Abstract
Applications of the concepts of complex networks for studying streamflow dynamics are gaining momentum at the current time. The present study applies a coupled phase space reconstruction–network construction method to examine the clustering property of the temporal dynamics of streamflow. The clustering of the temporal streamflow network is determined using clustering coefficient, which quantifies the tendency of a network to cluster (a measure of local density). Monthly streamflow time series observed from each of 639 stations (i.e. 639 networks) in the United States are studied. The presence of links between nodes (i.e. phase space reconstructed vectors) in each streamflow network (i.e. station) is identified using the Euclidean distance. Different distance thresholds are used to examine the influence of threshold on the clustering coefficient results and to identify the critical threshold. The results indicate that the distance threshold has significant influence on the clustering coefficient values of the temporal streamflow networks. With the critical distance threshold values, the clustering coefficients for the 639 stations are found to be between 0.15 and 0.81, suggesting very different types of network connections and dynamics. The clustering coefficient values are found to provide useful information on the influence of a given month (i.e. timestep) of the year on the temporal dynamics. Reliable interpretations of the clustering coefficient values in terms of catchment characteristics and flow properties are also possible.
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References
Agarwal A, Caesar L, Marwan N, Maheswaran R, Merz B, Kurths J (2019) Network-based identification and characterization of teleconnections on different time scales. Sci Rep 9, Article Number 8808
Agarwal A, Marwan N, Maheswaran R, Ozturk U, Kurths J, Merz B (2020) Optimal design of hydrometric station networks based on complex network analysis. Hydrol Earth Syst Sci 24(5):2235–2251
Alarcòn RR, Lozano S (2019) A complex network analysis of Spanish river basins. J Hydrol 578:124065
Antevs E (1952) Cenozoic climates of the Great basin. Geol Rundsch 40:94–108
Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512
Barrat A, Weigt M (2000) On the properties of small-world networks. Eur Phys J B 13:547–560
Braga AC et al (2016) Characterization of river flow fluctuations via horizontal visibility graphs. Phys A 444:1003–1011
Cao L, Mees A, Judd K (1998) Dynamics from multivariate time series. Physica D 121:75–88
Chen J, Shi H, Sivakumar B, Peart MR (2016) Population, water, food, energy and dams. Renew Sustain Energy Rev 56:18–28
Cook BI, Ault TR, Smerdon JE (2015) Unprecedented 21st century drought risk in the American Southwest and Central Plains. Sci Adv 1(1):e1400082. https://doi.org/10.1126/sciadv.1400005
Encyclopædia Britannica (2019) Great Basin. https://www.britannica.com/place/Great-Basin
Fang K, Sivakumar B, Woldemeskel FM (2017) Complex networks, community structure, and catchment classification in a large-scale river basin. J Hydrol 545:478–493. https://doi.org/10.1016/j.jhydrol.2016.11.056
Gao Z, Jin N (2009) Complex network from time series based on phase space reconstruction. Chaos 19(3):033137. https://doi.org/10.1063/1.3227736
Groisman PY, Knight RW, Karl TR (2001) Heavy precipitation and high streamflow in the contiguous United States: trends in the twentieth century. B Am Meteorol Soc 82(2):219–246. https://doi.org/10.1175/1520-0477
Halverson MJ, Fleming SW (2015) Complex network theory, streamflow, and hydrometric monitoring system design. Hydrol Earth Syst Sci 19(7):3301–3318. https://doi.org/10.5194/hess-19-3301-2015
Han X, Sivakumar B, Woldmeskel FM, Guerra de Aguilar M (2018) Temporal dynamics of streamflow: application of complex networks. Geosci Lett. https://doi.org/10.1186/s40562-018-0109-8
Han X, Ouarda TBMJ, Rahman A, Haddad K, Mehrotra R, Sharma A (2020) A network approach for delineating homogeneous regions in flood frequency analysis. Water Resour Res 56(3):e2019WR025910
Hossain F, Sivakumar B (2006) Spatial pattern of arsenic contamination in shallow wells of Bangladesh: regional geology and nonlinear dynamics. Stoch Environ Res Risk Assess 20(1–2):66–76
Kammerer JC (1990) Largest Rivers in the United States, US Geological Survey Fact Sheet, Open File Report 87-242
Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45(6):3403–3411
Kiang JE, Stewart DW, Archfield SA, Osborne EB, Eng K (2013) A national streamflow network gap analysis. US Geological Survey Scientific Investigations Report 2013-5013, Reston, Virginia, USA
Kim HS, Lee KH, Kyoung MS, Sivakumar B, Lee ET (2009) Measuring nonlinear dependence in hydrologic time series. Stoch Environ Res Risk Assess 23:907–916
Konapala G, Mishra AK (2017) Review of complex networks application in hydroclimatic extremes with an implementation to characterize spatio-temporal drought propagation in continental USA. J Hydrol 555:600–620
Kyoung MS, Kim HS, Sivakumar B, Singh VP, Ahn KS (2011) Dynamic characteristics of monthly rainfall in the Korean peninsula under climate change. Stoch Environ Res Risk Assess 25(4):613–625
Lins HF (2012) USGS Hydro-climatic data network 2009 (HCDN–2009). US Geological Survey Fact Sheet 2012-3047, US Geological Survey, Reston, VA, USA
Naufan I, Sivakumar B, Woldemeskel FM, Raghavan SV, Vu MT, Liong SY (2018) Spatial connections in regional climate model rainfall outputs at different temporal scales: application of network theory. J Hydrol 556:1232–1243
Newman MEJ (2001) The structure of scientific collaboration networks. Proc Natl Acad Sci USA 98:404–409
Packard NH, Crutchfield JD, Farmer JD, Shaw RS (1980) Geometry from a time series. Phys Rev Lett 45(9):712–716
Poff NL, Bledsoe BP, Cuhaciyan CO (2006) Hydrologic variation with land use across the contiguous United States: geomorphic and ecological consequences for stream ecosystems. Geomorphology 79:264–285
Porporato A, Ridolfi R (2001) Multivariate nonlinear prediction of river flows. J Hydrol 248(1–4):109–122
Pryor SC, Howe JA, Kunkel KE (2009) How spatially coherent and statistically robust are temporal changes in extreme precipitation in the contiguous USA? Int J Climatol 29(1):31–45. https://doi.org/10.1002/joc.1696
Robinson EB, Dietz JL (2019) Great plains. Encyclopædia Britannica. https://www.britannica.com/place/Great-Plains
Serinaldi F, Kilsby CG (2016) Irreversibility and complex network behavior of stream flow fluctuations. Phys A 450:585–600. https://doi.org/10.1016/j.physa.2016.01.043
Sivakumar B (2003) Forecasting monthly streamflow dynamics in the western United States: a nonlinear dynamical approach. Environ. Modell. Softw. 18:721–728
Sivakumar B (2009) Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward. Stoch Environ Res Risk Assess 23(7):1027–1036. https://doi.org/10.1007/s00477-008-0265-z
Sivakumar B (2015) Networks: a generic theory for hydrology? Stoch Environ Res Risk Assess 29:761–771
Sivakumar B (2017) Chaos in hydrology: bridging determinism and stochasticity. Springer, Dordrecht
Sivakumar B, Singh VP (2012) Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework. Hydrol Earth Syst Sci 16(11):4119–4131. https://doi.org/10.5194/hess-16-4119-2012
Sivakumar B, Woldemeskel FM (2014) Complex networks for streamflow dynamics. Hydrol Earth Syst Sci 18(11):4565–4578. https://doi.org/10.5194/hess-18-4565-2014
Sivakumar B, Woldemeskel FM (2015) A network-based analysis of spatial rainfall connections. Environ Model Softw 69:55–62
Sivakumar B, Berndtsson R, Persson M, Uvo CB (2005) A multi-variable time series phase space reconstruction approach to investigation of chaos in hydrological processes. Int J Civ Environ Eng 1(1):35–51
Slack JR, Landwehr VM (1992) Hydro climatic data network (HCDN): a US Geological Survey streamflow data set for United States for the study of climate variations, 1847-1988. US Geological Survey Open File Report, pp 92–129
Takens F (1981) Detecting strange attractors in turbulence. In: Rand DA, Young LS (eds) Dynamical systems and turbulence, vol 898. Lecture notes in mathematics. Springer-Verlag, Berlin, pp 366–381
The World Fact book. Central Intelligence Agency (2019). https://www.cia.gov/library/publications/resources/the-world-factbook/docs/notesanddefs.html#
The World Factbook. Central Intelligence Agency (2019). https://www.cia.gov/library/publications/the-world-factbook/fields/279.html#as
Tiwari S, Jha SK, Sivakumar B (2019) Reconstruction of daily rainfall data using the concepts of networks: accounting for spatial connections in neighborhood selection. J Hydrol 579:124185
Tongal H, Demirel MC, Booij MJ (2013) Seasonality of low flows and dominant processes in the Rhine River. Stoch Environ Res Risk Assess 27:489–503
Vignesh R, Jothiprakash V, Sivakumar B (2015) Streamflow variability and classification using false nearest neighbor method. J Hydrol 531:706–715. https://doi.org/10.1016/j.jhydrol.2015.10.056
Watts DJ, Strogatz SH (1998) Collective dynamics of small world networks. Nature 393(6684):440–444
Yasmin N, Sivakumar B (2018) Temporal streamflow analysis: coupling nonlinear dynamics with complex networks. J Hydrol 564:59–67
Acknowledgements
This study was supported by the Australian Research Council (ARC) Future Fellowship Grant (FT110100328). Bellie Sivakumar acknowledges the financial support from ARC through this Future Fellowship Grant. Nazly Yasmin acknowledges the financial support of the Australian Post Graduate Award (University of New South Wales). The authors thank the two reviewers and the Associate Editor for their constructive comments and useful suggestions on an earlier version of the manuscript.
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Yasmin, N., Sivakumar, B. Study of temporal streamflow dynamics with complex networks: network construction and clustering. Stoch Environ Res Risk Assess 35, 579–595 (2021). https://doi.org/10.1007/s00477-020-01931-9
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DOI: https://doi.org/10.1007/s00477-020-01931-9