*2.4. Model Evaluation*

Two parameters, α and β, were utilized for model calibration. The fine sediment filtration parameter, α, represents the removal of fine sediments from the water column by filtration and settling of fine sediments within the pore space of the sediment bed of the catchment and the bed erosion parameter, β, represents the erosion of the sediment bed during a flood event. The optimal values of model parameters (α and β) were determined by a reiterative trial and error process to minimize the root-mean-square error to data standard deviation ratio (RSR), using Equations (8)–(10).

The model performance was also evaluated based on values of the term R, which is defined as the ratio of the modeled sediment mass released to the observed sediment mass released. The model performance is considered satisfactory when RSR < 0.70 [50] and when R approaches 1 when there is a total agreement between observed and predicted values.

$$\mathbf{R} = \frac{\sum\_{\mathbf{j=1}}^{n} \mathbf{M}\_{\mathbf{f}|\text{model}}}{\sum\_{\mathbf{j=1}}^{n} \mathbf{M}\_{\mathbf{f}|\text{obs}}},\tag{8}$$

where n is the number of flood events in the entire simulation period.

$$\text{RSR} = \frac{\sqrt{\sum\_{i=1}^{n} \left(\mathbf{M}\_{\text{fi,obs}} - \mathbf{M}\_{\text{fi,model}}\right)^2}}{\sqrt{\sum\_{i=1}^{n} \left(\mathbf{M}\_{\text{fi,obs}} - \overline{\mathbf{M}\_{\text{f,obs}}}\right)^2}},\tag{9}$$

where n is the number of flood events and the mean observed mass released for all flood events is

$$\overline{\mathbf{M}\_{\rm f,obs}} = \frac{1}{\mathbf{n}} \sum\_{i=1}^{n} \mathbf{M}\_{\rm fi,obs} \tag{10}$$

The period of data available for model simulation varies for each catchment. For catchments with more than three years of observations, about two-thirds of the data were used for model calibration and the remaining data were used for validation, except for the Meuse River where 15 years of data were available. Due to the longer period of observations in the Meuse River, five years were used for model calibration, whereas data from the remaining 10 years were used for model validation, in order to test the applicability of the model in a longer period.
