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

Abstract 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.