Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model

Abstract

SUMMARYThe impact of one-and two-term extrapolated-trajectory schemes on the stability properties of centred semiimplicit semi-Lagrangian schemes is analysed by examining the behaviour of the discrete (acoustic) normal modes of a prototypical column model. It is found that, in the absence of any controlling mechanism, both extrapolated-trajectory schemes are unstable. Additionally, they can significantly distort the vertical structure of the modes. Though not studied herein, the analogous distortion of Rossby and gravity waves could be expected to be deleterious to a forecast model.

Dynamical kernel of the Aladin–NH spectral limited‐area model: Revised formulation and sensitivity experiments

“…However, as mentioned in Cullen (2001), in the case of 2-TL SL ICI schemes, using implicit winds available from the previously completed iteration is a better choice (see also Cordero et al, 2005). This approach is therefore implemented in Aladin-NH.…”

An iterative time‐stepping scheme for the Met Office's semi‐implicit semi‐Lagrangian non‐hydrostatic model

“…Additionally, as discussed in Section 3, time extrapolation of the wind field at t n+1/2 is required in order to compute the departure points. As shown recently by Cordero et al (2005), this may cause instability in an SISL non-hydrostatic model and significantly distort the vertical structure of the normal modes. However, if the time extrapolation is replaced by time interpolation, the instability is removed.…”

“…As mentioned above, a disadvantage of this approach is that the temporal extrapolation, Eqn (11), introduces an instability: see (Cordero et al, 2005) for a discussion.…”

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

“…This aspect has led to various approximations being used, for a discussion of some of which see [32]. As analyzed by [33] though, many of these approximations lead to instabilities. The advantage of employing an iterative scheme, as discussed in section 2.3, is that these issues can be avoided by embedding the departure point calculation within that iterative scheme so that, at convergence, expression (11) is recovered.…”

“…Here we follow in the steps of the analysis in [33,34] and report numerical results of ENDGame runs, evaluating the impact of different modelling choices. A standard direct method (Thomas's algorithm) was used for the solution of the tridiagonal solve in the simplified one-dimensional setting.…”