A comparison of time-parallel deferred correction methods for atmospheric modelling

Accurate and efficient time integration is a critical component of Numerical Weather Prediction (NWP) and climate modelling. Current approaches in the Met Office’s next‑generation dynamical core, GungHo, rely on a serial-in-time, low-order, iterative semi‑implicit timestepping scheme coupled with Flux‑Form Semi‑Lagrangian (FFSL) transport scheme. As model resolutions and computational scales increase, exploiting parallelism in the time dimension is becoming increasingly important.

This work evaluates the potential of time‑parallel Deferred Correction (DC) methods as a viable alternative to these traditional schemes. I examine two strategies for introducing temporal parallelism:

• Revisionist Integral Deferred Correction (RIDC), which parallelises across correction sweeps, and
• Spectral Deferred Correction (SDC) with time‑parallel (diagonal) preconditioners, which parallelises across collocation nodes.

Results are presented for a suite of standard dynamical core test cases for the compressible Euler equations. These experiments demonstrate how time‑parallel DC algorithms can improve temporal accuracy and offer meaningful opportunities for reducing wall‑clock time.

Together, these developments highlight the promise of DC-based integrators as a pathway toward more scalable and efficient time-stepping in next‑generation atmospheric models.