• Chorin, A. J., 1968: Numerical solution of the Navier–Stokes equations. Math. Comput., 22 , 745762.

  • Davies, L. A., and A. R. Brown, 2001: Assessment of which scales orography can be credibly resolved in a numerical model. Quart. J. Roy. Meteor. Soc., 127 , 12251237.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and R. B. Smith, 2003: Mountain waves over the Hohe Tauren: Influence of upstream diabatic effects. Quart. J. Roy. Meteor. Soc., 129 , 799823.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and Q. Jiang, 2006: Observations and numerical simulations of mountain waves in the presence of directional wind shear. Quart. J. Roy. Meteor. Soc., 132 , 18771905.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1986: Mountain waves. Mesoscale Meteorology and Forecasting, P. S. Ray, Ed., Amer. Meteor. Soc., 472–492.

  • Durran, D. R., 1999: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, 465 pp.

  • Garvert, M. F., B. Smull, and C. Mass, 2007: Multiscale mountain waves influencing a major orographic precipitation event. J. Atmos. Sci., 64 , 711737.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Grubišić, V., and Coauthors, 2008: The Terrain-Induced Rotor Experiment: A field campaign overview including observational highlights. Bull. Amer. Meteor. Soc., 89 , 15131533.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., 2006: Ensemble-based atmospheric data assimilation: A tutorial. Predictability of Weather and Climate, T. Palmer and R. Hagedorn, Eds., Cambridge University Press, 124–156.

    • Search Google Scholar
    • Export Citation
  • Hodur, R. M., 1997: The Naval Research Laboratory’s Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev., 125 , 14141430.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and R. Wilhelmson, 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35 , 10701096.

  • Klemp, J. B., W. C. Skamarock, and O. Furhrer, 2003: Numerical consistency of metric terms in terrain-following coordinates. Mon. Wea. Rev., 131 , 12291239.

    • Search Google Scholar
    • Export Citation
  • McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44 , 17751800.

    • Search Google Scholar
    • Export Citation
  • Mesinger, F., and A. Arakawa, 1976: Numerical Methods Used in Atmospheric Models. GARP Publication Series, Vol. 17, World Meteorological Organization, 64 pp.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., G. J. Shutts, and R. Swinbank, 1986: Alleviation of systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization. Quart. J. Roy. Meteor. Soc., 112 , 10011039.

    • Search Google Scholar
    • Export Citation
  • Peltier, W. R., and T. L. Clark, 1979: The evolution and stability of finite-amplitude mountain waves. II: Surface wave drag and severe downslope windstorms. J. Atmos. Sci., 36 , 14981529.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., 2006: Positive-definite and monotonic limiters for unrestricted-time-step transport schemes. Mon. Wea. Rev., 134 , 22412250.

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

  • Torn, R. D., G. J. Hakim, and C. Snyder, 2006: Boundary conditions for a limited-area ensemble Kalman filter. Mon. Wea. Rev., 134 , 24902502.

    • Search Google Scholar
    • Export Citation
  • Volkert, H., C. Keil, C. Kiemle, G. Poberaj, J. Chaboureau, and E. Richard, 2003: Gravity waves over the eastern Alps: A synopsis of the 25 October 1999 event (IOP 10) combining in situ and remote-sensing measurements with a high-resolution simulation. Quart. J. Roy. Meteor. Soc., 129 , 777797.

    • Search Google Scholar
    • Export Citation
  • Webster, S., A. R. Brown, D. R. Cameron, and C. P. Jones, 2003: Improvements to the representation of the orography in the Met Office Unified Model. Quart. J. Roy. Meteor. Soc., 129 , 19892010.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 218 218 218
PDF Downloads 1 1 1

The Overamplification of Gravity Waves in Numerical Solutions to Flow over Topography

View More View Less
  • 1 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
Restricted access

Abstract

The tendency of high-resolution numerical weather prediction (NWP) models to overpredict the strength of vertically propagating mountain waves is explored. Discrete analytic mountain-wave solutions are presented for the classical problem of cross-mountain flow in an atmosphere with constant wind speed and stability. Time-dependent linear numerical solutions are also obtained for more realistic atmospheric structures. On one hand, using second-order-accurate finite differences on an Arakawa C grid to model nonhydrostatic flow over what might be supposed to be an adequately resolved 8Δx-wide mountain can lead to an overamplification of the standing mountain wave by 30%–40%. On the other hand, the same finite-difference scheme underestimates the wave amplitude in hydrostatic flow over an 8Δx-wide mountain. Increasing the accuracy of the advection scheme to the fourth order significantly reduces the numerical errors associated with both the hydrostatic and nonhydrostatic discrete solutions. The Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model is used to generate two 70-member ensemble simulations of a mountain-wave event during the Terrain-Induced Rotor Experiment. It is shown that switching from second-order advection to fourth-order advection leads to as much as a 20 m s−1 decrease in vertical velocity on the lee side of the Sierra Nevada, and that the weaker fourth-order solutions are more consistent with observations.

* Current affiliation: National Research Council, Naval Research Laboratory, Monterey, California.

Corresponding author address: Patrick A. Reinecke, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. Email: alex.reinecke@nrlmry.navy.mil

This article included in the Terrain-Induced Rotor Experiment (T-Rex) special collection.

Abstract

The tendency of high-resolution numerical weather prediction (NWP) models to overpredict the strength of vertically propagating mountain waves is explored. Discrete analytic mountain-wave solutions are presented for the classical problem of cross-mountain flow in an atmosphere with constant wind speed and stability. Time-dependent linear numerical solutions are also obtained for more realistic atmospheric structures. On one hand, using second-order-accurate finite differences on an Arakawa C grid to model nonhydrostatic flow over what might be supposed to be an adequately resolved 8Δx-wide mountain can lead to an overamplification of the standing mountain wave by 30%–40%. On the other hand, the same finite-difference scheme underestimates the wave amplitude in hydrostatic flow over an 8Δx-wide mountain. Increasing the accuracy of the advection scheme to the fourth order significantly reduces the numerical errors associated with both the hydrostatic and nonhydrostatic discrete solutions. The Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model is used to generate two 70-member ensemble simulations of a mountain-wave event during the Terrain-Induced Rotor Experiment. It is shown that switching from second-order advection to fourth-order advection leads to as much as a 20 m s−1 decrease in vertical velocity on the lee side of the Sierra Nevada, and that the weaker fourth-order solutions are more consistent with observations.

* Current affiliation: National Research Council, Naval Research Laboratory, Monterey, California.

Corresponding author address: Patrick A. Reinecke, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. Email: alex.reinecke@nrlmry.navy.mil

This article included in the Terrain-Induced Rotor Experiment (T-Rex) special collection.

Save