Hybrid Physics–Machine Learning Framework for Forecasting Urban Air Circulation and Pollution in Mountain–Valley Cities

Background: Almaty, located in a mountain–valley basin, frequently experiences stagnant conditions that trap pollutants and cause sharp diurnal contrasts in air quality. Current forecasting systems either offer detailed physical realism at high computational cost or yield statistically accurate but physically inconsistent results. Urban air quality in mountain–valley cities is strongly shaped by thermal inversions and weak nocturnal ventilation that trap pollutants close to the surface. We present a hybrid physics–machine-learning framework that combines a Navier–Stokes surface-layer model with data-driven post-processing to produce short-term forecasts of wind, temperature, and particulate matter while preserving physical consistency. The approach captures diurnal ventilation patterns and the well-known negative linkage between near-surface wind and particulate loadings during wintertime inversions. Compared with purely statistical baselines, the hybrid system improves short-range forecast skill and maintains interpretability through physically grounded diagnostics. Beyond Almaty, the workflow is transferable to other mountain–valley environments and is directly actionable for early warning, traffic and heating-related emission management, and health-risk communication. By uniting physically meaningful fields with lightweight Machine Learning correction, the method offers a practical bridge between computational fluid dynamics and operational decision support for cities facing recurrent stagnation episodes. Aim: Develop and verify a method for the diagnostics and short-term forecasting of surface circulation and particle concentrations in Almaty (2024), ensuring physical consistency of fields, increased forecast accuracy on 6–24 h horizons, and interpretability of risk factors. Compared to purely statistical baselines (R2 ≈ 0.55 for PM forecasts), our hybrid framework achieved a 16% gain in explained variance and reduced RMSE by 25%. This improvement was most evident during winter inversion episodes. Methods: This study introduces a hybrid modeling framework that integrates the Navier–Stokes equations with machine-learning algorithms to diagnose and forecast surface air circulation and particulate matter concentrations. The approach ensures both physical consistency and improved predictive accuracy for short-term horizons (6–24 h). The Navier–Stokes equations in the Boussinesq approximation, the energy equation, and K-closure particulate matter transport were used. The numerical solution is based on the projection method (convection—TVD/QUICK, pressure—Poisson equation). The ML module is gradient boosting and decision trees for meteorological parameters, lags, and diagnostic quantities. The 2024 data are cleaned, normalized, and visualized. Results: The hybrid model reproduces the diurnal cycle of ventilation and concentrations, especially during winter inversions. For 6 h: wind RMSE ≈ 1.2 m/s (R2 ≈ 0.71), temperature RMSE ≈ 1.8 °C (R2 ≈ 0.78), and particles RMSE ≈ 0.012 mg/m3 (R2 ≈ 0.64). Errors are higher for 24 h. A negative relationship between wind and concentration was established: +1 m/s reduces the median by 10–15% during winter nights. Conclusions: The approach can be generalized to other mountain–valley cities beyond Almaty. Combining the physical model and ML correction improves short-term predictive ability and maintains physical consistency. The method is applicable for air quality risk assessment and decision support; further clarification of emissions and consideration of urban canyon geometry are required. The results support early-warning systems, health risk communication, and urban planning.