Skip to main content
SpringerLink
Log in

Spectral Methods in Global Climate and Weather Prediction Models

  • Chapter
Physically-Based Modelling and Simulation of Climate and Climatic Change

Part of the book series: NATO ASI Series ((ASIC,volume 243))

Abstract

Global models of atmospheric flow based on a spectral representation of the horizontal variation of dynamic variables have now become widely used in both research and operational environments. The detailed formulation of such models is discussed in the present chapter. Consideration is given to the properties of spherical harmonics, the principles of the transform method, primitive equation model formulation, model linearizations relevant to normal modes and semi-implicit time differencing, and to the current applications of spectral models in numerical weather prediction and in climate simulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Alexander, R. C., and R. L. Mobley, 1976: ‘Monthly average sea-surface temperatures and ice-pack limits on a 1° global grid.’ Mon. Wea. Rev. 104, 143–148.

    Article  Google Scholar 

  • Baede, A. P. M., M. Jarraud and U. Cubasch, 1979: ‘Adiabatic formulation and organisation of ECMWF’s spectral model.’ ECMWF Tech. Rep. No. 15, 40 pp.

    Google Scholar 

  • Baer, F., and J. J. Tribbia, 1977: ‘On complete filtering of gravity modes through nonlinear initialization.’ Mon. Wea. Rev., 105, 1536–1539.

    Article  Google Scholar 

  • Bennett, A. F., and D. B. Haidvogel, 1983: ‘Low resolution simulations of decaying two dimensional turbulence.’ J. Atmos. Sci., 40, 738–748.

    Article  Google Scholar 

  • Boer, G. J., and L. Steinberg, 1975: ‘Fourier series on spheres.’ Atmosphere, 13, 180–191.

    Google Scholar 

  • Bourke, W., 1972: ‘An efficient, one-level, primitive-equation spectral model.’ Mon. Wea. Rev., 100, 683–689.

    Article  Google Scholar 

  • Bourke, W., 1974: ‘A multi-level spectral model. I. Formulation and hemispheric integrations.’ Mon. Wea. Rev., 102, 687–701.

    Article  Google Scholar 

  • Bourke, W., B. Mvaney, K. Puri and R. Thurling, 1977: ‘Global modelling of atmospheric flow by spectral methods.’ Methods in Computational Physics, Vol. 17, ed. J. Chang, Academic Press, 267–324.

    Google Scholar 

  • Bourke, W., K. Puri, R. Seaman, B. Mvaney and J. Le Marshall, 1982: ‘ANMRC data assimilation for the southern hemisphere.’ Mon. Wea. Rev., 110, 1749–1771.

    Article  Google Scholar 

  • Boville, B. A, 1984: ‘The influence of the polar night jet on the tropospheric circulation.’ J. Atmos. Sci., 41, 1132–1142.

    Article  Google Scholar 

  • Boville, B. A., 1985: ‘The influence of wave damping on the winter lower stratosphere.’ J. Atmos. Sci., 42, 904–916.

    Article  Google Scholar 

  • Courant, R., and D. Hilbert, 1953: ‘Methods in Mathematical Physics,’ Volume 1. Interscience Publishers, Inc., New York, 561 pp.

    Google Scholar 

  • Daley, R., 1980: ‘The development of efficient time integration schemes using normal modes.’ Mon. Wea. Rev., 108, 100–110.

    Article  Google Scholar 

  • Daley, R., and Y. Bourassa, 1978: ‘Rhomboidal versus triangular spherical harmonic truncation: Some verification statistics.’ Atmosphere-Ocean, 16, 187–196.

    Article  Google Scholar 

  • Daley, R., C. Girard, J. Henderson and I. Simmonds, 1976: ‘Short term forecasting with a multi-level spectral primitive equation model.’ Atmosphere, 14, 98–134.

    Google Scholar 

  • Delsol, F., K. Miyakoda and R. H. Clarke, 1971: ‘Parameterized processes in the surface boundary layer of an atmospheric circulation model.’ Quart. J. Roy. Meteor. Soc., 97, 181–208.

    Article  Google Scholar 

  • Ellsaesser, H. W., 1966: ‘Expansion of hemispheric meteorological data in anti-symmetric surface spherical harmonic (Laplace) series.’ J. Appl. Meteor., 5, 263–276.

    Article  Google Scholar 

  • Eliasen, E., B. Machenhauer and E. Rasmussen, 1970: ‘On a numerical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields.’ Report No. 2, Institute for Theoretical Meteorology, University of Copenhagen.

    Google Scholar 

  • Errico, R., 1984: ‘The dynamical balance of a general circulation model.’ Mon. Wea. Rev., 112, 2439–2454.

    Article  Google Scholar 

  • Fels, S., 1985: ‘Radiative-dynamical interactions in the middle atmosphere.’ In Advances in Geophysics, 28A, ed. S. Manabe, 277–300.

    Google Scholar 

  • Fels, S., and M. D. Schwarzkopf, 1975: ‘The simplified exchange approximation: A new method for radiative transfer calculations.’ J. Atmos. Sci., 32, 1475–1488.

    Article  Google Scholar 

  • Frederiksen, J. S., and B. L Sawford., 1980: ‘Statistical dynamics of two dimensional inviscid flow on the sphere.’ J. Atmos. Sci., 37, 717–732.

    Article  Google Scholar 

  • Girard, C., and M. Jarraud, 1982: ‘Short and medium range forecast differences between a spectral and grid point model. An extensive quasi-operational comparison.’ ECMWF Tech. Rep. No. 32, 178 pp.

    Google Scholar 

  • Gordon, C. T., and W. F. Stern, 1982: ‘A description of the GFDL global spectral model.’ Mon. Wea. Rev., 110, 625–644.

    Article  Google Scholar 

  • Gordon, H. B. 1981: ‘A flux formulation of the spectral atmospheric equations suitable for use in long term climate modelling.’ Mon. Wea. Rev. 109, 56–64

    Article  Google Scholar 

  • Hart, T. L., W. Bourke, B. J. Mvaney, J. Mregor and B. Forgan, 1987: (In preparation).

    Google Scholar 

  • Hummel, J. R., and R. A. Reck, 1979: ‘A global surface albedo model.’ J. Appl. Meteor., 18, 239–253.

    Article  Google Scholar 

  • Iribarne, J. V., and W. L. Godson, 1973: Atmospheric Thermodynamics. D. Reidel Pub. Company, U.S.A., 222 pp.

    Google Scholar 

  • Jarraud, M., A. J. Simmons and M. Kanamitsu, 1985: ‘Development of the high resolution model.’ ECMWF Tech. Memorandum. No. 107.

    Google Scholar 

  • Jarraud, M., and A. J. Simmons, 1984: ‘The spectral technique.’ ECMWF Seminar on Numerical Methods for Weather Prediction, Vol. 2, 1–60.

    Google Scholar 

  • Kanamitsu, M., K. Tada, T. Kudo, N. Sato and S. Isa, 1983: ‘Description of the JMA operational spectral model.’ J. Meteor. Soc. Japan., 61, 812–828.

    Google Scholar 

  • Kasahara, A., 1976: ‘Normal modes of ultralong waves in the atmosphere.’ Mon. Wea. Rev., 104, 669–690.

    Article  Google Scholar 

  • Kuo, H. L., 1974: ‘Further studies of the parameterization of the influence of convection on large scale flow.’ J. Atmos. Sci., 31, 1232–1240.

    Article  Google Scholar 

  • Lacis, A. A., and J. E. Hansen, 1974: ‘A parameterization for the absorption of solar radiation in the earth’s atmosphere.’ J. Atmos. Sci., 31, 118–133.

    Article  Google Scholar 

  • Lorenz, E. N., 1960: ‘Maximum simplification of the dynamic equations.’ Tellus, 12, 243–254.

    Article  Google Scholar 

  • Louis, J.-F., 1979: ‘A parametric model of vertical eddy fluxes in the atmosphere.’ Bound. Lay. Meteor., 17, 187–202.

    Google Scholar 

  • Machenhauer, B., 1977: ‘On the dynamics of gravity oscillations in a shallow water model, with application to nonlinear normal mode initialization.’ Beitrage zur Physik der Atmosphare, 50, 253–271.

    Google Scholar 

  • achenhauer, B., 1979: ‘The spectral method.’ In Numerical Methods used in Atmospheric Models. GARP Publication Series No. 17, 121–275.

    Google Scholar 

  • Machenhauer, B., and R. Daley, 1972: ‘A baroclinic primitive equation model with a spectral representation in three dimensions.’ Report No. 4, Institute of Theoretical Meteorology, University of Copenhagen, 63 pp.

    Google Scholar 

  • Machenhauer, B., and E. Rasmussen, 1972: ‘On the integration of the spectral hydrodynamical equations by a transform method.’ Report No. 3, Institute for Theoretical Meteorology, University of Copenhagen, 44 pp.

    Google Scholar 

  • Manabe, S., and D. G. Hahn, 1981: ‘Simulation of atmospheric variability.’ Mon. Wea. Rev., 109, 2260–2286.

    Article  Google Scholar 

  • Manabe, S., and J. L. Holloway, 1975: ‘The seasonal variation of the hydrologic cycle as simulated by a global model of the atmosphere.’ J. Geoph. Res., 80, 1617–1649.

    Article  Google Scholar 

  • Manabe, S., J. Smagorinsky and R. F. Strickler, 1965: ‘Simulated climatology of a general circulation model with a hydrologic cycle.’ Mon. Wea. Rev., 93, 769–798.

    Article  Google Scholar 

  • Mvaney, B. J., 1985: Re-configuration of the ANMRC global spectral model for the Cyber 205. In Supercomputer Applications, ed. A. H. L. Emmen, North-Holland, Amsterdam, 151–169.

    Google Scholar 

  • Mvaney, B. J., W. Bourke and K. Puri, 1978: ‘A global spectral model for simulation of the general circulation.’ J. Atmos. Sci., 35, 1557–1583.

    Article  Google Scholar 

  • Merilees, P. E., 1973: ‘An alternative scheme for the summation of series of spherical harmonics.’ J. Appl. Meteor., 12, 224–227.

    Article  Google Scholar 

  • NMC, 1985: NMC Monthly Performance Summary, No. 4.

    Google Scholar 

  • Orszag, S. A., 1970: ‘Transform method for calculation of vector-coupled sums: Application to the spectral form of the vorticity equation.’ J. Atmos. Sci., 27, 890–895.

    Article  Google Scholar 

  • Orszag, S. A., 1971: ‘Numerical simulation of incompressible flows within simple boundaries: Accuracy.’ J. Fluid Mech., 49, 75–112.

    Article  Google Scholar 

  • Orszag, S. A., 1974: ‘Fourier series on spheres.’ Mon. Wea. Rev., 102, 56–75.

    Article  Google Scholar 

  • Payne, R. E., 1972: ‘Albedo of the sea-surface.’ J. Atmos. Sci., 29, 959–970.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Pitcher, E. J., R. C. Malone, V. Ramanathan, M. L. Blackmon, K. Puri and W. Bourke, 1983: ‘January and July simulations with a spectral general circulation model.’ J. Atmos. Sci., 40, 580–604.

    Article  Google Scholar 

  • Platzman, G. W., 1960: ‘The spectral form of the vorticity equation.’ J. Meteor., 17, 635–644.

    Article  Google Scholar 

  • Puri, K., 1984a: ‘Sensitivity of low latitude velocity potential field in a numerical weather prediction model to initial conditions, initialization and physical processes.’ Mon. Wea. Rev., 113, 449–466.

    Article  Google Scholar 

  • Puri, K., 1984b: ‘Normal mode initialization for the ANMRC spectral model.’ Aust. Met. Mag., 31, 85–96.

    Google Scholar 

  • Puri, K., and W. Bourke, 1974: ‘Implications of horizontal resolution in spectral model integrations.’ Mon. Wea. Rev., 102, 333–347.

    Article  Google Scholar 

  • Ramanathan, V., E. J. Pitcher, R. C. Malone and M. L. Blackmon, 1983: ‘The response of a spectral general circulation model to refinements in radiative processes.’ J. Atmos. Sci., 40, 605–630.

    Article  Google Scholar 

  • Rasch, P. J., 1985: ‘Developments in normal mode initialization, Part II: A new method and its comparison with currently used schemes.’ Mon. Wea. Rev., 113, 1753–1770.

    Article  Google Scholar 

  • Robert, A. J., 1966: ‘The integration of low order spectral form of the primitive meteorological equations.’ J. Meteor. Soc. Japan, 44, 237–244.

    Google Scholar 

  • Robert, A. J., 1969: ‘The integration of a spectral model of the atmosphere by the implicit method.’ Proc. WMO/IUGG Symp. Numer. Weather Predict. 1968, pp. VII-9-VII-23

    Google Scholar 

  • Robert, A. J., J. Henderson, C. Turnbull, 1972: ‘An implicit time integration scheme for baroclinic models of the atmosphere.’ Mon. Wea. Rev., 100, 329–335.

    Article  Google Scholar 

  • Sela, J. G., 1982: ‘The NMC spectral model.’ NOAA Tech. Report NWS 30, Dept. Commerce, NOAA, 36 pp.

    Google Scholar 

  • Silberman, I., 1954: ‘Planetary waves in the atmosphere.’ J. Meteor., 11, 27–34.

    Article  Google Scholar 

  • Simmons, A. J., and R. Strufing, 1981: ‘An energy and angular momentum conserving finite-difference scheme, hybrid coordinates and medium-range weather prediction.’ ECMWF Tech. Rep. No. 28, 67 pp.

    Google Scholar 

  • Slingo, J., and B. Ritter, 1985: ‘Cloud prediction in the ECMWF model.’ ECMWF Tech. Rep. No. 46, 49 pp.

    Google Scholar 

  • Stern, W. F., and J. J. Ploshay, 1983: ‘An assessment of GFDL’s continuous data assimilation system used for processing FGGE data.’ Prepr., Sixth Conf. Numer. Weather Predict., 1983, 90–95.

    Google Scholar 

  • Williamson, D. L., 1983: ‘Description of NCAR Community Climate Model (CCMOB). NCAR/TN-210+STR, 88 pp.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bureau of Meteorology Research Centre, GPO Box 1289K, 3001, Melbourne, Australia

    William Bourke

Authors
  1. William Bourke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon, USA

    M. E. Schlesinger

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Kluwer Academic Publishers

About this chapter

Cite this chapter

Bourke, W. (1988). Spectral Methods in Global Climate and Weather Prediction Models. In: Schlesinger, M.E. (eds) Physically-Based Modelling and Simulation of Climate and Climatic Change. NATO ASI Series, vol 243. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3041-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3041-4_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7867-2

  • Online ISBN: 978-94-009-3041-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation