小波变换分析降水时间序列的多分辨率特性研究

Research of multiresolution wavelet transform to rainfall time series

利用小波变换的多分辨率特性分析降水时间序列,其小波分解级数应是确定的。为解决此问题,提出一种新的框架:首先利用àtrous小波变换对降水时间序列进行分解,然后对分解的序列进行多尺度熵(MSE)分析以获取原始降水时间序列的一些潜在特征。分析表明,小波分解级数可以由不同尺度下近似信号MSE曲线的Mann-Kendall(MK)检验确定。对环渤海湾地区包括大连、锦州、天津、潍坊四个站点的降水时间序列复杂度进行多尺度分析比较,结果表明,利用MSE分析和MK检验可以得到较理想的小波分解级数。不同地方的降水时间序列复杂度分析可以为水资源的规划和应用提供参考。

The number of resolution levels of a wavelet transform to be used in the application to a rainfall time series should be determined. To resolve this problem, this paper presented a novel framework. First, the rainfall time series were decomposed using the a trous wavelet transform. Then, Multi-Scale Entropy （MSE） analysis that helps to elucidate some hidden characteristics of the original rainfall time series was applied to the decomposed rainfall time series. The analysis shows that the Mann-Kendall （MK） rank correlation test of MSE curves of residuals at various resolution levels could determine the number of resolution levels in the wavelet decomposition. The complexity of rainfall time series at four stations around Bohai Bay on a multi-scale was compared. The results reveal that the suggested number of resolution levels can be obtained using MSE analysis and MK test. The complexity of rainfall time series at various locations can also be analyzed to provide a reference for water resource planning and application.