29.2.5.4 Asymmetry of the barotropic equations in MOM 1

The barotropic equations presented to the solvers in MOM 1 were not symmetric, even when the implicit Coriolis parameter acor was set to zero. In an attempt to optimize the code to save a few floating point operations in the calculation of ${\bf A}{\bf x}$, each equation was divided by its diagonal coefficient, $\coeff_{i,jrow,0,0}$. Since these diagonal coefficients depend on topography and grid factors, they are not equal at neighboring cells, and the resulting equations are not symmetric. The asymmetry between a mid-ocean cell and a neighboring island perimeter is likely to be especially severe. It is possible that some of the problems arising with the use of conjugate gradient solvers in MOM 1 may be attributed to MOM 1's ``normalization'' of the elliptic equations and the resulting de-symmetrization of the coefficient array.