Hi Jose,
To put simply, the MPM coefficient modifies the intensity of the (bedload) sediment transport. This value is by default equal to 8 but can be modified and used as a calibration parameter. In the Exner equation, the divergence operator is applied to the sediment fluxes and therefore affecting the temporal variation of the bottom elevation. Please take a look to the Sisyphe's manual v7p2.
There are tons of articles, books, etc. about this topic. Please find below some good references.
*The (famous) e-book by Prof. Gary Parker
* W. Wu (2007). Computational River Dynamics, Taylor & Francis, UK, 494 p.
* Marcelo Garcia Sedimentation Engineering: Processes, Measurements, Modeling, and Practice
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