Semi-implicit finite-volume integrators for all-scale atmospheric dynamics

NCAR scientists have been working with ECMWF collaborators on a novel numerical approach for accurate and computationally efficient integrations of PDEs governing all-scale atmospheric dynamics. Such PDEs are not easy to handle, due to a huge disparity of spatial and temporal scales as well as a wide range of propagation speeds of natural phenomena captured by the equations. The novel Finite-Volume Module of the Integrated Forecasting System (IFS) at ECMWF (IFS-FVM) solves perturbation forms of the fully compressible Euler/Navier-Stokes equations under gravity and rotation using non-oscillatory forward-in-time semi-implicit time stepping and finite-volume spatial discretization. The IFS-FVM complements the established semi-implicit semi-Lagrangian spectral-transform IFS (IFS-ST) with the all-scale deep-atmosphere formulation cast in a generalized height-based vertical coordinate, fully conservative and monotone advection, flexible horizontal meshing and a predominantly local communication footprint. Yet, both dynamical cores can share the same quasi-uniform horizontal grid with collocated arrangement of variables, geospherical longitude-latitude coordinates and physics parameterizations, thus facilitating their synergetic relation. Relevant benchmark results and comparisons with corresponding IFS-ST results attest that IFS-FVM offers competitive solution quality and computational performance.

Left: Moist-precipitating baroclinic instability at day 15, near-surface pressure (hPa) obtained with IFS-FVM (top) and IFS-ST (bottom) coupled to the same IFS cloud microphysics parameterization. The simulations were performed at quasi-uniform grid with an approximate resolution 30 km. Right: Elapsed time to run 1 day of the dry baroclinic instability benchmark similar to the current ECMWF’s highest-resolution (≈9 km, with 137 vertical levels) deterministic forecast model, using the nonhydrostatic finite-volume dynamical core (left), spectral-transform hydrostatic dynamical core (center), and nonhydrostatic spectral-transform core (right); see Kühnlein et al, Geosci. Model Dev., 12, 651-676, 2019.
Figure A: Left: Moist-precipitating baroclinic instability at day 15, near-surface pressure (hPa) obtained with IFS-FVM (top) and IFS-ST (bottom) coupled to the same IFS cloud microphysics parameterization. The simulations were performed at quasi-uniform grid with an approximate resolution 30 km. Right: Elapsed time to run 1 day of the dry baroclinic instability benchmark similar to the current ECMWF’s highest-resolution (≈9 km, with 137 vertical levels) deterministic forecast model, using the nonhydrostatic finite-volume dynamical core (left), spectral-transform hydrostatic dynamical core (center), and nonhydrostatic spectral-transform core (right); see Kühnlein et al, Geosci. Model Dev., 12, 651-676, 2019.

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2012/ERC Grant agreement no. 320375), and from the ESIWACE project funded from the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement No 675191).