Described herein are various embodiments of an apparatus, a system, and a methods for reducing NOx emissions using ammonia storage on an SCR catalyst. For example, according to one embodiment, an apparatus for controlling an SCR system of an internal combustion engine system includes an ammonia storage module and a reductant dosing module. The ammonia storage module determines an ammonia storage surface coverage on an SCR catalyst of the SCR system and an ammonia compensation value based on one of an excess ammonia flow rate entering the SCR catalyst and an excess NOx flow rate entering the SCR catalyst. The reductant dosing module that generates a reductant dosing command based on the ammonia compensation value.