An engine exhaust aftertreatment system including an catalyst-based device configured to reduce an amount of NOx in exhaust gases produced by an engine using reductant stored in the catalyst-based device. The system includes a controller configured to determine a starting quantity of stored reductant in the catalyst-based device at the start of the engine. The starting quantity is based on a shutdown quantity of stored reductant in the catalyst-based device determined at the shutdown of the engine.