Inference On Streamflow Predictability Using Horizontal Visibility Graph Based Networks

Abstract

Streamflow is a dynamical process that integrates water movement in space and time within basin boundaries. The authors characterize the dynamics associated with streamflow time series data from about seventy-one U.S. Geological Survey (USGS) stream-gauge stations in the state of Iowa. They employ a novel approach called visibility graph (VG). It uses the concept of mapping time series into complex networks to investigate the time evolutionary behavior of dynamical system. The authors focus on a simple variant of VG algorithm called horizontal visibility graph (HVG). The tracking of dynamics and hence, the predictability of streamflow processes, are carried out by extracting two key pieces of information called characteristic exponent, λ of degree distribution and global clustering coefficient, GC pertaining to HVG derived network. The authors use these two measures to identify whether streamflow process has its origin in random or chaotic processes. They show that the characterization of streamflow dynamics is sensitive to data attributes. Through a systematic and comprehensive analysis, the authors illustrate that streamflow dynamics characterization is sensitive to the normalization, and the time-scale of streamflow time-series. At daily scale, streamflow at all stations used in the analysis, reveals randomness with strong spatial scale (basin size) dependence. This has implications for predictability of streamflow and floods. The authors demonstrate that dynamics transition through potentially chaotic to randomly correlated process as the averaging time-scale increases. Finally, the temporal trends of λ and GC are statistically significant at about 40% of the total number of stations analyzed. Attributing this trend to factors such as changing climate or land use requires further research.

Persistent Homology of Weighted Visibility Graph from Fractional Gaussian Noise

“…The advantage of this idea is that, one can apply many well-known techniques in networks and even in TDA such as PH for a time-series, helping for classification, discrimination and looking for exotic features hidden in the underlying time-series which could be robust in the presence of noise, trends and irregularities [36][37][38][39][40]. The notion of mapping the time-series to a network has been applied on different topics (see [41][42][43][44][45][46][47][48][49][50][51] and references therein).…”