Stochastic Dynamics of the Midlatitude Atmospheric Jet

Abstract

The innate tendency of the background straining field of the midlatitude atmospheric jet to preferentially amplify a subset of disturbances produces a characteristic response to stochastic perturbation whether the perturbations are internally generated by nonlinear processes or externally imposed. This physical property of enhanced response to a subset of perturbations is expressed analytically through the nonnormality of the linearized dynamical operator, which can be studied to determine the transient growth of particular disturbances over time through solution of the initial value problem or, alternatively, to determine the stationary response to continual excitation through solution of the related stochastic problem. Making use of the fact that the background flow dominates the strain rate field, a theory for the turbulent state can be constructed based on the nonnormality of the dynamical operator linearized about the background flow. While the initial value problem provides an explanation for individual cyclogenesis events, solution of the stochastic problem provides a theory for the statistics of the ensemble of all cyclones including structure, frequency, intensity, and resulting fluxes of heat and momentum, which together constitute the synoptic-scale influence on midlatitude climate. Moreover, the observed climate can be identified with the background thermal and velocity structure that is in self-consistent equilibrium with both its own induced fluxes and the imposed large scale thermal forcing. In order to approach the problem of determining the self-consistent statistical equilibrium of the midlatitude jet it is first necessary to solve the stochastic problem for the mixed baroclinic/barotropic jet because fluxes of both heat and momentum are involved in this balance. In this work the response to stochastic forcing of a linearized nonseparable quasigeostrophic model of the midlatitude jet is solved. The observed distribution of transient eddy variance with frequency and wavenumber, the observed vertical structures, and the observed heat and momentum flux distributions are obtained. Associated energetics and implications for maintenance of the climatological jet are discussed.