7.2.4 Atmospheric forcing and coupling
Dynamically, the ocean is forced at the surface
through the fluxes of momentum, heat and fresh
water. Errors in these fluxes, which are only
known to limited accuracy (cf. Liu and Katsaros,
Chapter 3.4), constitute a primary source of model
error, and future improvements in accuracy are
most urgent. Furthermore, the fluxes depend on
the state not only of the atmosphere, but also of
the ocean. This dependence represents the fundamental rationale for the two-way coupling of both
systems, and introduces a conceptual problem
for the flux formulation when an ocean model is
operated in stand-alone mode.
7.2.4.1 Local coupling
The flux of momentum is the principal driving
force for the ocean circulation. Except for a weak
dependence of the drag coefficient on near-surface
atmospheric stability, and hence effectively on sea
surface temperature, the wind stress depends only
on atmospheric parameters. Hence the momentum
flux coupling is essentially one-sided, and the wind
stress can be specified for ocean-only models. For
several aspects of the large-scale circulation, e.g.
for upper ocean transports, the dependence of circulation variables on wind stress is approximately
linear. In low latitudes, the accuracy of the wind
stress is a limiting factor for the accuracy of model
simulations. In high latitudes, the direct wind
effect on the circulation is somewhat weaker, but
changes in surface density, through wind-induced
mixing or through advection of sea-ice, can significantly influence the thermohaline circulation, as
discussed by Mauritzen and Hakkinen (1997).
The flux of heat constitutes the main driving
force for the thermohaline component of the circulation, and is likewise important for the atmosperic circulation. The net flux of heat depends
both on atmospheric parameters as well as on Sea
Surface Temperature (SST), and hence constitutes
a true coupling of both systems. The heat content
within the ocean is conserved, and obviously even
a small but systematic error in the basin-average
surface heat flux will in time have a big effect on
the overall heat budget. Moreover, errors in heat
flux can significantly distort the oceanic temperature distribution and hence its circulation patterns.
This has been demonstrated in an Atlantic model
driven with fixed mean heat fluxes derived from
the COADS (Comprehensive Ocean–Atmosphere
Data Set) data, where the oceanic response became
completely unrealistic after a few decades of integration (Schiller, 1995).
The net freshwater flux constitutes an important forcing for the thermohaline circulation. Its
dependence on ocean–atmosphere parameters corresponds to that of heat flux. Note that since the
freshwater flux does not depend on surface salinity, the (frequently employed) replacement by a
restoring condition for surface salinity has therefore no physical justification. As discussed by
Wijffels (Chapter 6.2), the accuracy of observed
estimates is far from satisfactory. As the overall
salt content of the ocean is conserved on usual
oceanic time scales, systematic errors in the freshwater budget add up and lead to a drift in the
salinity distribution.
7.2.4.2 Large-scale coupling
The difference in time scales between atmospheric
and oceanic motions leads to a fundamental difference when either system is considered in standalone mode, with the other system prescribed. The
atmospheric time scale is short compared with that
of the ocean, and hence it is sensible to run an
atmosphere-only model to study atmospheric
response to SST changes, by using the bulk formulae with prescribed SST. For ocean-only models,
the corresponding procedure would be to prescribe
the atmospheric parameters in these expressions.
Such a procedure would, however, ignore the
rapid atmospheric reaction to SST changes, and
lead to rather unrealistic fluxes. This may be
acceptable as long as only the sensitivity of the
ocean model is considered, but is clearly unacceptable for climate variability studies.
In principle, air–sea coupling on climate time
scales can only be properly simulated through
coupled ocean–atmosphere models (Wood and
Bryan, Chapter 2.3). Because these are extremely
demanding in terms of computational resources, at
least for investigations of qualitative aspects of
ocean climate variability, there is some value in
intermediate approaches that attempt to formulate
explicitly the atmospheric reaction, or more precisely the reaction of the various fluxes, to SST
changes. The situation is perhaps most obvious for
the flux of heat. The bulk formula that expresses
the net heat flux in terms of SST and atmospheric
parameters is often used in a linearized form,
7.2 Numerical Ocean Circulation Modelling: Present and Future
553
Willebrand and Haidvogel
Dynamically, the ocean is forced at the surface
through the fluxes of momentum, heat and fresh
water. Errors in these fluxes, which are only
known to limited accuracy (cf. Liu and Katsaros,
Chapter 3.4), constitute a primary source of model
error, and future improvements in accuracy are
most urgent. Furthermore, the fluxes depend on
the state not only of the atmosphere, but also of
the ocean. This dependence represents the fundamental rationale for the two-way coupling of both
systems, and introduces a conceptual problem
for the flux formulation when an ocean model is
operated in stand-alone mode.
7.2.4.1 Local coupling
The flux of momentum is the principal driving
force for the ocean circulation. Except for a weak
dependence of the drag coefficient on near-surface
atmospheric stability, and hence effectively on sea
surface temperature, the wind stress depends only
on atmospheric parameters. Hence the momentum
flux coupling is essentially one-sided, and the wind
stress can be specified for ocean-only models. For
several aspects of the large-scale circulation, e.g.
for upper ocean transports, the dependence of circulation variables on wind stress is approximately
linear. In low latitudes, the accuracy of the wind
stress is a limiting factor for the accuracy of model
simulations. In high latitudes, the direct wind
effect on the circulation is somewhat weaker, but
changes in surface density, through wind-induced
mixing or through advection of sea-ice, can significantly influence the thermohaline circulation, as
discussed by Mauritzen and Hakkinen (1997).
The flux of heat constitutes the main driving
force for the thermohaline component of the circulation, and is likewise important for the atmosperic circulation. The net flux of heat depends
both on atmospheric parameters as well as on Sea
Surface Temperature (SST), and hence constitutes
a true coupling of both systems. The heat content
within the ocean is conserved, and obviously even
a small but systematic error in the basin-average
surface heat flux will in time have a big effect on
the overall heat budget. Moreover, errors in heat
flux can significantly distort the oceanic temperature distribution and hence its circulation patterns.
This has been demonstrated in an Atlantic model
driven with fixed mean heat fluxes derived from
the COADS (Comprehensive Ocean–Atmosphere
Data Set) data, where the oceanic response became
completely unrealistic after a few decades of integration (Schiller, 1995).
The net freshwater flux constitutes an important forcing for the thermohaline circulation. Its
dependence on ocean–atmosphere parameters corresponds to that of heat flux. Note that since the
freshwater flux does not depend on surface salinity, the (frequently employed) replacement by a
restoring condition for surface salinity has therefore no physical justification. As discussed by
Wijffels (Chapter 6.2), the accuracy of observed
estimates is far from satisfactory. As the overall
salt content of the ocean is conserved on usual
oceanic time scales, systematic errors in the freshwater budget add up and lead to a drift in the
salinity distribution.
7.2.4.2 Large-scale coupling
The difference in time scales between atmospheric
and oceanic motions leads to a fundamental difference when either system is considered in standalone mode, with the other system prescribed. The
atmospheric time scale is short compared with that
of the ocean, and hence it is sensible to run an
atmosphere-only model to study atmospheric
response to SST changes, by using the bulk formulae with prescribed SST. For ocean-only models,
the corresponding procedure would be to prescribe
the atmospheric parameters in these expressions.
Such a procedure would, however, ignore the
rapid atmospheric reaction to SST changes, and
lead to rather unrealistic fluxes. This may be
acceptable as long as only the sensitivity of the
ocean model is considered, but is clearly unacceptable for climate variability studies.
In principle, air–sea coupling on climate time
scales can only be properly simulated through
coupled ocean–atmosphere models (Wood and
Bryan, Chapter 2.3). Because these are extremely
demanding in terms of computational resources, at
least for investigations of qualitative aspects of
ocean climate variability, there is some value in
intermediate approaches that attempt to formulate
explicitly the atmospheric reaction, or more precisely the reaction of the various fluxes, to SST
changes. The situation is perhaps most obvious for
the flux of heat. The bulk formula that expresses
the net heat flux in terms of SST and atmospheric
parameters is often used in a linearized form,
7.2 Numerical Ocean Circulation Modelling: Present and Future
553
Willebrand and Haidvogel