Potential vorticity in warm conveyor belt outflow

Warm conveyor belts (WCBs) are the main ascending air masses within extratropical cyclones. They often exhibit strong condensation and precipitation, associated with ascent on large scales or embedded convection. Most of the air outflows into the upper troposphere as part of a ridge. Such ridges are an integral part of Rossby waves propagating along the tropopause and are identified with a negative potential vorticity (PV) anomaly and associated anticyclonic circulation. It has been argued that diabatic modification of PV in WCBs has an important influence on the extent of the ridge, propagation of Rossby waves and weather impacts downstream. Following the coherent ensemble of trajectories defining a WCB, PV is expected to increase with time while below the level of maximum latent heating and then decrease as trajectories ascend above the heating maximum. In models, it is found that the net change is approximately zero, so that the average PV of the WCB outflow is almost equal to the PV of its inflow. Here, the conditions necessary for this evolution are explored analytically using constraints arising from the conservation of circulation. It is argued that the net PV change is insensitive to the details of diabatic processes and the PV maximum midway along a WCB depends primarily on the net diabatic transport of mass from the inflow to the outflow layer. The main effect of diabatic processes within a WCB is to raise the isentropic level of the outflow, rather than to modify PV.