Editorial Type:
Article
Article Type:
Research Article

A Finite-Difference GCM Dynamical Core with a Variable-Resolution Stretched Grid

Michael S. Fox-Rabinovitz University of Maryland at College Park, College Park, Maryland

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Georgiy L. Stenchikov University of Maryland at College Park, College Park, Maryland

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Max J. Suarez Goddard Space Flight Center, Greenbelt, Maryland

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Lawrence L. Takacs General Sciences Corporation, Laurel, Maryland

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Print Publication:
01 Nov 1997
DOI:
https://doi.org/10.1175/1520-0493(1997)125<2943:AFDGDC>2.0.CO;2
Page(s):
2943–2968
Restricted access

Abstract

A finite-difference atmospheric model dynamics, or dynamical core using variable resolution, or stretched grids, is developed and used for regional–global medium-term and long-term integrations.

The goal of the study is to verify whether using a variable-resolution dynamical core allows us to represent adequately the regional scales over the area of interest (and its vicinity). In other words, it is shown that a significant downscaling is taking place over the area of interest, due to better-resolved regional fields and boundary forcings. It is true not only for short-term integrations, but also for medium-term and, most importantly, long-term integrations.

Numerical experiments are performed with a stretched grid version of the dynamical core of the Goddard Earth Observing System (GEOS) general circulation model (GCM). The dynamical core includes the discrete (finite-difference) model dynamics and a Newtonian-type rhs zonal forcing, which is symmetric for both hemispheres about the equator. A flexible, portable global stretched grid design allows one to allocate the area of interest with uniform fine-horizontal (latitude by longitude) resolution over any part of the globe, such as the U.S. territory used in these experiments. Outside the region, grid intervals increase, or stretch, with latitude and longitude. The grids with moderate to large total (global) stretching factors or ratios of maximum to minimum grid intervals on the sphere are considered. Dynamical core versions with the total stretching factors ranging from 4 to 32 are used.

The model numerical scheme, with all its desirable conservation and other properties, is kept unchanged when using stretched grids. Two model basic horizontal filtering techniques, the polar or high-latitude Fourier filter and the Shapiro filter, are applied to stretched grid fields. Two filtering approaches based on the projection of a stretched grid onto a uniform one are tested. One of them does not provide the necessary computational noise control globally. Another approach provides a workable monotonic global solution. The latter is used within the developed stretched grid version of the GEOS GCM dynamical core that can be run in both the middle-range and long-term modes. This filtering approach allows one to use even large stretching factors.

The successful experiments were performed with the dynamical core for several stretched grid versions with moderate to large total stretching factors ranging from 4 to 32. For these versions, the fine resolutions (in degrees) used over the area of interest are 2 × 2.5, 1 × 1.25, 0.5 × 0.625, and 0.25 × 0.3125. Outside the area of interest, grid intervals are stretching to 4 × 5 or 8 × 10. The medium-range 10-day integrations with summer climate initial conditions show a pronounced similarity of synoptic patterns overthe area of interest and its vicinity when using a stretched grid or a control global uniform fine-resolution grid.

For a long-term benchmark integration performed with the first aforementioned grid, the annual mean circulation characteristics obtained with the stretched grid dynamical core appeared to be profoundly similar to those of the control run with the global uniform fine-resolution grid over the area of interest, or the United States. The similarity is also evident over the best resolved within the used stretched grid northwestern quadrant, whereas it does not take place over the least-resolved southeastern quadrant. In the better-resolved Northern Hemisphere, the jet and Hadley cell are close to those of the control run, which does not take place for the Southern Hemisphere with coarser variable resolution. The stretched grid dynamical core integrations have shown no negative computational effects accumulating in time.

The major result of the study is that a stretched grid approach allows one to take advantage of enhanced resolution over the region of interest. It provides a better representation of regional fields for both medium-term and long-term integrations.

The developed stretched grid model dynamics is supposed to be the first stage of the development of the full diabatic stretched grid GEOS GCM. It will be implemented, within a portable stretched grid approach, for various regional studies with a consistent representation of interactions between global and regional scales and phenomena.

Corresponding author address: Dr. Michael Fox-Rabinovitz, University of Maryland, Suite 200, 7501 Forbes Blvd., Seabrook, MD 20706.

Abstract

A finite-difference atmospheric model dynamics, or dynamical core using variable resolution, or stretched grids, is developed and used for regional–global medium-term and long-term integrations.

The goal of the study is to verify whether using a variable-resolution dynamical core allows us to represent adequately the regional scales over the area of interest (and its vicinity). In other words, it is shown that a significant downscaling is taking place over the area of interest, due to better-resolved regional fields and boundary forcings. It is true not only for short-term integrations, but also for medium-term and, most importantly, long-term integrations.

Numerical experiments are performed with a stretched grid version of the dynamical core of the Goddard Earth Observing System (GEOS) general circulation model (GCM). The dynamical core includes the discrete (finite-difference) model dynamics and a Newtonian-type rhs zonal forcing, which is symmetric for both hemispheres about the equator. A flexible, portable global stretched grid design allows one to allocate the area of interest with uniform fine-horizontal (latitude by longitude) resolution over any part of the globe, such as the U.S. territory used in these experiments. Outside the region, grid intervals increase, or stretch, with latitude and longitude. The grids with moderate to large total (global) stretching factors or ratios of maximum to minimum grid intervals on the sphere are considered. Dynamical core versions with the total stretching factors ranging from 4 to 32 are used.

The model numerical scheme, with all its desirable conservation and other properties, is kept unchanged when using stretched grids. Two model basic horizontal filtering techniques, the polar or high-latitude Fourier filter and the Shapiro filter, are applied to stretched grid fields. Two filtering approaches based on the projection of a stretched grid onto a uniform one are tested. One of them does not provide the necessary computational noise control globally. Another approach provides a workable monotonic global solution. The latter is used within the developed stretched grid version of the GEOS GCM dynamical core that can be run in both the middle-range and long-term modes. This filtering approach allows one to use even large stretching factors.

The successful experiments were performed with the dynamical core for several stretched grid versions with moderate to large total stretching factors ranging from 4 to 32. For these versions, the fine resolutions (in degrees) used over the area of interest are 2 × 2.5, 1 × 1.25, 0.5 × 0.625, and 0.25 × 0.3125. Outside the area of interest, grid intervals are stretching to 4 × 5 or 8 × 10. The medium-range 10-day integrations with summer climate initial conditions show a pronounced similarity of synoptic patterns overthe area of interest and its vicinity when using a stretched grid or a control global uniform fine-resolution grid.

For a long-term benchmark integration performed with the first aforementioned grid, the annual mean circulation characteristics obtained with the stretched grid dynamical core appeared to be profoundly similar to those of the control run with the global uniform fine-resolution grid over the area of interest, or the United States. The similarity is also evident over the best resolved within the used stretched grid northwestern quadrant, whereas it does not take place over the least-resolved southeastern quadrant. In the better-resolved Northern Hemisphere, the jet and Hadley cell are close to those of the control run, which does not take place for the Southern Hemisphere with coarser variable resolution. The stretched grid dynamical core integrations have shown no negative computational effects accumulating in time.

The major result of the study is that a stretched grid approach allows one to take advantage of enhanced resolution over the region of interest. It provides a better representation of regional fields for both medium-term and long-term integrations.

The developed stretched grid model dynamics is supposed to be the first stage of the development of the full diabatic stretched grid GEOS GCM. It will be implemented, within a portable stretched grid approach, for various regional studies with a consistent representation of interactions between global and regional scales and phenomena.

Corresponding author address: Dr. Michael Fox-Rabinovitz, University of Maryland, Suite 200, 7501 Forbes Blvd., Seabrook, MD 20706.

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  • Anthes, R. A., 1970: Numerical experiments with a two-dimensional horizontal variable grid. Mon. Wea. Rev.,98, 810–822.

  • ——, 1983: Regional models of the atmosphere in middle latitudes. Mon. Wea. Rev.,111, 1306–1335.

  • Arakawa, A., and V. R. Lamb, 1981: A potential enstrophy and energy conserving scheme for the shallow water equations. Mon. Wea. Rev.,109, 18–36.

  • ——, and M. J. Suarez, 1983: Vertical differencing of the primitive equations in sigma coordinates. Mon. Wea. Rev.,111, 34–45.

  • Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea.Rev.,100, 487–490.

  • Berger, M., and J. Oliger, 1984: Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys.,53, 484–512.

  • Brown, J. A., and K. Campana, 1978: An economical time-differencing system for numerical weather prediction. Mon. Wea. Rev.,106, 1125–1136.

  • Browning, M., O. Kreiss, and J. Oliger, 1973: Mesh refinements. Math. Comput.,27, 29–39.

  • Burridge, D. M., and J. Haseler, 1977: A model for medium range weather forecasting-adiabatic formulation. European Centre for Medium-Range Weather Forecasts Tech. Rep., 63 pp. [Available from European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, United Kingdom.].

  • Charney, J. G., 1966: Some remaining problems in numerical weather prediction. Advances in Numerical Weather Prediction, Travelers Research Center, 61–70. [Available from Archives and Special Collections Library, Building 14N-118, Massachusetts Institute of Technology, Cambridge, MA 02139.].

  • ——, R. Fjortoft, and J. von Neuman, 1950: Numerical integration of the barotropic vorticity equation. Tellus,2, 237–254.

  • Cotê, J., M. Roch, A. Staniforth, and L. Fillion, 1993: A variable-resolution semi-Lagrangian finite-element global model of the shallow-water equations. Mon. Wea. Rev.,121, 231–243.

  • Courtier, P., and J.-F. Geleyn, 1988: A global numerical weather prediction model with variable resolution: Application to the shallow-water equations. Quart. J. Roy. Meteor. Soc.,114, 1321–1346.

  • Davies, H. C., 1976: A lateral boundary formulation for multi-level prediction models. Quart. J. Roy. Meteor. Soc.,102, 405–418.

  • Déqué, M., and J. P. Piedelievre, 1995: High resolution climate simulation over Europe. Climate Dyn.,11, 321–339.

  • Dietachmayer, G. S., and K. K. Droegemeier, 1992: Application of continuous dynamic grid adaption techniques to meteorological modeling. Part I: Basic formulation and accuracy. Mon. Wea. Rev.,120, 1675–1706.

  • Fletcher, C. A. J., 1988: Computational Techniques for Fluid Dynamics. Vol. 2. Springer-Verlag, 541 pp.

  • Fox-Rabinovitz, M. S., 1974: Economical explicit and semi-implicit integration schemes for forecast equations. Sov. Meteor. Hydrol.,11, 11–19.

  • ——, 1988: Dispersion properties of some regular and irregular grids used in atmospheric models. Preprints, Eighth Conf. on Numerical Weather Prediction, Baltimore, MD, Amer. Meteor. Soc., 784–789.

  • Gates, W. L., 1992: AMIP: The Atmospheric Model Intercomparison Project. Bull. Amer. Meteor. Soc.,73, 1962–1970.

  • Giles, M. B., and W. T. Thompkins Jr., 1985: Propagation and stability of wavelike solutions of finite difference equations with variable coefficients. J. Comput. Phys.,58, 349–360.

  • Gravel, S., and A. Staniforth, 1992: Variable resolution and robustness. Mon. Wea. Rev.,120, 2633–2640.

  • Hardiker, V., 1997: A global numerical weather prediction model with variable resolution. Mon. Wea. Rev.,125, 59–73.

  • Held, I. M., and M. J. Suarez, 1994: A benchmark calculation for the dry dynamical cores of atmospheric generalcirculation models. Bull. Amer. Meteor. Soc.,75, 1825–1830.

  • Kalnay, E., M. Kanamitsu, J. Pfaendtner, J. Sela, M. Suarez, J. Stackpole, J. Tuccillo, L. Umscheid, and D. Williamson, 1989: Rules for the interchange of physical parameterizations, Bull. Amer. Meteor. Soc.,70, 620–622.

  • Koch, S. E., and J. T. McQueen, 1987: A survey of nested grid techniques and their potential for use within the MASS weather prediction model. NASA Tech. Memo. TM-87808, 25 pp. [Available from National Technical Information Service, Springfield, VA 22161.].

  • Kurihara, Y., 1965: Numerical integration of the primitive equations on a spherical grid. Mon. Wea. Rev.,93, 399–415.

  • Lindzen, R. S., and M. S. Fox-Rabinovitz, 1989: Consistent vertical and horizontal resolution. Mon. Wea. Rev.,117, 2575–2583.

  • Lorenz, E. N., 1960: Energy and numerical weather prediction. Tellus,12, 364–373.

  • Mesinger, F., and A. Arakawa, 1976: Numerical methods used in atmospheric models. WMO/ICSU Joint Organizing Committee, GARP Publications Series 17, 64 pp. [Available from World Meteorological Organization, C. P. No. 2300, CH. 1211 Geneva 2, Switzerland.].

  • Oliger, J., and A. Sundström, 1978: Theoretical and practical aspects of some initial boundary value problems in fluid dynamics. SIAM J. Appl. Math.,35, 419–446.

  • Paegle, J., 1989: A variable resolution global model based upon Fourier and finite-element representation. Mon. Wea. Rev.,117, 583–606.

  • Phillips, N. A., 1957: A coordinate system having some special advantages for numerical forecasting. J. Meteor.,14, 184–185.

  • ——, 1959: An example of non-linear computational instability. The Atmosphere and the Sea in Motion, Rossby Memorial Volume, Rockefeller Institute Press, 501–504.

  • ——, 1979: The nested grid model. NOAA Tech. Rep. NWS22, 80 pp. [Available from National Technical Information Service, Springfield, VA 22161.].

  • Pielke, R. A., and Coauthors, 1992: A comprehensive meteorological modeling system—RAMS. Meteor. Atmos. Phys.,49, 69–91.

  • Roache, P. J., 1976: Computational Fluid Dynamics. Hermosa Publishers, 446 pp.

  • Robert, A., 1966: The integration of low order spectral form of the primitive meteorological equations. J. Meteor. Soc. Japan,44, 237–245.

  • ——, and E. Yakimiw, 1986: Identification and elimination of an inflow boundary computational solution in limited area model integrations. Atmos.–Ocean,24, 369–385.

  • Sadourny, R., 1975: The dynamics of finite difference models of the shallow water equations. J. Atmos. Sci.,32, 680–689.

  • Schmidt, F., 1977: Variable fine mesh in a spectral global model. Beitr. Phys. Atmos.,50, 211–217.

  • Schuman, F. G., 1971: Resuscitation of an integration procedure. NMC Office Note 54, 55 pp. [Available from National Center for Environmental Prediction/NOAA, 5200 Auth Road, Camp Spring, MD 20746.].

  • Shapiro, R., 1970: Smoothing, filtering and boundary effects. Rev. Geophys. Space Phys.,8, 359–387.

  • Skamarock, W. C., 1989: Truncation error estimates for refinement criteria in nested and adaptive models.Mon. Wea. Rev.,117, 872–886.

  • ——, J. Oliger, and R. L. Street, 1989: Adaptive grid refinement for numerical weather prediction. J. Comput. Phys.,80, 27–60.

  • Staniforth, A., 1995: Regional modeling: Theoretical discussion. WMO PWPR Report Series 7, WMO/TD-No. 699, 72 pp. [Available from World Meteorological Organization, C. P. No. 2300, CH. 1211 Geneva 2, Switzerland.].

  • ——, and H. Mitchell, 1978: A variable resolution finite element technique for regional forecasting with primitive equations. Mon. Wea. Rev.,106, 439–447.

  • ——, J. Cotê, L. Fillion, and M. Roch, 1991: A variable-resolution finite-element semi-Lagrangian global model of the shallow water equations. Preprints, Ninth Conf. on Numerical Weather Prediction, Denver, CO, Amer. Meteor. Soc., 621–622.

  • Suarez, M. J., and L. L. Takacs, 1995: Documentation of the Aries/GEOS Dynamical Core Version 2. NASA Tech. Memo. 104606, 103 pp. [Available from NASA, Goddard Space Flight Center, Greenbelt, MD 20771.].

  • Takacs, L. L., and M. J. Suarez, 1996: Dynamical aspects of climate simulations using the GEOS GCM. NASA Tech. Memo. 104606, Vol. 10, 56 pp. [Available from NASA, Goddard Space Flight Center, Greenbelt, MD 20771.].

  • ——, A. Molod, and T. Wang, 1994: Goddard Earth Observing System (GEOS) General Circulation Model (GCM) Version 1. NASA Tech. Memo. 104606 Vol. 1, 97 pp. [Available from NASA, Goddard Space Flight Center, Greenbelt, MD 20771.].

  • Thompson, J. F., 1984: Grid generation techniques in computational fluid mechanics. AIAA J.,22, 1505–1523.

  • ——, Z. U. A. Warsi, and C. W. Mastin, 1985: Numerical Grid Generation: Foundations and Applications. North-Holland, 483 pp.

  • Vichnevetsky, R., 1987: Wave propagation and reflection in irregular grids for hyperbolic equations. Appl. Numer. Math.,2 (1–2), 133–166.

  • ——, and L. H. Turner, 1991: Spurious scattering from discontinuously stretching grids in computational fluid dynamics. J. Appl. Math.,8, 315–428.

  • Wilhelmson, R. B., and C. S. Chen, 1982: A simulation of the development of successive cells along a cold outflow boundary. J. Atmos. Sci.,39, 1466–1483.

  • Williamson, D., and G. L. Browning, 1974: Formation of the lateral boundary conditions for the NCAR limited area model. J. Appl. Meteor.,13, 8–15.

  • Yakimiw, E., and A. Robert, 1990: Validation experiments for a nested grid-point regional forecast model. Atmos.–Ocean,28, 466–472.

  • Yessad, K., and P. Benard, 1996: Introduction of a local mapping factor in the spectral part of the Meteo-France global variable mesh numerical forecast model. Quart. J. Roy. Meteor. Soc.,122, 1701–1719.

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