Ocean general circulation models frequently use nonuniform grids, espe
cially in the vertical direction. This paper clarifies the implication
s of using such grids on the consistency and accuracy of numerical sch
emes. It is emphasized that numerical schemes maintain their order of
accuracy on a nonuniform grid provided the grid can be related to a sm
ooth mapping. Additional metric terms appear in the truncation error,
which should not be interpreted simply as a numerical diffusion.