基于小波分析的我国台风风暴潮直接经济损失周期分析及预测

刘旭; 董剑希; 姜珊; 赵达君; 付翔; 王峥; 梁颖祺

doi:10.12284/hyxb2023109

基于小波分析的我国台风风暴潮直接经济损失周期分析及预测

doi: 10.12284/hyxb2023109

刘旭^{1, 2,},
董剑希¹,
姜珊¹,
赵达君³,
付翔¹,
王峥¹,
梁颖祺¹

1.
国家海洋环境预报中心，北京 100081
2.
北京林业大学经济管理学院，北京 100083
3.
新疆农业大学经济管理学院，新疆维吾尔自治区乌鲁木齐 830052

基金项目: 国家自然科学基金（41976221，41576029）；国家重点研发计划（2021YFB3900405）。

详细信息

作者简介:
刘旭（1986-），女，北京市人，博士，主要从事海洋灾害评估及系统分析。E-mail：fairyjujube@126.com

中图分类号: P458.1⁺24
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- 文章访问数: 208
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- 被引次数: 0
出版历程
- 收稿日期: 2022-08-31
- 修回日期: 2023-01-02
- 网络出版日期: 2023-08-08
- 刊出日期: 2023-07-01

Based on wavelet analysis of the direct economic loss of the typhoon storm surge in China cycle analysis and prediction

1.
National Marine Environmental Forecasting Center, Beijing 100081, China
2.
School of Economics & Management, Beijing Forestry University, Beijing 100083, China
3.
College of Economics and Management, Xinjiang Agricultural University, Urumqi 830052, China

摘要

摘要: 本文选取1989−2021年我国台风风暴潮直接经济损失统计数据，依据线性趋势法和Mann-Kendall非参数检验法进行分析，结果表明，32年间我国风暴潮灾害经济损失呈现显著下降趋势，整体呈厚尾分布特征，采用对数化处理后呈显著的正态分布特征。采用Morlet小波变换对我国台风风暴潮直接经济损失的周期变化规律进行分析，t检验结果显示，全域存在准两次高频振荡，1～2年及7～8年的周期振荡，但随时间变化年际周期逐渐缩短为3～5年，说明风暴潮经济损失序列存在高频振荡和多周期嵌套的低频振荡规律。在此基础上，采用Daubechies小波分解分离高频信号和低频信号，均方根误差和信噪比精度分析结果表明，当小波基设置消失矩为7，分解层数为2时，我国台风风暴潮直接经济损失时间序列具有最优分解重构效果。对各分解层进行小波系数平稳性检验和白噪声检验，建立的小波分解−ARMA组合模型的模拟精度和预测精度均优于传统的自回归移动平均模型和Fourier级数拓展模型，证明了小波分解法在我国台风风暴潮经济损失快速评估中具有可靠性和优越性。
- 风暴潮直接经济损失 /
- Mann-Kendall非参数检验 /
- Morlet小波变换 /
- Daubechies小波分解 /
- 自回归移动平均模型
Abstract: Based on the statistical data of direct economic losses of typhoon storm surge in China from 1989 to 2021, the economic losses of storm surge disasters in China during 32 years showed a significant downward trend, showing a thick-tailed distribution as a whole, and a normal distribution after logarithmic processing. The periodic changes of the direct economic losses of typhoon storm surge in China were analyzed by Morlet wavelet analysis method. According to the t-test, there were two quasi-high-frequency oscillations in the whole region, 1−2 years and 7−8 years oscillation , but the annual cycle gradually shortened to 3−5 years with the change of time. It indicated that the economic loss sequence of storm surge had high-frequency oscillation and multi-period nested low-frequency oscillation. On this basis, Daubechies wavelet decomposition was used to separate high frequency signal and low frequency signal. According to the results of root mean square error (RMSE) and signal-to-noise ratio, Daubechies wavelet base was set the vanishing moment is 7 and the number of decomposition layers is 2 for the direct economic loss time series of typhoon storm surges in China from 1989 to 2021, which had the optimal decomposition and reconstruction effect. Based on the results of stationarity test and white noise test of wavelet coefficients of each decomposition layer, the combined wavelet decomposed−ARMA model was established. The simulation accuracy and prediction accuracy were both better than that of single Autoregressive Integrated Moving Average model and Fourier series expansion model, which verified the reliability and superiority of wavelet decomposition method for rapid assessment of economic loss of typhoon storm surge in China.
- storm surge economic losses /
- Mann-Kendall nonparametric test /
- Morlet wavelet transform /
- Daubechies wavelet decomposition /
- autoregressive integrated moving average

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图 1 1989−2021年中国台风风暴潮直接经济损失时间序列

Fig. 1 Time series of direct economic losses of typhoon storm surges in China from 1989 to 2021

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图 2 频数分布

Fig. 2 Frequency distribution

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图 3 1989−2021年中国台风风暴潮直接经济损失周期分析图

a. 小波变换实部分布图；b. 小波能量谱图

Fig. 3 Cycle analysis of direct economic loss of typhoon storm surge in China from 1989 to 2021

a. Real part of wavelet transform; b. wavelet energy spectrum

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图 4 自相关性检验

Fig. 4 Autocorrelation test

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图 5 模型预测结果

Fig. 5 Model prediction results

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表 1 db2~db20小波分解重构信号误差

Tab. 1 Error of reconstructed signals by db2 to db20 wavelet decomposition

消失矩	harr	db4	db6	db8	db10	db12	db14	db16	db18	db20
均方根误差	234.1	84.4	76.9	151.4	187.8	133.5	1.3×10⁻⁹	1.3×10⁻⁹	1.3×10⁻⁹	1.3×10⁻⁹

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表 2 db7小波分解层数信噪比

Tab. 2 db7 wavelet decomposition layers signal-to-noise ratio

分解层数	1	2	3	4	5	6
信噪比	18.9	18.4	19.7	26.8	675.7	1291.8

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表 3 序列平稳性及白噪声显著性检验

Tab. 3 Series stationarity test and white noise significance test

检验方法	W1	V1	W2	V2	Y
ADF检验	0.01	0.01	0.01	0.01	0.01
PP检验	0.01	0.01	0.03	0.01	0.01
Q检验	0.02	0.64	0.30	0.19	0.00
结论	平稳非白噪声	平稳白噪声	平稳白噪声	平稳白噪声	平稳非白噪声

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表 4 ARMA模型参数检验

Tab. 4 ARMA model parameter test

	模型参数（p值）	结论
ARMA（1,1）	AR1 = −0.41(0.03)，MA1 = 0.12(0.55)，XMEAN = 85.07(0.00)	未通过
AR（2）	AR1 = −0.27(0.00)，AR2 = 0.06(0.43)，XMEAN = 85.09(0.00)	未通过
MA（2）	MA1 = −0.29(0.00)，MA2 = 0.19(0.00)，XMEAN = 85.13(0.00)	通过
AR（5）	AR1 = −0.61(0.00)， AR2 = −0.51(0.00)，AR3 = −0.44(0.00)，AR4 = −0.40(0.00)，AR5 = −0.19(0.01)	通过

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表 5 模型预测精度分析

Tab. 5 Analysis of model prediction accuracy

参数	Fourier级数拓展	小波分解	ARMA	Fourier级数拓展−ARMA	小波分解−ARMA
MSE	2469.13	1034.40	685.94	938.12	249.20
RMSE	49.69	32.16	26.19	30.63	15.79
MAE	46.82	21.01	18.77	25.05	6.40
ME	36.05	15.65	8.80	11.55	5.30

下载: 导出CSV

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