The
PV field at after 15 days as (i) computed from the (u,v,h) field
and (ii) as materially advected from the ICs:
The level of agreement is quite stunning.
This can be compared to a standard pseudospectral
discretization of the SWEs and TR/LF time-discretization.
Here is the PV field after 15 days (filtered to eliminate the
Gibbs ribbles but no hyperdiffusion is applied to SWEs)