Complex network theory, streamflow, and hydrometric monitoring system design

Abstract

Abstract. Network theory is applied to an array of streamflow gauges located in the Coast Mountains of British Columbia (BC) and Yukon, Canada. The goal of the analysis is to assess whether insights from this branch of mathematical graph theory can be meaningfully applied to hydrometric data, and, more specifically, whether it may help guide decisions concerning stream gauge placement so that the full complexity of the regional hydrology is efficiently captured. The streamflow data, when represented as a complex network, have a global clustering coefficient and average shortest path length consistent with small-world networks, which are a class of stable and efficient networks common in nature, but the observed degree distribution did not clearly indicate a scale-free network. Stability helps ensure that the network is robust to the loss of nodes; in the context of a streamflow network, stability is interpreted as insensitivity to station removal at random. Community structure is also evident in the streamflow network. A network theoretic community detection algorithm identified separate communities, each of which appears to be defined by the combination of its median seasonal flow regime (pluvial, nival, hybrid, or glacial, which in this region in turn mainly reflects basin elevation) and geographic proximity to other communities (reflecting shared or different daily meteorological forcing). Furthermore, betweenness analyses suggest a handful of key stations which serve as bridges between communities and might be highly valued. We propose that an idealized sampling network should sample high-betweenness stations, small-membership communities which are by definition rare or undersampled relative to other communities, and index stations having large numbers of intracommunity links, while retaining some degree of redundancy to maintain network robustness.

Assessing Catchment Resilience Using Entropy Associated with Mean Annual Runoff for the Upper Vaal Catchment in South Africa

“…The linkage between catchment resilience and sensitivity of streamflow to changing climate conditions was reported [13]. In addition, the relationship between resilience/stability and complex streamflow network was established for optimum design of the network [41] and entropy was used to characterize the optimum design of the river system network within a catchment or basin [41]. Similar to the resilience approach for urban sprawl systems [7], entropy was used in this study to measure indirectly catchment resilience.…”

Information theory‐based decision support system for integrated design of multivariable hydrometric networks

“…Also, Keum and Kaluarachchi [] combined a spatially distributed water quality model and the network density concept to determine adequate numbers of the salinity monitoring at a watershed scale in a large basin. Halverson and Fleming [] adapted complex network theory to hydrometric network design and conducted betweenness analyses to evaluate key stations. Dai et al .…”

Temporal dynamics of streamflow: application of complex networks

“…For the purpose of convenience in the present analysis, each year is considered to contain only 365 days (i.e., February 29th in leap year is excluded). Therefore, the network construction adopted in this study for temporal dynamics is more similar to the construction adopted in Sivakumar and Woldemeskel (2014) and Halverson and Fleming (2015) for spatial dynamics than to the one adopted in Tang et al (2010), Braga et al (2016), and Serinaldi and Kilsby (2016) for temporal dynamics.…”

“…Watts and Strogatz 1998;Jeong et al 2000;Newman 2001;Newman et al 2001;Tsonis and Roebber 2004;Suweis et al 2011;Scarsoglio et al 2013;Woldemeskel 2014, 2015;Halverson and Fleming 2015), suggesting that such networks are not classical random networks, but may be small-world networks or scale-free networks or some other types.…”

“…Applications of the concepts of complex networks in hydrology have been gaining momentum in the last few years. Thus far, they have included studies of river networks (Rinaldo et al 2006;Zaliapin et al 2010;Foufoula-Georgiou 2014, 2015;Rinaldo et al 2014), rainfall monitoring networks (Malik et al 2012;Boers et al 2013;Scarsoglio et al 2013;Sivakumar and Woldemeskel 2015;Jha et al 2015;Jha and Sivakumar 2017;Naufan et al 2017), and streamflow monitoring networks (Tang et al 2010;Sivakumar and Woldemeskel 2014;Halverson and Fleming 2015;Braga et al 2016;Serinaldi and Kilsby 2016;Fang et al 2017). Such studies have employed different methods, including degree centrality, clustering coefficient, degree distribution, closeness centrality, shortest path length, and community structure.…”