Hydrological prediction in Colombia using singular spectral analysis and the maximum entropy method

We explore Singular Spectrum Analysis (SSA) combined with maximum entropy method (MEM) to fit autorregresive models to predict monthly rainfall and streamflow river discharges in Colombia. These methods capture non-linear features of hydrological processes and also the strong influence of Ei Nino-Southern Oscillation on the hydro-climatology of Colombia. SSA is used to filter out the deterministic nonlinear component of a time series, whereas the MEM is used to determine the autoregressive models used for prediction. The original series is embedded in a higher dimensional space for the reconstruction of the atractor of the dynamic system producing the series. The method is equivalent to the expansion in Fourier series but instead of using prescribed sine and cosine functions, empirical eigen functions are used. The eigen-functions come from the eigen-vectors of the covariance matrix of the series in the phase space. Predictions are made extrapolating tendencies in the attractor The methods are applied to rainfall data in three basins in Antioquia, Colombia. Monthly predictions are performed for the period 1991-1992. Results again confirms the high degree of ENSO's influence on the hydro-climatology of the region. The results suggest that SSA in combination with MEM offer a promissing new tool for hydrological prediction in Colombia.