Identifying complexity of annual precipitation variation in Iran during 1960–2010 based on information theory and discrete wavelet transform

  • Kiyoumars Roushangar
  • Farhad Alizadeh
Original Paper


The hydrologic process and dynamic system of precipitation is influenced by many physical factors which are excessively complex and variable. Present study used a wavelet transform based multiscale entropy (WME) and wavelet-based multiscale relative entropy (WMRE) approach in order to analyze and gage the complexity of the precipitation series and spatially classify the raingauges in Iran. For this end, historical annual precipitation data of 51 years (1960–2010) from 31 raingauges was decomposed using WT in which smooth Daubechies (db) mother wavelet (db5–db10), optimal level of decomposition and boundary extensions were considered. Next, entropy concept was applied for components obtained from WT to measure of dispersion, uncertainty, disorderliness and diversification in a multi-scale form. Spatial classification of raingauges was performed using WME and WMRE values as input data to SOM and k-means approaches. Three validity indices namely Davis Bouldin (DB), Silhouette coefficient (SC) and Dunn index were used to validate the proposed model’s efficiency. Based on results, it was observed that k-means approach had better performance in determining homogenous areas with SC = 0.337, DB = 0.769 and Dunn = 1.42. Finally, spatial structure of precipitation variation in latitude and longitude directions demonstrated that WME and WMRE values had a decreasing trend with latitude, however, it was seen that WME and WMRE had an increasing relationship with longitude in Iran.


Precipitation regionalization Entropy concept Discrete wavelet transform (DWT) Self organizing maps (SOM) k-Means clustering Iran 



The funding was provided by University of Tabriz.

Supplementary material

477_2017_1430_MOESM1_ESM.xlsx (9 kb)
Supplementary material 1 (XLSX 9 kb)
477_2017_1430_MOESM2_ESM.xlsx (18 kb)
Supplementary material 2 (XLSX 18 kb)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Water Resources Engineering, Faculty of Civil EngineeringUniversity of TabrizTabrizIran

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