Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Hsu, Wu-Ron; Sun, Wen-Yih (2011)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article
In this paper, we present a numerical procedure for solving a 2-dimensional, compressible, andnonhydrostatic system of equations. A forward-backward integration scheme is applied to treathigh-frequency and internal gravity waves explicitly. The numerical procedure is shown to beneutral in time as long as a Courant–Friedrichs–Lewy criterion is met. Compared to the leapfrog-scheme most models use, this method involves only two time steps, which requires lessmemory and is also free from unstable computational modes. Hence, a time-filter is not needed.Advection and diffusion terms are calculated with a time step longer than sound-wave relatedterms, so that extensive computer time can be saved. In addition, a new numerical procedurefor the free-slip bottom boundary condition is developed to avoid using inaccurate one-sidedfinite difference of pressure in the surface horizontal momentum equation when the terraineffect is considered. We have demonstrated the accuracy and stability of this new model in bothlinear and nonlinear situations. In linear mountain wave simulations, the model results matchthe corresponding analytical solution very closely for all three cases presented in this paper.The analytical streamlines for uniform flow over a narrow mountain range were obtainedthrough numerical integration of Queney’s mathematical solution. It was found that Queney’soriginal diagram is not very accurate. The diagram had to be redrawn before it was used toverify our model results. For nonlinear tests, we simulated the famous 1972 Boulder windstormand a bubble convection in an isentropic enviroment. Although there are no analytical solutionsfor the two nonlinear tests, the model results are shown to be very robust in terms of spatialresolution, lateral boundary conditions, and the use of the time-split scheme.DOI: 10.1034/j.1600-0870.2001.01178.x
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Bacmeister, J. T. and Pierrehumbert, R. T. 1988. On high-drag states of nonlinear stratified flow over an obstacle. J. Atmos. Sci. 45, 63-80.
    • Carpenter, K. M. 1979. An experimental forecast using a non-hydrostatic mesoscale model. Quart. J. Roy. Meteor. Soc. 105, 629-655.
    • Chen, S. H. 1999. T he development of a nonhydrostatic model and a numerical study of flash flooding in the Ohio Valley. PhD thesis. Department of Earth and Atmospheric Sciences, Purdue University, 181 pp.
    • Chern, J. D. 1994. Numerical simulations of cyclogenesis over the western United States. PhD thesis. Department of Earth and Atmospheric Sciences, Purdue University, 178 pp.
    • Clark, T. L. 1977. A small scale dynamical model using a terrain following coordinate transformation. J. Comput. Phys. 24, 136-215.
    • Crowley, W. P. 1968. Numerical advection experiments. Mon. Wea. Rev. 96, 1-11.
    • Cullen, M. J. P. 1990. A test of a semi-implicit integration technique for a fully compressible non-hydrostatic model. Quart. J. Roy. Meteor. Soc. 116, 1253-1258.
    • Doyle, J. D., Durran, D. R., Chen, C., Colle, B. A., Georgelin, M., Grubisic, V., Hsu, W. R., Huang, C. Y., Landau, D., Lin, Y. L., Poulos, G. S., Sun, W. Y., Weber, D. B. Wurtele, M. G. and Xue, M. 2000. An intercomparison of model predicted wave breaking for the 11 January 1972 Boulder windstorm. Mon. Wea. Rev. 121, 1493-1513.
    • Dudhia, J. 1993. A nonhydrostatic version of the Penn State-NCAR Mesoscale Model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev. 128, 901-914.
    • Durran, D. R. 1986. Another look at downslope windstorms. Part I: The development of analogs of supercritical flow in an infinitely deep, continuously stratified fluid. J. Atmos. Sci. 43, 2527-2543.
    • Durran, D. R. 1990. Mountain waves and downslope winds. Atmospheric process over complex terrain, 23. Blumen, W. (ed.). AMS, 59-81.
    • Durran, D. R. and Klemp, J. B. 1982. The eVects of moisture on trapped mountain lee waves. Mon. Wea. Rev. 110, 2490-2506.
    • Durran, D. R. and Klemp, J. B. 1983. A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev. 111, 2341-2361.
    • Durran, D. R. and Klemp, J. B. 1987. Another look at downslope windstorms. Part II: Nonlinear amplification beneath wave-overturning layers. J. Atmos. Sci. 44, 3402-3412.
    • Gadd, A. J. 1978. A split explicit integration scheme for numerical weather prediction. Quart. J. Roy. Meteor. Soc. 104, 569-582.
    • Gill, A. E. 1982. Atmosphere-ocean dynamics. Academic Press, New York, 662 pp.
    • Hodur, R. M. 1997. The Naval Research Laboratory Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev. 125, 1414-1430.
    • Hsu, W. R. and Sun, W. Y. 1994. A numerical study of a low-level jet and its accompanying secondary circulation in a Mei-Yu system. Mon. Wea. Rev. 122, 324-340.
    • Ikawa, M. 1988. Comparison of some schemes for nonhydrostatic models with orography. J. Meteor. Soc. Japan. 66, 753-776.
    • Klemp, J. B. and Lilly, D. K. 1975. The dynamics of wave-induced downslope winds. J. Atmos. Sci. 32, 320-339.
    • Klemp, J. B. and Lilly, D. K. 1980. Mountain waves and momentum flux GARP Pub. Ser. 23. Orographic eVects in planetary flows. ICSU/WMO, 450 pp.
    • Klemp, J. B. and Wilhelmson, R. 1978. The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci. 35, 1070-1096.
    • Kundu, P. K. 1990. Fluid mechanics. Academic Press, New York, 638 pp.
    • Lilly, D. K. 1978. A severe downslope windstorm and aircraft turbulence induced by a mountain wave. J. Atmos. Sci. 35, 59-77.
    • Ogura, Y. and Phillips, N. A. 1962. Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci. 19, 173-179.
    • Peltier, W. R. and Clark, T. L. 1979. The evolution and stability of finite-amplitude mountain waves. Part II: Surface drag and severe downslope windstorms. J. Atmos. Sci. 36, 1498-1529.
    • Pielke, R. A., Cotton, W. R., Walko, R. L., Tremback, C. J., Lyons, W. A., Grasso, L. D., Nicholls, M. E., Moran, M. D., Wesley, D. A., Lee, T. J. and Copeland, J. H. 1992. A comprehensive meteorological modeling system - RAMS, Meteor. Atmos. Phys. 49, 69-91.
    • Pinty, J.-P., Benoit, R., Richard, E. and Laprise, R. 1995. Simple tests of a semi-implicit semi-Lagrangian model on 2D mountain wave problems. Mon. Wea. Rev. 123, 3042-3058.
    • Queney, P. 1948. The problem of airflow over mountains: A summary of theoretical studies. Bull. Amer. Meteor. Soc. 29, 16-26.
    • Robert, A. 1993. Bubble convection experiments with a semi-implict formulation of the Euler equations. J. Atmos. Sci. 50, 1865-1873.
    • Scorer, R. S. 1949. Theory of waves in the lee of mountains. Quart. J. Roy. Meteor. Soc. 75, 41-56.
    • Skamarock W. C. and Klemp, J. B. 1992. The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon. Wea. Rev. 120, 2109-2127.
    • Smith, R. B. 1979. The influence of mountains on the atmosphere. In: Advances in Geophysics, vol. 21 (B. Saltzman ed.), pp. 87-230. Academic Press.
    • Smith, R. B. 1985. On severe downslope winds. J. Atmos. Sci. 42, 2597-2603.
    • Smolarkiewicz, P. K. and Margolin, L. G. 1997. On forward-in-time diVerencing for fluids: An Eulerian/ semi-Lagrangian nonhydrostatic model for stratified flows. Atmos.-Ocean 35, 127-152.
    • Steppeler, J. 1995. Comments on ''A nonhydrostatic version of the Penn State-NCAR Mesoscale Model: Validation tests and simulations of an Atlantic cyclone and cold front.'' Mon. Wea. Rev. 123, 2572.
    • Sun, W. Y. 1980. A forward-backward time integration scheme to treat internal gravity waves. Mon. Wea. Rev. 108, 402-407.
    • Sun, W. Y. 1993. Numerical experiment for advection equation. J. Comput. Physics. 108, 264-271.
    • Sun, W. Y. and Hsu, W. R. 1988. Numerical study of cold air outbreak over the warm ocean. J. Atmos. Sci. 45, 1205-1227.
    • Sun, W. Y., Cherm, J. D., Wu. C. C. and Hsu, W. R. 1991. Numerical simulation of mesoscale circulation in Taiwan and surrounding area. Mon. Wea. Rev. 119, 2558-2573.
    • Tanquay, M., Robert, A. and Laprise, R. 1990. A semiimplicit semi-Lagrangian full compressible regional forecast model. Mon. Wea. Rev. 118, 1970-1980.
    • Tapp, M. C. and White, P. W. 1976. A non-hydrostatic mesoscale model. Quart. J. Roy. Meteor. Soc. 102, 277-296.
  • No related research data.
  • No similar publications.

Share - Bookmark

Funded by projects

  • NSF | The Importance of Halogen A...

Cite this article

Collected from