Nonlinear dynamics of the Great Salt Lake: System identification and prediction

A case study of the application of recent methods of nonlinear time series analysis is presented. The 1848-1992 biweekly time series of the Great Salt Lake (GSL) volume is analyzed for evidence of low dimensional dynamics and predictability. The spectrum of Lyapunov exponents indicates that the average predictability of the GSL is a few hundred days. Use of the false nearest neighbor statistic shows that the dynamics of the GSL can be described in time delay coordinates by four dimensional vectors with components lagged by about half a year. Local linear maps are used in this embedding of the data and their skill in forecasting is tested in split sample mode for a variety of GSL conditions: lake average volume, near the beginning of a drought, near the end of a drought, prior to a period of rapid lake rise. Implications for modeling low frequency components of the hydro-climate system are discussed.