A method is provided during which an aircraft powerplant is provided. The aircraft powerplant includes a combustor and a water recovery system. The water recovery system includes a condenser and a reservoir. Fuel is combusted within the combustor to provide combustion products. Water is extracted from the combustion products using the condenser. The water recovery system is operated in one of a plurality of modes based on likelihood of contrail formation. The modes include a first mode and a second mode, where the water is collected within the reservoir during the first mode, and where the water passes through the water recovery system during the second mode.