Abstract
Modeling nonhydrostatic atmospheric flow requires the solution of the vertical equation of motion and a prognostic or diagnostic equation for pressure. If the nonhydrostatic components of the flow are relatively small, they can be approximated and incorporated into a purely hydrostatic model, which usually is conceptually simpler and computationally more efficient. A method to do this for a linear model of local thermally-induced circulations is further developed and adapted to a non-linear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasi-nonhydrostatic version were used to simulate neutral flow over simple terrain features. One set of observations taken over a simple change in roughness and another set taken over a change in both roughness and terrain were simulated by both models to assess the capabilities of the quasi-nonhydrostatic technique.
It is found that (as expected) the pressure deviation from the hydrostatic state is negligible for the roughness change, but it is an important aspect of neutral flow over terrain. Thus, for flow encountering a simple roughness change, the hydrostatic approximation is good, even for small horizontal scales. However, the quasi-nonhydrostatic model qualitatively produces the features in the observations for flow over a terrain change that the hydrostatic model cannot produce.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, D. A., Tannehill, J. C., and Pletcher, R. H.: 1984, Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, p. 599.
Chang, L. P., Takle, E. S., and Sani, R. L.: 1982, ‘Development of a Two-Dimensional Finite-Element PBL Model and Two Preliminary Model Applications’, Mon. Wea. Rev. 110, 2025–2037.
Estoque, M. A.: 1974, ‘Numerical Modeling of the Planetary Boundary Layer’, in D. A. Haugen (ed.), Workshop on Micrometeorology, Amer. Meteorol. Soc., pp. 217–270.
Fast, J. D., and Takle, E. S.: 1988, ‘Application of a Quasi-Nonhydrostatic Parametrization for Modeling Neutral Flow over an Isolated Hill’, Boundary-Layer Meteorol. (in press).
Frost, W., Maus, J. R., and Fichtl, G. H.: 1974, ‘A Boundary-Layer Analysis of Atmospheric Motion over a Semi-Elliptical Surface Obstruction’, Boundary-Layer Meteorol. 7, 165–184.
Gresho, P. M. and Lee, R. L.: 1981, ‘Don't Suppress the Wiggles — They're Telling You Something!’, Comput. Fluids 9, 223–253.
Herwehe, J.: 1984, ‘Numerical Modeling of Turbulent Diffusion of Fugitive Dust from an Idealized Open-Pit Mine’, M. S. thesis, Library, Iowa State University, Ames, p. 336.
Hood, P. and Taylor, P.: 1974, ‘Navier-Stokes Equations Using Mixed Interpolation’, Proc. Int. Conf. on Finite Element Methods in Flow Problems, University of Alabama Press, pp. 121–132.
Jackson, P. S. and Hunt, J. C. R.: 1975, ‘Turbulent Wind Flow over a Low Hill’, Quart. J. Roy. Meteorol. Soc. 101, 929–955.
Koclas, P., Staniforth, A., and Wair, H.: 1986, ‘A Variable-Resolution Finite-Element Model of Frontogenesis’, Mon. Wea. Rev. 114, 1340–1353.
Mahrer, Y. and Pielke, R. A.: 1975, ‘A Numerical Study of the Air Flow over Mountains Using the Two-Dimensional Version of the University of Virginia Mesoscale Model’, J. Atmos. Sci. 32, 2144–2155.
Mahrer, Y. and Pielke, R. A.: 1977, ‘The Effects of Topography on Sea and Land Breezes in a Two-Dimensional Numerical Model’, Mon. Wea. Rev. 105, 1151–1162.
Martin, C. L.: 1981, ‘Numerical Accuracy in a Mesoscale Meteorological Model. University of Virginia Department of Environmental Sciences’, Report No. UVA-ENV SCI-MESO-1981-2, 86 pp.
Martin, C. L. and Pielke, R. A.: 1983, ‘The Adequacy of the Hydrostatic Assumption in Sea-Breeze Modeling over Flat Terrain’, J. Atmos. Sci. 40, 1472–1481.
Mason, P. J. and Sykes, R. I.: 1978, ‘A Simple Cartesian Model of Boundary Layer Flow over Topography’, J. Comput. Phys. 28, 198–210.
Mellor, G. L. and Blumberg, A. F.: 1985, ‘Modeling Vertical and Horizontal Diffusivities with the Sigma Coordinate System’, Mon. Wea. Rev. 113, 1379–1383.
Mulhearn, P. J.: 1977, ‘Relations Between Surface Fluxes and Mean Profiles of Velocity, Temperature and Concentration, Downwind of a Change in Surface Roughness’, Quart. J. Roy. Meteorol. Soc. 103, 785–802.
Neumann, J. and Mahrer, Y.: 1971, ‘A Theoretical Study of Land and Sea Breeze Circulations’, J. Atmos. Sci. 28, 532–542.
Orlanski, I.: 1981, ‘The Quasi-Hydrostatic Approximation’, J. Atmos. Sci. 38, 572–582.
Peterson, E. W.: 1969, ‘Modification of Mean Flow and Turbulent Energy by a Change in Surface Roughness Under Conditions of Neutral Stability’, Quart. J. Roy. Meteorol. Soc. 95, 561–575.
Peterson, E. W., Kristensen, L., and Su, C. C.: 1976, ‘Some Observations and Analysis of Wind over Non-Uniform Terrain’, Quart. J. Roy. Meteorol. Soc. 102, 857–869.
Peterson, E. W., Jensen, N. O., and Højstrup, J.: 1979, ‘Observations of Downwind Development of Wind Speed and Variance Profiles at Bognaes and Comparison with Theory’, Quart. J. Roy. Meteorol. Soc. 105, 521–529.
Peterson, E. W., Taylor, P. A., Højstrup, J., Jensen, N. O., Kristensen, L., and Petersen, E. L.: 1980, ‘Risø 1978: Further Investigations into the Effects of Local Terrain Irregularities on Tower-Measured Wind Profiles’, Boundary-Layer Meteorol. 19, 303–313.
Pielke, R. A.: 1972, ‘Comparison of a Hydrostatic and an Anelastic Dry Shallow Primitive Equation Model’, NOAA Tech. Memo., ERL OD-13, 47 pp.
Pielke, R. A.: 1984, Mesoscale Meteorological Modeling, Academic Press, New York, p. 612.
Rao, K. S., Wyngaard, J. C., and Cote, O. R.: 1974, ‘The Structure of the Two-Dimensional Internal Boundary Layer over a Sudden Change of Surface Roughness’, J. Atmos. Sci. 31, 738–746.
Russell, R. D. and Takle, E. S.: 1985, ‘A Numerical Study of the Effects of Synoptic Baroclinicity on Stable Boundary-Layer Evolution’, Boundary-Layer Meteorol. 31, 385–418.
Sani, R. L., Gresho, P. M., Lee, R. L., Griffiths, D., and Engelman, M.: 1981, ‘The Cause and Cure(?) of the Spurious Pressure Generated by Certain FEM Solutions of the Incompressible Navier-Stokes Equations’, in Int. J. Numerical Methods Fluids.
Sasaki, Y. K. and Chang, L. P.: 1982, ‘Methods in Numerical Weather Prediction: Where the Finite-Element Methods Stand?’, in T. Kawai (ed.), Finite Element Flow Analysis, University of Tokyo Press, pp. 27–33.
Song, J. L., Pielke, R. A., Segal, M., Arritt, R. W., and Kessler, R. C.: 1985, ‘A Method to Determine Nonhydrostatic Effects within Subdomains in a Mesoscale Model’, J. Atmos. Sci. 42, 2110–2120.
Tapp, M. C. and White, P. W.: 1976, ‘A Non-Hydrostatic Mesoscale Model’, Quart. J. Roy. Meteorol. Soc. 102, 277–296.
Taylor, P. A.: 1977, ‘Some Numerical Studies of Surface Boundary-Layer Flow Above Gentle Topography’, Boundary-Layer Meteorol. 11, 439–465.
Therry, G. and Lacarrℰe, P.: 1983, ‘Improving the Eddy Kinetic Energy Model for Planetary Boundary-Layer Description’, Boundary-Layer Metereol. 25, 66–88.
Author information
Authors and Affiliations
Additional information
Journal Paper No. J-12737 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2779.
Rights and permissions
About this article
Cite this article
Fast, J.D., Takle, E.S. Evaluation of an alternative method for numerically modeling nonhydrostatic flows over irregular terrain. Boundary-Layer Meteorol 44, 181–206 (1988). https://doi.org/10.1007/BF00117298
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00117298