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In this paper, a near-infrared laser heterodyne spectrometer developed by the laboratory is used to investigate the inversion of greenhouse gas column concentration and approximately evaluate the system measurement errors based on the optimal estimation algorithm. Firstly, the spectral database and the calculation results from the reference forward model are compared with the ground-based FTIR results, thereby selecting the detection window, the corresponding laser and detector. Secondly, the optimal estimation concentration inversion algorithm based on the reference forward model is established, and the Levenberg-Marquardt (LM) iterative method is adopted to realize the inversion of the concentration and vertical distribution profile of atmospheric CO2 column in the whole layer, and the long-term observation comparative experiment is carried out to verify the feasibility of this algorithm. Finally, by simulating the selected detection window spectrum in different white noise, the approximate corresponding relationship between the system signal-noise-ratio (SNR) and CO2 column concentration measuring error is eventually obtained. This research is an indispensable theoretical calculation part of the detection system and will conduce to improving the application of laser heterodyne technology in atmospheric observations.
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Keywords:
- laser heterodyne /
- measuring error /
- the reference forward model /
- CO2 column concentration
[1] 向亮, 高庆先, 周锁铨, 陈永立 2009 气候变化研究进展 5 278
Google Scholar
Xiang L, Gao Q X, Zhou S Q, Chen Y L 2009 Adv. Clim. Change Res. 5 278
Google Scholar
[2] 邵君宜, 林兆祥, 刘林美, 龚威 2017 物理学报 66 104206
Google Scholar
Shao J Y, Lin Z X, Liu L M, Gong W 2017 Acta Phys. Sin. 66 104206
Google Scholar
[3] 吴军 2013 博士学位论文 (合肥: 中国科学技术大学)
Wu J 2013 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[4] Knorr W 2009 Geophys. Res. Lett. 36 L21710
Google Scholar
[5] 丁武文, 孙利群, 衣路英 2017 物理学报 66 100702
Google Scholar
Ding W W, Sun L Q, Yi L Y 2017 Acta Phys. Sin. 66 100702
Google Scholar
[6] 管林强, 邓昊, 姚路, 聂伟, 许振宇, 李想, 臧益鹏, 胡迈, 范雪丽, 杨晨光, 阚瑞峰 2019 物理学报 68 084204
Google Scholar
Guan L Q, Deng H, Yao L, Nie W, Xu Z Y, Li X, Zang Y P, Hu M, Fan X L, Yang C G, Kan R F 2019 Acta Phys. Sin. 68 084204
Google Scholar
[7] Guo X Q, Zheng F, Li C L, Yang X F, Li N, Liu S, Wei J L 2019 Opt. Lasers Eng. 115 243
Google Scholar
[8] Sun K, Chao X, Sur R, Goldenstein C S, Jeffries J B, Hanson R K 2013 Meas. Sci. Technol. 24 125203
Google Scholar
[9] Sun C Y, Cao Y, Chen J J, Wang J J, Cheng g, Wang G S, Gao X M 2020 Chin. Phys. B 29 010704
Google Scholar
[10] 王薇, 刘文清, 张天舒, 2014 光学学报 34 0130003
Google Scholar
Wang W, Liu W Q, Zhang T S 2014 Acta Optic. Sin. 34 0130003
Google Scholar
[11] Zhao Y J, Wexler A S, Hase F, Pan Y, Mitloehner F M 2016 J. Environ. Prot. 7 1719
Google Scholar
[12] Sonnabend G, Wirtz D, Frank Schmülling, Schieder R 2002 Appl. Opt. 41 2978
Google Scholar
[13] Weidmann D, Reburn W J, Smith K M 2007 Appl. Opt. 46 7162
Google Scholar
[14] Tsai T R, Rose R A, Weidmann D, Wysocki G 2012 Appl. Opt. 51 8779
Google Scholar
[15] Wang J, Wang G, Tan T, Zhu G, Sun C, Cao Z, Chen W, Gao X 2019 Opt. Express 27 9610
Google Scholar
[16] 张尚露, 黄印博, 卢兴吉, 曹振松, 戴聪明, 刘强, 高晓明, 饶瑞中, 王英俭 2019 光谱学与光谱分析 39 1317
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Zhang S L, Huang Y B, Lu X j, Cao Z S, Dai C M, Liu Q, Gao X M, Zhong R R, Wang Y J 2019 Spectrosc. Spect. Anal. 39 1317
Google Scholar
[17] Dudhia A 2017 J. Quant. Spectrosc. Radiat. Transfer 186 243
Google Scholar
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Google Scholar
[19] Rodgers C D 2000 Inverse Methods for Atmospheric Sounding: Theory and Practise (1st Ed.) (Singapore: World Scientific Publishing)
[20] Rodgers C D 1990 J. Geophys. Res. 95 5587
Google Scholar
[21] 石广玉 2007 大气辐射学 (北京: 科学出版社)
Shi G Y 2007 Atmospheric Radiology (Beijing: Science Press) (in Chinese)
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图 1 激光外差系统整体技术路线
Figure 1. Overall technical route of laser heterodyne system.
图 2 基于RFM模拟的正向透过率谱及所选探测窗口
Figure 2. Forward transmittance spectrum based on RFM simulation and selected detection window.
图 3 激光外差实验结果 (a) CO2的高分辨率的外差信号; (b) 实时跟踪的太阳光信号; (c) 激光器的DC信号
Figure 3. Experimental results of the laser heterodyne: (a) The high-resolution heterodyne signal of CO2; (b) the sunlight signal tracked in real time; (c) the DC signal of the laser.
图 4 波数偏移校准原理 (a) 参考信号与实验信号之间的波数偏移; (b) 计算波数偏移的过程, 插图为相关系数的结果
Figure 4. Principle of the wavenumber shift calibration: (a) Wavenumber shift between the reference signal and real signal; (b) the process of calculating the wavenumber shift. The inset shows the result of correlation coefficients.
图 7 LHR数据反演结果 (a) 实验和拟合LHR谱图以及迭代过程的收敛性 (插图); (b) 残差; (c) 和 (d)分别获取的CO2的先验和反演的垂直浓度分布图
Figure 7. Inversion results of LHR data: (a) Experimental and fitted LHR spectrogram and convergence of iterative process (illustration); (b) residue; (c) and (d) obtained prior and inversion vertical concentration profiles of CO2, respectively.
图 5 (a) 温度和 (b) 压力廓线
Figure 5. (a) Temperature and (b) pressure profiles.
图 6 数据反演流程图 VMR, 体积混合比; ILS, 仪器线形; LM, Levenberg–Marquardt
Figure 6. Data inversion flow chart. VMR, volume mixing ratio; ILS, instrument linear; LM, Levenberg–Marquardt.
图 8 (a) 2019年3月14日从11:00至13:00的
$X_{{\rm{CO}}_2} $ 的反演结果; (b)$X_{{\rm{CO}}_2} $ 的外差结果和GOSAT结果的时间序列Figure 8. (a) Retrieval results of the
$X_{{\rm{CO}}_2} $ versus time from 11:00 to 13:00 on March 14, 2019; (b) time series of the LHR results and GOSAT results of$X_{{\rm{CO}}_2}$ .
图 9 (a) 叠加0.05幅度的白噪声后的透过率谱; (b) 叠加5000次后透过率谱最低点的变化
Figure 9. (a) The transmittance spectrum after adding white noise with the amplitude of 0.05; (b) change range of the lowest point of transmittance spectrum after adding 5000 times.
图 10 白噪声幅度0.001变化到幅度0.050引起的
$3 \sigma $ , Max, Min和SNR的变化Figure 10. Changes of
$ 3{\rm{\sigma }} $ , Max, Min, and SNR caused by the white noise amplitude increasing from 0.001 to 0.050.
图 11 (a) 最小值与廓线变化关系; (b)柱总量变化与最小值关系
Figure 11. (a) The relationship between the minimum value and the change of profile; (b) the relationship between the change of column total and the minimum.
图 12 SNR与测量误差间的对应关系
Figure 12. The relationship between SNR and measurement error.
表 1 数据反演中使用的状态向量的定义
Table 1. Definition of the state vector used in the data retrieval.
状态
向量先验值 定义 x (CO2) 1 先验廓线的比例因子
(ECMWF) 45层.a a0 基线中a0、b0和c0的多项式系数由对预处理的LHR信号与模型结果(去除吸收部分后)的比值进行二阶多项式拟合得到. b b0 c c0 
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[1] 向亮, 高庆先, 周锁铨, 陈永立 2009 气候变化研究进展 5 278
Google Scholar
Xiang L, Gao Q X, Zhou S Q, Chen Y L 2009 Adv. Clim. Change Res. 5 278
Google Scholar
[2] 邵君宜, 林兆祥, 刘林美, 龚威 2017 物理学报 66 104206
Google Scholar
Shao J Y, Lin Z X, Liu L M, Gong W 2017 Acta Phys. Sin. 66 104206
Google Scholar
[3] 吴军 2013 博士学位论文 (合肥: 中国科学技术大学)
Wu J 2013 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[4] Knorr W 2009 Geophys. Res. Lett. 36 L21710
Google Scholar
[5] 丁武文, 孙利群, 衣路英 2017 物理学报 66 100702
Google Scholar
Ding W W, Sun L Q, Yi L Y 2017 Acta Phys. Sin. 66 100702
Google Scholar
[6] 管林强, 邓昊, 姚路, 聂伟, 许振宇, 李想, 臧益鹏, 胡迈, 范雪丽, 杨晨光, 阚瑞峰 2019 物理学报 68 084204
Google Scholar
Guan L Q, Deng H, Yao L, Nie W, Xu Z Y, Li X, Zang Y P, Hu M, Fan X L, Yang C G, Kan R F 2019 Acta Phys. Sin. 68 084204
Google Scholar
[7] Guo X Q, Zheng F, Li C L, Yang X F, Li N, Liu S, Wei J L 2019 Opt. Lasers Eng. 115 243
Google Scholar
[8] Sun K, Chao X, Sur R, Goldenstein C S, Jeffries J B, Hanson R K 2013 Meas. Sci. Technol. 24 125203
Google Scholar
[9] Sun C Y, Cao Y, Chen J J, Wang J J, Cheng g, Wang G S, Gao X M 2020 Chin. Phys. B 29 010704
Google Scholar
[10] 王薇, 刘文清, 张天舒, 2014 光学学报 34 0130003
Google Scholar
Wang W, Liu W Q, Zhang T S 2014 Acta Optic. Sin. 34 0130003
Google Scholar
[11] Zhao Y J, Wexler A S, Hase F, Pan Y, Mitloehner F M 2016 J. Environ. Prot. 7 1719
Google Scholar
[12] Sonnabend G, Wirtz D, Frank Schmülling, Schieder R 2002 Appl. Opt. 41 2978
Google Scholar
[13] Weidmann D, Reburn W J, Smith K M 2007 Appl. Opt. 46 7162
Google Scholar
[14] Tsai T R, Rose R A, Weidmann D, Wysocki G 2012 Appl. Opt. 51 8779
Google Scholar
[15] Wang J, Wang G, Tan T, Zhu G, Sun C, Cao Z, Chen W, Gao X 2019 Opt. Express 27 9610
Google Scholar
[16] 张尚露, 黄印博, 卢兴吉, 曹振松, 戴聪明, 刘强, 高晓明, 饶瑞中, 王英俭 2019 光谱学与光谱分析 39 1317
Google Scholar
Zhang S L, Huang Y B, Lu X j, Cao Z S, Dai C M, Liu Q, Gao X M, Zhong R R, Wang Y J 2019 Spectrosc. Spect. Anal. 39 1317
Google Scholar
[17] Dudhia A 2017 J. Quant. Spectrosc. Radiat. Transfer 186 243
Google Scholar
[18] Gordon I E, Rothman L S, Hill C, Kochanov R V, Tan Y, Bernath P F, Chance K V 2017 J. Quant. Spectrosc. Radiat. Transfer 203 3
Google Scholar
[19] Rodgers C D 2000 Inverse Methods for Atmospheric Sounding: Theory and Practise (1st Ed.) (Singapore: World Scientific Publishing)
[20] Rodgers C D 1990 J. Geophys. Res. 95 5587
Google Scholar
[21] 石广玉 2007 大气辐射学 (北京: 科学出版社)
Shi G Y 2007 Atmospheric Radiology (Beijing: Science Press) (in Chinese)
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