The GAIA module handles sediment dynamics in the openTELEMAC system.For the transport of sediment in suspension in the context of the height-averaged Saint-Venant equations deriving a Rouse vertical concentration profile is crucial. However the computation of the Rouse vertical profile requires the quadrature of a Einstein integral which analysis in the 0 water-height limit is non-trivial. This difficulty might carry over into the numerics and lead to incongruous deposition profiles at the wet/dry interface. A new approximation of the Rouse profile hinging on convex analysis was proposed to allow for a proper deposition pattern at these spots