Effects of Spectral Truncation on General Circulation and Long-Range Prediction

Although atmospheric prediction models appear to yield results similar to observation, both their detailed predictive capability and their time-averaged forecasts depend on space truncation. Such dependence may be readily studied with a spectral model because of the ease of modifying truncation. A simple, two-level, quasi-geostrophic, forced general circulation model was represented in spectral form and nine cases of different truncation were integrated for the same forcing, starting with initial conditions generated from a state of rest. The truncations ranged from six to sixteen meridional waves, from five to ten degrees of freedom with latitude, and the models were integrated for about 60 days with finite-amplitude nonlinearity. Considering the kinetic energy in the vertical mean flow, and separating this energy into zonal and eddy, the results show that the general circulation may be predicted with as few as twelve planetary waves and eight latitudinal degrees of freedom, whereas detailed prediction for a period of 15–20 days requires at least sixteen planetary waves and eight to ten latitudinal degrees of freedom. The broad variation in solutions for different truncations observed in this study implies that care must be taken in selecting space truncation for any physical model chosen for integration.