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Networks: a generic theory for hydrology?

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An Erratum to this article was published on 23 September 2014

Abstract

Connections are ubiquitous. The hydrologic cycle is perhaps the best example: every component of this cycle is connected to every other component, but some connections are stronger than the others. Unraveling the nature and extent of connections in hydrologic systems, as well as their interactions with others, has always been a fundamental challenge in hydrology. Despite the progress in this direction, a strong scientific theory that is suitable for studying all types of connections in hydrology continues to be elusive. In this article, I argue that the theory of networks provides a generic theory for studying all types of connections in hydrology. After presenting a general discussion of complex systems as networks, I offer a brief account of the history of development of network theory and some basic concepts and measures of complex networks, and explain the relevance of complex network theory for hydrologic systems, with three specific examples.

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References

  • Albert R, Jeong H, Barabasi A-L (1999) Internet: diameter of the world wide web. Nature 401:130–131

    Article  CAS  Google Scholar 

  • Barabási A-L (2002) Linked: the new science of networks. Perseus, Cambridge, MA

    Google Scholar 

  • Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512

    Article  Google Scholar 

  • Barrat A, Weigt M (2000) On the properties of small-world networks. Eur Phys J B 13:547–560

    Article  CAS  Google Scholar 

  • Barrat A, Barthélemy M, Vespinani A (2008) Dynamical processes on complex networks. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Berge C (1962) The theory of graphs and its applications. Matheun, Ann Arbor

    Google Scholar 

  • Beven KJ (2006) A manifesto for the equifinality thesis. J Hydrol 320:18–36

    Article  Google Scholar 

  • Boers N, Bookhagen B, Marwan N, Kurths J, Marengo J (2013) Complex networks identify spatial patterns of extreme rainfall events of the South American Monsoon System. Geophys Res Lett 40:1–7. doi:10.1002/grl.50681

    Article  Google Scholar 

  • Bollobás B (1998) Modern graph theory. Springer, New York

    Book  Google Scholar 

  • Bondy JA, Murty USR (1976) Graph theory with applications. Elsevier Science, North-Holland

    Google Scholar 

  • Bouchaud J-P, Mézard M (2000) Wealth condensation in a simple model of economy. Phys A 282:536–540

    Article  Google Scholar 

  • Cayley A (1857) On the theory of the analytical forms called trees. Philos Mag, Ser IV 13(85):172–176

    Google Scholar 

  • Dalin C, Konar M, Hanasaki N, Rinaldo A, Rodriguez-Iturbe I (2012) Evolution of the global virtual water trade network. Proc Nat Acad Sci 109(16):5989–5994

    Article  CAS  Google Scholar 

  • Davis KF, D’Odorico P, Laio F, Ridolfi L (2013) Global spatio-temporal patterns in human migration: a complex network perspective. PLoS ONE 8(1):e53723. doi:10.1371/journal.pone.0053723

    Article  CAS  Google Scholar 

  • Dooge JCI (1967) The hydrologic cycle as a closed system. Int Assoc Sci Hydrol Bull 13(1):58–68

    Article  Google Scholar 

  • Dooge JCI (1986) Looking for hydrologic laws. Water Resour Res 22(9):46S–58S

    Article  Google Scholar 

  • Duan Q, Gupta HV, Sorooshian S, Rousseau AN, Turcotte R (2003) Calibration of watershed models. Water science and application 6. American Geophysical Union, Washington

    Book  Google Scholar 

  • Erdös P, Rényi A (1959) On random graphs, I. Publ Math (Debrecen) 6:290–297

    Google Scholar 

  • Erdös P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17–61

    Google Scholar 

  • Euler L (1741) Solutio problematis ad geometriam situs pertinentis. Comment Acad Sci Petropolitanae 8:128–140

    Google Scholar 

  • Grayson RB, Blöschl G (2000) Spatial patterns in catchment hydrology: observations and modeling. Cambridge University Press, Cambridge

    Google Scholar 

  • Harary F (1969) Graph theory. Addison-Wesley, Reading

    Google Scholar 

  • Hrachowitz M, Savenije HHG, Blöschl G, McDonnell JJ, Sivapalan M, Pomeroy JW, Arheimer B, Blume T, Clark MP, Ehret U, Fenicia F, Freer JE, Gelfan A, Gupta HV, Hughes DA, Hut RW, Montanari A, Pande S, Tetzlaff D, Troch PA, Uhlenbrook S, Wagener T, Winsemius HC, Woods RA, Zehe E, Cudennec C (2013) A decade of predictions in ungaged basins (PUB)—a review. Hydrol Sci J 58(6):1198–1255

    Article  Google Scholar 

  • Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási A-L (2000) The large-scale organization of metabolic networks. Nature 407:651–654

    Article  CAS  Google Scholar 

  • Karinthy F (1929) Chain-links. Everything is different

  • Konar M, Dalin C, Suweis S, Hanasaki N, Rinaldo A, Rodriguez-Iturbe I (2011) Water for food: the global virtual water trade network. Water Resour Res 47:W05520. doi:10.1029/2010WR010307

    Google Scholar 

  • Li C, Singh VP, Mishra AK (2012) Entropy theory-based criterion for hydrometric network evaluation and design: maximum information minimum redundancy. Water Resour Res 48:W05521. doi:10.1029/2011WR011251

    Google Scholar 

  • Liljeros F, Edling C, Amaral LN, Stanley HE, Åberg Y (2001) The web of human sexual contacts. Nature 411:907–908

    Article  CAS  Google Scholar 

  • Listing JB (1848) Vorstudien zur Topologie. Vandenhoeck und Ruprecht, Göttingen, pp 811–875

    Google Scholar 

  • Mandelbrot BB (1983) The fractal geometry of nature. W. H. Freeman and Company, New York

    Google Scholar 

  • Miguens J, Mendes J (2008) Weighted and directed network on traveling patterns. Biowire 5151:145–154

    Google Scholar 

  • Milgram S (1967) The small world problem. Psychol Today 2:60–67

    Google Scholar 

  • Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298:824–827

    Article  CAS  Google Scholar 

  • Mishra AK, Coulibaly P (2009) Developments in hydrometric network design: a review. Rev Geophys 47: RG2001/2009, 2007RG000243

  • Montanari A et al (2013) “Panta Rhei—Everything Flows”: change in hydrology and society—The IAHS Scientific Decade 2013–2022. Hydrol Sci J 58(6):1256–1275

    Article  Google Scholar 

  • Newman MEJ (2001) The structure of scientific collaboration networks. Proc Nat Acad Sci USA 98:404–409

    Article  CAS  Google Scholar 

  • Newman MEJ, Strogatz SH, Watts DJ (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E 64:021668

    Google Scholar 

  • Newman MEJ, Barabási A-L, Watts DJ (2003) The structure and dynamics of networks. Princeton University Press, Princeton

    Google Scholar 

  • Paola C, Foufoula-Georgiou E, Dietrich WE, Hondzo M, Mohrig D, Parker G, Power ME, Rodriguez-Iturbe I, Voller V, Wilcock P (2006) Toward a unified science of the Earth’s surface: opportunities for synthesis among hydrology, geomorphology, geochemistry, and ecology. Water Resour Res 42:W03S10. doi:10.1029/2005WR004336

    Google Scholar 

  • Rinaldo A, Banavar JR, Maritan A (2006) Trees, networks, and hydrology. Water Resour Res 42:W06D07. doi:10.1029/2005WR004108

    Google Scholar 

  • Scarsoglio S, Laio F, Ridolfi L (2013) Climate dynamics: a network-based approach for the analysis of global precipitation. PLoS ONE 8(8):e71129. doi:10.1371/journal.pone.0071129

    Article  CAS  Google Scholar 

  • Sivakumar B (2000) Chaos theory in hydrology: important issues and interpretations. J Hydrol 227(1–4):1–20

    Article  Google Scholar 

  • Sivakumar B (2003) Forecasting monthly streamflow dynamics in the western United States: a nonlinear dynamical approach. Environ Model Softw 18(8–9):721–728

    Article  Google Scholar 

  • Sivakumar B (2004a) Chaos theory in geophysics: past, present and future. Chaos Soliton Fract 19(2):441–462

    Article  Google Scholar 

  • Sivakumar B (2004b) Dominant processes concept in hydrology: moving forward. Hydrol Process 18(12):2349–2353

    Article  Google Scholar 

  • Sivakumar B (2008a) Dominant processes concept, model simplification and classification framework in catchment hydrology. Stoch Environ Res Risk Assess 22(6):737–748

    Article  Google Scholar 

  • Sivakumar B (2008b) The more things change, the more they stay the same: the state of hydrologic modeling. Hydrol Process 22:4333–4337

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Sivakumar B (2011a) Global climate change and its impacts on water resources planning and management: assessment and challenges. Stoch Environ Res Risk Assess 25(4):583–600

    Article  Google Scholar 

  • Sivakumar B (2011b) Water crisis: from conflict to cooperation–an overview. Hydrol Sci J 56(4):531–552

    Article  Google Scholar 

  • Sivakumar B (2014) Planning and management of shared waters: hydropolitics and hydropsychology—two sides of the same coin. Int J Wat Res Dev 30(2):200–210

    Article  Google Scholar 

  • Sivakumar B, Singh VP (2012) Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework. Hydrol Earth Syst Sci 16:4119–4131

    Article  Google Scholar 

  • Sivakumar B, Singh VP, Berndtsson R, Khan SK (2014) Catchment classification framework in hydrology: challenges and directions. ASCE J Hydrol Eng. doi:10.1061/(ASCE)HE.1943-5584.0000837

    Google Scholar 

  • Suweis S, Konar M, Dalin C, Hanasaki N, Rinaldo A, Rodriguez-Iturbe I (2011) Structure and controls of the global virtual water trade network. Geophys Res Lett 38:L10403. doi:10.1029/2011GL046837

    Article  Google Scholar 

  • Tsonis AA, Roebber PJ (2004) The architecture of the climate network. Phys A 333:497–504

    Article  Google Scholar 

  • Wasserman S, Faust K (1994) Social network analysis. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Watts DJ (1999) Small worlds: the dynamics of networks between order and randomness. Princeton University Press, Princeton

    Google Scholar 

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442

    Article  CAS  Google Scholar 

  • Yilmaz KK, Vrugt JA, Gupta HV, Sorooshian S (2010) Model calibration in watershed hydrology. In: Sivakumar B, Berndtsson R (eds) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore, pp 53–105

    Chapter  Google Scholar 

  • Young PC, Ratto M (2009) A unified approach to environmental systems modeling. Stoch Environ Res Risk Assess 23:1037–1057

    Article  Google Scholar 

Download references

Acknowledgments

This study is supported by the Australian Research Council (ARC). I acknowledge the financial support from ARC through the Future Fellowship grant (FT110100328). Fitsum Woldemeskel has provided help in the preparation of the figures. I would also like to thank the two reviewers for their comments, which helped improve the manuscript.

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Bellie Sivakumar

  2. Department of Land, Air and Water Resources, University of California, Davis, CA, 95616, USA

    Bellie Sivakumar

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  1. Bellie Sivakumar
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Correspondence to Bellie Sivakumar.

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Sivakumar, B. Networks: a generic theory for hydrology?. Stoch Environ Res Risk Assess 29, 761–771 (2015). https://doi.org/10.1007/s00477-014-0902-7

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