Nonlinear Dynamics of the Great Salt Lake: Nonparametric Short-Term Forecasting

Variations in the volume of closed basin lakes, such as the Great Salt Lake, are often driven by large-scale, persistent climatic fluctuations. There is growing evidence of structure in the recurrence patterns of such fluctuations, their relation to physical mechanisms, and their manifestation in hydrologic time series. Classical, linear methods for time series analysis and forecasting may be inappropriate for modeling such processes. Here we consider the time series of interest as the outcome of a finite-dimensional, nonlinear dynamical system and use nonparametric regression to recover the nonlinear, autoregressive “skeleton” of the underlying dynamics. The resulting model can be used for short-term forecasting, as well as for exploring other properties of the system. The utility of the approach is demonstrated with synthetic periodic data and data from low dimensional, chaotic, dynamical systems. An application to the 1847–1992 Great Salt Lake biweekly volume time series is also reported.

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