  Local conservation of mass and entropy are becoming increasingly desirable
properties for modern numerical weather and climate models. This work presents
a Flux-Form Semi-Lagrangian (FFSL) transport scheme, called SWIFT, that
facilitates this conservation for tracer variables, whilst maintaining other
vital properties such as preservation of a constant, monotonicity and
positivity. Importantly, these properties all hold for large Courant numbers
and multi-dimensional flow, making the scheme appropriate for use within a
dynamical core which takes large time steps.
  The SWIFT scheme presented here can be seen as an evolution of the FFSL
methods of Leonard et al and Lin and Rood. Two-dimensional and
three-dimensional schemes consist of a splitting into a sequence of
one-dimensional calculations. The new SWIFT splitting presented here allows
monotonic and positivity properties from the one-dimensional calculations to be
inherited by the multi-dimensional scheme. These one-dimensional calculations
involve separating the mass flux into terms that correspond to integer and
fractional parts of the Courant number. Key to achieving conservation is
coupling the transport of tracers to the transport of the fluid density,
through re-use of the discrete mass flux that was calculated from the fluid
density in the transport of the tracers. This work also describes how these
properties can still be attained when the tracer is vertically-staggered from
the density in a Charney-Phillips grid.
