Editorial Type:
Article
Article Type:
Research Article

Believable Scales and Parameterizations in a Spectral Transform Model

J. Lander Department of Meteorology, University of Reading, Reading, United Kingdom

Search for other papers by J. Lander in
Current site
Google Scholar
PubMed Close
and
B. J. Hoskins Department of Meteorology, University of Reading, Reading, United Kingdom

Search for other papers by B. J. Hoskins in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Feb 1997
DOI:
https://doi.org/10.1175/1520-0493(1997)125<0292:BSAPIA>2.0.CO;2
Page(s):
292–303
Restricted access

Abstract

Through analysis of the spectra of a Dirac delta function the notion of believable and unbelievable scales in a spectral transform model is quantified. The smallest resolved local features are shown to have an average wavenumber a factor of 2 less than that of the truncation, and a half-width 1.6 times greater than that associated with the smallest-scale waves and 2.4 times the maximum grid size of a quadratic transform grid. A reassessment of the philosophy of including parameterizations is introduced, the central point of which is a separation of the parameterization and dynamical truncation scales. The use of spectral filters applied to the input and output from gridpoint physical parameterization schemes and the use of a coarse “physics” grid are proposed. Diagnostics summarizing the noise in a spectral model are introduced, and a moist baroclinic wave life-cycle simulation and a one-dimensional analog to photochemistry at the terminator are discussed to demonstrate their use.

Corresponding author address: Dr. Jason Lander, Dept. of Meteorology, University of Reading, 2 Earley Gate, Whiteknights, Reading RG6 6AU United Kingdom.

Abstract

Through analysis of the spectra of a Dirac delta function the notion of believable and unbelievable scales in a spectral transform model is quantified. The smallest resolved local features are shown to have an average wavenumber a factor of 2 less than that of the truncation, and a half-width 1.6 times greater than that associated with the smallest-scale waves and 2.4 times the maximum grid size of a quadratic transform grid. A reassessment of the philosophy of including parameterizations is introduced, the central point of which is a separation of the parameterization and dynamical truncation scales. The use of spectral filters applied to the input and output from gridpoint physical parameterization schemes and the use of a coarse “physics” grid are proposed. Diagnostics summarizing the noise in a spectral model are introduced, and a moist baroclinic wave life-cycle simulation and a one-dimensional analog to photochemistry at the terminator are discussed to demonstrate their use.

Corresponding author address: Dr. Jason Lander, Dept. of Meteorology, University of Reading, 2 Earley Gate, Whiteknights, Reading RG6 6AU United Kingdom.

Save
Cover Monthly Weather Review
Monthly Weather Review

  • Bourke, W., B. McAvaney, K. Puri, and R. Thurling, 1977: Global modelling of atmospheric flow by spectral methods. Methods Comput. Phys,17, 267–324.

  • Fjørtoft, R., 1953: On the changes in the spectral distribution of kinetic energy of two-dimensional non-divergent flow. Tellus,5, 225–230.

  • Hoskins, B. J., 1980: Representation of the earth topography using spherical harmonics. Mon. Wea. Rev.,108, 111–115.

  • Jones, B., 1992: Effects of physical processes in baroclinic waves. Ph.D. thesis, University of Reading.

  • Machenhauer, B., and E. Rasmussen, 1972: On the integration of the spectral hydrodynamical equations. Report 3, Institut fir Teortisk Meteorologi, University of Copenhagen, 44 pp.

  • Navarra, A., W. F. Stern, and K. Miyakoda, 1994: Reduction of the Gibbs oscillation in spectral model simulations. J. Climate,7, 1169–1183.

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

  • Sardeshmukh, P. D., and B. J. Hoskins, 1984: Spatial smoothing on the sphere. Mon. Wea. Rev.,112, 2524–2529.

  • Trenberth, K. E., and A. Solomon, 1993: Implications of global atmospheric spatial spectra for processing and displaying data. J. Climate,6, 531–545.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 468 172 13
PDF Downloads 266 58 2