A hybrid wavelet-Lyapunov exponent model for river water quality forecast

The use of spectral theory and chaos theory on river water quality modeling is reported in a very limited way. This study proposes a wavelet-maximum Lyapunov exponent (WMLE) hybrid model for river water quality dynamics, combining spectral theory and chaos theory. The methodology involves the following major steps: (1) use of wavelet transformation to filter the noisy signal in the water quality time series; (2) reconstruction of phase space to embed the water quality time series and determine the trajectory of the underlying dynamics; and (3) identification of the presence/absence of chaos and prediction using the largest Lyapunov exponent value. Case studies on the Huaihe River in China and the Potomac River in the United States, as representatives of low-frequency and high-frequency forecast, show average relative errors on weekly dissolved oxygen (DO), chemical oxygen demand (COD), and ammonia nitrogen (NH3-N) data are 2.35%, 4.53%, and 18.85%, and on 15-minute based DO data are 1.185%. It also indicates that the hybrid model performs better to some extent when compared to the purely Lyapunov exponent model, ARMA model, and ANN model. This study is a proof that the combination of spectral theory and chaos theory is promising to describe and predict fluctuation of particular water quality indicators in rivers.