112
RAINER BLECK
in the subtropics are out of place in the relatively unstratified highlatitude waters and hence must exit the domain somewhere between the
subtropics and the subpolar latitude bands.
The hybridized depth-isopycnic coordinate (Bleck, 2002) developed
for the isopycnic model MICOM (Bleck et al., 1992) alleviates both
shortcomings just mentioned. It does so by not allowing coordinate
layers to outcrop, but rather forcing layers that are isopycnic in character
at low latitudes to turn into fixed-depth layers at high latitudes. Stated
differently, a coordinate layer associated with a chosen “target” isopycnal
adheres to the depth of that isopycnal as long as the latter exists in a
given water column. Near the outcrop latitude of the target isopycnal,
the coordinate layer turns horizontal and becomes a fixed-depth layer.
(The term fixed-depth here covers both constant-depth and bottomfollowing layer configurations.)
The approach just outlined creates fixed-depth coordinate layers at
the same rate at which the model loses isopycnic layers between the
equator and the poles. The new fixed-depth layers provide vertical resolution in unstratified high-latitude regions and on coastal shelves,
allowing the hybrid coordinate model to simulate turbulent mixing and
buoyant convection in a manner similar to z and σ coordinate models.
The term “hybrid vertical coordinate” has more than one meaning.
Often it refers to configurations (e.g., Bleck 1978) where the model domain is divided into a stack of subdomains, each filled with coordinate
surfaces defined independently of those in other subdomains. A simple
example is the combination, popular in weather prediction models, of
terrain-following coordinate surfaces in the lower atmosphere and isobaric surfaces in the upper atmosphere.
Our present hybrid scheme, which dates back to Bleck and Boudra
(1981), does not rely on rigidly defined subdomains. Instead, it permits temporal and lateral transitions between different coordinate types
– terrain-following, constant-depth, isopycnal – based on local conditions such as layer thickness and vertical density contrast. The scheme
has much in common with the ALE (Arbitrary Lagrangian-Eulerian)
technique of Hirt et al. (1974) but adds one important element to that
scheme, namely, a mechanism for keeping coordinate layers aligned with,
or for nudging them toward, their designated target isopycnals wherever
possible. The original ALE scheme only concerns itself with maintaining a finite separation between adjacent coordinate surfaces. While the
flexibility of coordinate placement in ALE-type schemes is disconcerting
to some users because grid point location in physical space cannot be
expressed in terms of a simple analytic formula, the flexibility inher-
RAINER BLECK
in the subtropics are out of place in the relatively unstratified highlatitude waters and hence must exit the domain somewhere between the
subtropics and the subpolar latitude bands.
The hybridized depth-isopycnic coordinate (Bleck, 2002) developed
for the isopycnic model MICOM (Bleck et al., 1992) alleviates both
shortcomings just mentioned. It does so by not allowing coordinate
layers to outcrop, but rather forcing layers that are isopycnic in character
at low latitudes to turn into fixed-depth layers at high latitudes. Stated
differently, a coordinate layer associated with a chosen “target” isopycnal
adheres to the depth of that isopycnal as long as the latter exists in a
given water column. Near the outcrop latitude of the target isopycnal,
the coordinate layer turns horizontal and becomes a fixed-depth layer.
(The term fixed-depth here covers both constant-depth and bottomfollowing layer configurations.)
The approach just outlined creates fixed-depth coordinate layers at
the same rate at which the model loses isopycnic layers between the
equator and the poles. The new fixed-depth layers provide vertical resolution in unstratified high-latitude regions and on coastal shelves,
allowing the hybrid coordinate model to simulate turbulent mixing and
buoyant convection in a manner similar to z and σ coordinate models.
The term “hybrid vertical coordinate” has more than one meaning.
Often it refers to configurations (e.g., Bleck 1978) where the model domain is divided into a stack of subdomains, each filled with coordinate
surfaces defined independently of those in other subdomains. A simple
example is the combination, popular in weather prediction models, of
terrain-following coordinate surfaces in the lower atmosphere and isobaric surfaces in the upper atmosphere.
Our present hybrid scheme, which dates back to Bleck and Boudra
(1981), does not rely on rigidly defined subdomains. Instead, it permits temporal and lateral transitions between different coordinate types
– terrain-following, constant-depth, isopycnal – based on local conditions such as layer thickness and vertical density contrast. The scheme
has much in common with the ALE (Arbitrary Lagrangian-Eulerian)
technique of Hirt et al. (1974) but adds one important element to that
scheme, namely, a mechanism for keeping coordinate layers aligned with,
or for nudging them toward, their designated target isopycnals wherever
possible. The original ALE scheme only concerns itself with maintaining a finite separation between adjacent coordinate surfaces. While the
flexibility of coordinate placement in ALE-type schemes is disconcerting
to some users because grid point location in physical space cannot be
expressed in terms of a simple analytic formula, the flexibility inher-