File last modified 3 December 1998
In this next section we will discuss some aspects of general circulation models. Some of these aspects they share with all modeling, but some are unique to GCMs.
All models have a scale at which they are no longer able to resolve what's going on. I suspect that unless someday we have the computational ability to model each and every molecule on an individual basis and their interactions with each other, subscale process parameterization will always be with us. In this particular case, the parameterization referred to deals with mixing at scales smaller than the scale of the grid the GCM is running on.
For example in the model run by Toggweiler et al. (1989a) the parameters Amh and Ahh are quite large due to the requirement for a smooth finite difference solution at this particular grid size. Toggweiler et al. assumed that Ahh would be larger in the upper ocean and used:
where
and no parameterization to allow along isopycnal surface mixing (instead of at "level" surfaces) was used. In the vertical, they assumed that Ahv would be greater at depth and used the following parameterization to account for subgrid scale mixing in the vertical:
where:
As always, the boundary conditions are very important. In this particular case we are dealing with the conditions at the surface and bottom of the ocean (as well as, by default, along the shores of the continents).
At the surface we have the following boundary conditions for wind stress: Hellerman and Rosenstein (1983) provide the monthly wind stresses turned into an annual mean and interpolated onto the Toggweiler et al. grid. This stress is applied as in the following:
For temperature and salinity they used anually averaged values of 
and S from Levitus (1982) at
both the surface and in the interior of the model domain (in what they called their "robust
diagnostic mode" only). Values at the surface were the upper 50 m average from Levitus to get
around the low salinity values found at some places in Levitus due to seasonal melt water.
Near the bottom Toggweiler et al. applied a simple linear drag to calculate:
The restoring parameter is well known to those that know it well. To the rest of the scientific community it sometimes comes as a bit of a shock. Essentially the restoring parameter is an adjustable parameter used in most general circulation models in an attempt to replicate the boundary fluxes of heat and freshwater at the air-sea interface. Rather than try to model the heat and freshwater fluxes at the surface explicitly, the modelers write:
where:
When the model was being run in "prognostic" mode, the restoring term was applied to the
surface only and was set to a value of 1/30 day-1 and when the model was run in "diagnostic"
mode it was applied tot he surface and the interior with value of 1/50 yr-1. Interestingly enough,
these values are the recommended values used in MOM-2 v2.2 today. The effect of this
parameter is to continuously push the model values of S and 
back towards the annual Levitus
average with the attendant effect on circulation.
As already mentioned, Toggweiler et al. Ran their GCM in two different modes (as do most
GCM operators do today still). In the "prognostic mode" the surface values of 
and S are forced
back to Levitus with a 
, in the interior 
is set to zero and thus the model is allowed to come
into geostrophic balance. A GCM needs to run out some 3500 model years to achieve a steady
state with a "chemical tracer" like 14C, this is known as the "spin-up" phase of running the model.
When run in the "diagnostic mode", the 
parameter, in effect, adds a small source of heat and
salt artificially to the interior of the model. In this manner the model can reach "equilibrium" in
as short a run as 300 model years and then is run out an additional 450 model years. When being
run in this mode Ahv = f(z) or Ahv = 1.0 cm2 s-1. Runs of the model were sampled every 5 model
years to produce average flow field for the 14C experiments. Both modes continuously check for
vertical density instabilities and mix convectively conserving 
, S and 14C.
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