On the Relationship of Barotropic Singular Modes to the Low-Frequency Variability of a General Circulation Model

Abstract

The hypothesis that extratropical low-frequency variability can be viewed as a linear barotropic response to spatially incoherent forcing is put to test. The recurrent ultra-low-frequency structures [i.e., the empirical orthogonal functions (E0Fs)] of a general circulation model are compared with the leading singular modes of the steady barotropic operator linearized about several mid- and upper-tropospheric levels. In a quasi-stochastically forced system these two sets of functions should approximately coincide. Although at each level one can find singular modes that closely replicate one of the EOFs, there does not exist a general correspondence at any one vertical level between the set of leading singular modes and the set of dominant EOFs, at least not for the same parameter range. The extratropical ultra-low-frequency variability cannot be understood as resulting solely from the organizing influence of horizontal asymmetries in the time-mean flow on randomly forced barotropic disturbances. The neglected processes, such as organized transient eddy forcing and diabatic heating, evidently play a crucial role in accounting for the prevalence of the observed patterns.