Hybrid Mixed-Effect Diffusion model (H-MED) for longitudinal air quality analysis


Tanrıverdi İ., Yozgatlıgil C.

ENVIRONMENTAL MODELLING & SOFTWARE, vol.195, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 195
  • Publication Date: 2026
  • Doi Number: 10.1016/j.envsoft.2025.106746
  • Journal Name: ENVIRONMENTAL MODELLING & SOFTWARE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, Environment Index, Geobase, Greenfile, INSPEC, Public Affairs Index
  • Middle East Technical University Affiliated: Yes

Abstract

Air pollution poses severe threats to global public health and environmental sustainability, with complex spatiotemporal dynamics. Traditional air quality models face limitations in capturing longitudinal dependencies and managing computational costs at scale. To address these challenges, we propose the Hybrid MixedEffect Diffusion (H-MED) model, a novel framework integrating mixed-effects regression, Gaussian-Process Regression (GPR), Long Short-Term Memory (LSTM), and diffusion-based learning for enhanced predictive accuracy and uncertainty quantification. Applied to a comprehensive longitudinal dataset spanning 61 countries (2013-2023), H-MED demonstrated superior performance, achieving the lowest prediction errors (MAE:0.1423, RMSE:0.1925), while maintaining computational efficiency (5.69 s). The model significantly outperformed state-of-the-art approaches including advanced spatiotemporal models such as HITS, DCRNN, ST-GCN, and DeepAR by 15%-20% across all metrics. By incorporating country-level random effects and providing SHAP-based feature attribution, H-MED delivers interpretable, high-resolution forecasts that capture regional pollution heterogeneity and enable targeted policy interventions, a critical advantage over black-box deep learning models that lack explainability for environmental decision-making.