Can overshooting convection dehydrate the tropical tropopause layer?

A numerical model is used to investigate the potential for irreversible dehydration near the tropical tropopause caused by overshooting deep convection. We show that convective updrafts overshooting the cold point tropopause can generate extremely cold, dry air within the updrafts. However, the updrafts contain sufficient mass in small (<=20 mm radius) ice crystals that do not sediment out of the short-lived overshoots, such that when the overshoots collapse and warm back to the ambient temperature, these small crystals sublimate and rehydrate the air, resulting in no irreversible dehydration. Despite maximizing crystal size (and fall speed) by assuming low aerosol concentrations and using large ice-ice collection efficiencies, we find no evidence to support the hypothesis that overshooting convection can dehydrate the tropical tropopause layer (TTL) when it is initially ice subsaturated. Only when the TTL is initially supersaturated with respect to ice do we find that deep convection can draw down the humidity, as vapor in excess of saturation condenses on the ice crystals. The overall impact of deep convection on the TTL water vapor budget depends on the climatology of TTL relative humidity in convective regions.