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.