Dynamics of Atmospheric Regression Patterns: Regional Mountain Torque Events

Abstract

Abstract The regression of atmospheric fields against a parameter P with lag τ is a standard procedure in meteorology. Here, the torque exerted by a mountain massif is chosen as a parameter in order to study the interaction of weather systems with orography on a statistical basis. It is normally found that the amplitudes of the correlation patterns increase with τ → 0 and decrease for increasing positive lag. It is proposed to explain this ubiquitous feature in the orographic case on the basis of the covariance equations that govern these regressions. Two examples are discussed. First, a version of the low-order Charney–DeVore model of β-plane flow over a mountain is considered where stochastic forcing stirs a Rossby wave mode. It is found that the general increase of covariance amplitudes for τ → 0 (if it occurs) is mainly due to the forcing, but triple covariances of mountain torque and vorticity advection are important as well. A new covariance energy equation is derived to demonstrate that the frictional decay for τ > 0 is supported by these triple covariances while the stationary wave acts as a source for τ > 0. A dynamical interpretation of the triple terms is given. Next, data from the ECMWF 40-yr Re-Analysis (ERA-40) set are used to study mountain torque events in winter near Greenland, where the covariances of all standard variables with the torque P exhibit a rapid quasi-barotropic increase with τ → 0 near Greenland. This amplification process is investigated by looking at the barotropic vorticity equation adapted to this statistical problem. This equation captures the evolution of the regression patterns reasonably well in the range −2 ≤ τ ≤ 2 days. The triple covariances of torque and nonlinear vorticity advection play the key role in the amplification process. In particular, covariance enstrophy is generated and destroyed by these terms, a process without counterpart in the standard vorticity equation. Stochastic forcing is presumably unimportant. The interpretation of the triple terms is difficult in contrast to that of the other “linear” terms of the vorticity equation. The angular momentum in the Greenland domain decreases during events of positive torque.