This model was originally proposed by Exner (1925). Assuming a smooth initial condition,

(ζ - *z *)

2

(11)

where *c*z is the propagation speed of the bed. As is well known, non-linear hyperbolic equations

such as Eq. (10), depending on the initial conditions, will develop steep gradients (and eventually

discontinuities or shocks) which provide a rigorous test for a numerical method. A similar model

was examined by Johnson and Zyserman (2002) in the context of testing a finite difference

scheme.

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