Analysis of Near Sea-Surface Optical Turbulence Characters Based on Hilbert-Huang Transform

Hanjiu Zhang; Gang Sun; Kun Zhang; Yang Wu; Feifei Wang; Xuebin Li; Shengcheng Cui; Qing Liu; Ningquan Weng

doi:10.3788/LOP202259.1201001

Laser & Optoelectronics Progress, Volume. 59, Issue 12, 1201001(2022)

Analysis of Near Sea-Surface Optical Turbulence Characters Based on Hilbert-Huang Transform

Hanjiu Zhang^1,2, Gang Sun^2、*, Kun Zhang^1,2, Yang Wu^1,2, Feifei Wang², Xuebin Li², Shengcheng Cui², Qing Liu², and Ningquan Weng^1,2

Author Affiliations

¹School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei 230026, Anhui , China

²Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, Anhui , China

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Figures & Tables(8)

$Instrument and Cn2 daily change. (a) Instrument installation environment; (b) daily change of refractive index structure constant on November 16, 2019$

Fig. 1. Instrument and $C_{n}^{2}$ daily change. (a) Instrument installation environment; (b) daily change of refractive index structure constant on November 16, 2019

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Fig. 2. IMF and IMF frequency spectra. (a) $C_{n}^{2}$ time series and corresponding IMF at noon on November 16, 2019; (b) IMF FFT frequency spectra

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Fig. 3. Relationship between m and T of IMF. (a) m-T; (b) m-lnT

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Fig. 4. IMF reconstruction with different scales and corresponding relation with original signal. (a)(b) Different IMF combinations; (c)(d) relation between reconstructed combination and original signal

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Fig. 5. Spectrum analysis. (a) Time-frequency-energy distribution of IMF obtained by HHT; (b) HHT marginal spectrum and FFT spectrum; (c) normalized marginal spectra of meteorological elements and $C_{n}^{2}$ in unstable layer condition; (d) as Fig.5(c) but in stable layer condition

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Table 1. Character analysis of each IMF

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Table 1. Character analysis of each IMF

Parameter	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	R
Correlation	0.67	0.43	0.33	0.27	0.26	0.15	0.10	0.02	0.13
Period number	246	119.5	60	29.5	11.5	5	2.5	1
Period /s	14.263	30.13	60	122.03	313.04	720	1440	3600
Energy /（10^-28·m^-4/9·s）	1.15	2.45	1.98	1.35	2.31	14.45	33.80	9.80	3.96
Mean energy /（10^-31·m^-4/9·s）	4.68	20.50	33.08	45.83	201.04	2890	13520	9800

Table 2. RMSE of IMF combinations in many days

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Table 2. RMSE of IMF combinations in many days

Combination	11.02	11.07	11.09	11.11	11.13	11.21	11.22	11.26
IMF2‒IMF9	0.043	0.118	0.152	0.211	0.041	0.069	0.040	0.073
IMF3‒IMF9	0.068	0.114	0.161	0.212	0.062	0.085	0.065	0.110
IMF4‒IMF9	0.079	0.140	0.177	0.246	0.083	0.095	0.071	0.129
IMF5‒IMF9	0.075	0.235	0.150	0.297	0.088	0.095	0.067	0.136
IMF6‒IMF9	0.071	0.153	0.142	0.297	0.086	0.094	0.068	0.136
IMF7‒IMF9	0.062	0.195	0.145	0.234	0.074	0.056	0.030	0.217

Table 3. Cross correlation of meteorological elements and $C_{n}^{2}$ marginal spectra

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Table 3. Cross correlation of meteorological elements and $C_{n}^{2}$ marginal spectra

Cross correlation coefficient	Daytime		Night
Cross correlation coefficient	All scales	log₁₀T≥2	All scales	log₁₀T≥2
R（ $C_{n}^{2}$ and humidity）	0.9012	0.8893	0.7493	0.4992
R（ $C_{n}^{2}$ and temperature）	0.8489	0.7350	0.7294	0.6102
R（ $C_{n}^{2}$ and wind speed）	0.8357	0.5520	0.7550	0.4554
R（temperature and wind speed）	0.9217	0.8534	0.9660	0.9609

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Hanjiu Zhang, Gang Sun, Kun Zhang, Yang Wu, Feifei Wang, Xuebin Li, Shengcheng Cui, Qing Liu, Ningquan Weng. Analysis of Near Sea-Surface Optical Turbulence Characters Based on Hilbert-Huang Transform[J]. Laser & Optoelectronics Progress, 2022, 59(12): 1201001

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