几种统计预测方法对1998年南京降水的跨季节预测试验及分析

胡凤良; 王丽琼; 左瑞亭; 张舰齐

doi:10.3878/j.issn.1006-9585.2016.15251

几种统计预测方法对1998年南京降水的跨季节预测试验及分析

doi: 10.3878/j.issn.1006-9585.2016.15251

1.
解放军理工大学气象海洋学院, 南京 211101
2.
中国人民解放军95871部队, 衡阳 421002

基金项目:

国家自然科学基金项目 (NSFC, Grants 41490642 and 41475071)

详细信息

作者简介:
胡凤良,男,1993年出生,硕士研究生,主要从事气候数值模拟研究。E-mail:15895904544@163.com

通讯作者:
左瑞亭,E-mail:ratinzuo@126.com

中图分类号: P468.0⁺24
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- 被引次数: 0
出版历程
- 收稿日期: 2015-11-10
- 网络出版日期: 2016-05-23
- 刊出日期: 2017-02-01

Extra-seasonal Predicting Tests and Analyses of Several Statistical Forecasting Methods on Precipitation over Nanjing in 1998

1.
Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101
2.
95871 Troop, People's Liberation Army of China, Hengyang 421002

Funds:

National Natural Science Foundation of China (NSFC, Grants 41490642 and 41475071)

摘要

摘要: 对1998年南京降水分别设计并开展了求和自回归滑动平均（Auto-Regressive Integrated Moving Average，ARIMA）模型预测、经验模态分解（Empirical Mode Decomposition，EMD）预测和基于Hilbert变换（HilbertTransformation，HT）的幅频分离预测等3种跨季节统计预测试验。结果表明：ARIMA模型预测结果存在明显的系统性误差且对夏季的降水突变现象预测困难；EMD分解预测的结果虽在降水演变趋势上有明显提高，但仍未能预测出夏季的强降水突变现象，究其原因可能是对高频分量预测效果不好所致；而基于Hilbert变换的幅频分离预测方法能够对各模态分量的瞬时频率和瞬时振幅实施隔离预测，消除两者的相互影响，显著改善高频模态的预测效果，使得最终预测结果最为理想，不仅具有最高的趋势相关性和最小的偏差，而且还较好地预测出了夏季两次强降水过程。不仅如此，在对2003年的降水预测验证中，基于Hilbert变换的幅频分离预测方法同样具有最好的预测效果，表明该方法预测效果较为稳定，为改进跨季节短期气候统计预测技术提供了一个新思路。
- 短期气候预测 /
- 求和自回归滑动平均(ARIMA) /
- 经验模态分解(EMD) /
- Hilbert变换(HT) /
- 最小二乘支持向量机
Abstract: Three statistical forecasting methods, i.e. ARIMA (Auto-Regressive Integrated Moving Average) model prediction, EMD (Empirical Mode Decomposition) decomposition prediction, and isolated prediction of frequency and amplitude based on Hilbert transformation, are designed and employed to make extra-seasonal prediction tests on the precipitation over Nanjing in 1998. Results show that the ARIMA model exhibits severe system errors and is hard to reproduce the abrupt variation of precipitation. Although the EMD decomposition prediction makes an obvious improvement in the evolution trend of precipitation, it still fails in the depiction of precipitation catastrophes in the summer due to its incapability of predicting high frequency modes. The isolated prediction method improves the prediction of high frequency modes since it can separately predict the frequency and amplitude of each mode and their interactions are avoided. Thereby the isolated prediction method gives a pretty good final prediction with the highest trend correlation and the smallest deviation. The two precipitation catastrophes in the summer of 1998 are realistically predicted. Additionally, a further verification of the precipitation prediction for 2003 also indicates that the isolated prediction method performs best among the three methods proposed in this study. The above results suggest that the isolated prediction method may provide a new idea for the technological improvement on extra-seasonal short-term climate prediction.
- Short-term climate prediction /
- Auto-Regressive Integrated Moving Average (ARIMA) /
- Empirical mode decomposition /
- Hilbert transformation /
- Least square support vector machine

HTML全文

图 1 1998 年3～9 月南京地区(a)逐日降水量和对应的(b)降水候距平

Figure 1. Daily precipitation and(b)pentad-mean precipitation anomalies in Nanjing from Mar to Sep in 1998

下载: 全尺寸图片幻灯片

图 2 ARIMA 模型对历史训练序列的拟合

Figure 2. Fitting results of the ARIMA model to the historical training series

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图 3 1998 年3～9 月各预测试验降水候距平结果对比

Figure 3. Comparison of the pentad-mean precipitation anomalies from the prediction tests and the real data for the period of Mar to Sep of 1998

下载: 全尺寸图片幻灯片

图 4 1994 年3 月至1998 年9 月共330 候降水距平EMD 分解结果

Figure 4. EMD decomposition results of 330 pentad-mean precipitation anomalies from Mar 1994 to Sep 1998

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图 5 1998 年3～9 月降水候距平前4 个IMF 高频分量的预测结果(粗实线表示近似真值，细实线表示试验2 结果，虚线表示试验3 结果)

Figure 5. The first four IMFs of pentad-mean precipitation anomalies from Mar to Sep of 1998(the bold solid line indicates the real data, the thin solid line indicates the results of test 2, and the dash line indicates the results of test 3)

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图 6 1994 年3 月至1998 年2 月降水候距平序列EMD 分解各特征模态的振幅和频率

Figure 6. Instantaneous amplitudes and frequencies of IMFs for pentad-mean precipitation anomalies from Mar 1993 to Feb 1998

下载: 全尺寸图片幻灯片

图 7 2003 年3～9 月各预测试验降水候距平结果对比

Figure 7. Comparison of pentad-mean precipitation anomalies of prediction tests and the real data from Mar to Sep of 2003

下载: 全尺寸图片幻灯片

表 1 各模态分量的方差贡献率和累积贡献

Table 1. Variance contribution rates of each component and cumulative contribution

	方差贡献率	累积贡献
IMF1	43.9%	43.9%
IMF2	34.9%	78.8%
IMF3	9.5%	88.3%
IMF4	7.0%	95.3%
IMF5	1.4%	96.7%
IMF6	2.3%	99.0%
IMF7	0.1%	99.1%
RES	0.9%	100.0%

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表 2 全序列与历史样本序列EMD 分解的差异对比

Table 2. Differences between the EMD decomposition results of the whole sequences and historical sample sequences

	r	R_RMSE	k_e
IMF1	0.9994	0.0350	1.0%
IMF2	0.9955	0.0955	5.6%
IMF3	0.9929	0.1193	4.5%
IMF4	0.9958	0.0928	8.3%
IMF5	0.9626	0.2746	17.0%
IMF6	0.9160	0.4444	26.4%
IMF7	0.8234	0.8321	99.0%
RES	0.7182	0.6410	89.2%

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表 3 试验2 预测模型各模态分量的γ和σ 值

Table 3. γ andσ of each component of prediction model inexperiment 2

	γ(×10⁵	σ
IMF1	1.6	130
IMF2	1.0	4000
IMF3	0.3	500
IMF4	4.5	24
IMF5	1.4	2100
IMF6	1.0	20
IMF7	1.4	2
RES	16.0	0.8

下载: 导出CSV

表 4 高频分量模态预测结果与EMD 分解结果之间的相关系数和均方根误差

Table 4. Correlation coefficients and RMSEs of predicted high frequency components and EMD decomposition results

	r			RMSE/mm
	试验1	试验2	试验3	试验1	试验2	试验3
IMF1	−	0.29	0.42	−	4.73	4.51
IMF2	−	0.20	0.45	−	3.66	3.54
IMF3	−	0.41	0.35	−	1.84	1.81
IMF4	−	0.33	0.76	−	1.77	1.31
剩余分量	−	0.63	−0.22	−	1.75	0.93
合成	0.11	0.29	0.47	7.32	6.51	6.26

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表 5 预测结果与近似真值的相关系数和均方根误差

Table 5. Correlation coefficients and RMSEs between the predicted results and the approximate real values

	r		RMSE
	振幅	频率	振幅	频率
IMF1	0.52	0.14	3.31	0.12
IMF2	0.48	0.32	2.60	0.04
IMF3	0.28	−0.40	1.32	0.03
IMF4	0.78	0.03	0.54	0.02

下载: 导出CSV

表 6 2003 年3～9 月各预测试验降水候距平与观测数据之间的相关系数和均方差

Table 6. Correlation coefficients and RMSEs between the predicted pentad-mean precipitations anomalies and observed data from Mar to Sep of 2003

	r	RMSE
ARIMA试验	0.03	14.06
EMD分解预测试验	0.18	10.24
Hilbert预测试验	0.42	9.32

下载: 导出CSV

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