An optimized semi-empirical physical approach for satellite-based PM_2.5 retrieval: embedding machine learning to simulate complex physical parameters

Abstract. Satellite remote sensing of PM_2.5 mass concentration has become one of the most popular atmospheric research aspects, resulting in the development of different models. Among them, the semi-empirical physical approach constructs the transformation relationship between the aerosol optical depth (AOD) and PM_2.5 based on the optical properties of particles, which has strong physical significance. Also, it performs the PM_2.5 retrieval independently of the ground stations. However, due to the complex physical relationship, the physical parameters in the semi-empirical approach are difficult to calculate accurately, resulting in relatively limited accuracy. To achieve the optimization effect, this study proposes a method of embedding machine learning into a semi-physical empirical model (RF-PMRS). Specifically, based on the theory of the physical PM_2.5 remote sensing approach (PMRS), the complex parameter (VE_f, a columnar volume-to-extinction ratio of fine particles) is simulated by the random forest model (RF). Also, a fine mode fraction product with higher quality is applied to make up for the insufficient coverage of satellite products. Experiments in North China show that the surface PM_2.5 concentration derived by RF-PMRS has an average annual value of 57.92 μg/m³ versus the ground value of 60.23 μg/m³. Compared with the original method, RMSE decreases by 39.95 μg/m³, and the relative deviation reduces by 44.87%. Moreover, validation at two AERONET sites presents a trend closer to the true values, with an R of about 0.80. This study is also a preliminary attempt to combine model-driven and data-driven models, laying a foundation for further atmospheric research on optimization methods.