Bayesian spatio--temporal disaggregation modeling using a diffusion-SPDE approach: a case study of Aerosol Optical Depth in India

Accurate estimation of Aerosol Optical Depth (AOD) is crucial for understanding climate change and its impacts on public health, as aerosols are a measure of air quality conditions. AOD is usually retrieved from satellite imagery at coarse spatial and temporal resolutions. However, producing high-resolution AOD estimates in both space and time can better support evidence-based policies and interventions. We propose a spatio-temporal disaggregation model that assumes a latent spatio--temporal continuous Gaussian process observed through aggregated measurements. The model links discrete observations to the continuous domain and accommodates covariates to improve explanatory power and interpretability. The approach employs Gaussian processes with separable or non-separable covariance structures derived from a diffusion-based spatio-temporal stochastic partial differential equation (SPDE). Bayesian inference is conducted using the INLA-SPDE framework for computational efficiency. Simulation studies and an application to nowcasting AOD at 550 nm in India demonstrate the model's effectiveness, improving spatial resolution from 0.75{\deg} to 0.25{\deg} and temporal resolution from 3 hours to 1 hour.