Temporal variation in deterministic chaos: the influence of Kainji dam on downstream stations along lower Niger River.

Complex systems such as river flow do not obey the law of linearity but most often than not behave in a nonlinear manner. In this study, the dynamics of the River Niger discharge along two stations located in Nigeria were investigated using the methods of phase space reconstruction, correlation dimension and Lyapunov exponent. The analysis was carried out by using the daily data for three different periods — 1914–1939 (period 1), 1940–1964 (period 2), and 1966–1991 (period 3) spanning before and after the Kainji dam construction. Time delay embedding values at Baro and Lokoja for the three time periods were used to reconstruct the phase space of the river discharge at both locations. The embedding dimension represents the number of variables to completely describe the system. The presence of chaos was confirmed with positive values of Lyapunov exponents in both locations at the three different periods considered. The Lyapunov exponents at Baro were in the range 0.0014–0.0150 while the range at Lokoja was 0.007–0.0145. Significant correlation dimension values obtained at Baro (2.11–2.81) and Lokoja (2.28–4.51) are indicative of low dimensional chaos. A possible explanation for this could be the temporal sequence in the dam installation. The forecast horizon, the inverse of the largest Lyapunov exponents, gives a prediction boundary on a chaotic time series. In this study, the forecast horizon for both locations is expected to be in the range of 40–58 days into the future. [ABSTRACT FROM AUTHOR]