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Estimation of accuracy of different high-resolution, sound-filtered, pressure-coordinate models is carried out by modeling their response to orographic forcing. Evaluated models are the elastic nonhydrostatic model (EFM), the anelastic nonhydrostatic model (AEM), and the hydrostatic primitive equation model (HSM). These models are compared to the exact, nonfiltered, nonhydrostatic, pressure-coordinate dynamics (ExM). All model equations are linearized, a wave equation for vertical displacements of air particles is derived, and exact analytical stationary solutions for each model are compared for uniform flow over given smooth orography (bell-shaped mountain). These linear solutions reveal that compressible (ExM, EFM) and incompressible (AEM, HSM) models are different at long horizontal scales l ∼ 1000 km. Differences are especially large in the vertical velocity field (up to 100%) at the medium and upper levels of the atmosphere, where incompressible models give systematic reductions of wave ampl...

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller–Pearce–White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

Pressure (isobaric or p-) coordinates in non-hydrostatic (NH) dynamics with pressure in the role of the vertic al coordinate were first introduced by (1974), and generalized to sigma-coordinate framework by (1984). First numerical applicat ions of the NH model in pressure related coordinates where developed by (1991) for twodimensional case, and by (1992) for three-dimensional motion.

A nonhydrostatic pressure-coordinate model of atmospheric dynamics is developed. The model filters acoustic mode. Internal acoustic waves are filtered using the assumption of non-divergence of motion in pressure-space. External (Lamb mode) waves are filtered using the surface pressure adjustment. The model is implemented in the framework of the numerical weather prediction model HIRLAM (High Resolution Limited Area Model) as an extension to the hydrostatic kernel. The integration scheme is either the explicit or semi-implicit Eulerian leapfrog time stepping. Due to the acoustic filtration, the explicit scheme supports quite large time-steps. To check the validity of the model, several flow experiments with artificial orography are performed. The hydrostatic and nonhydrostatic flow regimes are investigated. The results of different models are compared mutually and with the analytic solutions. The real situation simulations are also presented to show the model’s forecasting capabilities. DOI: 10.1034/j.1600-0870.2003.00018.x