An empirical model of barotropic atmospheric dynamics and its response to tropical forcing

A linear empirical model of barotropic atmospheric dynamics is constructed in which the streamfunction tendency field is optimally predicted using the concurrent streamfunction state as a predictor. The prediction equations are those resulting from performing a linear regression between tendency and state vectors. Based on the formal analogy between this model and the linear nondivergent barotropic vorticity equation, this empirical model is applied to problems normally addressed with a conventional model based on physical principles. It is found to qualitatively represent the horizontal dispersion of energy and to skillfully predict how a general circulation model will respond to steady tropical heat sources. Analysis of model solutions indicates that the empirical model's dynamics include processes that are not represented by conventional nondivergent linear models. Most significantly, the influence of internally generated midlatitude divergence anomalies and of anomalous vorticity fluxes by high-frequency transients associated with low-frequency anomalies are automatically incorporated into the empirical model. The results suggest the utility of empirical models of atmospheric dynamics in situations where estimates of the response to external forcing are needed or as a standard of comparison in efforts to make models based on physical principles more complete.