**4. Discussion**

The storage and re-suspension model developed by Park et al. [32] was applied to multiple catchments in contrasted climatic conditions with different catchment areas and other catchment characteristics (e.g., soil properties, and land use). Area dependency of the filtration parameter was observed, and it is notable that five catchments with Mediterranean-type climates show consistency in α, with ranges from 10 to 20 regardless of catchment scale. Relatively larger values of α (>100) were observed in larger catchments (i.e., Owenabue, Bandon, Hopland, Guerneville, and Meuse) where climatic conditions and bed material compositions were more variable (Table 1). In the case of the bed erosion parameter, the values were within a narrow range. It is clear that both α and β were affected by various environmental characteristics in each catchment. Understanding the effects of these various environmental characteristics on the model parameters, including the reason for the possible area dependency of α and relative consistency of α in the five catchments of Mediterranean-type climate, is suggested as a subject for future study.

The purpose of this study was to verify the general applicability of the storage and re-suspension model for catchments with various environmental characteristics and to understand the effect of environmental characteristics on the model performance. Therefore, providing specific values of model parameters for each catchment was out of the scope of this paper. Model calibration in 13 catchments shows a good fit with the real observations and thus verifies the possible applicability of the model, whereas there are certain areas where the applicability of the model can be improved in future studies, as described below.

(i) The first is to minimize uncertainties in determining the model input parameters Qc, Qmax, Cb, and Mmax for each catchment. Uncertainties in the determination of these model parameters can have various causes, such as limited periods of observation in the catchment and variability of sediment dynamics in the natural river system, which induce noticeable scatter of Qs, even at the same water discharge. For example, as shown in the previous study [32], a larger peak flow rate (1050 m3/s) than Qmax (890 m3/s) was observed in Guerneville on 12 December 2014, during the validation period, which was not observed during the calibration period. The model-estimated mass of fine sediments released from the sediment bed was 72,600 Mg, which is only ~50% of the amount during the flood event [32].

In Carapelle, a Qmax of 37 m3/s and Mmax of 23,000 Mg were observed on 5 March 2009, where the maximum flow rate during the model calibration period was 120 m3/s, registered on 6 March 2009. It is interesting that the flood with the largest mass of fine sediment release in Carapelle had a flow rate of only one third of the highest flow rates on record. As in Cantalice et al. [21], this could be explained by the fact that C in the first flood is related to the re-suspension of deposited sediments, whereas it decreases in the subsequent events as considerable amount of sediment was re-suspended in the previous flood event. This suggests that high rates of fine sediment erosion are possible also at moderate flow rates.

An example of model parameter uncertainty can also be drawn from the model simulation result for the Isabena. There is relatively greater disagreement between the model estimation and observations of the fine sediment mass released from the sediment bed in the Isabena, where the RSR of the model calibration is 0.97. This disagreement may be attributed to the wide range in observed suspended sediment concentrations during flood recession periods and baseflows, leading to considerable uncertainty in the assumed dependence of the background suspended sediment concentration on Q. In the Isabena, Cb was hardly discernable in the linear scale plot; thus, Cb was determined from the log–log scale (Figure S2). The wide ranges of scatter in the relationship between C and Q in the two subalpine regions, Galabre and Bès, also cause uncertainty in the determination of Qc and Cb in the two catchments. Unlike the Isabena, even with these constraints with respect to the application of the model, the calibrated model provides good representations of the fine sediment release during flood events, with 5% and 7% bias of the observation in the two catchments, Galabre and Bès, respectively.

Overall, model calibration and validation results in this study provide a good estimation of the observed sediment dynamics. However, consistent and longer-term observations will reduce possible uncertainties, including model parameter determination, and further improve model performance.

(ii) Secondly, there are possible issues that can cause considerable model bias, such as episodic events that may produce bank erosion. For example, the model reasonably estimated the observed mass of fine sediments released from the sediment bed in Violettes (Table 2). The observed mass of fine sediments released from the sediment bed (Mf, obs) was less than 1 Mg when Q was less than 0.1 m3/s, except for the two flood events on 16 and 27 October 2002. The model-estimated mass of fine sediments released from the sediment bed (Mf, model) was less than 1 Mg for all flood events including the two events specified above, while Mf, obs was 3.5 Mg and 2.1 Mg, where the Q of the two flood events on 16 and 27 October was 0.09 m3/s and 0.06 m3/s, respectively. Thus, a considerable underestimation of Mf, obs was observed for these two flood events. This underestimation by the model may be related to the additional supply of sediment by episodic events, such as bank erosion, associated with cattle trampling in riparian pastures from March to October [33,42].

The two model parameters in this study, α and β, successfully accounted for all variability despite contrasting environmental conditions, whereas episodic events may be considered little and may increase the uncertainty of the numerical model as it was assumed that the mass of fine sediment re-suspended from the sediment bed is proportional to the bed erosion depth which is considered as an exponential function of bed shear stress. Thus, better insights into the characteristics and episodic events of each catchment would provide a better understanding of the possible reasons for the model bias and thus clues for improving the model in future studies.

Various natural characteristics can affect fine sediment dynamics, and thus should be considered for the development of sediment dynamics models for rivers. For example, in catchments with low geomorphic activity, it is possible to obtain statistically significant multivariate models to predict suspended sediment concentrations [36]. However, in catchments with greater sedimentary activity, the results of these models fail to be significant through all the time, which indicates that sediment supply and the role of the riverbed acting as a sediment source or sink play fundamental roles [55]. Riverbed sediment clogging by cohesive sediment (<63 μm) is also one of factors that have possible effect on sediment transport processes and it can be considered that in sites with sandy or sand-gravel such as the Incline Creek, the Hopland and the Guerneville, the bed material is not dominantly cohesive while the sediment is cohesive in sites with clay or silty bed material dominated such as the Violettes, the Moulinet, and the Isábena. The limitation of available information for the detailed characteristics and conditions of field sites limits the practical applicability of sediment model in many cases. Including more parameters would improve model performance but would also increase model complexity, and would require more effort for data observation and thus reduce the practical applicability of the model [32,56]. The model developed in this study includes only two model parameters, α and β, but shows good ability for estimating fine sediment storage mass in 13 catchments with various environmental characteristics, which is an obvious benefit of this model.

## **5. Conclusions**

The general applicability of a storage and re-suspension model was tested in this study. The model was applied to 13 catchments with different climatic conditions (e.g., precipitation and hydrological conditions) and catchment area. The initial model parameters, Qc, Qmax, Cb, and Mmax, were determined from the observed data. The observed cumulative mass of fine sediments released from the bed in relation to the total suspended load during the model calibration period ranges from 18 to 65%.

The model performance was evaluated using the statistical parameters RSR and R. The optimal model simulation parameters, α and β, were determined to be values that minimize the RSR based on trial and error. The RSR of the model calibration ranges from 0.33 to 0.97, with an average value of 0.54, and the R value ranges from 0.83 to 1.23, with an average of 1.01. The value of the filtration parameter, α, ranges from 0.022 to 1650 m3/s; a clear area dependency was observed up to an approximate catchment area of less than 100 km2. The bed erosion parameter, β, was set within a narrower range than α, between 2.4 and 5.3.

It is also noticeable that relatively small values of α from 10 to 20 were observed in five catchments located around the Mediterranean Sea with similar climate, while larger values of α (>100) were observed in five catchments with largest area.

Overall, the model estimated the mass of fine sediments released from the sediment bed in the 13 catchments within ~23% bias.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4441/11/5/878/s1, Figure S1: Q vs Qs, Figure S2: Background line, Figure S3: Hysteresis analysis, Figure S4: Sensitivity analysis, Figure S5: Model calibration, Table S1: Study sites.

**Author Contributions:** Conceptualization: J.P.; Methodology: J.P.; Software: J.P.; Validation: J.P., R.J.B., F.B., M.E., F.G., J.R.H., O.N., J.A.L.-T., D.V.; Formal analysis: J.P., R.J.B., F.B., M.E., F.G., J.R.H., O.N., J.A.L.-T., D.V.; Investigation: J.P., R.J.B., F.B., M.E., F.G., J.R.H., O.N., J.A.L.-T., D.V.; Resources: J.P.; R.J.B., F.B., M.E., F.G., J.R.H., O.N., J.A.L.-T., D.V.; Data curation: J.P., R.J.B., F.B., M.E., F.G., J.R.H., O.N., J.A.L.-T., D.V.; Writing—original draft preparation: J.P.; Writing—review and editing: J.P., R.J.B., F.B., M.E., F.G., J.R.H., O.N., J.A.L.-T., D.V.; Visualization: J.P.; Supervision: J.P.; Project administration: J.P.; Funding acquisition: R.J.B., F.B., M.E., F.G., J.R.H., O.N., J.A.L.-T., D.V.

**Funding:** J. A. López-Tarazón is in receipt of a Vicenç Mut postdoctoral fellowship (CAIB PD/038/2016), while Damià Vericat is a a Serra Húnter Fellow at the University of Lleida. Authors acknowledge the support from the Economy and Knowledge Department of the Catalan Government through the Consolidated Research Group 2017 SGR 459 Fluvial Dynamics Research Group (RIUS). The data in Galabre and Bès were collected during the STREAMS (Sediment TRansport and Erosion Across Mountains) project, funded by the French National Research Agency (ANR/ BLAN06-1\_13915).

**Acknowledgments:** This study applied a filtration and bed erosion model developed from the analysis of the United States Geological Survey field monitoring data, which was easily accessed from "California datacube" developed by the UC Berkeley Water Center in collaboration with the Lawrence Berkeley National Laboratory and Microsoft Research. Great thanks to Dr. Jacques L. Langlois for kindly provided data in Incline Creek, also thanks to Professor Hans Middelkoop at Utrecht University, the Netherlands, for kindly provided link to the flow and suspended sediment data for Meuse River.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
