HYBRID VERTICAL COORDINATES
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seek to exploit “some symmetry or conservation laws inherent in the underlying physics” with the goal of improving the accuracy of the numerical solution. Foremost among those conservation laws is the one stating
that adiabatic motion follows surfaces of constant entropy or its proxy,
potential density. Thus, if one uses potential density as vertical coordinate, adiabatic flow that is 3-dimensional in Cartesian space is rendered
2-dimensional in potential density space. This makes it particularly easy
to satisfy adiabatic constraints while modeling lateral transport of tracers, including temperature and salinity.
The above advantage actually holds for resolved as well as a wide range
of unresolved scales of motion. Lateral stirring processes in the ocean
are known to mix properties predominantly along isentropic surfaces.
Hence, a model based on potential density (which in this particular
case must be locally referenced) should be able to simulate the effects
of subgridscale stirring, typically parameterized as an eddy diffusion
process, more accurately than a model in which lateral isentropic stirring
must be projected onto the Cartesian x, y, z axes.
The principal design element of isopycnic (potential density) coordinate models, in relation to conventional Cartesian coordinate models, is
that depth (alias layer thickness) and potential density trade places as
dependent and independent variables. This switch does not affect the
number of prognostic equations, nor does it alter the familiar mix of
wave modes and processes by which information is transmitted in the
ocean. This is to say that both model types solve the same physical
problem. However, since the two models are based on different sets of
differential equations, their numerical properties should be expected to
be very different as well.
Wind-forced process models framed in isopycnic coordinates have
been in use since the 1960s (e.g., Welander, 1966; Holland and Lin,
1975a,b; Bleck and Boudra, 1981). With the addition of thermohaline
forcing (Bleck et al., 1992; Oberhuber, 1993; Hu, 1997; Sun and Bleck,
2001; Cheng et al., 2004), these models have become sufficiently comprehensive to be useful in studying the oceanic general circulation.
The focus in this article is on one particular extension of the isopycnic coordinate concept that addresses certain shortcomings of potential
density as vertical coordinate. These shortcomings are
coordinate surfaces intersecting the sea surface (the outcropping
problem);
lack of vertical resolution in unstratified water columns.
Note that these are two sides of the same coin. In a global model,
most density surfaces required to span the top-to-bottom density range
111
seek to exploit “some symmetry or conservation laws inherent in the underlying physics” with the goal of improving the accuracy of the numerical solution. Foremost among those conservation laws is the one stating
that adiabatic motion follows surfaces of constant entropy or its proxy,
potential density. Thus, if one uses potential density as vertical coordinate, adiabatic flow that is 3-dimensional in Cartesian space is rendered
2-dimensional in potential density space. This makes it particularly easy
to satisfy adiabatic constraints while modeling lateral transport of tracers, including temperature and salinity.
The above advantage actually holds for resolved as well as a wide range
of unresolved scales of motion. Lateral stirring processes in the ocean
are known to mix properties predominantly along isentropic surfaces.
Hence, a model based on potential density (which in this particular
case must be locally referenced) should be able to simulate the effects
of subgridscale stirring, typically parameterized as an eddy diffusion
process, more accurately than a model in which lateral isentropic stirring
must be projected onto the Cartesian x, y, z axes.
The principal design element of isopycnic (potential density) coordinate models, in relation to conventional Cartesian coordinate models, is
that depth (alias layer thickness) and potential density trade places as
dependent and independent variables. This switch does not affect the
number of prognostic equations, nor does it alter the familiar mix of
wave modes and processes by which information is transmitted in the
ocean. This is to say that both model types solve the same physical
problem. However, since the two models are based on different sets of
differential equations, their numerical properties should be expected to
be very different as well.
Wind-forced process models framed in isopycnic coordinates have
been in use since the 1960s (e.g., Welander, 1966; Holland and Lin,
1975a,b; Bleck and Boudra, 1981). With the addition of thermohaline
forcing (Bleck et al., 1992; Oberhuber, 1993; Hu, 1997; Sun and Bleck,
2001; Cheng et al., 2004), these models have become sufficiently comprehensive to be useful in studying the oceanic general circulation.
The focus in this article is on one particular extension of the isopycnic coordinate concept that addresses certain shortcomings of potential
density as vertical coordinate. These shortcomings are
coordinate surfaces intersecting the sea surface (the outcropping
problem);
lack of vertical resolution in unstratified water columns.
Note that these are two sides of the same coin. In a global model,
most density surfaces required to span the top-to-bottom density range