Abstract

This study reported the analyses of daily–recorded variability of the Total Solar Irradiance (TSI) (daily means) measurements using chaos theory such as mutual information, false nearest neighbours (FNN), Lyapunov exponent, phase space reconstruction and power spectrum. In an attempt to identify the temporal correlation of the TSI data, Space- time separation plots were also analysed. Wavelet power spectrum (WPS) which splits the time series into different scales and monitors energy distribution in each scale was also computed. Our analyses revealed that FNN had its first at an embedding dimension of four. The phase space reconstruction for TSI time series using time delay embedding for τ = 15 and m = 4 was also reported. The power spectrum calculated was broadband in nature and also decays exponentially, an indication of the possibility of chaotic behaviour. Analysis of space- time separation plot for TSI time series shows oscillations covering a small scale range and as such there is no prominent temporal correlation in the data. The divergence in the trajectories of TSI data as given by largest Lyapunov exponent curve indicated a very strong possibility of chaos. WPS analysis reveals the multi-scale and non-stationary behaviour of the data with greater concentration of power between 1024 and 204 minutes bands. Sequel to all analyses conducted, it could be inferred that TSI data could be modeled and predicted with a minimum of four dynamical variables since the first minimum of the false nearest neighbours plot occurred at an embedding dimension of four.