Investigating Chaos and Nonlinear Forecasting in Short Term and Mid-term River Discharge

Abstract

In the present study, an attempt is made to investigate and identify chaos using various techniques as well as river flow forecasting in short-term (daily) and mid-term (monthly) scales using nonlinear local approximation method (NLA) and ARIMA method. Daily and monthly flow data of Daintree River in Australia from 1969 to 2011 are used. In this respect, seven nonlinear dynamic methods including (1) average mutual information function; (2) phase space reconstruction; (3) false nearest neighbour algorithm; (4) method of surrogate data; (5) correlation dimension method; (6) Lyapunov exponent method; and (7) nonlinear local approximation are employed. The Takens’ theorem, mutual information and false nearest neighbour are used to determine the delay time and embedding dimension for the phase space reconstruction. The correlation dimensions obtained for the short term and mid-term river flow are 6.7 and 3.3, respectively. The finite dimensions obtained for the short term and mid-term river flow time series indicate the possible existence of chaos. The comparative analyses show that the NLA method is superior to ARIMA in mid-term scale while both models are acceptable for short term scale forecasting.