基于季节调整和趋势分解的水文序列小波周期分析模型及其应用  

Hydrological Series Wavelet Periodic Model Based on Seasonal Adjustment and Trend Decomposition with Its Application

作　　者：王红瑞[1] 刘达通[2] 王成[1] 高雄[1] 

机构地区：[1]北京师范大学水科学研究院水沙科学教育部重点实验室,北京100875 [2]中国人民大学统计学院,北京100872

出　　处：《应用基础与工程科学学报》2013年第5期823-836,共14页Journal of Basic Science and Engineering

基　　金：国家自然科学基金项目(51279006);国家科技支撑计划资助项目(2012BAB02B04)

摘　　要：针对季节要素、不规则要素以及趋势要素在水文序列小波周期研究中常被忽略的情况,建立了基于季节调整和趋势分解的小波周期分析模型.首先建立乘积ARIMA模型延长原序列并且检验条件异方差性;其次利用Census X12季节调整得到趋势循环项;再次利用BP滤波趋势分解得到循环项;最后基于分离出来的循环项,利用Mexhat小波对水文过程周期进行分析.本文以上海1958—2007年的月尺度降水序列为例进行了应用研究,结果表明,上海降水有着4.17年的周期,而直接使用原始数据进行周期分析并不能得到周期值,经对比分析表明所建模型效果更好,并采用方差分析周期检验方法作了可靠性讨论.Given that seasonal factor, irregular factor, and tendency factor are often ignored in the study of wavelet cycle on hydrological data sequence, a new wavelet cycle model was established in this paper based on the seasonal adjustment and tendency decomposition. A product ARIMA model was first built up to extend the original data sequence and tested the conditional heteroskedasticity in order to provide a series of complement for seasonal adjustment. The series of tendency and cycle was then obtained by Census X12 seasonal adjustment. Furthermore, the series of pure cycle was retrieved via BP filtering tendency decomposition. Finally, the period of the hydrological process was analyzed with Mexhat wavelet based on the separated series of cycle. The proposed model was verified with the monthly precipitation data series between 1958 and 2007 in Shanghai. The results indicated that the precipitation in Shanghai showed a cycle of 4.17 years, while this period cannot be obtained from the direct analysis of the original data without seasonal adjustment and tendency decomposition. The comparison with the traditional wavelet analysis confirmed that the proposed model performs better. The model reliability was also discussed in the paper.

关 键 词：条件异方差 季节调整 趋势分解 小波分析 水文过程周期分析 上海降水站 

分 类 号：P333[天文地球—水文科学]