Covariance Analysis of the Global Atmospheric Axial Angular Momentum Budget
Monthly Weather Review
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
... covariance function of M with increasing lag is slow and almost linear for 20 Ͻ Ͻ 280 days. That of the friction torque T f is exponential with a decay rate of ϳ5 days. The autocovariance of the mountain torque T o decays even faster. The torque T g 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 T f . The contribution by T g is small. The cross covariance of T o and T f 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 T g and M. A regressive model for M, T o , and T f is presented.