Analysis of daily solar irradiation variability and predictability in space and time is important for energy resources planning, development, and management. The natural intermittency of solar irradiation is mainly triggered by atmospheric turbulent conditions, radiative transfer, optical properties of cloud and aerosol, moisture and atmospheric stability, orographic and thermal forcing, which introduce additional complexity into the phenomenological records. To address this question for daily solar irradiation data recorded during the period 2011–2015, at 32 stations measuring solar irradiance on La Reunion French tropical Indian Ocean Island, we use the tools of non-linear dynamics: the intermittency and chaos analysis, the largest Lyapunov exponent, Sample entropy, the Kolmogorov complexity and its derivatives (Kolmogorov complexity spectrum and its highest value), and spatial weighted Kolmogorov complexity combined with Hamming distance to assess complexity and corresponding predictability. Finally, we have clustered the Kolmogorov time (that quantifies the time span beyond which randomness significantly influences predictability) for daily cumulative solar irradiation for all stations. We show that under the record-breaking 2011–2012 La Nina event and preceding a very strong El-Nino 2015–2016 event, the predictability of daily incident solar energy over La Réunion is affected.