Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective

Abstract

The semi-Lagrangian numerical method, in conjunction with semi-implicit time integration, provides numerical weather prediction models with numerical stability for large time steps, accurate modes of interest, and good representation of hydrostatic and geostrophic balance. Drawing on the legacy of dynamical cores at the Met Office, the use of the semi-implicit semi-Lagrangian method in an operational numerical weather prediction context is surveyed, together with details of the solution approach and associated issues and challenges. The numerical properties and performance of the current operational version of the Met Office's numerical model are then investigated in a simplified setting along with the impact of different modelling choices.

A Semi-Implicit Compressible Model for Atmospheric Flows with Seamless Access to Soundproof and Hydrostatic Dynamics

“…Examples of operational dynamical cores using semi-implicit timeintegrations strategies are the ECMWF 1 's IFS [19], that discretizes the hydrostatic primitive equations, and the UK Met Office's ENDGame [9,50]. In particular, ENDGame uses a double-loop structure in the implicit solver entailing four solves per time step in its operational incarnation, a strategy carried over in recent developments [30], and allowing non-operational configurations to run stably and second-order accurately without additional numerical damping (for operational forecasts, a small amount of off-centering is usually employed for safety reasons).…”

Instabilities in the Shallow-Water System with a Semi-Lagrangian, Time-Centered Discretization

“…This polynomial-based interpolation no longer preserves wave amplitudes, and instead it dissipates waves in proportion to their wavenumber (relative to the grid scale) and the distance between the interpolated, off-grid point and the nearest on-grid location. For example, bilinear interpolation "semi-implicit," while Benacchio and Wood (2016) suggests the phrase "iterative implicit" for a nonlinear, implicit system solved with a fixed number of iterations.…”

A modern-day Mars climate in the Met Office Unified Model: dry simulations

“…For this study, we take the Global Atmosphere 7.0 science configuration of the UM (Walters et al, 2019) and adapt it to Martian conditions. The UM dynamical core (ENDGame, described by Wood et al, 2014) simulates the atmosphere as a non-hydrostatic fully compressible fluid and its numerical formulation uses a semi-implicit timestep and semi-Lagrangian advection scheme (Benacchio and Wood, 2016). A full description of the model's dynamical core is given by Wood (2003, 2008); Wood et al (2014), with a global climate configuration further detailed by Walters et al (2019).…”