The expression for
is similar to equation (85) except that **S** replaces
in equations
(86) and (87).
The expressions for and are also similar
except that in addition, we can safely ignore the second term in
square brackets of equations (86) and (87)
since along isopycnal
diffusion of and is quite small in the deep ocean, because
of the very small magnitudes of and . Therefore, unlike
and **S**, there is not a threat of significant drift in water mass
properties for long term integrations.

The expressions for horizontal viscosities and can also be simplified to considerable computational advantage and negligible loss in accuracy [41]: