## 1. Introduction

[2] Static stability is among the most fundamental quantities describing the state of the atmosphere. Equivalent to the vertical temperature structure of the atmosphere, the static stability determines the buoyancy frequency of dry perturbations in the vertical, the speed of gravity waves, and the magnitude of the greenhouse effect. In the midlatitudes in particular, the static stability is a key ingredient to any theory of the general circulation.

[3] The determination of the static stability of the tropical troposphere is relatively well understood: there moist convection occurs over warm waters, and sets the upper tropospheric temperatures. The temperature structure there is thus approximately given by the moist adiabat [*Xu and Emanuel*, 1989]. The moist adiabatic structure then results in upper tropospheric amplification of global warming within the tropics, and hence a more stable troposphere in terms of dry stability with increases in temperature. In observations, there remain discrepancies between model predictions and observations in the tropics, but large observational uncertainties make it difficult to determine whether this theoretical understanding is flawed [*Climate Change Science Program*, 2006].

[4] In the midlatitudes, on the other hand, the determination of the static stability is much less well understood from a theoretical perspective. Early theories relied on dry baroclinic eddy dynamics to understand midlatitude static stability [*Stone*, 1972; *Held*, 1982]. Theories by *Stone* [1978] and *Held* [1982] derive a constraint that relates the static stability to meridional temperature gradients:

with θ the potential temperature, *f* and *β* the Coriolis parameter and its gradient, and *H* some depth scale. However recent studies have shown that the detailed predictions of these theories are not borne out in a general circulation model (GCM) [*Thuburn and Craig*, 1997] or in reanalysis data [*Juckes*, 2000]. Recently, instead, focus has been turned to moist convection as being important in the determination of the midlatitude stability, as it is in the tropics [*Juckes*, 2000]. In this argument, moist convection occurs within the warm cores of baroclinic eddies (as it is observed to in the work of *Emanuel* [1988]), setting a minimum stability. The net moist stability of the midlatitudes is then determined by the standard deviation of the surface equivalent potential temperature, which can be related to meridional gradients through mixing length-like closures. The end result relates the moist stability to surface equivalent potential temperature gradients [*Frierson et al.*, 2006a]:

where θ_{e} is the equivalent potential temperature.

[5] The predictions of equation 2 have been found to be accurate for a simplified moist general circulation model [*Frierson et al.*, 2006a]. Equation 2 predicts an increase in dry stability with moisture content and thus with the mean temperature of the atmosphere; in this sense the argument could additionally be used to explain the increase in static stability with sea surface temperature (SST) seen in the aquaplanet full GCM simulations of *Caballero and Langen* [2005].

[6] Simulations of global warming provide a unique test of the determination of the midlatitude static stability. The temperature changes in the more extreme scenarios can be significantly larger than interannual variability within observations, but clearly not outside the range of realism. Further, using the best models of various climate modeling groups around the world and their associated parameterizations of clouds, convection, and other physics provides a measure of robustness to physical parameterization that is impossible with a single model. In this paper we analyze the changes in bulk (vertically integrated) measures of the static stability in global warming scenarios in 21 coupled GCM's, and compare with the various theories listed above.