The slope of isentropes in the extratropical troposphere

Tapio Schneider Atmospheric and Oceanic Sciences Program, Princeton University Isaac M. Held Geophysical Fluid Dynamics Laboratory, NOAA Introduction. The static stability @z  and the meridional gradient @y  of the longitudinally averaged potential temperature  both play prominent roles in theories for baroclinic eddy uxes (Stone 1972; Green 1970). Despite much ongoing work, there is still no consensus on how radiative and dynamic processes interact to maintain the static stability and the mean meridional potential temperature gradient in the extratropics. Establishing relationships between these quantities is therefore an important step towards enhancing our understanding of fundamental atmospheric dynamics. Here we focus on the isentropic slope I = @z =@y , which relates the static stability to the meridional potential temperature gradient. It is convenient to normalize the isentropic slope I via multiplication by the ratio HT =a, where HT denotes the height of the tropopause and a the Earth's radius. We write (HT =a) I = z= y, where z = HT @z  and y = a @y  represent approximate potential temperature di erences between tropopause and surface and between equator and pole, respectively. Fig. 1 shows a latitude-pressure cross section of the longitudinally averaged potential temperature for mean January conditions. Included in this gure is the 3.5-PVU contour of the isentropic potential vorticity, where 1PVU = 10 6m2Ks 1 kg 1 denotes the potential vorticity unit. Outside the tropics, the 3.5-PVU potential vorticity surface approximates the tropopause (Hoerling et al. 1991). From Fig. 1, we infer that the lowest isentrope that crosses the tropopause also grazes the Earth's surface in the tropics. More precisely, we observe that, in the extratropics, the mean potential temperature di erences between surface and tropopause and between equator and pole are approximately equal; that is, y z. This has often been regarded as a chance coincidence (see, e.g., Hoskins (1991)). 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80 90 100 Latitude P re ss ur e [k P a]