How to reduce the computational error is a key issue of using 
-coordinate coastal ocean models. Due to the fact that the higher the order
of the difference scheme, the less the truncation error and the more
complicated the computation, we introduce two sixth-order difference schemes
(ordinary and compact) for the -coordinate coastal models in order to
reduce error without increasing much complexity of the computation. After the
analytical error estimation, the Semi-Spectral Primitive Equation Model (SPEM)
is used to demonstrate the benefit of using these schemes and to compare the
difference among the three six-order schemes. Over a wide range of parameter
space as well as a great parametric domain of numerical stability, the
ordinary sixth-order scheme is shown to have error reductions by factors of 50
comparing to the second-order difference scheme and the compact sixth-order
scheme is shown to have more than 50% error reduction comparing to the
ordinary sixth-order scheme.