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. It was developed by the Austrian meteorologist and sedimentologist Felix Maria Exner, from whom it derives its name. It is typically applied to sediment in a fluvial system such as a river.

, times the negative divergence of sediment flux,

equals the bed porosity.

for natural systems range from 0.45 to 0.75. A typical value for spherical grains is 0.64, as given by random close packing. An upper bound for close-packed spherical grains is 0.74048 (see sphere packing for more details); this degree of packing is extremely improbable in natural systems, making random close packing the more realistic upper bound on grain packing density.

, as one is typically interested in the downstream distribution of erosion and deposition though a river reach

is scalar sediment flux in the downstream direction.

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