making a small correction to the hydrostatic pressure. QH has good energetic credentials  they are the same as for HPE. Importantly, however, it has the same angular momentum principle as the full nonhydrostatic model (NH)  see Marshall et.al., 1997a. As in HPE only a 2d elliptic problem need be solved.
1.3.4.3 Nonhydrostatic and quasinonhydrostatic formsThe MIT model presently supports a full nonhydrostatic ocean isomorph, but only a quasinonhydrostatic atmospheric isomorph.
1.3.4.3.1 Nonhydrostatic OceanIn the nonhydrostatic ocean model all terms in equations Eqs.(1.29 1.31) are retained. A three dimensional elliptic equation must be solved subject to Neumann boundary conditions (see below). It is important to note that use of the full NH does not admit any new `fast' waves in to the system  the incompressible condition eq(1.3) has already filtered out acoustic modes. It does, however, ensure that the gravity waves are treated accurately with an exact dispersion relation. The NH set has a complete angular momentum principle and consistent energetics  see White and Bromley, 1995; Marshall et.al. 1997a.
1.3.4.3.2 Quasinonhydrostatic AtmosphereIn the nonhydrostatic version of our atmospheric model we approximate in the vertical momentum eqs(1.28) and (1.30) (but only here) by:
where is the hydrostatic pressure.
1.3.4.4 Summary of equation sets supported by model
1.3.4.4.1 AtmosphereHydrostatic, and quasihydrostatic and quasi nonhydrostatic forms of the compressible nonBoussinesq equations in coordinates are supported.
1.3.4.4.1.1 Hydrostatic and quasihydrostaticThe hydrostatic set is written out in coordinates in appendix Atmosphere  see eq(1.59).
1.3.4.4.1.2 QuasinonhydrostaticA quasinonhydrostatic form is also supported.
1.3.4.4.2 Ocean
1.3.4.4.2.1 Hydrostatic and quasihydrostaticHydrostatic, and quasihydrostatic forms of the incompressible Boussinesq equations in coordinates are supported.
1.3.4.4.2.2 NonhydrostaticNonhydrostatic forms of the incompressible Boussinesq equations in coordinates are supported  see eqs(1.99) to (1.104).
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