2.3.3 Model drift and flux adjustment
Large-scale general circulation models of both the
atmosphere and the ocean have been developed
over a number of years. One might think that,
given a ‘good’ model of each subsystem, it would
be a relatively simple matter to exchange surface
fluxes and boundary layer properties between the
two, as described in Section 2.3.2 above, and
obtain a ‘good’ model of the coupled system. The
history of the development of coupled models has
shown this task to be harder than might be imagined, partly because it has only recently become
clear what is meant by a ‘good’ model in this
context. In one of the pioneering coupled models
(Manabe et al., 1979), little of the model’s ocean
surface temperature was within 2°C of the
observed values, and the whole of the Southern
Ocean circumpolar region was 6–10°C too warm.
Because of the fundamental importance of surface
energy exchanges in the climate system, studies of
long-term climate variability or anthropogenic climate change using such a model would be subject
to considerable uncertainty, because the incorrect
surface temperatures would distort the highly nonlinear atmospheric feedbacks that determine the
response of the system to a given perturbation.
A way around this problem was developed by
Sausen et al. (1988). The method is known as ‘flux
correction’ or ‘flux adjustment,’ and involves simply adding in an additional, prescribed term to the
surface fluxes of heat, fresh water and (sometimes)
momentum that drive the ocean component of the
coupled model. The ‘flux adjustments’ are chosen
in such a way as to ensure that the sea surface
temperature and salinity remain reasonably close
to observed values. They may be fixed in time or
seasonally varying, but never vary on longer than
annual time scales. Usually they are prescribed as
two-dimensional surface fields, but sometimes
zonal-mean values (dependent on latitude only)
have been used. It is important to understand that
the flux adjustments are prescribed, and do not
change in response to changing surface conditions.
A common way of choosing the flux adjustments
(e.g. Manabe et al., 1991; Johns et al., 1997b) is to
make a preliminary run of the model to near equilibrium, with the addition of a relaxation term on
the surface temperature and salinity that ensures
that they remain close to the desired climatology:
Surface flux:q;(T 0 9T model )
where q is the surface flux computed from the
model’s surface fields, T 0 is the climatological
surface temperature or salinity, T model is the model
surface temperature or salinity, and is a relaxation constant chosen to keep T model ‘suitably’
close to T 0 . At the end of the preliminary run the
relaxation fluxes are diagnosed, and these are
applied as fixed flux-adjustment terms in the main
model run:
Surface flux:q;q FA
where q FA is simply the (suitably time averaged)
value of (T 0 9T model ) from the preliminary run.
Because the preliminary run was in near equilibrium (no long-term drifts), the expectation is that
the main run will simply continue on this equilibrium. This can indeed be achieved in practice.
During the 1990s a number of coupled models
were developed that were able to maintain stable
climatologies over many centuries, using flux
adjustments. The advantage of flux adjustment is
that it allows such long runs to be made, with surface climatologies that are (by definition) close to
reality. For some applications, this may be preferable to a model without flux adjustments that has
a poorer surface climatology. For example, in
order to obtain realistic ENSO-like variability in a
coupled model, it may be important that the
model maintains the strong zonal SST gradient in
the tropical Pacific. A flux-adjusted model that
maintained this gradient might show better ENSO
variability than a parallel non-flux-adjusted model
in which the SST gradient was too weak.
On the other hand, the flux adjustments have
no physical basis, and are ‘correcting’ for a model
error, which may originate in the interior dynamics of the atmosphere or ocean model, by adjusting
the surface fluxes. For typical models, flux adjustments can locally be as large as the model fluxes
themselves. This clearly leads to uncertainty in
interpreting any experiments with the model, and
by masking the model errors makes it harder for
the modeller to diagnose the causes of those errors
(especially when they are of an inherently ‘coupled’
nature).
During the late 1990s coupled models began to
emerge that maintained acceptable surface climatologies without flux adjustments. A key element
in achieving this appears to be a correct and consistent simulation of the large-scale heat budget of
the atmosphere and ocean. The fundamentals of
SECTION 2 OBSERVATIONS AND MODELS
84
Large-scale general circulation models of both the
atmosphere and the ocean have been developed
over a number of years. One might think that,
given a ‘good’ model of each subsystem, it would
be a relatively simple matter to exchange surface
fluxes and boundary layer properties between the
two, as described in Section 2.3.2 above, and
obtain a ‘good’ model of the coupled system. The
history of the development of coupled models has
shown this task to be harder than might be imagined, partly because it has only recently become
clear what is meant by a ‘good’ model in this
context. In one of the pioneering coupled models
(Manabe et al., 1979), little of the model’s ocean
surface temperature was within 2°C of the
observed values, and the whole of the Southern
Ocean circumpolar region was 6–10°C too warm.
Because of the fundamental importance of surface
energy exchanges in the climate system, studies of
long-term climate variability or anthropogenic climate change using such a model would be subject
to considerable uncertainty, because the incorrect
surface temperatures would distort the highly nonlinear atmospheric feedbacks that determine the
response of the system to a given perturbation.
A way around this problem was developed by
Sausen et al. (1988). The method is known as ‘flux
correction’ or ‘flux adjustment,’ and involves simply adding in an additional, prescribed term to the
surface fluxes of heat, fresh water and (sometimes)
momentum that drive the ocean component of the
coupled model. The ‘flux adjustments’ are chosen
in such a way as to ensure that the sea surface
temperature and salinity remain reasonably close
to observed values. They may be fixed in time or
seasonally varying, but never vary on longer than
annual time scales. Usually they are prescribed as
two-dimensional surface fields, but sometimes
zonal-mean values (dependent on latitude only)
have been used. It is important to understand that
the flux adjustments are prescribed, and do not
change in response to changing surface conditions.
A common way of choosing the flux adjustments
(e.g. Manabe et al., 1991; Johns et al., 1997b) is to
make a preliminary run of the model to near equilibrium, with the addition of a relaxation term on
the surface temperature and salinity that ensures
that they remain close to the desired climatology:
Surface flux:q;(T 0 9T model )
where q is the surface flux computed from the
model’s surface fields, T 0 is the climatological
surface temperature or salinity, T model is the model
surface temperature or salinity, and is a relaxation constant chosen to keep T model ‘suitably’
close to T 0 . At the end of the preliminary run the
relaxation fluxes are diagnosed, and these are
applied as fixed flux-adjustment terms in the main
model run:
Surface flux:q;q FA
where q FA is simply the (suitably time averaged)
value of (T 0 9T model ) from the preliminary run.
Because the preliminary run was in near equilibrium (no long-term drifts), the expectation is that
the main run will simply continue on this equilibrium. This can indeed be achieved in practice.
During the 1990s a number of coupled models
were developed that were able to maintain stable
climatologies over many centuries, using flux
adjustments. The advantage of flux adjustment is
that it allows such long runs to be made, with surface climatologies that are (by definition) close to
reality. For some applications, this may be preferable to a model without flux adjustments that has
a poorer surface climatology. For example, in
order to obtain realistic ENSO-like variability in a
coupled model, it may be important that the
model maintains the strong zonal SST gradient in
the tropical Pacific. A flux-adjusted model that
maintained this gradient might show better ENSO
variability than a parallel non-flux-adjusted model
in which the SST gradient was too weak.
On the other hand, the flux adjustments have
no physical basis, and are ‘correcting’ for a model
error, which may originate in the interior dynamics of the atmosphere or ocean model, by adjusting
the surface fluxes. For typical models, flux adjustments can locally be as large as the model fluxes
themselves. This clearly leads to uncertainty in
interpreting any experiments with the model, and
by masking the model errors makes it harder for
the modeller to diagnose the causes of those errors
(especially when they are of an inherently ‘coupled’
nature).
During the late 1990s coupled models began to
emerge that maintained acceptable surface climatologies without flux adjustments. A key element
in achieving this appears to be a correct and consistent simulation of the large-scale heat budget of
the atmosphere and ocean. The fundamentals of
SECTION 2 OBSERVATIONS AND MODELS
84