Complex network analysis and robustness evaluation of spatial variation of monthly rainfall

TONGAL H., Sivakumar B.

Stochastic Environmental Research and Risk Assessment, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.1007/s00477-023-02578-y
  • Journal Name: Stochastic Environmental Research and Risk Assessment
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Agricultural & Environmental Science Database, CAB Abstracts, Compendex, Environment Index, Geobase, Index Islamicus, Pollution Abstracts, zbMATH, Civil Engineering Abstracts
  • Keywords: Complex network, Correlation threshold, Gaussian process regression, Local and global network measures, Spatial rainfall variability, Variation of information
  • Süleyman Demirel University Affiliated: Yes


Recently, complex network-based approaches are shown to be efficient for spatial analysis of rainfall variation. One of the most critical limitations of correlation-based networks is using some assumed threshold levels to identify the existence of links that lead to different topological and community structures. A hypothesis test is formulated for the robustness analysis of recovered community structures for monthly rainfall data of Tasmania, Australia. To this aim, variation of information (VI) curves are constructed for the original and random networks. Then Gaussian process regression method is applied for these curves at different correlation threshold values (i.e., 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90) to obtain maximum likelihoods as forms of Bayes factors. The networks are analyzed on a local and global scale by using node strength, node efficiency, edge density, and global efficiency measures to reveal the features of the rainfall network in the basin. Mainly, local strengths and efficiencies show that the networks are more efficient for threshold values higher than of 0.70. Global measures (i.e., edge density and global efficiency) decrease as the threshold increases except for the threshold of 0.80. In a rainfall forecasting exercise, using the robust network with the threshold value of 0.80 increases the coefficient of determination, Nash–Sutcliffe, and Kling-Gupta efficiencies from 0.29, 0.27, and 0.43 to 0.41, 0.36, and 0.61, respectively, leading to about 41%, 33%, and 41% improvement. Therefore, the results could be useful for determining robust network structures for various hydrological purposes such as filling missing values, regional flood analysis, and forecasting.