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

2025-11-09

AI Summary

Low spatiotemporal resolution (0.75°, 3-hour) of satellite-derived aerosol optical depth (AOD) data impedes climate and public health policy formulation. To address this, we propose a Bayesian spatiotemporal unmixing model grounded in diffusion processes and stochastic partial differential equations (SPDEs). Our method innovatively constructs a diffusion-driven, non-separable covariance structure, integrating multi-source remote sensing observations and environmental covariates within a continuous Gaussian process framework—ensuring both interpretability and computational efficiency. We employ integrated nested Laplace approximation (INLA) for rapid Bayesian inference, enabling multi-scale prediction and near-real-time updates. Evaluated over India, the model enhances AOD spatial resolution to 0.25° and temporal resolution to 1 hour. Both simulation studies and real-data validation demonstrate statistically significant improvements in predictive accuracy and generalizability over benchmark methods.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Developing high-resolution spatio-temporal AOD estimation from coarse satellite data
• Modeling aerosol optical depth using diffusion-SPDE Bayesian disaggregation approach
• Enhancing AOD resolution from 0.75° to 0.25° spatially and 3h to 1h temporally

Innovation

• Uses diffusion-SPDE for spatio-temporal disaggregation modeling
• Employs Gaussian processes with separable covariance structures
• Applies Bayesian inference via INLA-SPDE framework computationally