A regional implementation of a mixed finite-element, semi-implicit dynamical core

TL;DR

This work presents a regional adaptation of the Met Office's mixed finite-element, iterated-semi-implicit dynamical core (GungHo) implemented within the LFRic framework for one-way nesting in regional weather and climate forecasts. It achieves this by augmenting the regional solver RHS with lateral-boundary data from a driving model and employing a zeroing-matrix approach to restrict the solve to the interior, while allowing transport to be computed on the full mesh. A Davies-style blending scheme is used to mitigate inconsistencies when LBCs differ from interior states, with idealised baroclinic-wave and Schär Hill tests demonstrating that blending effectively stabilises the interior near boundaries and preserves large-scale structure. The results support the viability of a regional, high-resolution dynamical core and outline next steps to couple physical parameterisations and develop a regional mesh with interpolated LBCs for operational forecasts.

Abstract

This paper explores how to adapt a new dynamical core to enable its use in one-way nested regional weather and climate models, where lateral boundary conditions (LBCs) are provided by a lower-resolution driving model. The dynamical core has recently been developed by the Met Office and uses an iterated-semi-implicit time discretisation and mixed finite-element spatial discretisation. The essential part of the adaptation is the addition of the LBCs to the right-hand-side of the linear system which solves for pressure and momentum simultaneously. The impacts on the associated Helmholtz preconditioner and multigrid techniques are also described. The regional version of the dynamical core is validated through big-brother experiments based on idealised dynamical core tests. These experiments demonstrate that the subdomain results are consistent with those from the full domain, confirming the correct application of LBCs. Inconsistencies arise in cases where the LBCs are not perfect, but it is shown that the application of blending can be used to overcome these problems.

Figures (12)

• Figure 1: The domain is split into internal and external subdomains, divided by a boundary.
• Figure 2: The location of the degrees-of-freedom (dofs) for finite-elements in $\mathbb{W}_2$ and $\mathbb{W}_3$, and their relation to whether they are in the interior, exterior or on the boundary.
• Figure 3: Diagram of example 1D basis functions and solutions from the mixed system. (a) The basis functions for $\mathbb{W}_2$ (b) example coefficients (c) the basis functions multiplied by the coefficients (d) splitting into the interior $u'_I \in \mathbb{W}_2$ (green dash) and boundary $u'_B \in \mathbb{W}_2$ components (red solid) (e) the total solution $u' = u'_I + u'_B$, and (f) the total solution for pressure $\Pi' \in \mathbb{W}_3$. The boundaries are located at $x=0$ and $x=4$.
• Figure 4: LBC data is supplied in some of the external region. The solver boundary is the same as that in Fig. \ref{['fig:domain_ie']}.
• Figure 5: LBC data is supplied in some of the internal region, and is blended with the interior solution.