Justin Dong

Justin Dong, Sean P. Santos, Steven B. Roberts et al.

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 solutions from becoming unstable. We show that in the latest version of Energy Exascale Earth System Model, E3SMv3, the rain microphysics provided by the Predicted Particle Properties (P3) scheme is underresolved in time at the model's default 300s time step. The P3 scheme requires limiters to guarantee stability, but those limiters make large discretization errors more difficult to detect. When the time step of the P3 scheme is reduced to sufficiently capture correct microphysics behavior, wall clock time of the simulation is increased by nearly a factor of 40. Instead of reducing the microphysics time step, we recommend using higher-order time integrators based on Runge-Kutta methods, which offer improved solution accuracy at comparable computational costs. A key to obtaining computationally efficient microphysics results is the use of adaptive time stepping, which also eliminates the need for specialized substepping procedures in the sedimentation process. We also analyze individual microphysical processes by extracting inverse timescales from Jacobians of the process rates, which gives 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. The proposed integrators can achieve the accuracy level required to correctly model rain microphysics parameterizations more than 10x faster than the P3 scheme.

Mark Ainsworth, Justin Dong

We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence of neural networks. The finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.