Exner equation

The Exner equation is a statement of conservation of mass that applies to sediment in a fluvial system such as a river. It was developed by the Austrian meteorologist and sedimentologist Felix Maria Exner, from whom it derives its name.

The Exner equation describes conservation of mass between sediment in the bed of a channel and sediment that is being transported. It states that bed elevation increases (the bed aggrades) proportionally to the amount of sediment that drops out of transport, and conversely decreases (the bed degrades) proportionally to the amount of sediment that becomes entrained by the flow.

The equation states that the change in bed elevation, ${\displaystyle \eta }$, over time, ${\displaystyle t}$, is equal to one over the grain packing density, ${\displaystyle \varepsilon _{o}}$, times the negative divergence of sediment flux, ${\displaystyle q_{s}}$.

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