Abstract
Many features of the general circulation of the atmosphere shift upward in response to warming in simulations of climate change with both general circulation models (GCMs) and cloud-system-resolving models. The importance of the upward shift is well known, but its physical basis and the extent to which it occurs coherently across variables are not well understood. A transformation is derived here that shows how an upward shift of a solution to the moist primitive equations gives a new approximate solution with higher tropospheric temperatures. According to the transformation, all variables shift upward with warming but with an additional modification to the temperature and a general weakening of the pressure velocity. The applicability of the vertical-shift transformation is explored using a hierarchy of models from adiabatic parcel ascents to comprehensive GCMs. The transformation is found to capture many features of the response to climate change in simulations with an idealized GCM, including the mid- and upper-tropospheric changes in lapse rate, relative humidity, and meridional wind. The transformation is less accurate when applied to simulations with more realistic GCMs, but it nonetheless captures some important features. Deviations from the simulated response are primarily due to the surface boundary conditions, which do not necessarily conform to the transformation, especially in the case of the zonal winds. The results allow for a physical interpretation of the upward shift in terms of the governing equations and suggest that it may be thought of as a coherent response of the general circulation of the mid- and upper troposphere.
