2.2.2. Fine Sediment Re-Suspension

In Phase 2, during the rising flood with dQ/dt > 0 and Q > Qc, fine sediments are released from the sediment bed into the water column, because the bed materials become fluidized when Q exceeds Qc, initiating mobilization of the bed material.

An analysis of the data from Haschenburger [49] leads to the assumption that the erosion depth of the sediment bed during a flood event is an exponential function of the peak flow rate (Qpeak). From this approach, it is assumed that the maximum bed erosion occurs at the maximum flow rate (Qmax) during the observation period, when the release of all fine sediment particles within the sediment bed is expected. Thus Mmax is observed at Qmax (Appendix A.1).

In the model, the ratio of fine sediments mass released from the sediment bed, Mf,model, to the maximum possible mass of fine sediments in storage, Mmax, is expressed as an exponential function of the ratio of Qpeak to Qmax. Thus, the mass of fine sediments released from the sediment bed by flood event i is

$$\mathbf{M}\_{\text{fi,model}} = \mathbf{M}\_{\text{max}} \exp\left[ -\beta \left( 1 - \frac{\mathbf{Q}(\mathbf{t}\_{\text{p,i}})}{\mathbf{Q}\_{\text{max}}} \right) \right] \tag{2}$$

where tp,i is time at Qpeak of flood event i and β a dimensionless sediment bed erosion parameter.

The mass of fine sediments remaining in the pore space of the sediment bed immediately after flood event i is estimated from the difference between the accumulated fine sediment mass in the sediment bed before flood event i and the mass of fine sediments released from the sediment bed by flood event i, as

$$\mathbf{M}(\mathbf{t}\_{\mathrm{p},i}) = \mathbf{M}(\mathbf{t}\_{\mathrm{s},i}) - \mathbf{M}\_{\mathrm{max}} \exp\left[-\beta \left(1 - \frac{\mathbf{Q}(\mathbf{t}\_{\mathrm{p},i})}{\mathbf{Q}\_{\mathrm{max}}}\right)\right],\tag{3}$$

where M(t) is the fine sediment mass accumulated in the sediment bed at time t, and ts,i is the time at the beginning of flood event i. In the model simulation, M(tp,i) is restricted to be non- negative.

#### 2.2.3. Fine Sediment Accumulation during Flood Recession

Finally, in Phase 3, in the falling limb with dQ/dt < 0 and Q > Qc, fine sediments can be removed by filtration through hyporheic flow and stored within the pore space of the sediment bed. During flood recession, the available capacity for sediment storage is limited by partial fluidization of the sediment bed, which reduces the volume of porous media available for sediment accumulation (Appendix A.2). In the model, the available capacity for sediment storage in the sediment bed during the flood recession of a flood event, Mcap, is represented as

$$\mathbf{M}\_{\rm cap}[\mathbf{Q}(\mathbf{t})] = \mathbf{M}\_{\rm max} \left\{ 1 - \exp \left[ -\beta \left( 1 - \frac{\mathbf{Q}(\mathbf{t})}{\mathbf{Q}\_{\rm max}} \right) \right] \right\},\tag{4}$$

The change of accumulated fine sediments mass during the flood recession period is estimated by substituting Mcap[Q(t)] for Mmax in Equation (1) as

$$
\Delta \mathbf{M}(\mathbf{t}) = \alpha \mathbf{C}(\mathbf{t}) \left\{ 1 - \frac{\mathbf{M}(\mathbf{t})}{\mathbf{M}\_{\text{cap}}[\mathbf{Q}(\mathbf{t})]} \right\} \Delta \mathbf{t} \qquad \text{for } \mathbf{Q} > \mathbf{Q}\_c \text{ and } \mathbf{d} \mathbf{Q}/\text{dt} < 0,\tag{5}
$$
