Evaluation of Potential Vorticity Changes Near the Tropopause, and the Related Vertical Motions, Vertical Advection of Vorticity and Flow of Radioactive Debris from Stratosphere to Troposphere

Abstract

Individual potential vorticity change, vertical motion, vertical advection of vorticity and flow from stratosphere to troposphere are evaluated at different levels and for different times in an extratropical disturbancec Vertical motions are obtained from trajectories on three isentropic surfaces for two different times. The isentropes pass through or near a front in the upper troposphere, the lower stratosphere, and the high troposphere on the cold side of the front. Vertical motion is also evaluated at 500 mb from an adiabatic method designed to give instantaneous values to the extent that the system moves without change of shapeo Negative extremes of 8 to 10 cm sec-1 occur in the upper air front, with positive extremes of the same magnitude a short distance to the northeast, coinciding with the eastern exit of the frontal zone. From theory it is shown that potential vorticity is not conserved if there is either a gradient of diabatic heating or a component of curl, normal to the isentropic surface, of frictional force. The sum of these two effects is evaluated over the United States for two 12-hr periods on two isentropic surfaces which were common to parts of the lower stratosphere, upper troposphere and a front in middle and upper troposphere. Generally large, positive potential vorticity changes occur in the lower stratosphere and in the upper troposphere on the cold side of the front. Large negative values occur in the frontal zone and around the entire periphery of the positive area, or around the periphery of the trough in the upper air. The potential vorticity changes are related to simultaneous stability and vorticity changes of like sign. The potential vorticity changes are positive in the region of the so-called 1 tropopause funnel 1 ; changes everywhere appear attributable to vertical gradient of diabatic heating rather than curl of frictional force. ' ( I The terms in the vorticity equation which contain vertical velocity (vertical advection of vorticity and tilting terms) are shown by means of the thermal wind equation to depend only on the vertical motion and temperature fields in an isobaric surface. For the frequent case where negative motion is centered in the baroclinic or frontal zone and rising motion centered at the exit of the zone, each of the vertical motion terms has the same characteristic distribution. Positive values occur on the cold side of the zone and to the right of the downwind exit of the zone, and negative values occur on the warm side of the zone and to the left of the downwind exit of the zone. The vertical advection and the sum of vertical advection and tilting terms are evaluated at 500 mb. Magnitudes obtained compare with those of the divergence term, although magnitude depends considerably on the distances over which finite differences are evaluated. Isentropic trajectories trace air initially in the lower stratosphere downward to within 5000 ft of the surface within 24 hr. Diabatic incorporation into the troposphere is also noted. The total adiabatic mass flow into the troposphere associated with the number of typical upper air disturbances in existence at any time is estimated and found to be sufficient to give the observed short residence times of a few months for radioactive debris injected into the stratosphere by nuclear detonations.