Building a sophisticated forecasting framework for solar and photovoltaic power production in geographic zones with severe meteorological conditions is very challenging. This difficulty is linked to the high variability of the global solar radiation on which the energy production depends. A suitable forecasting framework might take into account this high variability and could be able to adjust/re-adjust model parameters to reduce sensitivity to estimation errors. The framework should also be able to re-adapt the model parameters whenever the atmospheric conditions change drastically or suddenly—this changes according to microscopic variations. This work presents a new methodology to analyze carefully the meaningful features of global solar radiation variability and extract some relevant information about the probabilistic laws which governs its dynamic evolution. The work establishes a framework able to identify the macroscopic variations from the solar irradiance. The different categories of variability correspond to different levels of meteorological conditions and events and can occur in different time intervals. Thereafter, the tool will be able to extract the abrupt changes, corresponding to microscopic variations, inside each level of variability. The methodology is based on a combination of probability and possibility theory. An unsupervised clustering technique based on a Gaussian mixture model is proposed to identify, first, the categories of variability and, using a hidden Markov model, we study the temporal dependency of the process to identify the dynamic evolution of the solar irradiance as different temporal states. Finally, by means of some transformations of probabilities to possibilities, we identify the abrupt changes in the solar radiation. The study is performed in Guadeloupe, where we have a long record of global solar radiation data recorded at 1 Hertz.