** Next:** Free-surface boundary condition
** Up:** Improvements introduced in POP
** Previous:** Improvements introduced in POP
** Contents**

##

Surface-pressure formulation of barotropic mode

The barotropic streamfunction formulation in the standard
BCS models required an additional equation to be solved for each
continent and island that penetrated the ocean surface. This was
costly even on machines like Cray parallel-vector-processor computers,
which had fast memory access. To reduce the number of equations to
solve with the barotropic streamfunction formulation, it was common
practice to submerge islands, connect them to nearby continents with
artificial land bridges, or merge an island chain into a single mass
without gaps. The first modification created artificial gaps,
permitting increased flow, while the latter two closed channels that
should exist.

On distributed-memory parallel computers, these added equations
were even more costly because each required gathering data from an
arbitrarily large set of processors to perform a line-integral around
each landmass. This computational dilemma was addressed by developing
a new formulation of the barotropic mode based on surface pressure.
The boundary condition for the surface pressure at a land-ocean
interface point is local, which eliminates the non-local line-integral.

Consequently, the surface-pressure formulation permits any
number of islands to be included at no additional computational cost,
so all channels can be treated as precisely as the resolution of the
grid permits.

Another problem with the barotropic streamfunction formulation is that
the elliptic problem to be solved is ill-conditioned if bottom
topography has large spatial gradients. The bottom topography must be
smoothed to maintain numerical stability. Although this reduces the
fidelity of the simulation, it does have the "desirable" side effect
(given the other limitations of the streamfunction approach mentioned
above) of submerging many islands, thereby reducing the number of
equations to be solved. In contrast, the surface-pressure formulation
allows more realistic, unsmoothed bottom topography to be used with
no reduction in time step.

** Next:** Free-surface boundary condition
** Up:** Improvements introduced in POP
** Previous:** Improvements introduced in POP
** Contents**
2010-01-14