*Appendix A.1. Fine Sediment Re-Suspension*

An analysis of the data from Haschenburger [49] leads to an assumption that the average depth of bed erosion was an exponential function of bed shear stress as

$$\text{bed version depth at } \mathbf{Q\_{peak}} \propto \exp\left(\boldsymbol{\beta}' \mathbf{Q\_{peak}}\right) \tag{A1}$$

where β is a bed erosion parameter.

From this approach, it is assumed that the maximum bed erosion depth occurs at Qmax during the observation period as

$$\text{Maximum bed region depth at } \text{Q}\_{\text{max}} \propto \exp\left(\beta^{\prime} \text{Q}\_{\text{max}}\right), \tag{A2}$$

The mass of fine sediments released from the sediment bed by a flood with Qpeak is assumed to be proportional to the bed erosion depth and thus, Mmax would be expected at Qmax. The ratio of Mf,model, to Mmax is

$$\frac{\mathbf{M}\_{\text{f,model}}}{\mathbf{M}\_{\text{max}}} = \exp\left[\boldsymbol{\beta}^{\prime}\mathbf{Q}\_{\text{peak}} - \boldsymbol{\beta}^{\prime}\mathbf{Q}\_{\text{max}}\right] = \exp\left[-\boldsymbol{\beta}\left(1 - \frac{\mathbf{Q}\_{\text{peak}}}{\mathbf{Q}\_{\text{max}}}\right)\right] \tag{A3}$$

where β, a dimensionless sediment bed erosion parameter, is defined as β Qmax.

Thus, the mass of fine sediments released form the sediment bed by flood event i is

$$\mathbf{M}\_{\text{fi,model}} = \mathbf{M}\_{\text{max}} \exp\left[ -\beta \left( 1 - \frac{\mathbf{Q}(\mathbf{t}\_{\text{p},i})}{\mathbf{Q}\_{\text{max}}} \right) \right] \tag{A4}$$

where tp,i is time at Qpeak of flood event i.
