A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core

Abstract

An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge-Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank-Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%-20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

Multigrid preconditioners for the mixed finite element dynamical core of the LFRic atmospheric model

“…Since advective transport is about an order of magnitude slower than acoustic pressure oscillations, CFL h ≈ 10 and L ≈ 4 irrespective of the model resolution. As was demonstrated in [2,5], this "shallow" multigrid works well, and avoids expensive global communications. It also significantly simplifies the parallel decomposition, since it is only necessary to (horizontally) partition the coarsest grid, which still has a large number of cells and allows a relative fine-grained domain decomposition.…”

“…An exception is the recent implementation of the MPAS model. In [5] it is shown that a semiimplicit methods with a multigrid solver can be competitive with fully explicit time integrators. A conditional semi-coarsening multigrid for the ENDGame dynamical core [48] used by the Met Office is described in [49] and currently implemented in the Unified Model code.…”

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

“…For example, the choice of a loose linear solver tolerance improves efficiency but can prevent overall nonlinear convergence. Similar efforts to tease out the performance trade-offs with iterative schemes also recommend the fewest iterations to maintain stability and yet minimize cost (Sandbach et al, 2015). For the test cases analyzed presently, the optimal tolerance depends on the spatial grid and time step size.…”

“…However, it has been shown that subcycling can present new errors and instabilities associated with time splitting in related applications (Estep et al, 2008). Other models use a form of semi-implicit methods (Å ström et al, 2012;Sandbach et al, 2015), which take advantage of scale separation to isolate and solve the relatively fast linear gravity waves efficiently. For high resolution configurations, semi-implicit schemes still require subcycling within subcomponents, and that can result in reduced solution accuracy, depending on the splitting strategy (Knoll et al, 2003).…”

A nestable, multigrid‐friendly grid on a sphere for global spectral models based on Clenshaw–Curtis quadrature

“…While such an approach has been applied and proved effective in the context of grid‐based atmospheric models (e.g. Heikes et al ; Sandbach et al ), implementing it on current spectral models is not straightforward because the aforementioned non‐nested nature of Gaussian quadrature necessitates some form of accurate off‐grid interpolation (Jones, ; Ullrich et al ) from higher‐ to lower‐resolution grid (and vice versa). Appendix C gives further discussion.…”