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RAINER BLECK
where the models are used outside their “design range” and therefore
generate results that do not always live up to the expectations of the
various user communities. Ocean models clearly need to be developed
further to satisfy those communities.
There are essentially three ways in which ocean models can be
improved. One can
1 increase grid resolution;
2 improve model physics;
3 improve model numerics.
Increasing grid resolution (item 1), in theory, allows a numerically obtained solution to approach that of the underlying differential equation.
However, given the huge spectral range of unresolved processes in the
ocean, truncation errors continue to cast their shadow even over what
we call “high-resolution” models.
Efforts in model physics improvement (item 2) in most cases boil down
to improvements in the parameterization of spatially unresolved processes. This is a never-ending process: parameterization schemes tend
to be sensitive to where the transition between resolved and unresolved
scales occurs and therefore must evolve in lockstep with refinements in
mesh size.
Improved numerics (item 3) is a non-exclusive alternative to higher
grid resolution; both approaches lower the truncation error in the finite
difference equations that constitute the ocean model.
Model numerics can be improved in several ways. One approach is
to switch to higher-order finite difference approximation (“order” here
refers to the power of the spatial or temporal mesh size in truncation
error expressions; the higher the power, the faster the error goes to zero
with increased grid resolution). Another approach is to revive techniques
developed in pre-computer days when a problem became solvable only
by transforming the equations into a coordinate system that exploited
some symmetry or conservation laws inherent in the underlying physics.
The geophysical fluid dynamics community is doing some of this already
by formulating its equations in a coordinate system whose z axis points
in the direction of gravity rather than, say, the center of our galaxy. But
the concept of manipulating the equations to make them easier to solve
or improve the accuracy of the solutions can be extended much further.
The recent proliferation of unconventional vertical coordinates in geophysical modeling should be viewed as one particular attempt to improve
ocean model numerics along the lines of item 3 above. Repeating the
phrase just used, the new coordinates currently being experimented with
RAINER BLECK
where the models are used outside their “design range” and therefore
generate results that do not always live up to the expectations of the
various user communities. Ocean models clearly need to be developed
further to satisfy those communities.
There are essentially three ways in which ocean models can be
improved. One can
1 increase grid resolution;
2 improve model physics;
3 improve model numerics.
Increasing grid resolution (item 1), in theory, allows a numerically obtained solution to approach that of the underlying differential equation.
However, given the huge spectral range of unresolved processes in the
ocean, truncation errors continue to cast their shadow even over what
we call “high-resolution” models.
Efforts in model physics improvement (item 2) in most cases boil down
to improvements in the parameterization of spatially unresolved processes. This is a never-ending process: parameterization schemes tend
to be sensitive to where the transition between resolved and unresolved
scales occurs and therefore must evolve in lockstep with refinements in
mesh size.
Improved numerics (item 3) is a non-exclusive alternative to higher
grid resolution; both approaches lower the truncation error in the finite
difference equations that constitute the ocean model.
Model numerics can be improved in several ways. One approach is
to switch to higher-order finite difference approximation (“order” here
refers to the power of the spatial or temporal mesh size in truncation
error expressions; the higher the power, the faster the error goes to zero
with increased grid resolution). Another approach is to revive techniques
developed in pre-computer days when a problem became solvable only
by transforming the equations into a coordinate system that exploited
some symmetry or conservation laws inherent in the underlying physics.
The geophysical fluid dynamics community is doing some of this already
by formulating its equations in a coordinate system whose z axis points
in the direction of gravity rather than, say, the center of our galaxy. But
the concept of manipulating the equations to make them easier to solve
or improve the accuracy of the solutions can be extended much further.
The recent proliferation of unconventional vertical coordinates in geophysical modeling should be viewed as one particular attempt to improve
ocean model numerics along the lines of item 3 above. Repeating the
phrase just used, the new coordinates currently being experimented with