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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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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).
    [1]

    饶瑞中 2022 红外与激光工程 51 22Google Scholar

    Rao R Z 2022 Infrared Laser Eng. 51 22Google Scholar

    [2]

    Beland R 1993 The Infrared and Electro-Optical Systems Handbook (Bellingham, WA: SPIE, Optical Engineering Press) pp211–224

    [3]

    吴晓庆, 曾宗泳, 马成胜, 翁宁泉, 肖黎明 1996 量子电子学报 13 385

    Wu X Q, Zeng Z Y, Ma C S, Weng N Q, Xiao L M 1996 Chin. J. Quantum Electron. 13 385

    [4]

    Coulman C, Vernin J, Coqueugniot Y, Caccia J 1988 Appl. Opt. 27 155Google Scholar

    [5]

    Dewan E M, Good R E, Beland B, Brown J 1993 A Model for Cn2 Profiles Using Radiosonde Rata (Phillips Laboratory, Hansom Air Force Base) PL-TR-93-2043

    [6]

    Trinquet H, Vernin J 2007 Environ. Fluid Mech. 7 397Google Scholar

    [7]

    Tatarski V I 1961 Wave Propagation in a Turbulent Medium (New York: McGraw-Hill)

    [8]

    Jumper G Y, Beland R R 2000 31st AIAA Plasmadynamics and Lasers Conference Denver, CO, USA, June 19–22, 2000, AIAA-2000-2355

    [9]

    Parenti R R, Sasiela R J 1994 J. Opt. Soc. Am. A 11 288Google Scholar

    [10]

    Battles F P, Murphy E A, Noonan J P 1988 Phys. Scripta 37 151Google Scholar

    [11]

    吴晓庆, 钱仙妹, 黄宏华, 汪平, 崔朝龙, 青春 2014 天文学报 55 144Google Scholar

    Wu X Q, Qian X M, Huang H H, Wang P, Cui C L, Qing C 2014 Acta Astron. Sin. 55 144Google Scholar

    [12]

    Good R, Beland R, Murphy E, Brown J, Dewan E 1988 SPIE 928 165

    [13]

    蔡俊, 李学彬, 詹国伟, 武鹏飞, 徐春燕, 青春, 吴晓庆 2018 物理学报 67 014206Google Scholar

    Cai J, Li X B, Zhan G W, Wu P F, Xu C Y, Qing C, Wu X Q 2018 Acta Phys. Sin. 67 014206Google Scholar

    [14]

    Han Y J, Wu X Q, Luo T, Qing C, Yang Q K, JinX M, Liu N N, Wu S, Su C D 2020 J. Opt. Soc. Am. A 37 995Google Scholar

    [15]

    Beland R R, Brown J H, Good R E, Murphy E A 1985 Optical Turbulence Characterization of AMOS Report AFGL-TR-88-xxxx

    [16]

    Tyson R K 1996 Appl. Opt. 35 3640

    [17]

    程知, 侯再红, 靖旭, 李菲, 陆茜茜, 于龙昆 2013 红外与激光工程 42 1562

    Cheng Z, Hou Z H, Jing X, Li F, Lu Q Q, Yu L K 2013 Infrared Laser Eng. 42 1562

    [18]

    Cheng Z, Tan F F, Jing X, He F, Qin L A, Hou Z H 2017 Chin. Opt. Lett. 15 020101Google Scholar

    [19]

    Balaley B, Peterson V L 1981 J. Appl. Meteor. 20 266Google Scholar

  • 图 1  湍流模式$ C_T^2 $, $ C_n^2 $, $ \rho $$(P/T^2)^2$的廓线

    Figure 1.  Profiles of $ C_T^2 $, $ C_n^2 $, $ \rho $ and $(P/T^2)^2$ by models.

    图 2  5个实验点$ C_n^2 $实测和拟合廓线的比较

    Figure 2.  Comparison of $ C_n^2 $ measured and fitting profiles of five sites.

    图 3  5实验点$ C_T^2 $, $ C_n^2 $ , $ \rho $$(P/T^2)^2$的廓线

    Figure 3.  Profiles of $ C_T^2 $, $ C_n^2 $ , $ \rho $ and $(P/T^2)^2$ by measured in five sites.

    图 4  大柴旦各单次探空$ C_n^2 $廓线积分值$ {r_0} $与平均廓线积分值的比对

    Figure 4.  Comparison between $ {r_0} $ of each sounding profile and $ {r_0} $ of fitting profle in Dachaidan.

    图 5  气象雷达和探空测量的低平流层$ C_n^2 $递减率随纬度的变化(*表示用气象雷达测量, #表示微温探空, 数据来自文献[10, 19])

    Figure 5.  Variation of $ C_n^2 $ lapse rate of low stratosphere with latitude measured by meteorological rada and thermosonde (*refers to meteorological radar measurement, # refers to thermosonde, data are from Ref. [10, 19]).

    表 1  几种有代表性的$ C_n^2 $廓线模式简介

    Table 1.  Brief introduction of several typical $ C_n^2 $ profile models.

    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
    SLC3.0620 (相对高度)几何平均光闪烁亚热带海洋
    大气湍流
    AFGL AMOS3.0630 (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 I1.2430 (海拔高度)算术平均探空低对流层风速
    下沙漠型湍流
    DownLoad: CSV

    表 2  模式廓线计算的$ {r_0} $, $ {\varepsilon _{{\text{FWHM}}}} $, $ {\theta _0} $, $ {\tau _0} $, $ \overline h $$ \overline V $

    Table 2.  The $ {r_0} $, $ {\varepsilon _{{\text{FWHM}}}} $, $ {\theta _0} $, $ {\tau _0} $, $ \overline h $ and $ \overline V $ calculated by $ C_n^2 $ models.

    $ {r_0} $/cm$ {\varepsilon _{{\text{FWHM}}}} $/μrad$ {\theta _0} $/μrad$ {\tau _0} $/ms$ \overline h $/m (AGL)$ \overline V $/(m·s–1)
    AFGL night8.95.5212.25.72260.74.9
    AFGL day7.36.714.43.55191.46.5
    AFGL sunrise15.33.215.35.39016.99.1
    H-V (5/7)5.09.846.91.92271.98.4
    CLEAR I night11.34.338.514.84179.12.4
    修正CLEAR I5.68.776.58.22684.22.1
    DownLoad: CSV

    表 3  模式中各大气层$ {r_0} $(i)对整层$ {r_0} $贡献占比

    Table 3.  Integrated contribution of coherence length from each atmosphere layer.

    AFGL nightAFGL dayAFGL sunriseH-V (5/7)CLEAR I night
    SL/%BL/%FA/%SL/%BL/%FA/%SL/%BL/%FA/%SL/%BL/%FA/%SL/%BL/%FA/%
    11.081.37.740.336.722.93.343.852.930.458.610.950.412.137.4
    DownLoad: CSV

    表 4  模式中各大气层等晕角$ {\theta _0} $(i)对整层等晕角$ {\theta _0} $贡献占比

    Table 4.  Integrated contribution of isoplanatic angle from each atmosphere layer.

    AFGL nightAFGL dayAFGL sunriseH-V (5/7)CLEAR I night
    SL/%BL/%FA/%SL/%BL/%FA/%SL/%BL/%FA/%SL/%BL/%FA/%SL/%BL/%FA/%
    0.06.593.50.00.499.60.00.799.30.03.396.60.41.797.4
    DownLoad: CSV

    表 5  修正的CLEAR I夜晚模式表达式

    Table 5.  Modified CLEAR I night model.

    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 ≤ 2.132.13 < h ≤ 10.3410.34 < h ≤ 301.23 < h ≤ 2.132.13 < h ≤ 10.3410.34 < h ≤ 30
    a = –10.7025a = –16.2897a = –17.0577a = –9.7025a = –16.0897a = –16.6577
    b = –4.3507b = 0.0335b = –0.0449b = –4.3507b = 0.0435b = –0.0449
    c = 0.8141c = –0.0134c = –0.0005c = 0.6541c = –0.0134c = –0.0005
    d = 0.6181d = 0.1981
    e = 15.5617e = 15.5617
    f = 3.4666f = 3.4666
    DownLoad: CSV

    表 6  湍流模式各大气层$ C_T^2 $, $ C_n^2 $ , $ \rho $$(P/T^2)^2$的递减率

    Table 6.  Drop-off rate of $ C_T^2 $, $ C_n^2 $, $ \rho $ and $(P/T^2)^2$ in each atmosphere layer.

    $ {\text{DR}}(C_T^2) $$ {\text{DR}}(C_n^2) $$ {\text{DR}}(\rho ) $ ${\text{DR} }((P/T^2)^2)$
    SLBLFASLBLFASLBLFASLBLFA
    AFGL night9.6211.37–0.6110.3012.050.850.430.440.700.680.691.46
    AFGL day67.1514.84–0.8867.8315.530.580.430.440.700.680.691.46
    AFGL sunrise5.015.28–0.545.695.970.920.430.440.700.680.691.46
    H-V (5/7)41.9810.770.7642.6211.422.160.420.430.690.640.651.40
    CLEAR I17.361.72–0.6917.932.260.760.390.390.690.570.541.45
    修正 CLEAR I22.393.22–0.7222.963.760.730.390.390.690.570.541.45
    DownLoad: CSV

    表 7  外场探空实验基本信息

    Table 7.  Basic information of field thermosonde.

    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°E323732.45178
    拉萨29.39°N, 91.08°E366031.194711
    大柴旦37.44°N, 95.20°E318337.00121325
    茂名21.27°N, 111.18°E1135.567411
    荣成36.46°N, 122.11°E8031.377613
    DownLoad: CSV

    表 8  5个测量点算术平均拟合的$ C_n^2 $廓线公式系数

    Table 8.  Coefficient of $ C_n^2 $ formula fitted by arithmetic average of five sites.

    abcdfig
    高美古$ 1 \times {10^{ - 40}} $33.310.393$ 6.2 \times {10^{ - 17}} $6.45$ 1.95 \times {10^{ - 15}} $0.0871
    拉萨$ 2.29 \times {10^{ - 22}} $9.101.227$ 6.62 \times {10^{ - 17}} $10.468$ 2.50 \times {10^{ - 16}} $0.0247
    大柴旦$ 4.45 \times {10^{ - 18}} $3.591.81$ 3.88 \times {10^{ - 17}} $13.24$ 7.14 \times {10^{ - 16}} $0.0459
    茂名$ 5.65 \times {10^{ - 20}} $5.462.31$ 2.12 \times {10^{ - 16}} $5.02$ 1.4 \times {10^{ - 15}} $0.305
    荣成$ 3.24 \times {10^{ - 24}} $13.200.767$ 1.58 \times {10^{ - 16}} $7.37$ 5.68 \times {10^{ - 15}} $0.0073
    DownLoad: CSV

    表 9  实测$ C_n^2 $廓线的校正后拟合决定系数(Radj-Square)

    Table 9.  Adjusted R square of fitting $ C_n^2 $ profile.

    高美古拉萨大柴旦茂名荣成
    $ C_n^2/{m^{ - 2/3}} $0.7730.7980.8340.7040.874
    DownLoad: CSV

    表 10  5实验点算术平均和几何平均廓线计算的$ {r_0} $, $ {\varepsilon _{{\text{FWHM}}}} $, $ {\theta _0} $, $ {\tau _0} $, $ \overline h $$ \overline V $

    Table 10.  The $ {r_0} $, $ {\varepsilon _{{\text{FWHM}}}} $, $ {\theta _0} $, $ {\tau _0} $, $ \overline h $ and $ \overline V $ calculated by $ C_n^2 $ profiles from arithmetic average and geometric average in five sites.

    $ {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11.018.24.52.75.210.91.63.06.6745.26822.219.1
    拉萨6.49.87.75.11.72.81.72.711.53311.06311.911.5
    大柴旦6.614.97.53.32.04.80.92.210.1729.65922.221.8
    茂名3.17.615.76.50.82.00.61.512.99311.77517.315.9
    荣成5.39.19.25.41.83.50.71.59.4548.17923.019.7
    DownLoad: CSV

    表 11  5实验点各大气层$ C_T^2 $, $ C_n^2 $以及$ \rho $$(P/T^2)^2$廓线的递减率

    Table 11.  Drop-off rate of $ C_T^2 $, $ C_n^2 $ , $ \rho $ and $(P/T^2)^2$ in each atmosphere layer of five sites.

    算术平均$ {\text{DR}}(C_T^2) $$ {\text{DR}}(C_n^2) $$ {\text{DR}}(\rho ) $${\text{DR} }((P/T^2)^2)$
    SLBLFASLBLFASLBLFASLBLFA
    高美古5.463.01–0.716.233.720.950.410.460.770.610.721.66
    拉萨9.95–0.80–0.6110.65–0.180.990.400.410.740.560.591.60
    大柴旦21.490.03–0.6722.870.610.970.410.400.760.640.551.64
    茂名18.072.94–0.9119.213.800.790.430.470.770.700.851.70
    荣成63.520.88–0.4866.591.710.990.440.470.710.710.821.47
    DownLoad: CSV

    表 12  模式廓线和实测廓线在低平流层的递减率

    Table 12.  Drop-off rate of model profile and measured profile in low stratosphere.

    ModelAFGL nightAFGL dayAFGL sunriseH-V(5/7)CLEAR I修正CLEAR高美古拉萨大柴旦茂名荣成
    ASL/km25—2925—2925—2917—2325—2925—2918—2618—2618—2618—2618—26
    DR($ C_n^2 $)0.850.580.922.160.760.730.950.990.970.790.99
    DR($ C_T^2 $)–0.61–0.88–0.540.76–0.69–0.72–0.71–0.61–0.67–0.91–0.48
    DR($ \rho $)0.700.700.700.690.690.690.770.740.760.770.71
    ${\text{DR} } \big(\big(P/T^2\big)^2\big)$ 1.461.461.461.401.451.451.661.601.641.701.47
    DownLoad: CSV
  • [1]

    饶瑞中 2022 红外与激光工程 51 22Google Scholar

    Rao R Z 2022 Infrared Laser Eng. 51 22Google Scholar

    [2]

    Beland R 1993 The Infrared and Electro-Optical Systems Handbook (Bellingham, WA: SPIE, Optical Engineering Press) pp211–224

    [3]

    吴晓庆, 曾宗泳, 马成胜, 翁宁泉, 肖黎明 1996 量子电子学报 13 385

    Wu X Q, Zeng Z Y, Ma C S, Weng N Q, Xiao L M 1996 Chin. J. Quantum Electron. 13 385

    [4]

    Coulman C, Vernin J, Coqueugniot Y, Caccia J 1988 Appl. Opt. 27 155Google Scholar

    [5]

    Dewan E M, Good R E, Beland B, Brown J 1993 A Model for Cn2 Profiles Using Radiosonde Rata (Phillips Laboratory, Hansom Air Force Base) PL-TR-93-2043

    [6]

    Trinquet H, Vernin J 2007 Environ. Fluid Mech. 7 397Google Scholar

    [7]

    Tatarski V I 1961 Wave Propagation in a Turbulent Medium (New York: McGraw-Hill)

    [8]

    Jumper G Y, Beland R R 2000 31st AIAA Plasmadynamics and Lasers Conference Denver, CO, USA, June 19–22, 2000, AIAA-2000-2355

    [9]

    Parenti R R, Sasiela R J 1994 J. Opt. Soc. Am. A 11 288Google Scholar

    [10]

    Battles F P, Murphy E A, Noonan J P 1988 Phys. Scripta 37 151Google Scholar

    [11]

    吴晓庆, 钱仙妹, 黄宏华, 汪平, 崔朝龙, 青春 2014 天文学报 55 144Google Scholar

    Wu X Q, Qian X M, Huang H H, Wang P, Cui C L, Qing C 2014 Acta Astron. Sin. 55 144Google Scholar

    [12]

    Good R, Beland R, Murphy E, Brown J, Dewan E 1988 SPIE 928 165

    [13]

    蔡俊, 李学彬, 詹国伟, 武鹏飞, 徐春燕, 青春, 吴晓庆 2018 物理学报 67 014206Google Scholar

    Cai J, Li X B, Zhan G W, Wu P F, Xu C Y, Qing C, Wu X Q 2018 Acta Phys. Sin. 67 014206Google Scholar

    [14]

    Han Y J, Wu X Q, Luo T, Qing C, Yang Q K, JinX M, Liu N N, Wu S, Su C D 2020 J. Opt. Soc. Am. A 37 995Google Scholar

    [15]

    Beland R R, Brown J H, Good R E, Murphy E A 1985 Optical Turbulence Characterization of AMOS Report AFGL-TR-88-xxxx

    [16]

    Tyson R K 1996 Appl. Opt. 35 3640

    [17]

    程知, 侯再红, 靖旭, 李菲, 陆茜茜, 于龙昆 2013 红外与激光工程 42 1562

    Cheng Z, Hou Z H, Jing X, Li F, Lu Q Q, Yu L K 2013 Infrared Laser Eng. 42 1562

    [18]

    Cheng Z, Tan F F, Jing X, He F, Qin L A, Hou Z H 2017 Chin. Opt. Lett. 15 020101Google Scholar

    [19]

    Balaley B, Peterson V L 1981 J. Appl. Meteor. 20 266Google Scholar

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Metrics
  • Abstract views:  2695
  • PDF Downloads:  86
  • 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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