Effect of the Kinematic Lower Boundary Condition on the Spectral and Autocorrelation Structure of Annular Variability in the Troposphere

Abstract

Abstract The dynamical origin of the spectral and autocorrelation structure of annular variability in the troposphere is investigated by a deductive approach. Specifically, the structure of the power spectrum and autocorrelation function of the zonal-mean geopotential is analyzed for the case of a quasigeostrophic spherical atmosphere subject to a white noise mechanical forcing applied in a single Hough mode and concentrated at a particular level in the vertical, with vertically uniform Newtonian cooling and Rayleigh drag concentrated at a rigid lower boundary. Analytic expressions for the power spectrum are presented together with expressions for an approximate red noise (i.e., a Lorentzian-shaped) power spectrum. It is found that for an infinitely deep atmosphere the power spectrum can be well approximated by a red noise process for the first few Hough modes (associated with large Rossby heights), provided the distance from the forcing is not larger than about one Rossby height. When a frictional rigid lower boundary is included, however, the approximation is generally bad. The high-frequency part of the power spectrum exhibits near-exponential behavior and the autocorrelation function shows a transition from a rapid decay at short lags to a much slower decay at longer lags, if the thermal and mechanical damping time scales are sufficiently well separated. Since observed annular variability exhibits the same characteristics, the above results lead to the hypothesis that these characteristics may, to some extent, be intrinsic to the linear zonal-mean response problem—although the need for an additional contribution from eddy feedbacks is also implied by the results.