Dynamical System Analysis of Reference Evapotranspiration using Chaos Models in Some Selected States in Northern Nigeria

Abstract

This study analyzed the dynamical system of reference evapotranspiration using chaos and maximum entropy models in some selected states in Northern Nigeria. The study covered 16 states in Northern Nigeria which were selected using purposive sampling techniques. The materials used for the study consist of secondary data of daily mean records of air temperature, wind speed, solar radiation and relative humidity from 1^st January 1984 to December 2022.  From the data, the daily reference Evapotranspiration were computed using Penman-Monteith equation. The reference evapotranspiration obtained was further analyzed using Phase portrait, recurrent plot and Lyapunov exponent to characterize the dynamical system.  The results showed that the dynamical system has a random and nonlinear trend which is aperiodic. The phase portrait exhibits sponge-like structures having distinct curves which indicates a low degree deterministic chaos. Also, the recurrent plots in 16 states had a dark short diagonal line diagonals and white ribbons which indicates seasonal variations. The largest Lyapunov exponents of the 16 states are all positive and range between 0.001983/day – 0.004419/day. This positive result indicated that the dynamical system is deterministic and chaotic in behavior.