A method of adjusting the dosage of a reductant for an SCR catalyst, comprising: determining (110) an expected temperature profile in at least one axial section of the catalyst (70) for a defined period of time (tSim); firstly simulating (120) the resulting amount of reductant beyond the at least one section of the catalyst with a first defined dosage of the reductant depending on the expected temperature profile determined; comparing the first simulated amount of reductant with a limit; depending on the result of the comparison, choosing a second defined dosage and secondly simulating (130, 160) a resulting amount of reductant beyond the at least one section of the catalyst (70) with the second dosage; comparing the second simulated amount of reductant with the limit; and adjusting (140, 150, 170, 180, 190, 195) the dosage for injection of the reductant into the catalyst based on the first and/or second comparison.