2.2.1. Fine Sediment Accumulation

In Phase 1, when Q is less than the critical flow rate (Qc) to initiate sediment bed material mobilization, the fine sediments in the water column are accumulated in the sediment bed through hyporheic flow. The change of accumulated fine sediments mass during the time period from t to t + Δt is represented by Equation (1), which was derived by considering that the mass of fine sediments accumulated in the sediment bed is proportional to the fine sediment concentration in surface water, C(t).

$$
\Delta \mathbf{M}(\mathbf{t}) = \alpha \mathbf{C}(\mathbf{t}) \left[ 1 - \frac{\mathbf{M}(\mathbf{t})}{\mathbf{M}\_{\text{max}}} \right] \Delta \mathbf{t} \qquad \text{for } \mathbf{Q} < \mathbf{Q}\_{\text{c}'} \tag{1}
$$

where M is the mass of fine sediments accumulated within the pore space of the sediment bed. The maximum value of M, Mmax, represents the sediment particle accumulation capacity of the sediment bed. The sediment particle removal parameter, α (L3/T), represents the filtration and settling of fine sediment particles within the sediment bed.
