To establish a more sustainable future, Saudi Arabia is striving to reduce its dependency on fossil fuels and promote renewable energies. Solar energy is a major resource in Saudi Arabia because of the country’s geographical location with year-round clear skies and plentiful sunlight. However, although solar energy is a clean and safe renewable energy resource, it can be quite unpredictable. Therefore, solar irradiance needs to be forecasted and simulated as accurately as possible on both regional and national scales in the Kingdom to assist in planning for reserve usage, switching sources, and short-term power purchases. Based on an hourly solar diffuse horizontal irradiance (DHI) dataset from 45 different Saudi Arabian solar monitoring stations, this study proposes a novel spatio-temporal model. We identify the temporal dependency of DHI as cyclostationary and incorporate this key observation in the model. This feature helps yield accurate (i.e., significantly close to the ground truth and with narrow confidence bands) probabilistic forecasts and realistic simulations in near-future time points and at new locations. Then, the proposed model is compared to a stationary model that fails to recognize the cyclostationarity structure in the data. The proposed model produces significantly better predictions and simulations than the stationary model. Further, we calculate the photovoltaic power outputs using the simulated samples from both the models and the original observations and then compare them. The simulated samples from the proposed model afford photovoltaic power output estimates that are significantly closer to the original observed data than those from the stationary model and, therefore, they can better assist photovoltaic power output operators in assessing solar energy production and operational pre-planning to mitigate impacts by the uncertain nature of solar irradiance.