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Accuracy of reduced‐grid calculations
Author(s) -
Williamson David L.,
Rosinski James M.
Publication year - 2000
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712656604
Subject(s) - eulerian path , grid , advection , adiabatic process , mathematics , interpolation (computer graphics) , algorithm , meteorology , mathematical optimization , physics , geometry , classical mechanics , lagrangian , motion (physics) , thermodynamics
The accuracy of calculations on reduced grids is examined from a climate modelling perspective. It is demonstrated that an adiabatic Eulerian spectral‐transform model run on an e ‐digit grid is accurate to e digits for short integrations. The error introduced by the reduced grid grows as expected for a turbulent atmosphere, and the growth is not accelerated by the reduced grid. The errors from an adiabatic semi‐Lagrangian spectral‐transform model can be significantly larger than those from an Eulerian model because the interpolation required in the semi‐Lagrangian method will not maintain more than a few digits of accuracy. Adiabatic model errors are put in perspective by illustrating errors introduced by arbitrary aspects of model specification such as the longitude of the first grid point. For the Eulerian adiabatic model there appears to be no justification in using a higher‐digit grid than the 2‐digit one. A higher‐digit grid may be desirable for an adiabatic semi‐Lagrangian model. Results from a cosine‐bell advection test are presented. All reduced grids tested have the same error for Eulerian spectral‐transform advection. The semi‐Lagrangian advection shows some increase in error with greater reduction in the grid, but the variation is comparable with the difference in error from choosing different interpolants or different time steps. There is little reason to choose a higher‐digit grid than the 4‐digit grid. In fact the 3‐, 2‐ and 1‐digit grids might be considered satisfactory for semi‐Lagrangian advection. Finally, multiple‐year climate simulations with full and reduced grids are presented. The overall impression is that the mean climates produced by the models run on the reduced grids are all very similar. There is no indication that the reduced grids introduce pathological errors that contaminate the simulations. A few select fields which are particularly sensitive to model changes are shown to quantify the differences, and to indicate that the differences are comparable with those which arise from the natural variability of the model. The results indicate that even a 1‐digit grid is suitable for climate modelling with both Eulerian and semi‐Lagrangian spectral‐transform models.