Laplace transform integration of the shallow-water equations. Part 2: Lagrangian formulation and orographic resonance

In this paper we combine the Laplace transform (LT) scheme with a semi-
Lagrangian advection scheme, and implement it in a shallow water model. It
is compared to a reference model using the semi-implicit (SI) scheme, with both
Eulerian and Lagrangian advection. We show that the LT scheme is accurate
and computationally competitive with these reference schemes. We also show,
both analytically and numerically, that the LT scheme is free from the problem
of orographic resonance that is found with semi-implicit schemes.