  A positivity-preserving conservative semi-Lagrangian transport model by
multi-moment finite volume method has been developed on the cubed-sphere grid.
In this paper, two kinds of moments, i.e. point values (PV moment) at cell
boundaries and volume integrated average (VIA) value, are defined within a
single cell. The PV moment is updated by a conventional semi-Lagrangian method,
while the VIA moment is cast by the flux form formulation that assures the
exact numerical conservation. Different from the spatial approximation used in
CSL2 (conservative semi-Lagrangian scheme with second order polynomial
function) scheme, a monotonic rational function which can effectively remove
non-physical oscillations and preserve the shape, is reconstructed in a single
cell by the PV moment and VIA moment. The resulting scheme is inherently
conservative and can allow a CFL number larger than one. Moreover, the scheme
uses only one cell for spatial reconstruction, which is very easy for practical
implementation. The proposed model is evaluated by several widely used
benchmark tests on cubed-sphere geometry. Numerical results show that the
proposed transport model can effectively remove unphysical oscillations
compared with the CSL2 scheme and preserve the numerical non-negativity, and it
has the potential to transport the tracers accurately in real atmospheric
model.
