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

From this fit design experiment, the ANOVA summarized in Table 7 indicates that all factors and interactions considered are significant. With all P values smaller than 0.05, all the calibration parameters have a statistically significant effect on OWIST, MF, when considering a confidence level of 95%.

The homoscedasticity plot in Figure 6 did not show any unusual structure. As for Normality verification, a chi-square normality test was performed, where the OWIST, MF residues were distributed into 16 equally probable classes, and each class was then compared with the expected number of observations. Using Statgraphics software for this analysis, a *P*-value was obtained equal to 0.9273 for this normality test, which is greater than or equal to 0.05. This prevents rejecting the hypothesis that OWIST, MF residues do not come from a normal distribution, with statistical confidence level of 95%.

The assumption of data independence was verified from the plot of Residues vs. Execution order in Figure 6. As in the 2k experiment, the results shown in this figure indicate that the residuals did not follow a trend in terms of their execution order. The plot of residues in Figure 6 suggests that there is no autocorrelation among the residuals of the ANOVA.

After verifying the fit of the qualitative parameters, it can be summarized that the optimal calibration for this case study for the Meta River occurs at these experimental conditions: Van Rijn transport equation; Ks = 0.5 and Kb = 0.1. As result, the modelers obtained an OWIST, MF = 0.8293 and a global OWI = 0.8571.

#### *4.4. Additional Remarks*

As previously stated, the method proposed in this paper is based on DOE theory, and because of this, it shares some of its limitations:


It is also worth noting that the goodness of fit might considerably vary depending on the numeric model used and its capacity to recreate the hydrodynamic, sedimentologic and morphological processes under analysis.

#### **5. Conclusions**

By including principles of design of experiments (DOE), the method presented in this paper improves the reliability of the calibration process of hydromorphological models. This becomes even more relevant for rivers whose hydrodynamics depends on morphological processes. Within this context, this paper presented a calibration method based on DOE, which consists of a systematic approach for evaluating the qualitative and quantitative performance of a hydromorphological numerical model based on its corresponding calibration parameters, with the aim of allowing the modelers to get a better understanding and of the effects of these parameters on the adjustment indicators.

Using a 75 km reach of the Meta River as case study, and the MIKE-21C model, the method and its results were described and discussed, along with some of its limitations. The calibration parameters for this case study were the roughness coefficient, the sediment transport equation, the riverbed and suspended load factors, the transverse slope coefficient and the transverse slope power. An optimal overall weighted indicator, which can be defined as an integrated measure of the performance of the model was found for the example, with a value of 85.71%.

The method is versatile in terms of number of calibration parameters and selection of adjustment indicators, because their selection depends on the modeling objective and characteristics of the analyzed section. This method can be applied to unidimensional or multidimensional hydromorphological models.

Based on the findings of this study, some future research directions are:


**Author Contributions:** Conceptualization, G.J.A. and H.A.; Methodology, G.J.A. and H.A.; Formal Analysis, G.J.A. and H.A.; Writing and Original Draft Preparation, G.J.A. and F.A.C.; Writing, Review and Editing, G.J.A. and F.A.C.; Funding acquisition, H.A.

**Funding:** This research was funded by the Universidad del Norte, Colombia.

**Acknowledgments:** The authors acknowledge the teamwork with the Institute of Hydraulic and Environmental Studies of the Universidad del Norte and data from the project "Update of the Studies and Designs for the Navigation of the Meta River between Cabuyaro (K804) and Puerto Carreño (K0)".

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

#### *Article*
