58
STEPHEN GRIFFIES
to be preserved over large space and time scales (e.g., basin and
decade scales). This property of the ocean interior is critical to represent in a numerical simulation of ocean climate. An isopycnal
coordinate framework is well suited to this task, whereas geopotential and sigma models have problems associated with numerical
truncation errors. As discussed by Griffies et al., 2000b, the problem becomes more egregious as the model resolution is refined, due
to the enhanced levels of eddy activity that pumps tracer variance
to the grid scale. Quasi-adiabatic dissipation of this variance is
difficult to maintain in non-isopycnal models.
Ocean bottom: The solid earth bottom topography directly influences the overlying currents. In an unstratified ocean, the balanced
flow generally follows lines of constant f /H, where f is the Coriolis parameter and H ocean depth. Additionally, there are several
regions where density driven currents (overflows) and turbulent
bottom boundary layer (BBL) processes act as a strong determinant of water mass characteristics. Many such processes are crucial
for the formation of deep water properties in the World Ocean, and
for representing coastal processes in regional models. It is for this
reason that sigma models have been developed over the past few
decades, with their dominant application focused on the coastal
and estuarine problem.
These three regimes impact on the design of vertical coordinates for
ocean models. In this section, we detail some vertical coordinates and
summarize their strengths and weaknesses, keeping in mind the above
physical considerations.
6.1
Depth based vertical coordinates
We use depth based vertical coordinates in this section to discretize
the Boussinesq equations.14 Depth based coordinates are also known as
volume based coordinates, since for a Boussinesq model which uses depth
as the vertical coordinate, the volume of interior grid cells is constant
in the absence of sources. Correspondingly, depth based coordinates are
naturally suited for Boussinesq fluids.
14Greatbatch and McDougall, 2003 discuss an algorithm for non-Boussinesq dynamics in a
z-model. Their methods are implemented in the MOM4 code of Griffies et al., 2004. This
approach may be of special use for non-Boussinesq non-hydrostatic z-models. However, when
focusing on hydrostatic models as we do here, pressure based vertical coordinates discussed
in Section 6.2 are more convenient.
STEPHEN GRIFFIES
to be preserved over large space and time scales (e.g., basin and
decade scales). This property of the ocean interior is critical to represent in a numerical simulation of ocean climate. An isopycnal
coordinate framework is well suited to this task, whereas geopotential and sigma models have problems associated with numerical
truncation errors. As discussed by Griffies et al., 2000b, the problem becomes more egregious as the model resolution is refined, due
to the enhanced levels of eddy activity that pumps tracer variance
to the grid scale. Quasi-adiabatic dissipation of this variance is
difficult to maintain in non-isopycnal models.
Ocean bottom: The solid earth bottom topography directly influences the overlying currents. In an unstratified ocean, the balanced
flow generally follows lines of constant f /H, where f is the Coriolis parameter and H ocean depth. Additionally, there are several
regions where density driven currents (overflows) and turbulent
bottom boundary layer (BBL) processes act as a strong determinant of water mass characteristics. Many such processes are crucial
for the formation of deep water properties in the World Ocean, and
for representing coastal processes in regional models. It is for this
reason that sigma models have been developed over the past few
decades, with their dominant application focused on the coastal
and estuarine problem.
These three regimes impact on the design of vertical coordinates for
ocean models. In this section, we detail some vertical coordinates and
summarize their strengths and weaknesses, keeping in mind the above
physical considerations.
6.1
Depth based vertical coordinates
We use depth based vertical coordinates in this section to discretize
the Boussinesq equations.14 Depth based coordinates are also known as
volume based coordinates, since for a Boussinesq model which uses depth
as the vertical coordinate, the volume of interior grid cells is constant
in the absence of sources. Correspondingly, depth based coordinates are
naturally suited for Boussinesq fluids.
14Greatbatch and McDougall, 2003 discuss an algorithm for non-Boussinesq dynamics in a
z-model. Their methods are implemented in the MOM4 code of Griffies et al., 2004. This
approach may be of special use for non-Boussinesq non-hydrostatic z-models. However, when
focusing on hydrostatic models as we do here, pressure based vertical coordinates discussed
in Section 6.2 are more convenient.