SOME OCEAN MODEL FUNDAMENTALS
29
assimilation (see the lectures at this school from Jens Schr¨ oter as
well as Thuburn and Haine, 2001).
How should the model treat the Coriolis force? On the B-grid, it
is common to do so implicitly or semi-implicitly in time, but this
method is not available on the C-grid since the velocity components
are not coincident in space. Also, the C-grid spatial averaging of
the Coriolis force can lead to problematical null modes (Adcroft
et al., 1999).
What about the pressure gradient calculation? We return to this
question in Section 5, where comments are made regarding the
difficulties of computing the pressure gradient.
1.3
Two themes
There are two themes emphasized in these lectures.
How the vertical coordinate is treated is the most fundamental
element of an ocean model design.
The development of ocean model algorithms should be based on
rational formulations starting from fundamental principles.
The first theme concerns the central importance of vertical coordinates
in ocean model design. Their importance stems from the large distinctions at present between algorithms in models with differing vertical
coordinates. Further differences arise in analysis techniques. These fundamental and pervasive distinctions have led to disparate research and
development communities oriented around models of a particular class of
vertical coordinate. One purpose of these lectures is to describe methods
whereby these distinctions at the formulation stage are minimized, thus
in principle facilitating the design of a single code capable of employing
many vertical coordinates.
The second theme is a “motherhood” statement. What scientist or
engineer would disagree? Nonetheless, it remains nontrivial to satisfy for
three reasons. First, there are many important elements of the ocean
that we do not understand. This ignorance hinders our ability to prescribe rational forms for the very important SGS operators. Second,
some approximations (e.g., Boussinesq approximation, rigid lid approximation, virtual tracer fluxes), made years ago for good reasons then,
often remain in use today yet need not be made with our present-day
modelling capabilities and requirements. These legacy approximations
often compromise a model’s ability to realistically simulate certain aspects of the ocean and/or its interactions with other components of the
29
assimilation (see the lectures at this school from Jens Schr¨ oter as
well as Thuburn and Haine, 2001).
How should the model treat the Coriolis force? On the B-grid, it
is common to do so implicitly or semi-implicitly in time, but this
method is not available on the C-grid since the velocity components
are not coincident in space. Also, the C-grid spatial averaging of
the Coriolis force can lead to problematical null modes (Adcroft
et al., 1999).
What about the pressure gradient calculation? We return to this
question in Section 5, where comments are made regarding the
difficulties of computing the pressure gradient.
1.3
Two themes
There are two themes emphasized in these lectures.
How the vertical coordinate is treated is the most fundamental
element of an ocean model design.
The development of ocean model algorithms should be based on
rational formulations starting from fundamental principles.
The first theme concerns the central importance of vertical coordinates
in ocean model design. Their importance stems from the large distinctions at present between algorithms in models with differing vertical
coordinates. Further differences arise in analysis techniques. These fundamental and pervasive distinctions have led to disparate research and
development communities oriented around models of a particular class of
vertical coordinate. One purpose of these lectures is to describe methods
whereby these distinctions at the formulation stage are minimized, thus
in principle facilitating the design of a single code capable of employing
many vertical coordinates.
The second theme is a “motherhood” statement. What scientist or
engineer would disagree? Nonetheless, it remains nontrivial to satisfy for
three reasons. First, there are many important elements of the ocean
that we do not understand. This ignorance hinders our ability to prescribe rational forms for the very important SGS operators. Second,
some approximations (e.g., Boussinesq approximation, rigid lid approximation, virtual tracer fluxes), made years ago for good reasons then,
often remain in use today yet need not be made with our present-day
modelling capabilities and requirements. These legacy approximations
often compromise a model’s ability to realistically simulate certain aspects of the ocean and/or its interactions with other components of the