*3.3. Fit Design—3<sup>k</sup> Experiment*

This second DOE, of the 3<sup>k</sup> type, allows specifying the calibration value of the parameters. The parameters and levels at which the second design was evaluated are shown in Table 4. However, since some 2nd and 3rd order significant interactions were found at Table 5, they cannot be excluded from the experiment. Nevertheless, if all these interactions are considered, the necessary degrees of freedom in the residues will not be enough to perform the analysis of variance. Therefore, the modelers decided to vary the TSP as a replica generator, because it is one of the original main parameters whose effect was recognized as not significant at Figure 4. As previously defined at Table 4, the TSP was varied within the range from 0.5 to 1.

Based on the previous consideration, the parameters and levels at which this second design was evaluated are shown in Table 6, and the ANOVA results for this experiment are shown in Table 7, where all *F*-ratios are based on the mean square of residual error. The R2 statistic indicates that this fit model explains 97.69% of the variability in OWIST, MF. As in the 2k experiment, verification tests were performed for Homoscedasticity, Normality and Independence assumptions. Homoscedasticity and Independence charts are presented in Figure 6.


**Table 6.** Factors (Calibration parameters) for 3k experimental design.


**Table 7.** ANOVA results for the 3k experiment.

**Figure 6.** Graphic verification of Homoscedasticity and Independence—Experiment 3k.

From the analysis of the individual behavior and interactions of the main parameters of this case study, the modelers observed that the higher OWIST, MF values were obtained when using the Van Rijn Transport equation.

Optimal calibration has as its objective to maximize OWIST, MF within the boundaries of the experimental region. From this, the best OWIST, MF result found was 0.864, associated with the following conditions: Van Rijn transport equation; Ks = 0.5; Kb = 0.1.

As described in the method section and summarized in Figure 1, once the morphological and sedimentological calibration has been performed and quantified by means of the OWIST, MF, the hydrodynamic component of OWI has to be checked in order to determine if its calibration remains valid.

For this case study, the water level (WL) and flow distribution (FD) were calculated by the model using the conditions previously mentioned for optimizing OWIST, MF. An OWIHD of 0.90 was obtained from using those results. The qualitative calibration parameters related to velocity vectors and morphological evolution were also evaluated for this optimal case. For two sections of the river reach used as case study, Figure 7 displays the comparison between observed and modeled velocity vectors, where a good fit was observed both for magnitude and direction.

**Figure 7.** Comparison between Velocity Vectors in two sections of the reach for the optimal case.

The morphological evolution was assessed and verified, with no significant instabilities or bathymetric changes found.

#### **4. Discussion**

#### *4.1. Hydrodynamic Calibration*

For the three different options of C, the error found between the simulated and observed values did not exceed 1.7%. Consequently, for this case study, the model sensitivity to this parameter is low, because in general, all the evaluated cases achieved an excellent adjustment when estimating water levels and flow distribution through river branches.

The visual inspection showed a good adjustment of the direction and magnitude of the average vectors extracted from the ADCP measurements with respect to the velocity vectors with respect to the simulated ones. The morphological behavior developed properly. There were no significant instability or abrupt changes in the bottom morphology of the river.
