-
分层是大气湍流特别是高空湍流显著特征. 在某一固定高度真实光学湍流
$ C_n^2 $ 值在平均值上有1—2个量级甚至更大的起伏. 以观测数据建立的湍流廓线模式, 是一个统计平均的结果. 既不能代表某次实际大气湍流廓线的分层特征, 也没有预报功能, 不能完全满足光学工程需求. 受限于计算机的容量和速度, 无法通过DNS (direct numerical simulation)以及LES (large eddy simulation)求解Navier-Stokes方程来预报光学湍流, 解决方案是通过中尺度天气数值预报模式MM5/WRF, 预报出常规气象参数, 再由湍流参数化方案计算出$ C_n^2 $ . 本文介绍了近地面层、边界层和自由大气层$ C_n^2 $ 预报方法和研究成果, 从湍流动能预报方程和温度脉动方差预报方程详细推导出Tatarski公式, 归纳出该公式所隐含的物理意义和适用条件. 重点介绍了神经网络预报$ C_n^2 $ 和$ C_n^2 $ 估算和预报方法在南极天文选址的最新研究进展. 分析了以实验数据拟合的经验模式、建立在Kolmogorov湍流理论基础之上含有常规气象参数的参数模式、与中尺度气象模式有关的预报模式、基于数据驱动的神经网络方法等不同模式的特点和差异. 强调Kolmogorov湍流理论是现有大气光学湍流参数模式的理论基础.-
关键词:
- 大气光学湍流 /
- 湍流模式 /
- Tatarski公式 /
- 神经网络预报$ C_n^2 $ /
- 南极天文选址
Stratification is a significant characteristic of atmospheric turbulence, especially high-altitude turbulence. At a fixed height, the real optical turbulence value fluctuates by 1–2 orders of magnitude or even greater on the average value. The turbulence profile model based on the observed data is a statistical average result. It can neither represent the stratification characteristics of an actual atmospheric turbulence profile nor have the prediction function, and can not fully meet the demand of optical engineering. Owing to the limitation of the capacity and speed of the computer, it is impossible to solve the Navier Stokes equation through direct numerical simulation (DNS) and large eddy simulation (LES) to predict the optical turbulence. The solution is to predict the conventional gas parameters through the mesoscale weather numerical prediction model MM5/ WRF, and then calculate the turbulence parameters through the turbulence parameterization scheme. In this paper, the prediction methods and research results of$ C_n^2 $ in surface layer,boundary layer and free atmosphere layer are introduced. Tatarski formula is derived in detail from the turbulence kinetic energy prediction equation and the temperature fluctuation variance prediction equation, and the physical meaning and applicable conditions of the formula are summarized. The latest research progress of neural network prediction and Antarctic astronomical site selection is mainly introduced. The characteristics and differences among different models, such as the empirical model fitted with experimental data, the parameter model with conventional meteorological parameters based on Kolmogorov turbulence theory, the prediction model related to mesoscale meteorological model, and the neural network method based on data driving and so on, are analyzed. It is emphasized that Kolmogorov turbulence theory is the theoretical basis of the existing atmospheric optical turbulence parameter models.-
Keywords:
- atmospheric optical turbulence /
- turbulence model /
- Tatarski formula /
- neural network prediction of $ C_n^2 $ /
- astronomical site selection
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[2] 吴晓庆, 马成胜, 曾宗泳 1996 量子电子学 13 385
Wu X Q, Ma C S, Zeng Z Y 1996 Chin. J. Quantum Electron. 13 385
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[11] Davidson K L, Schacher G E, Fairall C W, Goroch A K 1981 Appl. Opt. 20 2919Google Scholar
[12] Rachele H, Tunick A 1992 Proceedings, Battlefield Atmospherics Conference, White Sands Missile Range New Mexico, SPIE 1688 251
[13] Tunick A D 1998 U. S. Army Research Laboratory, ARL-TR-1615
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[17] Walters D L, Kunkel K E 1981 J. Opt. Soc. Am. 71 397Google Scholar
[18] Kukharets V P, Tsvang L R 1980 Izv. Atmos. Oceanic Phys. 16 73
[19] Murphy E A, Dewan E M, Sheldon S M 1985 in Adaptive Optics, Proc. SPIE 551 156
[20] Andrews L C, Phillips R L, Crabbs R, Wayne D, Leclerc T, Sauer P 2010 Proc. SPIE 7588 758809Google Scholar
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[22] 吴晓庆, 朱行听, 黄宏华, 胡顺星 2012 光学学报 32 0701004Google Scholar
Wu X Q, Zhu X T, Huang H H, Hu S X 2012 Acta Opt. Sin. 32 0701004Google Scholar
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Wu X Q, Wang Y J, Zeng Z Y, Gong Z 2002 High Power Laser Part. Beams 14 819
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[28] 许利明 2008 硕士论文 (合肥: 中国科学院大学)
Xu L M 2008 M. S. Thesis (Hefei: University of Chinese Academy of Sciences) (in Chinese)
[29] Qing C, Wu X Q, Li X B, Zhu W Y, Qiao C H, Rao R Z, Mei H P 2016 Opt. Express 24 13303Google Scholar
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[33] 吴晓庆 2019 安徽师范大学学报自然科学版 (特约稿) 42 511
Wu X Q 2019 J. Anhui Normal Univ. (Nat. Sci.) 42 511
[34] 吴晓庆 2014 安徽师范大学学报(自然科学版) (特约稿) 37 511
Wu X Q 2014 J. Anhui Normal Univ. (Nat. Sci.) 37 511
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[40] Ruggiero F H, DeBenedictis D A 2002 HPCMP Users Group Conference Austin, Texas, January 13–14, 2002 p11
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[42] Basu S 2015 Opt. Lett. 40 4130Google Scholar
[43] 胡晓丹, 吴晓庆, 青春 2019 极地研究 31 301
Hu X D, Wu X Q, Qing C 2019 Chin. J. Polar Res. 31 301
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[46] Wu S, Wu X Q, Su C D, YangQ K, Xu J Y, Luo T, Huang C, Qing C 2021 Opt. Express 29 12455
[47] 青春, 吴晓庆, 李学彬, 黄宏华, 蔡俊 2015 强激光与粒子束 27 061009Google Scholar
Qing C, Wu X Q, Li X B, Huang H H, Cai J 2015 High Power Laser Part. Beams 27 061009Google Scholar
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Qing C, Wu X Q, Li X B, Zhu W Y, Rao R Z, Mei H P 2015 Chin. J. Lasers 42 0913001Google Scholar
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Qing C, Wu X Q, Li X B, Zhu W Y, Huang Y B, Rao R Z, Cai J 2016 Acta Opt. Sin. 36 0501001Google Scholar
[50] Su C D, Wu X Q, Wu S, Yang Q K, Han Y J, Qing C, Luo T, Liu Y 2021 Mon. Not. R. Astron. Soc. 506 3430Google Scholar
[51] Travouillon T, Ashley M C B, Burton M G, Storey J W V, Loewenstein R F 2003 Astron. Astrophys. 400 1163Google Scholar
[52] Lawrence J S, Ashley M C B, Tokovinin A, Travouillon T 2004 Nature 431 278Google Scholar
[53] Agabi A, Aristidi E, Azouit M, Fossat E, Martin F, Sadibekova T, Vernin J, Ziad A 2006 PASP 118 344Google Scholar
[54] Aristidi E, Fossat E, Agabi A, Mékarnia D, Jeanneaux F, Bondoux E, Challita Z, Ziad A, Vernin J, Trinquet H 2009 Astron. Astrophys. 499 955Google Scholar
[55] Ma B, Shang Z H, Hu Y, Hu K L, Jiang P 2020 Nature 583 771Google Scholar
[56] Wu X Q, Tian Q G, Jiang P, Chai B, Qing C, Cai J, Jin X M, Zhou H Y 2015 Adv. Polar Sci. 26 305
[57] Qing C, Wu X Q, Huang H H, Tian Q G, Zhu W Y, Rao R Z, Li X B 2016 Opt. Express 24 20424Google Scholar
[58] Qing C, Li X B, Wu X Q, TianQ G, Liu D, Rao R Z, Zhu W Y 2018 Astron. J. 155 13
[59] Yang Q K, Wu X Q, Han Y J, Qing C 2021 Appl. Opt. 60 4084Google Scholar
[60] Yang Q K, Wu X Q, Wu S, Han Y J, Su C D, Zhang S T, Qing C 2021 J. Opt. Soc. Am. 38 1483Google Scholar
[61] Yang Q K, Wu X Q, Han Y J, Qing C, Wu S, Su C D, Wu P F, Luo T, Zhang S T 2021 Opt. Express 29 44000Google Scholar
[62] Yang Q K, Wu X Q, Han Y J, Qing C, Wu S, Su C D, Wu P F, Zhang S T 2021 Opt. Express 29 35238Google Scholar
-
图 8 Polar WRF模拟的2014年1月30日(UTC)南极高原2 m高度处
$C_n^2$ 的日变化. 等高线表示地形高度(m), 太阳图标引出的红色箭头表示太阳光照射方向, 黑色五角星表示泰山站位置, 灰色同心圆表示间隔为5°的纬度Fig. 8. Polar WRF simulated diurnal evolution of
$C_n^2$ at 2 m above model surface of Antarctic Plateau on 30 January, 2014 (UTC), represented by colors.The contours represent the terrain height(m). There are red arrows drawn with a tail at the center of the Sun symbol; the direction of each arrow indicates the direction of sunlight. The black stars show the location of the Taishan Station. The interval of the gray concentric circles representing the latitudes is 5°.表 1 三种
$ C_n^2 $ 估算方法的比对结果Table 1. Comparison results of
$ C_n^2 $ by three estimation methods.Gradient AGA-BP Polar WRF RMSE 0.41 0.29 0.40 ${R_{xy}}$ 0.61 0.90 0.67 表 2 6条实测
$C_n^2$ 廓线与SA-BP预测和HMNSP99估算的$C_n^2$ 廓线定量比对(RMSE/$ {R_{xy}} $ )Table 2. Quantitative comparison of 6 measured
$ C_n^2 $ profiles with prediction by SA-BP and by HMNSP99 (RMSE/$ {R_{xy}} $ ).气球编号 探空日期 探空时间 HMNSP99 (RMSE/$ {R_{xy}} $) SA-BP (RMSE/$ {R_{xy}} $) 1 13/08/2020 20:03 1.30/0.65 0.49/0.72 2 14/08/2020 20:11 1.24/0.61 0.67/0.72 3 15/08/2020 20:05 1.34/0.43 0.75/0.77 4 20/08/2020 07:25 0.76/0.47 0.46/0.71 5 21/08/2020 07:17 0.74/0.76 0.43/0.80 6 22/08/2020 07:10 0.76/0.50 0.36/0.83 -
[1] Beland R 1993 The Infrared and ElectroOpticalSystems Handbook, SPIE (Bellingham, WA: Optical Engineering Press) p211
[2] 吴晓庆, 马成胜, 曾宗泳 1996 量子电子学 13 385
Wu X Q, Ma C S, Zeng Z Y 1996 Chin. J. Quantum Electron. 13 385
[3] 吴晓庆, 杨期科, 黄宏华, 青春, 胡晓丹, 王英俭 2023 物理学报 72 069201Google Scholar
Wu X Q, Yang Q K, Huang H H, Qing C, Hu X D, Wang Y J 2023 Acta Phys. Sin. 72 069201Google Scholar
[4] 张兆顺, 崔桂香, 许春晓 2002 力学与实践 24 1Google Scholar
Zhang Z S, Cui G X, Xu C X 2002 Mech. Eng. 24 1Google Scholar
[5] 吴晓庆 2017 激光与光电子学进展 54 010001Google Scholar
Wu X Q 2017 Laser Optoelectron. Prog. 54 010001Google Scholar
[6] Coulman C E, Andre J C, Lacarrere P, Guillingham P R 1986 Publ. Astron. Soc. Pac. 98 376Google Scholar
[7] Masciadri E, Vernin J, Bougeault P 1999 Astron. Astrophys. Suppl. Ser. 137 185Google Scholar
[8] Lascaux F, Masciadri E, Hagelin S 2010 Mon. Not. R. Astron. Soc. 403 1714Google Scholar
[9] Wyngaard J C, Izumi Y, Collins S A 1971 J. Opt. Soc. Am. 61 1646Google Scholar
[10] AndreasE L 1988 J. Opt. Soc. Am. 5 481Google Scholar
[11] Davidson K L, Schacher G E, Fairall C W, Goroch A K 1981 Appl. Opt. 20 2919Google Scholar
[12] Rachele H, Tunick A 1992 Proceedings, Battlefield Atmospherics Conference, White Sands Missile Range New Mexico, SPIE 1688 251
[13] Tunick A D 1998 U. S. Army Research Laboratory, ARL-TR-1615
[14] Hill R J 1980 J. Opt. Soc. Am. 70 1192Google Scholar
[15] Wyngaard J C 1973 On Surface Layer Turbulence, in Workshop of Micrometeorology (Boston: American Meteorological Society) pp101–149
[16] Kaimal J C, Wyngaard J C, Haugen D A, Cote O R, Izumi Y 1976 J. Atmos. Sci. 33 2152Google Scholar
[17] Walters D L, Kunkel K E 1981 J. Opt. Soc. Am. 71 397Google Scholar
[18] Kukharets V P, Tsvang L R 1980 Izv. Atmos. Oceanic Phys. 16 73
[19] Murphy E A, Dewan E M, Sheldon S M 1985 in Adaptive Optics, Proc. SPIE 551 156
[20] Andrews L C, Phillips R L, Crabbs R, Wayne D, Leclerc T, Sauer P 2010 Proc. SPIE 7588 758809Google Scholar
[21] Andrews L C, Phillips R L, Crabbs R, Wayne D, Leclerc T, Sauer P 2012 Proc. SPIE 8238 82380FGoogle Scholar
[22] 吴晓庆, 朱行听, 黄宏华, 胡顺星 2012 光学学报 32 0701004Google Scholar
Wu X Q, Zhu X T, Huang H H, Hu S X 2012 Acta Opt. Sin. 32 0701004Google Scholar
[23] 吴晓庆, 田启国, 金鑫淼, 姜鹏, 青春, 蔡俊, 周宏岩 2017 物理学报 66 039201Google Scholar
Wu X Q, Tian Q G, Jin X M, Jiang P, Qing C, Cai J, Zhou H Y 2017 Acta Phys. Sin. 66 039201Google Scholar
[24] 吴晓庆, 王英俭, 曾宗泳, 马成胜, 袁仁民 2002 气象学报 60 1Google Scholar
Wu X Q, Wang Y J, Zeng Z Y, Ma C S, Yuan R M 2002 Acta Meteorol. Sin. 60 1Google Scholar
[25] Burk S D 1980 J. Appl. Meteor. 19 562Google Scholar
[26] 吴晓庆, 王英俭, 曾宗泳, 龚知本 2002 强激光与粒子束 14 819
Wu X Q, Wang Y J, Zeng Z Y, Gong Z 2002 High Power Laser Part. Beams 14 819
[27] Cheinet S, Beljaars A 2011 Boundary-Layer Meteorol 138 453Google Scholar
[28] 许利明 2008 硕士论文 (合肥: 中国科学院大学)
Xu L M 2008 M. S. Thesis (Hefei: University of Chinese Academy of Sciences) (in Chinese)
[29] Qing C, Wu X Q, Li X B, Zhu W Y, Qiao C H, Rao R Z, Mei H P 2016 Opt. Express 24 13303Google Scholar
[30] Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533Google Scholar
[31] Wang Y, Basu S 2016 Opt. Lett. 41 2334Google Scholar
[32] Su C D, Wu X Q, Luo T, Wu S, Qing C 2020 Appl. Opt. 59 3699Google Scholar
[33] 吴晓庆 2019 安徽师范大学学报自然科学版 (特约稿) 42 511
Wu X Q 2019 J. Anhui Normal Univ. (Nat. Sci.) 42 511
[34] 吴晓庆 2014 安徽师范大学学报(自然科学版) (特约稿) 37 511
Wu X Q 2014 J. Anhui Normal Univ. (Nat. Sci.) 37 511
[35] Corrsin S 1951 J. Appl. Phys. 22 469Google Scholar
[36] Dewan E M 1980 Optical Turbulence Forecasting: A turorial Air Force Geophysics Laboratory Technical Report No. AFGL-TR-80-0030, ADA 086863
[37] Horne J D 2004 M. S. Thesis (Monterey, CA: Naval Postgraduate School) p163
[38] Hodur R M 1997 Mon. Weather Rev. 125 1414Google Scholar
[39] Dewan E M, Good R E, Beland B, Brown J 1993 Environmental Research Paper (Phillips Laboratory, Hansom Air Force Base) No. 1121 PL-TR-93-2043, ADA 279399
[40] Ruggiero F H, DeBenedictis D A 2002 HPCMP Users Group Conference Austin, Texas, January 13–14, 2002 p11
[41] Coulman C, Vernin J, Coqueugniot Y, Caccia J 1988 Appl. Opt. 27 155Google Scholar
[42] Basu S 2015 Opt. Lett. 40 4130Google Scholar
[43] 胡晓丹, 吴晓庆, 青春 2019 极地研究 31 301
Hu X D, Wu X Q, Qing C 2019 Chin. J. Polar Res. 31 301
[44] 胡晓丹, 苏昶东, 罗涛, 青春, 孙刚, 刘庆, 李学彬, 朱文越, 吴晓庆 2019 强激光与粒子束 31 081002Google Scholar
Hu X D, Su C D, Luo T, Qing C, Sun G, Liu Q, Li X B, Zhu W Y, Wu X Q 2019 High Power Laser Part. Beams 31 081002Google Scholar
[45] Wu S, Su C D, Wu X Q, Luo T, Li X B 2020 Publ. Astron. Soc. Pac. 132 084501Google Scholar
[46] Wu S, Wu X Q, Su C D, YangQ K, Xu J Y, Luo T, Huang C, Qing C 2021 Opt. Express 29 12455
[47] 青春, 吴晓庆, 李学彬, 黄宏华, 蔡俊 2015 强激光与粒子束 27 061009Google Scholar
Qing C, Wu X Q, Li X B, Huang H H, Cai J 2015 High Power Laser Part. Beams 27 061009Google Scholar
[48] 青春, 吴晓庆, 李学彬, 朱文越, 饶瑞中, 梅海平 2015 中国激光 42 0913001Google Scholar
Qing C, Wu X Q, Li X B, Zhu W Y, Rao R Z, Mei H P 2015 Chin. J. Lasers 42 0913001Google Scholar
[49] 青春, 吴晓庆, 李学彬, 朱文越, 黄印博, 饶瑞中, 蔡俊 2016 光学学报 36 0501001Google Scholar
Qing C, Wu X Q, Li X B, Zhu W Y, Huang Y B, Rao R Z, Cai J 2016 Acta Opt. Sin. 36 0501001Google Scholar
[50] Su C D, Wu X Q, Wu S, Yang Q K, Han Y J, Qing C, Luo T, Liu Y 2021 Mon. Not. R. Astron. Soc. 506 3430Google Scholar
[51] Travouillon T, Ashley M C B, Burton M G, Storey J W V, Loewenstein R F 2003 Astron. Astrophys. 400 1163Google Scholar
[52] Lawrence J S, Ashley M C B, Tokovinin A, Travouillon T 2004 Nature 431 278Google Scholar
[53] Agabi A, Aristidi E, Azouit M, Fossat E, Martin F, Sadibekova T, Vernin J, Ziad A 2006 PASP 118 344Google Scholar
[54] Aristidi E, Fossat E, Agabi A, Mékarnia D, Jeanneaux F, Bondoux E, Challita Z, Ziad A, Vernin J, Trinquet H 2009 Astron. Astrophys. 499 955Google Scholar
[55] Ma B, Shang Z H, Hu Y, Hu K L, Jiang P 2020 Nature 583 771Google Scholar
[56] Wu X Q, Tian Q G, Jiang P, Chai B, Qing C, Cai J, Jin X M, Zhou H Y 2015 Adv. Polar Sci. 26 305
[57] Qing C, Wu X Q, Huang H H, Tian Q G, Zhu W Y, Rao R Z, Li X B 2016 Opt. Express 24 20424Google Scholar
[58] Qing C, Li X B, Wu X Q, TianQ G, Liu D, Rao R Z, Zhu W Y 2018 Astron. J. 155 13
[59] Yang Q K, Wu X Q, Han Y J, Qing C 2021 Appl. Opt. 60 4084Google Scholar
[60] Yang Q K, Wu X Q, Wu S, Han Y J, Su C D, Zhang S T, Qing C 2021 J. Opt. Soc. Am. 38 1483Google Scholar
[61] Yang Q K, Wu X Q, Han Y J, Qing C, Wu S, Su C D, Wu P F, Luo T, Zhang S T 2021 Opt. Express 29 44000Google Scholar
[62] Yang Q K, Wu X Q, Han Y J, Qing C, Wu S, Su C D, Wu P F, Zhang S T 2021 Opt. Express 29 35238Google Scholar
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