SOME OCEAN MODEL FUNDAMENTALS
57
many regions. Hence, they expose the calculation to nontrivial numerical truncation errors which can lead to spurious pressure gradients that
spin up an unforced fluid with initially flat isopycnals. Significant effort
has gone into reducing such pressure gradient errors, especially in terrain following models where undulations of the coordinate surfaces can
be large with realistic bottom topography (e.g., see Figure 12). Some
of these issues are summarized, with references, in Section 2 of Griffies
et al., 2000a. Perhaps the most promising approach is that proposed
by Shchepetkin and McWilliams, 2002. It is notable that difficulties
with pressure gradient errors have largely been responsible for the near
absence of sigma models being used for long term global ocean climate
simulations. l3
6.
Elements of vertical coordinates
As discussed in Griffies et al., 2000a, there are broadly three regimes
of the ocean germane to the considerations of a vertical coordinate.
w Upper ocean mixed layer: This is a generally turbulent region
dominated by transfers of momentum, heat, freshwater, and tracers with the overlying atmosphere, sea ice, rivers, etc. It is of prime
importance for climate system modelling and operational oceanography. It is typically very well mixed in the vertical through threedimensional convective/turbulent processes. These processes involve non-hydrostatic physics which requires very high horizontal
and vertical resolution (i.e., a vertical to horizontal grid aspect ratio near unity) to explicitly represent. A parameterization of these
processes is therefore necessary in primitive equation ocean models. In this region, it is essential to employ a vertical coordinate
that facilitates the representation and parameterization of these
highly turbulent processes. Geopotential and pressure coordinates,
or their relatives, are the most commonly used coordinates as they
facilitate the use of very refined vertical grid spacing, which can
be essential to simulate the strong exchanges between the ocean
and atmosphere, rivers, and ice.
w Ocean interior: Tracer transport processes in the ocean interior
predominantly occur along neutral directions (McDougall, 1987).
The transport is dominated by large scale currents and mesoscale
eddy fluctuations. Water mass properties in the interior thus tend
1 3 ~ h e
work of Diansky et al., 2002 is the only case known by the author of a global sigma
model used for climate purposes.
57
many regions. Hence, they expose the calculation to nontrivial numerical truncation errors which can lead to spurious pressure gradients that
spin up an unforced fluid with initially flat isopycnals. Significant effort
has gone into reducing such pressure gradient errors, especially in terrain following models where undulations of the coordinate surfaces can
be large with realistic bottom topography (e.g., see Figure 12). Some
of these issues are summarized, with references, in Section 2 of Griffies
et al., 2000a. Perhaps the most promising approach is that proposed
by Shchepetkin and McWilliams, 2002. It is notable that difficulties
with pressure gradient errors have largely been responsible for the near
absence of sigma models being used for long term global ocean climate
simulations. l3
6.
Elements of vertical coordinates
As discussed in Griffies et al., 2000a, there are broadly three regimes
of the ocean germane to the considerations of a vertical coordinate.
w Upper ocean mixed layer: This is a generally turbulent region
dominated by transfers of momentum, heat, freshwater, and tracers with the overlying atmosphere, sea ice, rivers, etc. It is of prime
importance for climate system modelling and operational oceanography. It is typically very well mixed in the vertical through threedimensional convective/turbulent processes. These processes involve non-hydrostatic physics which requires very high horizontal
and vertical resolution (i.e., a vertical to horizontal grid aspect ratio near unity) to explicitly represent. A parameterization of these
processes is therefore necessary in primitive equation ocean models. In this region, it is essential to employ a vertical coordinate
that facilitates the representation and parameterization of these
highly turbulent processes. Geopotential and pressure coordinates,
or their relatives, are the most commonly used coordinates as they
facilitate the use of very refined vertical grid spacing, which can
be essential to simulate the strong exchanges between the ocean
and atmosphere, rivers, and ice.
w Ocean interior: Tracer transport processes in the ocean interior
predominantly occur along neutral directions (McDougall, 1987).
The transport is dominated by large scale currents and mesoscale
eddy fluctuations. Water mass properties in the interior thus tend
1 3 ~ h e
work of Diansky et al., 2002 is the only case known by the author of a global sigma
model used for climate purposes.