Unfolding Community Structure in Rainfall Network of Germany Using Complex Network-Based Approach

Many natural systems can be represented as networks of dynamical units with a modular structure in the form of communities of densely interconnected nodes. Unfolding structure of such densely interconnected nodes in hydro-climatology is essential for reliable parameter transfer, model inter-comparison, prediction in ungauged basins, and estimating missing information. This study presents the application of complex network-based approach for regionalization of rainfall patterns in Germany. As a test case study, daily rainfall records observed at 1,229 rain gauges were selected throughout Germany. The rainfall data, when represented as a complex network using event synchronization, exhibits small-world and scale-free network topology which are a class of stable and efficient networks common in nature. In total, eight communities were identified using Louvain community detection algorithm. Each of the identified communities has a sufficient number of rain gauges which show distinct statistical and physical rainfall characteristics. The method used has wide application in most of the real systems which can be represented by network enabling to understand modular patterns through time series analysis.

[1]  Norbert Marwan,et al.  Non-linear time series analysis of precipitation events using regional climate networks for Germany , 2015, Climate Dynamics.

[2]  Béla Bollobás,et al.  Random Graphs , 1985 .

[3]  David Gfeller,et al.  Spectral coarse graining of complex networks. , 2007, Physical review letters.

[4]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Ankit Agarwal,et al.  Hydrologic regionalization using wavelet-based multiscale entropy method , 2015 .

[6]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[7]  Bruno Merz,et al.  An event synchronization method to link heavy rainfall events and large‐scale atmospheric circulation features , 2018 .

[8]  N Marwan,et al.  Prediction of extreme floods in the eastern Central Andes based on a complex networks approach , 2014, Nature Communications.

[9]  Hoshin Vijai Gupta,et al.  Diagnostic evaluation of conceptual rainfall–runoff models using temporal clustering , 2010 .

[10]  Long Yang,et al.  Urban signatures in the spatial clustering of summer heavy rainfall events over the Beijing metropolitan region , 2014 .

[11]  Jian Yu,et al.  Node Attribute-enhanced Community Detection in Complex Networks , 2017, Scientific Reports.

[12]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[13]  Vinit Sehgal,et al.  A non-linear and non-stationary perspective for downscaling mean monthly temperature: a wavelet coupled second order Volterra model , 2017, Stochastic Environmental Research and Risk Assessment.

[14]  Bruno Merz,et al.  Multi-scale event synchronization analysis for unravelling climate processes , 2017 .

[15]  Marco Franchini,et al.  Regional analysis of flow duration curves for a limestone region , 1996 .

[16]  Donald H. Burn,et al.  Estimation of hydrological parameters at ungauged catchments , 1993 .

[17]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[18]  Sheng-Tun Li,et al.  Clustering spatial-temporal precipitation data using wavelet transform and self-organizing map neural network , 2010 .

[19]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[20]  Bellie Sivakumar,et al.  Complex networks for streamflow dynamics , 2014 .

[21]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[22]  Jürgen Kurths,et al.  Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka , 2014 .

[23]  Alexander Y. Sun,et al.  Patterns of precipitation and soil moisture extremes in Texas, US: A complex network analysis , 2018 .

[24]  Ankit Agarwal,et al.  Optimal design of hydrometric station networks based on complex network analysis , 2020, Hydrology and Earth System Sciences.

[25]  Nitesh V. Chawla,et al.  An exploration of climate data using complex networks , 2009, SensorKDD '09.

[26]  Olaf Sporns,et al.  Weight-conserving characterization of complex functional brain networks , 2011, NeuroImage.

[27]  Manuel E. Mendoza,et al.  Hydrogeographical Regionalisation: An Approach for Evaluating the Effects of Land Cover Change in Watersheds. A Case Study in the Cuitzeo Lake Watershed, Central Mexico , 2009 .

[28]  Copernicus Publications,et al.  Complex network theory, streamflow, and hydrometric monitoring system design , 2014 .

[29]  J. Kurths,et al.  Wavelet Spectrum and Self-Organizing Maps-Based Approach for Hydrologic Regionalization -a Case Study in the Western United States , 2016, Water Resources Management.

[30]  O. de Weck,et al.  Overview of metrics and their correlation patterns for multiple-metric topology analysis on heterogeneous graph ensembles. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Bruno Merz,et al.  Quantifying the roles of single stations within homogeneous regions using complex network analysis , 2018, Journal of Hydrology.

[32]  Nitesh V. Chawla,et al.  Complex networks as a unified framework for descriptive analysis and predictive modeling in climate science , 2011, Stat. Anal. Data Min..

[33]  Betül Saf.  Regional Flood Frequency Analysis Using L-Moments for the West Mediterranean Region of Turkey , 2009 .

[34]  Paulin Coulibaly,et al.  Streamflow Prediction in Ungauged Basins: Review of Regionalization Methods , 2013 .

[35]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[36]  Mark Newman,et al.  Detecting community structure in networks , 2004 .

[37]  Vazken Andréassian,et al.  Spatial proximity, physical similarity, regression and ungaged catchments: A comparison of regionalization approaches based on 913 French catchments , 2008 .

[38]  R Quian Quiroga,et al.  Performance of different synchronization measures in real data: a case study on electroencephalographic signals. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Bellie Sivakumar,et al.  Network theory and spatial rainfall connections: An interpretation , 2015 .

[40]  Isameldin A. Atiem,et al.  Assessment of Regional Floods Using L-Moments Approach: The Case of The River Nile , 2006 .

[41]  O. Korup,et al.  Rare flash floods and debris flows in southern Germany. , 2018, The Science of the total environment.

[42]  S. Havlin,et al.  Scale-free networks are ultrasmall. , 2002, Physical review letters.

[43]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[44]  Vinit Sehgal,et al.  Application of multi-scale wavelet entropy and multi-resolution Volterra models for climatic downscaling , 2018 .

[45]  A. Ramachandra Rao,et al.  Regionalization of Watersheds , 2008 .

[46]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[47]  Steven L. Markstrom,et al.  Parameter regionalization of a monthly water balance model for the conterminous United States , 2015 .

[48]  G..  SCALE ISSUES IN HYDROLOGICAL MODELLING : A REVIEW , 2006 .

[49]  Guanrong Chen,et al.  Spectral coarse graining of complex clustered networks , 2013, Commun. Nonlinear Sci. Numer. Simul..