Problems
393
(b) Show that the vertical finite-difference scheme for the o-coordinate
primitive-equation model described in Section 7.6.3 will conserve total
mass if nonconservative effects due to time-differencing and the horizontal
spectral representation are neglected.
(c) Suppose that instead of predicting In Ps as in (7.115) , the actual surface
pressure was predicted using (7.104). Show that except for nonconservative
effects due to time-differencing, total mass will be exactly conserved in a
numerical model in which the Galerkin spectral method is used to evaluate
the horizontal derivatives , and the vertical derivative is approximated by
(7.119) . This approach is not used in practice because it generates a noisier
solution that that obtained using In Ps as the prognostic variable (Kiehl et aI.
1996, p. 15).
393
(b) Show that the vertical finite-difference scheme for the o-coordinate
primitive-equation model described in Section 7.6.3 will conserve total
mass if nonconservative effects due to time-differencing and the horizontal
spectral representation are neglected.
(c) Suppose that instead of predicting In Ps as in (7.115) , the actual surface
pressure was predicted using (7.104). Show that except for nonconservative
effects due to time-differencing, total mass will be exactly conserved in a
numerical model in which the Galerkin spectral method is used to evaluate
the horizontal derivatives , and the vertical derivative is approximated by
(7.119) . This approach is not used in practice because it generates a noisier
solution that that obtained using In Ps as the prognostic variable (Kiehl et aI.
1996, p. 15).