Leveraging higher-order time integration methods for improved computational efficiency in a rainshaft model

Abstract

Cloud and precipitation microphysics packages in atmospheric general circulation models typically use first-order time integration methods with a large time step, requiring ad hoc limiters and substepping of the sedimentation scheme to prevent numerical instability. We investigate alternative methods for rain microphysical processes in the current Energy Exascale Earth System Model (E3SMv3), provided by the Predicted Particle Properties (P3) scheme. Using an offline rainshaft model containing P3's rain microphysics as a proxy for E3SMv3, we find that rain microphysics is underresolved in time at E3SMv3's default 300s time step. Accurately resolving the rainshaft model processes in time requires an over 100x reduction in time step, increasing wall clock time by 40x. However, higher-order time integrators based on Runge-Kutta methods offer improved solution accuracy for a given computational cost. Adaptive time stepping is key to obtaining computationally efficient microphysics results, eliminating the need for specialized substepping procedures in the sedimentation process. An adaptive second-order Runge-Kutta method approximates a high-temporal-resolution reference solution at only 2.6x the cost of the default P3 scheme; this method achieves high accuracy greater than 15x more efficiently than simply reducing the time step of P3 in the rainshaft model. We also analyze the timescales of the rain processes to obtain insight about the maximum time step each process is able to take while maintaining stability and accuracy, and about how individual processes should be grouped together for most efficient results.