Zonally symmetric adjustment in the presence of artificial relaxation

Abstract Numerical experiments, presented in a companion paper, have been performed in which the zonal-mean state of the stratosphere in a comprehensive, stratosphere-resolving, general circulation model is strongly relaxed (or “nudged”) toward the evolution of a reference sudden warming event in order to investigate its influence on the freely evolving troposphere below. Similar approaches have been used in a number of other studies. This raises the question of whether such an artificial relaxation induces the adiabatic and diabatic adjustments expected below the region of nudging, even in the absence of the stratospheric wave driving responsible for the reference event. Motivated by this question, the zonally symmetric quasigeostrophic diabatic response to zonal forces (representing wave driving) in a system nudged to a time-dependent reference state is studied. In the presence of wave driving in the nudging region that differs from the reference state, the meridional mass circulation of the reference state is reproduced only in the region below the nudging up to a correction that is inversely proportional to the strength of the nudging. The anomalous circulation is confined because of an effective boundary condition at the interface of the nudging layer. The nudging also produces an artificial “sponge-layer feedback” immediately below the region of the nudging in response to differences in the tropospheric wave driving. The strength of this artificial feedback is closely related to the strength of the effective boundary condition; however, the time scale required for the sponge-layer feedback to be established is typically much longer than that required for the confinement.This is the final version. It first appeared at http://journals.ametsoc.org/doi/abs/10.1175/JAS-D-14-0013.1