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Selective catalytic reduction (SCR) of NOx is coming into widespread use for diesel exhaust emissions control in passenger cars, light trucks, and commercial vehicles. Because of the transient nature of these applications, modeling is a critical element of the controls development process. For software-in-the-loop simulation, the model must run in real-time while still retaining first order accuracy. Furthermore, if used as an embedded system or nonlinear observer, the allowable time step must not be shorter than the control module clock rate. Unfortunately, the time scales for ammonia storage decrease exponentially with temperature. The end result is a trade-off between spatial resolution, real-time performance, and temperature range. If the SCR catalyst is placed downstream of a particulate filter, this issue is even more acute due to the high temperatures that occur during regeneration. A switched catalyst model is proposed that breaks this trade-off.