Simulation of Global Cloud Water Acidity Based on the Adaptive Damped Newton's Method

Abstract Cloud water pH is a critical parameter in atmospheric chemistry, regulating the phase partitioning of semivolatile species, the dissolution of trace metals, and the kinetic processes of aqueous‐phase reactions, thereby influencing secondary aerosol formation and aerosol‐cloud‐radiation interactions. Current approaches for calculating cloud water acidity in widely used atmospheric chemistry numerical models range from the early fixed‐value assumption and analytical solutions (e.g., Cardano's Formula for cubic equations) to iterative techniques such as the bisection and standard Newton's methods. However, these existing approaches often struggle to maintain a balance between computational efficiency, numerical stability, and the ability to generalize across diverse and highly nonlinear chemical regimes. In this study, we developed an adaptive damped Newton's method by introducing a dynamic step‐size damping factor. This method retains the rapid convergence feature of the standard Newton's method while ensuring robust global numerical stability. Our results demonstrate that the adaptive damped Newton's method effectively eliminates unphysical cloud pH overestimations and the subsequent overestimation of sulfate production rates in regions enriched with alkaline dust and sea salt. This work offers a robust and scalable numerical framework that enhances the fidelity of cloud pH calculations across varying spatial scales—from mechanistic box models to global chemical transport models—thereby refining our understanding of pH‐dependent atmospheric processes and the non‐linear evolution of secondary aerosols.