Spatial and Temporal Non-Linear Dynamics Analysis and Predictability of Solar Radiation Time Series for La Reunion Island (France)

Abstract

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.

Algorithmic Probability Method Versus Kolmogorov Complexity with No-Threshold Encoding Scheme for Short Time Series: An Analysis of Day-To-Day Hourly Solar Radiation Time Series over Tropical Western Indian Ocean

“…To compute KC of the hourly solar radiation time series , we need firstly to encode the time series before using the Lempel-Ziv algorithm [ 7 ] in order to replace it by a new set of binary values such as: where is a threshold value [ 8 , 9 ]. Usually, the mean of the time series is used as a threshold.…”

“…Commonly, Lempel-Ziv’s algorithm is a widely-used universal lossless data compression tool to achieve this goal [ 7 ]. Recent studies on daily solar radiation emphasize that the use of such algorithmic method (through the Kolmogorov time that is inverse to KC) remains a reliable tool for estimating solar resource predictability over small tropical islands [ 8 , 9 ]. Nevertheless, there is a weakness about predictability with Kolmogorov time on solar radiation because of the drawback in encoding procedure of time series for calculation of KC.…”

“…To overcome this problem, Mihailovic et al [ 10 ] introduced the Kolmogorov complexity spectrum to assess how the computation of KC is sensitive to the threshold value used to encode the time series. Bessafi et al [ 9 ] showed that, for 5-years daily solar radiation time series, the mean is an optimum threshold. Furthermore, they mentioned the ability of KC computation to give an estimation of daily solar radiation predictability but emphasizing the limitation of this method for shorter time series.…”

“…Furthermore, they mentioned the ability of KC computation to give an estimation of daily solar radiation predictability but emphasizing the limitation of this method for shorter time series. To embed the purpose of this study, it is pointed out that the two previous studies [ 8 , 9 ] focused on complexity of solar radiation at La Réunion with spatially sparse daily dataset. The former study was achieved using 11 laboratory solar radiation stations throughout the 2013–2015 period to assess the spatial complexity pattern over the island.…”

Evaluation of WRF-DART (ARW v.3.9.1.1 and DART manhattan release) multi-phase cloud water path assimilation for short-term solar irradiance forecasting in a tropical environment

“…These sites are both located in the west of the island at 800 m and 1200 m respectively, meaning these sites are typically in the lee of the trade winds at altitudes where thermally driven convective clouds often form. This leads to lower GHI values (Badosa et al, 2013) and produces the most complex solar irradiance conditions (Bessafi et al, 2018) compared to the other sites. This explains the high positive MBE for these two sites.…”