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Original Research Papers

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

Authors:

Rein Rõõm ,

Institute of Environmental Physics, Tartu University, likooli 18, 50090 Tartu, EE
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Aarne Männik,

Institute of Environmental Physics, Tartu University, likooli 18, 50090 Tartu, EE
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Andres Luhamaa

Institute of Environmental Physics, Tartu University, likooli 18, 50090 Tartu, EE
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Abstract

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.

How to Cite: Rõõm, R., Männik, A. and Luhamaa, A., 2007. Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme. Tellus A: Dynamic Meteorology and Oceanography, 59(5), pp.650–660. DOI: http://doi.org/10.1111/j.1600-0870.2007.00252.x
  Published on 01 Jan 2007
 Accepted on 19 Mar 2007            Submitted on 9 Aug 2006

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