Baroclinic Empirical Orthogonal Functions as Basis Functions in an Atmospheric Model

Abstract

In this study, empirical orthogonal functions (EOFs) are used as basis functions in a spectral model of the atmospheric circulation. Two hypotheses are tested. The first hypothesis is that a basis of EOFs is more efficient in describing large-scale atmospheric dynamics compared to spherical harmonics. The second hypothesis is that, by using EOFs as basis functions, the forecast skill and climatology of the model can be improved. Two experiments are performed with a three-level, quasigeostrophic, hemispheric spectral T21 model. In the first experiment, a perfect model approach is taken. In the second, T21 is used to produce forecasts for the Northern Hemisphere in winter. In the perfect model experiment, EOFs are determined from a long model integration; in the second experiment, EOFs are determined from 10 winters of ECMWF analyses. The first hypothesis is tested by comparing the forecast skill of EOF truncated versions of T21 with the skill of a T17 version. In both experiments it is found that with less than half the number of degrees of freedom the EOF model beats T17. However, although the EOF model is more efficient with respect to the number of degrees of freedom, it is more expensive to integrate numerically. The second hypothesis is tested in the perfect model experiment by producing forecasts of the T21 circulation with T17, filtered on the leading EOFs, in an attempt to reduce the error propagation from the trailing EOFs and thus improve the forecast skill of T17. In contrast to previously obtained results in the barotropic case, the filter does not improve the forecast skill. With an empirically determined dissipation on the EOFs as a closure for neglected interactions, both the forecast skill and the climatology of T17 show some improvement. In the second experiment T21 is filtered on the leading atmospheric EOFs. Also in this experiment, the EOF filter does not improve the forecast skill of T21. By introducing an empirically determined dissipation on the EOFs, the variability of T21 shows some improvement.