  In this paper, we develop and present an arbitrary high order well-balanced
finite volume WENO method combined with the modified Patankar Deferred
Correction (mPDeC) time integration method for the shallow water equations. Due
to the positivity-preserving property of mPDeC, the resulting scheme is
unconditionally positivity preserving for the water height. To apply the mPDeC
approach, we have to interpret the spatial semi-discretization in terms of
production-destruction systems. Only small modifications inside the classical
WENO implementation are necessary and we explain how it can be done. In
numerical simulations, focusing on a fifth order method, we demonstrate the
good performance of the new method and verify the theoretical properties.
