• Alaka, M. A., Ed., 1960: The airflow over mountains. WMO Tech. Rep. 34, 135 pp.

  • Baines, P. G., 1995: Topographic Effects in Stratified Flows. Cambridge University Press, 482 pp.

  • Bubnova, R., G. Hello, P. Benard, and J. F. Geleyn, 1995: Integration of the fully elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/Aladin NWP system. Mon. Wea. Rev.,123, 515–535.

  • Eliassen, A. 1949: The quasi-static equations of motion with pressure as independent variable. Geofys. Publ. (Oslo),17 (3), 44 pp.

  • Hereil, Ph., and R. Laprise, 1996: Sensitivity of internal gravity waves solutions to the time step of a semi-implicit semi-Lagrangian nonhydrostatic model. Mon. Wea. Rev.,124, 972–999.

  • Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3d ed. Academic Press, 511 pp.

  • Laprise, R., 1992: The Euler equations of motion with hydrostatic pressure as an independent variable. Mon. Wea. Rev.,120, 197–207.

  • ——, and W. R. Peltier, 1989: On the structural characteristics of steady finite-amplitude mountain waves over bell-shaped topography. J. Atmos. Sci.,46, 586–595.

  • Lin, Y.-L., and T.-A. Wang, 1996: Flow regimes and transient dynamics of two-dimensional stratified flow over an isolated mountain ridge. J. Atmos. Sci.,53, 139–158.

  • Long, R. R., 1953: Some aspects of the flow of stratified fluids. Part I: A theoretical investigation. Tellus,5, 42–58.

  • Miller, M. J., and R. P. Pearce, 1974: A three-dimensional primitive equation model of cumulonimbus convection. Quart. J. Roy. Meteor. Soc.,100, 133–154.

  • Miranda, P. M. A., and I. N. James, 1992: Non-linear three-dimensional effects on gravity-wave drag: Splitting flow and breaking waves. Quart. J. Roy. Meteor. Soc.,118, 1057–1081.

  • ——, and M. A. Valente, 1997: Critical level resonance in three-dimensional flow past isolated mountains. J. Atmos. Sci.,54, 1574–1588.

  • Nance, L. B., and D. R. Durran, 1994: A comparison of the accuracy of three anelastic systems and the pseudo-incompressible system. J. Atmos. Sci.,51, 3549–3565.

  • Queney, P., 1948: The problem of airflow over mountains: A summary of theoretical studies. Bull. Amer. Meteor. Soc.,29, 16–26.

  • Rõõm, R., 1989: The general form of dynamical equations of the atmosphere in the isobaric coordinate space. Proc. Est. Acad. Sci., Phys., Math.,38, 368–371.

  • ——, 1990: General form of the dynamical equations for the ideal atmosphere in the isobaric coordinate system. Izv. SSSR, Fiz. Atmos. Okeana,26, 17–26.

  • ——, 1997: Nonhydrostatic atmospheric dynamics in pressure-related coordinates. Tech. Rep., Estonian Science Foundation Grant 172, Tartu Observatory, 105 pp.

  • ——, 1998: Acoustic filtering in nonhydrostatic pressure coordinate dynamics: A variational approach. J. Atmos. Sci.,55, 654–668.

  • ——, and A. Ülejõe, 1996: Nonhydrostatic acoustically filtered equations of atmospheric dynamics in pressure coordinates. Proc. Est. Acad. Sci., Phys., Math.,45, 421–429.

  • Salmon, R., and L. M. Smith, 1994: Hamiltonian derivation of the nonhydrostatic pressure-coordinate model. Quart. J. Roy. Meteor. Soc.,120, 1409–1413.

  • Scorer, R. S., 1949: Theory of waves in the lee of mountains. Quart. J. Roy. Meteor. Soc.,75, 41–56.

  • ——, 1953: Theory of airflow over mountains: II—The flow over a ridge. Quart. J. Roy. Meteor. Soc.,79, 70–83.

  • ——, 1954: Theory of airflow over mountains: III—Airstream characteristics. Quart. J. Roy. Meteor. Soc.,80, 417–428.

  • ——, 1956: Airflow over an isolated hill. Quart. J. Roy. Meteor. Soc.,82, 75–81.

  • Smith, R. B., 1979: The influence of mountains on the atmosphere. Advances in Geophysics, Vol. 21, Academic Press, 87–230.

  • White, A. A., 1989: An extended version of nonhydrostatic, pressure coordinate model. Quart. J. Roy. Meteor. Soc.,115, 1243–1251.

  • Xue, M., and A. J. Thorpe, 1991: A mesoscale numerical model using the nonhydrostatic pressure-based sigma-coordinate equations: Model experiments with dry mountain flows. Mon. Wea. Rev.,119, 1168–1185.

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Responses of Different Nonhydrostatic, Pressure-Coordinate Models to Orographic Forcing

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  • 1 Tartu Observatory, Toravere, Estonia
  • | 2 Tartu University, Tartu, Estonia
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Abstract

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 amplitudes. All models are effectively incompressible and coincide with high precision in the region 10 km < l < 500–700 km. As expected, the first critical scale is l ∼ 10 km, below which the HSM fails. The second critical scale is at l ∼ 100 m (moderate winds) to l ∼ 1000 m (strong winds), below which the AEM becomes inconsistent with the other models in temperature fluctuation presentation. The EFM represents a universal approximation, valid at all scales.

Corresponding author address: Dr. Rein Rõõm, Tartu Observatory, EE2444 Tartumaa, Toravere, Estonia.

Email: room@aai.ee

Abstract

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 amplitudes. All models are effectively incompressible and coincide with high precision in the region 10 km < l < 500–700 km. As expected, the first critical scale is l ∼ 10 km, below which the HSM fails. The second critical scale is at l ∼ 100 m (moderate winds) to l ∼ 1000 m (strong winds), below which the AEM becomes inconsistent with the other models in temperature fluctuation presentation. The EFM represents a universal approximation, valid at all scales.

Corresponding author address: Dr. Rein Rõõm, Tartu Observatory, EE2444 Tartumaa, Toravere, Estonia.

Email: room@aai.ee

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