Complexity of streamflows in the west-flowing rivers of India

Adequate knowledge of the complexity of streamflows in river basins is important for proper assessment, planning, and management of our water resources. However, identification of the complexity of streamflows is very challenging, due to the various mechanisms governing the streamflow process both in space and in time. The present study examines the complexity of daily streamflows in the west-flowing rivers of India. The false nearest neighbor (FNN) algorithm, a nonlinear dynamic-based method, is employed to determine the dimensionality of streamflow time series and, hence, to examine the complexity. The FNN method uses reconstruction of the single-variable streamflow time series in a multi-dimensional phase space, and identifies the FNNs in the reconstructed phase space. Daily streamflow time series from 13 gaging stations in the Tapi to Tadri basin are analyzed. The effect of delay time on the FNN dimension estimation of the 13 streamflow series is also investigated, by considering four different delay time values to represent different kinds of separation of elements in the phase space reconstruction vector (daily, annual, autocorrelation, mutual information). Collectively considering the different delay time values, the FNN dimensions for the 13 streamflow series are found to have a wide range of variability (with dimensions ranging from 5 to 20), indicating a wide range of complexity in the dynamics of streamflow in the Tapi to Tadri basin. The results generally reveal that: (1) for any given station, the FNN dimensions change with changes in delay time; and (2) for any given delay time, the FNN dimensions change for the different stations. There does not seem to be any clear pattern in the spatial variability of streamflow across the entire basin, although there are small pockets of local similarity. Based on the FNN dimension results, potential issues in the application of the FNN method to the streamflow series in the Tapi to Tadri basin (and streamflow, more broadly) are also discussed. The outcomes of the present study have important implications for streamflow data monitoring, streamflow modeling and forecasting, flood frequency analysis, environmental flow requirements, and water resource assessment, among others.