Complex networks, 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 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, has 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 results did not clearly suggest 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 community detection algorithm identified 10 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). Betweenness analyses additionally suggest a handful of key stations which serve as bridges between communities and might therefore be highly valued. We propose that an idealized sampling network should sample high-betweenness stations, as well as small-membership communities which are by definition rare or undersampled relative to other communities, while retaining some degree of redundancy to maintain network robustness.