A Nonlinear Dynamical Systems‐Based Modeling Approach for Stochastic Simulation of Streamflow and Understanding Predictability 10.1029/2018WR023650
Balaji Rajagopalan1,2, Solomon Tassew Erkyihun1,3,4, Upmanu Lall5, Edith Zagona1,3, and Kenneth Nowak6
1Civil, Environmental and Architectural Engineering, University of Colorado Boulder, Boulder, CO, USA, 2Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado Boulder, Boulder, CO, USA, 3Center for Advanced Decision Support for Water and Environmental Systems (CADSWES), University of Colorado Boulder, Boulder, CO, USA, 4Now at Tampa Bay Water, Clearwater, FL, USA, 5Earth and Environmental Engineering, Columbia University, New York, NY, USA, 6Bureau of Reclamation, Technical Services Center, Denver, CO, USA
Abstract: We propose a time series modeling approach based on nonlinear dynamical systems to recover the underlying dynamics and predictability of streamflow and to produce projections with identifiable skill. First, a wavelet spectral analysis is performed on the time series to identify the dominant quasiperiodic bands. The time series is then reconstructed across these bands and summed to obtain a signal time series. This signal is embedded in a D‐dimensional space with an appropriate lag τ to reconstruct the phase space in which the dynamics unfolds. Time‐varying predictability is assessed by quantifying the divergence of trajectories in the phase space with time, using Local Lyapunov Exponents. Ensembles of projections from a current time are generated by block resampling trajectories of desired projection length, from the K‐nearest neighbors of the current vector in the phase space. This modeling approach was applied to the naturalized historical and paleoreconstructed streamflow at Lees Ferry gauge on the Colorado River, which offered three interesting insights. (i) The flows exhibited significant epochal variations in predictability. (ii) The predictability of the flow quantified by Local Lyapunov Exponent is related to the variance of the flow signal and selected climate indices. (iii) Blind projections of flow during epochs identified as highly predictable showed good skill in capturing the distributional and threshold exceedance statistics and poor performance during low predictability epochs. The ability to assess the potential skill of these long lead projections opens opportunities to perceive hydrologic predictability and consequently water management in a new paradigm.