We introduce rigorously defined air masses as a diagnostic of tropospheric transport. The fractional contribution from each air mass partitions air at any given point according to either where it was last in the planetary boundary layer or where it was last in contact with the stratosphere. The utility of these air-mass fractions is demonstrated for the climate of a dynamical core circulation model and its response to specified heating. For an idealized warming typical of end-of-century projections, changes in air-mass fractions are in the order of 10% and reveal the model's climate change in tropospheric transport: poleward-shifted jets and surface-intensified eddy kinetic energy lead to more efficient stirring of air out of the midlatitude boundary layer, suggesting that, in the future, there may be increased transport of black carbon and industrial pollutants to the Arctic upper troposphere. Correspondingly, air is less efficiently mixed away from the subtropical boundary layer. The air-mass fraction that had last stratosphere contact at midlatitudes increases all the way to the surface, in part due to increased isentropic eddy transport across the tropopause. Correspondingly, the air-mass fraction that had last stratosphere contact at high latitudes is reduced through decreased downwelling across the tropopause. A weakened Hadley circulation leads to decreased interhemispheric transport in the model's future climate.