An emissions control system for treating exhaust gas containing NOx emissions from an internal combustion engine comprises a selective catalytic reduction (SCR) device that stores reductant that reacts with the NOx emissions, a reductant supply system configured to inject the reductant according to a reductant storage model; NOx module(s) configured to generate an NOx concentration signal indicating an NOx concentration, temperature module(s) configured to generate a temperature signal indicating an SCR temperature of the SCR device, and a control module operably connected to the reductant supply system, the NOx module, and the temperature module. The control module is configured to determine an amount of the reductant that is parasitically oxidized based on the NOx concentration signal and the temperature signal, and to determine a correction factor based on the amount of parasitically oxidized reductant to modify the reductant storage model.