\begin{document}$ C_n^2 $\end{document}) profile is an important parameter to evaluate the turbulence effects. This paper summarizes several representative \begin{document}$ C_n^2 $\end{document} profile models and analyzes the data using balloon-borne microthermal probes at five sites i.e. Gaomeigu, Lhasa, Dachaidan, Maoming, and Rongcheng. The atmospheirc optical parameters are calculated, such as coherence length, seeing, isoplanatie angle, coherence time, equivalent height, equivalent wind speed, drop-off rate and integrated contribution from each atmosphere layer. The formulas of five sites are developed by fitting the arithmetic average of measurements. Several troubling basic problems such as suspicion the H-V (5/7) model, the model developed by arithmetic average or geometric average, the problem whether there is a uniform lapse rate in the low stratosphere, are discussed and solved. The modified CLEAR I night model is given."> Study of <inline-formula><tex-math id="M2">\begin{document}${\boldsymbol C_{\boldsymbol n}^{\boldsymbol 2}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20221985_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20221985_M2.png"/></alternatives></inline-formula> profile model by atmospheric optical turbulence model - 必威体育下载

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    Study of ${\boldsymbol C_{\boldsymbol n}^{\boldsymbol 2}}$ profile model by atmospheric optical turbulence model

    Wu Xiao-Qing, Yang Qi-Ke, Huang Hong-Hua, Qing Chun, Hu Xiao-Dan, Wang Ying-Jian
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    • Owing to the existence of atmospheric turbulence, a series of turbulence effects such as phase fluctuation and light intensity scintillation will occur when the electromagnetic waves propagates through the atmosphere, which seriously affects the performance of the electro-optic system, resulting in the difficulty of astronomical observation. The atmospheric refractive index structure constant ( $ C_n^2 $ ) profile is an important parameter to evaluate the turbulence effects. This paper summarizes several representative $ C_n^2 $ profile models and analyzes the data using balloon-borne microthermal probes at five sites i.e. Gaomeigu, Lhasa, Dachaidan, Maoming, and Rongcheng. The atmospheirc optical parameters are calculated, such as coherence length, seeing, isoplanatie angle, coherence time, equivalent height, equivalent wind speed, drop-off rate and integrated contribution from each atmosphere layer. The formulas of five sites are developed by fitting the arithmetic average of measurements. Several troubling basic problems such as suspicion the H-V (5/7) model, the model developed by arithmetic average or geometric average, the problem whether there is a uniform lapse rate in the low stratosphere, are discussed and solved. The modified CLEAR I night model is given.
          Corresponding author:Wu Xiao-Qing,xqwu@aiofm.ac.cn
        • Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 91752103, 41576185) and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. CXJJ-19S028).
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      • 模式名称 模式种类 海拔高度/km 有效高度/km 平均方式 数据来源 代表性
        夜晚 白天 日出
        SLC 3.06 20 (相对高度) 几何平均 光闪烁 亚热带海洋
        大气湍流
        AFGL AMOS 3.06 30 (海拔高度) 算术平均 探空 亚热带海洋
        大气湍流
        H-V(5/7) 含有高空风速的$ C_n^2 $参数公式 实际海拔
        高度/km
        24 (海拔高度) 算术平均 光闪烁、探空 中纬度大气湍流
        CLEAR I 1.24 30 (海拔高度) 算术平均 探空 低对流层风速
        下沙漠型湍流
        DownLoad: CSV

        $ {r_0} $/cm $ {\varepsilon _{{\text{FWHM}}}} $/μrad $ {\theta _0} $/μrad $ {\tau _0} $/ms $ \overline h $/m (AGL) $ \overline V $/(m·s–1)
        AFGL night 8.9 5.52 12.2 5.7 2260.7 4.9
        AFGL day 7.3 6.71 4.4 3.5 5191.4 6.5
        AFGL sunrise 15.3 3.21 5.3 5.3 9016.9 9.1
        H-V (5/7) 5.0 9.84 6.9 1.9 2271.9 8.4
        CLEAR I night 11.3 4.33 8.5 14.8 4179.1 2.4
        修正CLEAR I 5.6 8.77 6.5 8.2 2684.2 2.1
        DownLoad: CSV

        AFGL night AFGL day AFGL sunrise H-V (5/7) CLEAR I night
        SL/% BL/% FA/% SL/% BL/% FA/% SL/% BL/% FA/% SL/% BL/% FA/% SL/% BL/% FA/%
        11.0 81.3 7.7 40.3 36.7 22.9 3.3 43.8 52.9 30.4 58.6 10.9 50.4 12.1 37.4
        DownLoad: CSV

        AFGL night AFGL day AFGL sunrise H-V (5/7) CLEAR I night
        SL/% BL/% FA/% SL/% BL/% FA/% SL/% BL/% FA/% SL/% BL/% FA/% SL/% BL/% FA/%
        0.0 6.5 93.5 0.0 0.4 99.6 0.0 0.7 99.3 0.0 3.3 96.6 0.4 1.7 97.4
        DownLoad: CSV

        边界层内    $ \lg (C_n^2)= a + bh + c{h^2} $   对流层内  $ \lg (C_n^2)= a + bh + c{h^2} $
        低平流层下   $\lg (C_n^2)= a + bh + c{h^2} + d\exp \big\{ { - 0.5 { {[{ {(h - e)} }/{f}]}^2} } \big\}$
        CLEAR I night模式/km 修正CLEAR I night模式/km
        1.23 <h≤ 2.13 2.13 <h≤ 10.34 10.34 <h≤ 30 1.23 <h≤ 2.13 2.13 <h≤ 10.34 10.34 <h≤ 30
        a= –10.7025 a= –16.2897 a= –17.0577 a= –9.7025 a= –16.0897 a= –16.6577
        b= –4.3507 b= 0.0335 b= –0.0449 b= –4.3507 b= 0.0435 b= –0.0449
        c= 0.8141 c= –0.0134 c= –0.0005 c= 0.6541 c= –0.0134 c= –0.0005
        d= 0.6181 d= 0.1981
        e= 15.5617 e= 15.5617
        f= 3.4666 f= 3.4666
        DownLoad: CSV

        $ {\text{DR}}(C_T^2) $ $ {\text{DR}}(C_n^2) $ $ {\text{DR}}(\rho ) $ ${\text{DR} }((P/T^2)^2)$
        SL BL FA SL BL FA SL BL FA SL BL FA
        AFGL night 9.62 11.37 –0.61 10.30 12.05 0.85 0.43 0.44 0.70 0.68 0.69 1.46
        AFGL day 67.15 14.84 –0.88 67.83 15.53 0.58 0.43 0.44 0.70 0.68 0.69 1.46
        AFGL sunrise 5.01 5.28 –0.54 5.69 5.97 0.92 0.43 0.44 0.70 0.68 0.69 1.46
        H-V (5/7) 41.98 10.77 0.76 42.62 11.42 2.16 0.42 0.43 0.69 0.64 0.65 1.40
        CLEAR I 17.36 1.72 –0.69 17.93 2.26 0.76 0.39 0.39 0.69 0.57 0.54 1.45
        修正 CLEAR I 22.39 3.22 –0.72 22.96 3.76 0.73 0.39 0.39 0.69 0.57 0.54 1.45
        DownLoad: CSV

        地点 经纬度 海拔高度/m 平均最大探测
        海拔高度/km
        早晨有效
        探空数
        夜晚有效
        探空数
        总有效
        探空数
        高美古 26.41°N, 100.01°E 3237 32.45 1 7 8
        拉萨 29.39°N, 91.08°E 3660 31.19 4 7 11
        大柴旦 37.44°N, 95.20°E 3183 37.00 12 13 25
        茂名 21.27°N, 111.18°E 11 35.56 7 4 11
        荣成 36.46°N, 122.11°E 80 31.37 7 6 13
        DownLoad: CSV

        a b c d f i g
        高美古 $ 1 \times {10^{ - 40}} $ 33.31 0.393 $ 6.2 \times {10^{ - 17}} $ 6.45 $ 1.95 \times {10^{ - 15}} $ 0.0871
        拉萨 $ 2.29 \times {10^{ - 22}} $ 9.10 1.227 $ 6.62 \times {10^{ - 17}} $ 10.468 $ 2.50 \times {10^{ - 16}} $ 0.0247
        大柴旦 $ 4.45 \times {10^{ - 18}} $ 3.59 1.81 $ 3.88 \times {10^{ - 17}} $ 13.24 $ 7.14 \times {10^{ - 16}} $ 0.0459
        茂名 $ 5.65 \times {10^{ - 20}} $ 5.46 2.31 $ 2.12 \times {10^{ - 16}} $ 5.02 $ 1.4 \times {10^{ - 15}} $ 0.305
        荣成 $ 3.24 \times {10^{ - 24}} $ 13.20 0.767 $ 1.58 \times {10^{ - 16}} $ 7.37 $ 5.68 \times {10^{ - 15}} $ 0.0073
        DownLoad: CSV

        高美古 拉萨 大柴旦 茂名 荣成
        $ C_n^2/{m^{ - 2/3}} $ 0.773 0.798 0.834 0.704 0.874
        DownLoad: CSV

        $ {r_0} $/cm $ {\varepsilon _{{\text{FWHM}}}} $/μrad $ {\theta _0} $/μrad $ {\tau _0} $/ms $ \overline h $/km (AGL) $ \overline V $/(m·s–1)
        算术 几何 算术 几何 算术 几何 算术 几何 算术 几何 算术 几何
        高美古 11.0 18.2 4.5 2.7 5.2 10.9 1.6 3.0 6.674 5.268 22.2 19.1
        拉萨 6.4 9.8 7.7 5.1 1.7 2.8 1.7 2.7 11.533 11.063 11.9 11.5
        大柴旦 6.6 14.9 7.5 3.3 2.0 4.8 0.9 2.2 10.172 9.659 22.2 21.8
        茂名 3.1 7.6 15.7 6.5 0.8 2.0 0.6 1.5 12.993 11.775 17.3 15.9
        荣成 5.3 9.1 9.2 5.4 1.8 3.5 0.7 1.5 9.454 8.179 23.0 19.7
        DownLoad: CSV

        算术平均 $ {\text{DR}}(C_T^2) $ $ {\text{DR}}(C_n^2) $ $ {\text{DR}}(\rho ) $ ${\text{DR} }((P/T^2)^2)$
        SL BL FA SL BL FA SL BL FA SL BL FA
        高美古 5.46 3.01 –0.71 6.23 3.72 0.95 0.41 0.46 0.77 0.61 0.72 1.66
        拉萨 9.95 –0.80 –0.61 10.65 –0.18 0.99 0.40 0.41 0.74 0.56 0.59 1.60
        大柴旦 21.49 0.03 –0.67 22.87 0.61 0.97 0.41 0.40 0.76 0.64 0.55 1.64
        茂名 18.07 2.94 –0.91 19.21 3.80 0.79 0.43 0.47 0.77 0.70 0.85 1.70
        荣成 63.52 0.88 –0.48 66.59 1.71 0.99 0.44 0.47 0.71 0.71 0.82 1.47
        DownLoad: CSV

        Model AFGL night AFGL day AFGL sunrise H-V(5/7) CLEAR I 修正CLEAR 高美古 拉萨 大柴旦 茂名 荣成
        ASL/km 25—29 25—29 25—29 17—23 25—29 25—29 18—26 18—26 18—26 18—26 18—26
        DR($ C_n^2 $) 0.85 0.58 0.92 2.16 0.76 0.73 0.95 0.99 0.97 0.79 0.99
        DR($ C_T^2 $) –0.61 –0.88 –0.54 0.76 –0.69 –0.72 –0.71 –0.61 –0.67 –0.91 –0.48
        DR($ \rho $) 0.70 0.70 0.70 0.69 0.69 0.69 0.77 0.74 0.76 0.77 0.71
        ${\text{DR} } \big(\big(P/T^2\big)^2\big)$ 1.46 1.46 1.46 1.40 1.45 1.45 1.66 1.60 1.64 1.70 1.47
        DownLoad: CSV
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      Metrics
      • Abstract views:4143
      • PDF Downloads:114
      • Cited By:0
      Publishing process
      • Received Date:17 October 2022
      • Accepted Date:03 January 2023
      • Available Online:07 January 2023
      • Published Online:20 March 2023

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