A hierarchical Bayesian spatio-temporal model for estimating solar radiation from sunshine duration records

Abstract

Estimating surface solar radiation is essential for applications in climatology, agriculture, and renewable energy, yet direct radiation measurements are often sparse or unavailable. This study presents a hierarchical Bayesian spatio-temporal model for estimating daily solar radiation from sunshine duration records, using an extended version of the Angström–Prescott (A–P) empirical relationship. The model incorporates fixed effects, elevation-dependent covariates, spatially and temporally structured latent fields, and unstructured random effects, estimated using the Integrated Nested Laplace Approximation (INLA) and the Stochastic Partial Differential Equation (SPDE) approach. Applied to a comprehensive observational dataset covering mainland Spain (1973–2024), the model reveals coherent spatial and seasonal patterns in the A–P coefficients, including a strong altitude effect on the slope parameter and opposing seasonal cycles for the intercept and slope. Validation against observed radiation data shows excellent agreement for most aspects of the distribution, with remaining discrepancies explained by known limitations in the sunshine duration measurements, particularly under overcast conditions. Long-term temporal trends in the slope suggest changes in atmospheric transmissivity, potentially linked to air quality and aerosol dynamics. The proposed framework provides a flexible, computationally efficient, and physically interpretable tool for reconstructing solar radiation fields in data-scarce regions, offering broad relevance for environmental and climate-related applications.