A review of existing solution methodology for non-hydrostatic atmospheric models identified the split-explicit timestepping approach as the preferred solution method for a new non-hydrostatic atmospheric model. The linear advectionequation was used for stability analysis of different combinations of time integration and advection schemes beforethe third order Runge-Kutta (RK3) time integration scheme was chosen. A number of one- and two-dimensional testproblems were then applied to the linear advection equation to study the robustness of the different finite differenceadvection schemes. It was found that the third and fifth order upwind advection schemes have good phase propertiesand are generally robust even in coarse grid resolutions. The RK3 time integration scheme with third and fifth orderupwind advection schemes were then applied to the split explicit formulation for the new non-hydrostatic atmosphericmodel. The model was verified with well known test cases of increasing complexity. The performance of the new modelwas compared with other established non-hydrostatic models. Due to the highly non-linear ow in the test case, therewas some variability in simulation results from the other models. Our new model simulation results were all withinthe average of the majority of the models and was not an outlier.A two-dimensional version of the new model was used to study mountain waves in the middle atmosphere over thesouthern Andes. Using realistic temperatures, winds and topography, the model simulations generate large amplitudelong wavelength breaking mountain waves in the middle atmosphere that compare favourably with satellite measure-ments. Modelled waves have preferred horizontal wavelengths. Spectral analysis reveals correspondences betweenwavelengths and peaks in the spectrum of Andean topographic elevations. The shorter waves reach the stratospherewell before the longer ones, consistent with group velocity arguments, with longer wavelengths ultimately dominating.At later times we find evidence of downward propagating secondary waves produced by upper level breaking of theprimary waves.
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