Streamflow variability and classification using false nearest neighbor method

Understanding regional streamflow dynamics and patterns continues to be a challenging problem. The present study introduces the false nearest neighbor (FNN) algorithm, a nonlinear dynamic-based method, to examine the spatial variability of streamflow over a region. The FNN method is a dimensionality-based approach, where the dimension of the time series represents its variability. The method uses phase space reconstruction and nearest neighbor concepts, and identifies false neighbors in the reconstructed phase space. The FNN method is applied to monthly streamflow data monitored over a period of 53 years (1950-2002) in an extensive network of 639 stations in the contiguous United States (US). Since selection of delay time in phase space reconstruction may influence the FNN outcomes, analysis is carried out for five different delay time values: monthly, seasonal, and annual separation of data as well as delay time values obtained using autocorrelation function (ACF) and average mutual information (AMI) methods. The FNN dimensions for the 639 streamflow series are generally identified to range from 4 to 12 (with very few exceptional cases), indicating a wide range of variability in the dynamics of streamflow across the contiguous US. However, the FNN dimensions for a majority of the streamflow series are found to be low (less than or equal to 6), suggesting low level of complexity in streamflow dynamics in most of the individual stations and over many sub-regions. The FNN dimension estimates also reveal that streamflow dynamics in the western parts of the US (including far west, northwestern, and southwestern parts) generally exhibit much greater variability compared to that in the eastern parts of the US (including far east, northeastern, and southeastern parts), although there are also differences among 'pockets' within these regions. These results are useful for identification of appropriate model complexity at individual stations, patterns across regions and sub-regions, interpolation and extrapolation of data, and catchment classification. An attempt is also made to relate the FNN dimensions with catchment characteristics and streamflow statistical properties. (C) 2015 Elsevier B.V. All rights reserved.