*3.1. Model Parameters*

The model parameters (i.e., Qc, Cb, Mmax, and Qmax) were determined from analysis of observed data in each of the 13 catchments (Figures S1 and S2 in Supplementary Materials) and are summarized in Table 1; a complete set of figures for all catchments is presented in Supplementary Materials, and in the next we present some observations on the data.

Slope breaks in the relationship between Qs to Q were observed at flow rates of 5 m3/s for Owenabue and 10 m3/s for Bandon (Figure S1). The falling limb flow recessions asymptotically approached a linear relationship between C and Q, which defined the assumed background suspended sediment concentration dependence on Q as Cb(Q) = 1.5Q for Owenabue and Cb(Q) = 0.1Q for Bandon (Figure 2).

**Figure 2.** Fine sediment concentration data during falling limb recession of each flood event for Owenabue from 15 September 2009, to 15 September 2010 (**a**), and Bandon from 10 February 2010, to 9 February 2011 (**b**). The symbols with different colors and shapes represent different flood events.

Unlike in the other catchments, the range in Q was rather small for Incline Creek; that is, 0.15 to 0.45 m3/s. In addition, the flow rates above 0.28 m3/s are reported only within a resolution of 1 cfs (cubic feet per second), thus 0.028 m3/s, which was the minimum resolution of the flow rate measurement for this USGS gauging site, leading to limited resolution of the recession curve and vertically aligned data beyond flow rates of 0.28 m3/s (Figure S1).

The relationship of Qs to Q for water discharge above 1 m3/s for the Ribera Salada showed noticeable expansion of vertical scatter. Thus, Qc was determined to be 1 m3/s, which corresponds to previous observations [51]. In three catchments, Ribera Salada, Isabena, and Carapelle, considerable scatter was observed in the relationship between Qs and Q, and power laws show a reasonably good fit with the falling limb recession of flood events (Figure S2). Thus, power laws were utilized for the estimation of the background fine sediment concentrations (Table 1). The Qc values in two subalpine regions, Galabre and Bès, were determined to be 1 m3/s and 10 m3/s, respectively (Figure S1).

The hysteresis analysis of sequential flood events provides better insight into model parameter determination. For example, much less hysteresis is observed during the second flood event of the two sequential events with similar peak flow rates between 9 and 10 August 2002, in Moulinet, France (Figure 3). This represents the depletion of stored suspended sediments by the preceding flood event and suggests that the suspended sediments were mostly supplied from the catchment during the second flood event. The observed mass of the fine sediments released from the sediment bed was 2.0 Mg for the first flood and 0.6 Mg for the second flood. The background suspended sediment concentration relationship Cb = 300 Q for Moulinet shows consistency with the suspended sediment concentration during the recession of the two flood events (Figure 3). A similar pattern of fine sediment dynamics in sequential flood events was also observed in the examples of hysteresis analysis between Q and C in other catchments. For example, much less hysteresis was observed during the second flood event of the two sequential flood events at Owenabue between 5 and 10 December 2009, at Incline Creek between 4 and 6 May 2000 and at the largest catchment Meuse between 1 December 1999 and 26 January 2000 (Figure S3). The background suspended sediment concentration relationship also shows consistency with the suspended sediment concentration during the recession of the two flood events at each site.

**Figure 3.** (**a**) Hydrograph (date format: month-day hour:min) and (**b**) hysteresis of sediment concentration (C) to suspended sediment load (Q) for sequential floods in Moulinet between 9 and 10 August 2002.

#### *3.2. Model Calibration*

Model calibration results are summarized in Table 2. The model was calibrated for each catchment to determine optimal model parameters (α and β) that minimize RSR (Figure S4 in Supplementary Materials). Figure 4 shows examples of model calibrations for two catchments, Owenabue and Bandon in Ireland, where the RSR was 0.49 and 0.36, respectively. The number of flood events in each catchment ranged from 22 to 79 during the calibration period. The filtration parameter, α, ranged from 0.022 to 1650 m3/s, whereas relative consistency was observed for the bed erosion parameter, β, ranging from

2.4 to 5.3 (Figure S4 in Supplementary Materials). The model parameter sensitivity analysis shows that the model calibration stably converges to optimal values, and is more sensitive to change in α rather than β, in the two small catchments in France (Violettes and Moulinet), the snowmelt-dominated Incline Creek, and Carapelle (Figure S4). In the relatively larger catchments of Isabena, Guerneville, and Meuse, the model calibration also converges to optimal values, although it is more sensitive to change in β rather than α (Figure S4 and Park et al. [32]). In the other six catchments, Galabre, Owenabue, Bandon, Bès, Ribera Salada, and Hopland, the model calibrations are less sensitive to the change of α than to that of β when α is larger than the optimal value (Figure S4 and Park et al. [32]).

**Figure 4.** Model calibration output for (**a**) Owenabue from 15 September 2009 to 15 September 2010 and (**b**) Bandon from 10 February 2010 to 9 February 2011. The dashed magenta line represents the storage capacity of the sediment bed for fine sediments, Mcap [Q(t)], and the dotted black line represents the mass of the fine sediments stored in the sediment bed, M(t). The black line with triangles represents the observed cumulative mass of fine sediments released from the sediment bed by the first i flood events (Ai,obs) and the red line with circles represents the modeled cumulative mass of sediments released for the first i flood events (Ai,model).

The model-estimated cumulative mass of fine sediments released from the sediment bed shows a good fit to the observations for the 13 catchments (Table 2 and Figure S5). The average RSR value in these 13 catchments is 0.54, ranging from 0.33 to 0.97, where the largest RSR of 0.97 is observed in the Isabena catchment. The model also estimated an observation bias of less than 20% in 12 catchments, except for Violettes, where R was 1.23 (Table 2).

The mass of fine sediments released from channel beds, that is, the cumulative sum of Mf, obs, ranged from 18% to 65% of the total suspended sediment load in the 13 catchments during the model calibration periods (Table 2), which is consistent with previous studies [52–54].



*Water* **2019**, *11*, 878
