The set of equations governing the atmospheric motions employed in the operational Met Office NWP and global climate model is the non-hydrostatic and deep-atmosphere form of the Navier-Stokes equation set. The equations are discretised on a uniform lat-long Arakawa C-grid in the horizontal and a Charney-Phillips grid in the vertical using a semi-implicit semi-Lagrangian finite difference time integration (``New Dynamics'').

A key aspect in the development and testing of the New Dynamics was the creation of 1D and 2D versions of the model. These versions were used to investigate the numerical stability of the scheme, and to test its behaviour in the presence of orography and for different top and bottom boundary conditions. Some results from these idealised models have been presented at previous ``PDEs on the sphere''

workshops.

In order to bridge the gap between these experiments and various linear analyses, the linear normal modes of the exact 2D New Dynamics discretisation have been computed. The program has the flexibility to be used to analyse the 1D discretisation and different vertical staggering of the variables, and includes switches to change the top and bottom boundary conditions.

At present it has been used to compute the normal modes of the 1D column model with both an isentropic and an isothermal basic state. In the isentropic basic state case, the numerical results are found to agree well with the analytic ones. The normal modes of the isothermal basic state 1D column model have been used to initialise the 1D New Dynamics: some of the numerical results will be presented.

Future work will include: completing the analysis of the properties of the 1D and 2D versions of the existing discretisation, for different boundary conditions and vertical staggering of the variables; using the established normal mode model as a tool to analyse the properties of improved alternative discretisations, before implementing them in the full NWP model; and extending the program to include the trajectory calculation.