New and improved four-parameter non-linear Muskingum model

There are two mathematical forms of the non-linear Muskingum model, which involves a storage parameter, weighting parameter and an exponent parameter. In the first form, the exponent parameter is associated with the inflow and outflow variables of the storage equation; in the second form, it is associated with the weighted storage term of that equation. The second form has been more popular as it is easier to estimate and produces a better fit to observed data. This paper proposes a new four-parameter non-linear Muskingum model that assumes a power function of the channel storage and in effect combines the two known mathematical forms of the model. The resulting model provides more degrees of freedom in fitting observed data. The problem is formulated as a mathematical optimisation model that minimises the sum of the squared deviations between observed and estimated outflows. A constraint among the four model parameters is developed to ensure non-negative outflows. Application of the proposed model shows that it could substantially (up to almost 80%) improve the fit to observed outflows.