Surface modification of the sediment transport

Internally the model stores the masses of each fraction in each layer:

\[ m_{j,i} = \text{mass of fraction } i \text{ in layer } j \]

Equation: Notation for the mass of a sediment fraction stored in a bed layer.

The so-called surface modification involves the factors \(F_{i}\), which are calculated as:

\[ F_{i} = f\left( \frac{\Delta_{1}}{\Delta_{a}} \right)\ \frac{m_{1,i}}{\sum m_{1,i}} \]

Equation: Surface modification factor for a sediment fraction.

This is the relative mass of the fraction in the bed surface multiplied by the function \(f\), which is given by:

\[ f(x) = \begin{cases} x, & x < 1 \\ 1, & x \geq 1 \end{cases} \]

Equation: Scaling function applied when the active layer is below its target thickness.

The modification for relative mass is the standard surface modification, while the second modification only has an influence if the active layer thickness (\(\Delta_{1}\)) is below the target thickness. That situation can only occur under the following conditions:

• 1-layer model with the active layer below its target thickness
• 2-layer model in which the local passive layer is empty and therefore the active layer can go below the target thickness (cannot happen unless the passive layer is empty)

Both situations represent sediment starved conditions, and the modification scales down the sediment transport (\(f(x) < 1\)).