  In this paper, we are concerned with the shallow water flow model over
non-flat bottom topography by high-order schemes. Most of the numerical schemes
in the literature are developed from the original mathematical model of the
shallow water flow. The novel contribution of this study consists in designing
a finite-difference weighted essentially non-oscillatory (WENO) scheme based on
the alternative formulation of the shallow water flow model, denoted as
"pre-balanced" shallow water equations and introduced in [Journal of
Computational Physics 192 (2003) 422-451]. This formulation greatly simplifies
the achievement of the well-balancing of the present scheme. Rigorous numerical
analysis, as well as extensive numerical results all, verify that the current
scheme preserves the exact conservation property. It is important to note that
this resulting scheme also maintains the non-oscillatory property near
discontinuities and keep high-order accuracy for smooth solutions at the same
time.
