Analysis of atmospheric optical turbulence model— methods and progress

Wu Xiao-Qing; Yang Qi-Ke; Huang Hong-Hua; Qing Chun; Hu Xiao-Dan; Wang Ying-Jian

doi:10.7498/aps.72.20221986

Abstract

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

Authors and contacts

1.
Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China
2.
Advanced Laser Technology Laboratory of Anhui Province, Hefei 230037, China
3.
Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Wu Xiao-Qing, xqwu@aiofm.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 91752103, 41576185), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. CXJJ-19S028).

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References

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Cited By

图 1 不同大气稳定度下模式估算不确定度

Figure 1. The uncertainty of $ C_n^2 $ estimated by model under different stability parameter.

DownLoad: Full-Size Img PowerPoint

图 2 一维边界层模式估算的合肥地区近地面层$ C_n^2 $随季节的日变化

Figure 2. Seasonal and diurnal variation of $ C_n^2 $ at surface layer in Hefei area estimated by one-dimensional boundary layer model.

DownLoad: Full-Size Img PowerPoint

图 3 中尺度气象模式预报$ C_n^2 $流程图

Figure 3. Flow chart of Forecasting $ C_n^2 $ With mesoscale numerical model.

DownLoad: Full-Size Img PowerPoint

图 4 AGA-BP 神经网络结构

Figure 4. AGA-BP neural network architecture.

DownLoad: Full-Size Img PowerPoint

图 5 三种方法$ C_n^2 $估算值与实测值的比对结果

Figure 5. Comparison results of estimated and measured $ C_n^2 $ of three methods.

DownLoad: Full-Size Img PowerPoint

图 6 SA-BP 神经网络的结构图

Figure 6. SA-BP neural network architecture.

DownLoad: Full-Size Img PowerPoint

图 7 SA-BP 神经网络算法流程图

Figure 7. Block diagram of the SA-BP neural network.

DownLoad: Full-Size Img PowerPoint

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

Figure 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°.

DownLoad: Full-Size Img PowerPoint

图 9 南极昆仑站整层视宁度估算与实测比较(实测视宁度数据来自文献[55])　(图9(b)是平均风速廓线, (d)是平均气温廓线, (f)是视宁度的统计分布)

Figure 9. Comparison of seeing estimated and measured of whole layer at Kunlun station, Antarctica (The seeing data measured from literature [55]).

DownLoad: Full-Size Img PowerPoint

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

DownLoad: CSV

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

DownLoad: CSV

[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 069201 Google Scholar Wu X Q, Yang Q K, Huang H H, Qing C, Hu X D, Wang Y J 2023 Acta Phys. Sin. 72 069201 Google Scholar
[4]	张兆顺, 崔桂香, 许春晓 2002 力学与实践 24 1 Google Scholar Zhang Z S, Cui G X, Xu C X 2002 Mech. Eng. 24 1 Google Scholar
[5]	吴晓庆 2017 激光与光电子学进展 54 010001 Google Scholar Wu X Q 2017 Laser Optoelectron. Prog. 54 010001 Google Scholar
[6]	Coulman C E, Andre J C, Lacarrere P, Guillingham P R 1986 Publ. Astron. Soc. Pac. 98 376 Google Scholar
[7]	Masciadri E, Vernin J, Bougeault P 1999 Astron. Astrophys. Suppl. Ser. 137 185 Google Scholar
[8]	Lascaux F, Masciadri E, Hagelin S 2010 Mon. Not. R. Astron. Soc. 403 1714 Google Scholar
[9]	Wyngaard J C, Izumi Y, Collins S A 1971 J. Opt. Soc. Am. 61 1646 Google Scholar
[10]	AndreasE L 1988 J. Opt. Soc. Am. 5 481 Google Scholar
[11]	Davidson K L, Schacher G E, Fairall C W, Goroch A K 1981 Appl. Opt. 20 2919 Google 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 1192 Google 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 2152 Google Scholar
[17]	Walters D L, Kunkel K E 1981 J. Opt. Soc. Am. 71 397 Google 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 758809 Google Scholar
[21]	Andrews L C, Phillips R L, Crabbs R, Wayne D, Leclerc T, Sauer P 2012 Proc. SPIE 8238 82380F Google Scholar
[22]	吴晓庆, 朱行听, 黄宏华, 胡顺星 2012 光学学报 32 0701004 Google Scholar Wu X Q, Zhu X T, Huang H H, Hu S X 2012 Acta Opt. Sin. 32 0701004 Google 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 039201 Google Scholar Wu X Q, Tian Q G, Jin X M, Jiang P, Qing C, Cai J, Zhou H Y 2017 Acta Phys. Sin. 66 039201 Google Scholar
[24]	吴晓庆, 王英俭, 曾宗泳, 马成胜, 袁仁民 2002 气象学报 60 1 Google Scholar Wu X Q, Wang Y J, Zeng Z Y, Ma C S, Yuan R M 2002 Acta Meteorol. Sin. 60 1 Google Scholar
[25]	Burk S D 1980 J. Appl. Meteor. 19 562 Google 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 138 453 Google 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 13303 Google Scholar
[30]	Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533 Google Scholar
[31]	Wang Y, Basu S 2016 Opt. Lett. 41 2334 Google Scholar
[32]	Su C D, Wu X Q, Luo T, Wu S, Qing C 2020 Appl. Opt. 59 3699 Google 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. 22 469 Google 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 1414 Google 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. 27 155 Google Scholar
[42]	Basu S 2015 Opt. Lett. 40 4130 Google 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 081002 Google 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 081002 Google Scholar
[45]	Wu S, Su C D, Wu X Q, Luo T, Li X B 2020 Publ. Astron. Soc. Pac. 132 084501 Google 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 061009 Google Scholar Qing C, Wu X Q, Li X B, Huang H H, Cai J 2015 High Power Laser Part. Beams 27 061009 Google 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 0913001 Google Scholar Qing C, Wu X Q, Li X B, Zhu W Y, Rao R Z, Mei H P 2015 Chin. J. Lasers 42 0913001 Google 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 0501001 Google 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 0501001 Google 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 3430 Google Scholar
[51]	Travouillon T, Ashley M C B, Burton M G, Storey J W V, Loewenstein R F 2003 Astron. Astrophys. 400 1163 Google Scholar
[52]	Lawrence J S, Ashley M C B, Tokovinin A, Travouillon T 2004 Nature 431 278 Google Scholar
[53]	Agabi A, Aristidi E, Azouit M, Fossat E, Martin F, Sadibekova T, Vernin J, Ziad A 2006 PASP 118 344 Google 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. 499 955 Google Scholar
[55]	Ma B, Shang Z H, Hu Y, Hu K L, Jiang P 2020 Nature 583 771 Google 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 20424 Google 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 4084 Google 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 1483 Google 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 44000 Google 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 35238 Google Scholar

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Vol. 72, Issue 4 - 2023-02-20

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