Explicit solutions to stochastic global angular momentum equations
Weickmann et al. (2000) proposed a stochastic model for the global angular momentum budget where the mountain torque To is modelled as red noise whereas the friction torque Tf is composed of a red noise component and a damping term for the angular momentum M. It has been demonstrated by these authors that this model captures quite well the covariance functions of M, To and Tf as observed. Here analytic solutions to the covariance equations of this model are derived in order to better understand the reasons for the success and partial failures of this model. Moreover, the estimate of the key damping parameter of the model is improved. The agreement with the observations as well as nearly all discrepancies between observations and model results can be explained on the basis of these solutions. A new relation is found between the covariance of To, M and the covariance of To, Tf. Moreover, an extension and improvement of the model is proposed following recent ideas on stochastic modelling of mountain torques.