Leveraging physics-based and explainable machine learning approaches to quantify the relative contributions of rain and air pollutants to wet deposition

A quantitative understanding of the roles of rainfall and pollutant concentrations in wet deposition is important because they critically influence terrestrial and aquatic ecosystems. However, their relative contributions to wet deposition, which vary across regions, have not yet been identified. We propose two methods that quantitatively separate the contributions of rain and pollutant concentrations to wet deposition: one is based on simplified equations describing the wet scavenging of pollutants and the other is based on random forest models employing SHapley Additive exPlanations. Three-dimensional long-term air quality simulations from 2003 to 2019 are used as inputs for both the physics-based and machine learning models. Remarkably, the results drawn from the explainable machine learning model are consistent with those from the physics-based approach: overall, rain is a more important limiting factor than pollutant concentrations and the relative contribution of rain is larger than that of pollutants by up to a factor of 3-4 in polluted regions. In polluted regions, pollutant concentrations can remain relatively high even in the presence of precipitation owing to continuous and intense emissions; therefore, wet deposition is limited by rainfall. The contribution of rainfall is larger by 1.5-2.5 than that of pollutant concentrations in regions even with low emissions and this considerably large role of rain suggests that regional or transboundary pollutant transport plays a key role in modulating wet deposition. However, in very remote regions, once the rainfall amount exceeds a certain value, rainfall no longer contributes to increasing wet deposition because atmospheric pollutants are readily removed by rain. So, the contributions of the two factors are comparable in pristine regions. Our results can serve as a basis for explaining interannual variations in wet deposition and for future projections of wet deposition under emission control plans and climate change scenarios across regions.