A nonlinear dynamical systems based modeling approach for understanding predictability and stochastic simulation of stream flow


A nonlinear dynamical systems based time series approach to recover the underlying dynamics and understand the predictability of streamflow variability. Further, this information is used to produce skillful projections. The signal component of the time series is isolated using wavelet spectral analysis. This signal is embedded in a D-dimensional space with an appropriate lag tau to reconstruct the phase space (or ‘attractor’) in which the dynamics unfolds. The parameters D and tau are obtained using False Nearest Neighbor and Mutual Information, respectively. Then, time varying predictability is assessed by quantifying the divergence of trajectories in the phase space with time, as 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 paleo reconstructed streamflow at Lees Ferry gauge on the Colorado River which offered three interesting insights: (i) The flows exhibited significant epochal variations in predictability – with recent decades indicating low predictability. (ii) The temporal variability of, predictability and the signal variance of the flow and large scale climate, are strongly related – indicating high predictability during periods of low variability in flow and large scale signal and vice-versa. (iii) Blind projections of flows during high predictable epochs showed good skill in capturing the distributional, drought and surplus statistics and poor performance during low predictability epochs. These results provoke an adaptive and flexible water management approach.

Apr 14, 2015 3:30 PM — 4:30 PM
Bechtel Collaboratory, Discovery Learning Center
Engineering Center, University of Colorado at Boulder, Boulder, CO 80309

University of Colorado Boulder