A soot discharge amount is calculated by multiplying a “steady discharge amount” by a “transient correction value.” The steady discharge amount is a soot discharge amount in a steady operation state, and is acquired through table search. For each of a plurality of factors which affect the soot discharge amount, a steady value (value obtained through table search) of the factor and a transient value (current value) of the factor are substituted for a characteristic equation which represents a change in the soot discharge amount with the value of the factor, whereby a steady characteristic value and a transient characteristic value are acquired. The “ratio between the steady characteristic value and the transient characteristic value” is then calculated for each factor. The transient correction value is obtained by multiplying together all values of the “ratio between the steady characteristic value and the transient characteristic value” obtained for the factors.