Capturing Aerosol-Cloud-Precipitation Interactions: A Physics-Informed Sparse Regression Approach for a Coupled Multiscale System With Time Delay

Aerosols exert a net cooling effect on the climate system by reflecting solar radiation, both directly and indirectly through their role in cloud formation, known as aerosol-cloud interactions. The multiscale nature of aerosol-cloud interactions, and especially their mesoscale adjustments and associated challenges for their representation in climate models, makes the aerosol forcing a key uncertainty of climate projections. Here we show that a physics-informed data-driven approach in the form of delay differential equations (DDEs) for coupled cloud-rain dynamics of mesoscale adjustments can combine the interpretability of conceptual models with the quantitative reliability of large-eddy simulations (LESs). Applied to a conceptual model that describes the coupled system as a predator-prey relationship between cloud depth H and cloud droplet number concentration N, the proposed approach faithfully reconstructs the known DDEs when providing information about the microscale physics in the form of an assumed rain-formation function. We further apply our approach to approximate governing DDEs for the complex aerosol-cloud adjustments modeled by LESs. Capturing the governing cloud-rain dynamics as coupled DDEs also requires providing macroscale physics, which translates into separating the rain and nonrain regimes and assumptions about their asymptotic behavior. These governing equations offer a quantitative pathway for predicting the emergent behaviors of aerosol-cloud-precipitation interactions.