A multiscale time-space approach to analyze and categorize the precipitation fluctuation based on the wavelet transform and information theory concept

The present study proposed a time-space framework using discrete wavelet transform-based multiscale entropy (DWE) approach to analyze and spatially categories the precipitation variation in Iran. To this end, historical monthly precipitation time series during 1960–2010 from 31 rain gauges were used in this study. First, wavelet-based de-noising approach was applied to diminish the effect of noise in precipitation time series which may affect the entropy values. Next, Daubechies (db) mother wavelets (db5–db10) were used to decompose the precipitation time series. Subsequently, entropy concept was applied to the sub-series to measure the uncertainty and disorderliness at multiple scales. According to the pattern of entropy across scales, each cluster was assigned an entropy signature that provided an estimation of the entropy pattern of precipitation in each cluster. Spatial categorization of rain gauges was performed using DWE values as input data to k-means and self-organizing map (SOM) clustering techniques. According to evaluation criteria, it was proved that k-means with clustering number equal to 5 with Silhouette coefficient = 0.33 , Davis–Bouldin = 1.18 and Dunn index = 1.52 performed better in determining homogenous areas. Finally, investigating spatial structure of precipitation variation revealed that the DWE had a decreasing and increasing relationship with longitude and latitude, respectively, in Iran.