大气光学湍流模式研究—方法和进展

吴晓庆; 杨期科; 黄宏华; 青春; 胡晓丹; 王英俭

doi:10.7498/aps.72.20221986

摘要

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:

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

作者及机构信息

1.
中国科学院合肥物质科学研究院安徽光学精密机械研究所, 中国科学院大气光学重点实验室, 合肥　230031

2.
先进激光技术安徽省实验室, 合肥　230037

3.
中国科学技术大学研究生院科学岛分院, 合肥　230026

通信作者: 吴晓庆, xqwu@aiofm.ac.cn

基金项目: 国家自然科学基金(批准号: 91752103, 41576185)和中国科学院战略性先导科技专项(A类) (批准号: CXJJ-19S028)资助的课题.

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).

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 不同大气稳定度下模式估算不确定度

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

下载: 全尺寸图片幻灯片

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

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

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图 3 中尺度气象模式预报$ C_n^2 $流程图

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

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图 4 AGA-BP 神经网络结构

Fig. 4. AGA-BP neural network architecture.

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图 5 三种方法$ C_n^2 $估算值与实测值的比对结果

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

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图 6 SA-BP 神经网络的结构图

Fig. 6. SA-BP neural network architecture.

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图 7 SA-BP 神经网络算法流程图

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

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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°.

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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)

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

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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

下载: 导出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

下载: 导出CSV

map

[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
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[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
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[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
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[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
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[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
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[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
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