>D</mi><mo>></mo><mo>∼</mo><mn mathvariant="normal">1.0</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="bd74489f43ac34ca8ed46fa25c6fe69f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00008.svg" width="46pt" height="10pt" src="amt-18-1193-2025-ie00008.png"/></svg:svg></span></span> km. (3) Hourly mean <span class="inline-formula"><i>ε</i><sub>DL</sub></span> averaged over the [100–300] m height range and hourly mean <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M21" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">DS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="b7168c5cde330e477a552370c5ce60b2"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00009.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00009.png"/></svg:svg></span></span> averaged over the [400–500] m height range with <span class="inline-formula"><i>L</i>∼0.1<i>D</i></span> are identical on average. Consistent with the fact that <span class="inline-formula"><i>ε</i></span> is expected to decrease slightly with height in the mixed layer, results (2) and (3) imply an uncertainty as to the exact value of the <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M24" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>L</mi><mo>/</mo><mi>D</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="23pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="7f7a3c178d855b237cdbf2fb0ae49128"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00010.svg" width="23pt" height="14pt" src="amt-18-1193-2025-ie00010.png"/></svg:svg></span></span> ratio: <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M25" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>∼</mo><mn mathvariant="normal">0.1</mn><mi>D</mi><mo><</mo><mi>L</mi><mo><</mo><mo>∼</mo><mn mathvariant="normal">0.2</mn><mi>D</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="99pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="0c2920cfcad5fdbd3b1308e542f44a1f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00011.svg" width="99pt" height="10pt" src="amt-18-1193-2025-ie00011.png"/></svg:svg></span></span>. We have also studied in detail the case of a shallow (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M26" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>D</mi><mo><</mo><mo>∼</mo><mn mathvariant="normal">0.6</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="d0123f3adf61ea73127a90c2450ae182"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00012.svg" width="46pt" height="10pt" src="amt-18-1193-2025-ie00012.png"/></svg:svg></span></span> km) convective boundary layer that developed under low atmospheric pressure and cloudy conditions. Despite the fact that hourly mean <span class="inline-formula"><i>ε</i><sub>DL</sub></span> averaged over the [100–300] m height range and hourly mean <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M28" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">TS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="4a9674608032cc97556f6dd65a1d1280"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00013.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00013.png"/></svg:svg></span></span> averaged over the [400–500] m height range show more significant discrepancies, maybe due to the different properties of the shallow convection, the time–height cross-sections of <span class="inline-formula"><i>ε</i><sub>DL</sub></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M30" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">ε</mi><mrow><mi mathvariant="normal">LQ</mi><mn mathvariant="normal">7</mn></mrow><mi mathvariant="normal">DS</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="18pt" class="svg-formula" dspmath="mathimg" md5hash="414f2727191f7ae4e816b9727929f771"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-18-1193-2025-ie00014.svg" width="24pt" height="18pt" src="amt-18-1193-2025-ie00014.png"/></svg:svg></span></span> show more consistent patterns and levels.</p> |
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| ISSN: | 1867-1381 1867-8548 |