Zonally symmetric adjustment in the presence of artificial relaxation
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') towards 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 studies. This raises the question of whether such an arti cial relaxation would induce 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, we study the zonally symmetric quasigeostrophic diabatic response to zonal forces (representing wave driving) in a system nudged to a time-dependent reference state. In the presence of wave driving that di ers from the reference state, the nudging does not reproduce the meridional mass circulation of the reference state. However, the circulation is reproduced in the region below the nudging up to up to a correction that is inversely proportional to the strength of the nudging. This is acheived due to an e ffective boundary condition at the interface of the nudging layer. The nudging also produces an arti cial 'sponge-layer feedback' immediately below the region of the nudging in response to di fferences in the tropospheric wave driving. The strength of this arti cial feedback is closely related to the strength of the eff ective boundary condition, however, the timescale required for the sponge-layer feedback to be established is typically much longer than that required for the confinement.