  In this work a simple but accurate shallow model for bedload sediment
transport is proposed. The model is based on applying the moment approach to
the Shallow Water Exner model, making it possible to recover the vertical
structure of the flow. This approach allows us to obtain a better approximation
of the fluid velocity close to the bottom, which is the relevant velocity for
the sediment transport. A general Shallow Water Exner moment model allowing for
polynomial velocity profiles of arbitrary order is obtained. A regularization
ensures hyperbolicity and easy computation of the eigenvalues. The system is
solved by means of an adapted IFCP scheme proposed here. The improvement of
this IFCP type scheme is based on the approximation of the eigenvalue
associated to the sediment transport. Numerical tests are presented which deal
with large and short time scales. The proposed model allows to obtain the
vertical structure of the fluid, which results in a better description on the
bedload transport of the sediment layer.
