华南热带气旋相关物理量场的线性及非线性统计分析研究

谭金凯; 刘合香; 陈燕璇

doi:10.16032/j.issn.1004-4965.2017.01.013

华南热带气旋相关物理量场的线性及非线性统计分析研究

doi: 10.16032/j.issn.1004-4965.2017.01.013

广西师范学院数学与统计科学学院，广西南宁 530023

基金项目:

国家自然科学基金 41665006

国家自然科学基金 41465003

国家自然科学基金 11561009

广西科学研究与技术开发项目 1355010-8

广西科学研究与技术开发项目桂科合1599005-2-13

广西研究生教育创新计划项目 YCSZ2015185

详细信息

通讯作者:
刘合香, 女, 山东省人, 教授, 研究方向为：概率统计、数学模型、自然灾害风分析。E-mail: hx_post@163.com

中图分类号: P444
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出版历程
- 收稿日期: 2015-08-03
- 修回日期: 2016-07-28
- 刊出日期: 2017-02-01

THE LINEAR AND NONLINEAR STATISTICAL STUDY OF WESTERN PACIFIC PHYSICAL FIELD WITH TROPICAL CYCLONES IN SOUTH CHINA

College of Mathematics and Statistics Sciences, Guangxi Teachers Education University, Nanning 530023, China

摘要

摘要: 选取西太平洋海平面温度场、海平面气压场、500 hPa位势高度场作为物理因子场，并普查计算1949—2013年影响我国华南地区的热带气旋的年均频数、年均最低气压、年均最大风速作为相关物理量场。对因子场分别应用主成分分析 (PCA) 与核主成分分析 (KPCA) 算法进行主成分提取，在此基础上，对因子场的前六主成分进行功率谱估计与凝聚谱分析。最后，利用典型相关分析 (CCA) 与核典型相关分析 (KCCA) 算法对因子场与物理量场进行典型相关分析。结果表明，基于非线性的KPCA算法提取出西太平洋物理因子场前六成分的解释方差贡献率，均高于PCA算法；海温场、海压场、高度场的第一成分各自存在大概18年的周期性振荡变化，同时，在周期为2~3年的范围内，这三者的振荡频率的互相关性最强；而因子场与物理量场的非线性典型相关系数，明显高于线性典型相关系数。
- 热带气旋 /
- 主成分 /
- 谱估计 /
- 周期 /
- 典型相关
Abstract: Western Pacific sea surface temperatures (SST), sea level pressure (SLP), 500 hPa geopotential height (HGT) were selected into a physical factors field, and the average frequency of each TC in the south of China, values of average annual lowest air pressure, and annual maximum wind speed were used as a physical field that were surveyed and calculated for the time from 1949 to 2013. Principal component analysis (PCA) and kernel principal component analysis (KPCA) algorithms were used to extract principal component factor fields. On this basis, the first six games of the principal components were taken for power spectrum estimation and cohesion spectrum analysis. Finally, canonical correlation analysis (CCA) and kernel canonical correlation analysis (KCCA) algorithms were used for canonical correlation analysis on the factor field and physical field. The results show that based on KPCA the explained variance contribution rates of the first six components are higher than that with PCA. The first components of SST, SLP and HGT fields have periodic fluctuations of about 18 years. Meanwhile, for the fluctuation of 2 to 3 years, the cross correlation of oscillation frequency is the strongest. The nonlinear canonical correlation coefficient is higher than the linear coefficient.
- tropical cyclone /
- principal component /
- power spectrum estimation /
- period /
- canonical correlation

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图 1 SST、SLP、HGT的前六个主成分解释方差贡献率

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图 2 SST、SLP、HGT的前六主成分功率谱估计曲线

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图 3 CCA与KCCA的变量散点图及回归曲线

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表 1 SST、SLP、HGT的前六个主成分解释方差贡献率 (%)

主成分数		1	2	3	4	5	6
SST	KPCA	73.55	12.44	8.08	3.44	1.34	1.16
SST	PCA	70.97	12.00	7.84	3.42	1.25	1.08
SLP	KPCA	86.32	6.61	4.24	1.07	0.97	0.79
SLP	PCA	85.05	5.80	4.26	0.98	0.86	0.64
HGT	KPCA	83.14	8.64	3.87	2.33	1.33	0.68
HGT	PCA	82.93	8.48	3.81	2.29	1.30	0.56

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表 2 SST、SLP、HGT的功率谱估计

L T		0 ∞	1 18	2 9	3 6	4 4.5	5 3.6	6 3	7 2.6	8 2.3	9 2
	P_k	0.203 8	0.274 0	0.110 4	0.070 7	0.046 3	0.039 4	0.057 4	0.071 6	0.081 9	0.044 1
SST	P	0.203 7	0.274 0	0.110 4	0.070 7	0.046 3	0.039 4	0.057 4	0.071 6	0.082 0	0.044 1
	${\tilde P}$	0.372 1	0.333 9	0.257 7	0.190 9	0.144 9	0.115 3	0.096 7	0.085 5	0.079 4	0.077 5
	P_k	0.175 6	0.230 3	0.094 0	0.097 1	0.1174	0.106 3	0.068 8	0.042 6	0.044 0	0.023 4
SLP	P	0.175 5	0.230 2	0.094 0	0.097 3	0.117 4	0.106 3	0.068 8	0.042 6	0.044 0	0.023 4
	${\tilde P}$	0.381 1	0.339 8	0.259 0	0.189 8	0.143 0	0.113 3	0.094 7	0.083 6	0.077 6	0.075 8
	P_k	0.166 4	0.217 6	0.094 2	0.090 8	0.099 5	0.094 1	0.078 8	0.075 1	0.060 8	0.022 1
HGT	P	0.172 9	0.220 3	0.093 3	0.100 7	0.110 2	0.095 5	0.070 2	0.062 9	0.053 2	0.020 3
	${\tilde P}$	0.404 3	0.354 5	0.261 7	0.186 7	0.138 2	0.108 3	0.089 9	0.079 0	0.073 3	0.071 4

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表 3 因子场凝聚谱估计

T		18	9	6	4.5	3.6	3	2.6	2.3	2
	R_k	0.223 8	0.036 2	0.037 7	0.003 8	0.304 4	0.510 1	0.6119	0.474 1	0.446 2
SST-SLP	R	0.223 6	0.035 9	0.037 4	0.003 7	0.304 0	0.510 4	0.611 5	0.474 0	0.446 9
	F	3.031 7	0.587 5	0.271 5	0.166 4	5.646 0	12.76 4	20.728	13.502	12.26 5
	R_k	0.490 6	0.170 6	0.232 4	0.133 3	0.199 5	0.219 9	0.2939	0.107 9	0.001 0
SST-HGT	R	0.529 0	0.149 6	0.236 5	0.146 2	0.266 8	0.340 4	0.415 8	0.180 4	0.025 0
	F	15.218	2.810 0	5.409 9	3.652 3	6.120 1	10.290	15.406	6.188 0	2.016 4
	R_k	0.292 5	0.285 1	0.496 6	0.718 8	0.793 3	0.565 0	0.397 6	0.304 0	0.243 4
SLP-HGT	R	0.374 1	0.359 2	0.571 7	0.759 9	0.8120	0.646 6	0.479 8	0.324 9	0.251 5
	F	7.385 2	6.736 7	14.627	32.701	51.304	25.460	14.958	5.269 8	1.310 2

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表 4 KCCA与CCA的典型相关系数及检验

主成分		1	2	3
CCA	r	0.602 6	0.199 5	0.052 2
CCA	χ²	29.427	2.579 5	0.162 4
KCCA	r	0.638 2	0.456, 2	0.367 1
KCCA	χ²	53.621	22.495	8.613 0

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