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 - H. Luce; M. Yabuki (Atmospheric Measurement Techniques)
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 ε 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 W from mean W time series (TS method) was applied to DL (εDL). The same method was also applied to 1 min LQ7 data (<msubsup>εLQ7TS</msubsup><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>​​​​​​​) 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 (<msubsup>εLQ7DS</msubsup><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>) from the 10 min average profiles. We tested recently proposed models of the form ε=σ3/L<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>, where σ is half the spectral width corrected for non-turbulent effects, and L is assumed to be a constant or a fraction of the depth D of the convective boundary layer (CBL). The main results are the following: (1) For the deepest CBLs (max⁡(D)>∼1.0<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> km) that develop under high atmospheric pressure, the time–height cross-sections of <msubsup>εLQ7DS</msubsup><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> and εDL show very consistent patterns and do not show any substantial gaps in the transition region of 300–400 m when <msubsup>εLQ7DS</msubsup><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> is evaluated with L∼70 m, which is found to be about one-tenth of the average of the CBL depth (L∼0.1D). (2) Hourly mean εDL averaged over the [100–300] m height range is on average about twice the hourly mean <msubsup>εLQ7TS</msubsup><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> averaged over the [400–500] m height range when D>∼1.0<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> km. (3) Hourly mean εDL averaged over the [100–300] m height range and hourly mean <msubsup>εLQ7DS</msubsup><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> averaged over the [400–500] m height range with L∼0.1D are identical on average. Consistent with the fact that ε 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 L/D<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> ratio: ∼0.1D<L<∼0.2D<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>. We have also studied in detail the case of a shallow (D<∼0.6<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> km) convective boundary layer that developed under low atmospheric pressure and cloudy conditions. Despite the fact that hourly mean εDL averaged over the [100–300] m height range and hourly mean <msubsup>εLQ7TS</msubsup><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> 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 εDL and <msubsup>εLQ7DS</msubsup><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> show more consistent patterns and levels.