Covariance Analysis of the Global Atmospheric Axial Angular Momentum Budget

Abstract

Given the budget equation for the global axial angular momentum M, the related covariance equations are derived. These equations allow one to study the response of the global angular momentum to the forcing by mountain and friction torques in a statistical framework. ECMWF reanalysis (ERA) data are used to evaluate the terms of these equations and to assess their relative importance. Moreover, a new test of the quality of these data is provided this way. The decay of the autocovariance function of M with increasing lag τ is slow and almost linear for 20 < τ < 280 days. That of the friction torque Tf is exponential with a decay rate of ?5 days. The autocovariance of the mountain torque To decays even faster. The torque Tg due to the gravity wave drag is more persistent than the mountain torque. When inserting the observed covariance functions in the respective equations, it is found that the mountain torque is generally more important than Tf. The contribution by Tg is small. The cross covariance of To and Tf is a major contributor in the covariance equations of these torques. However, both torques act on M as if they were almost independent. All covariance equations are satisfied quite well, particularly for the covariance of Tg and M. A regressive model for M, To, and Tf is presented.