supercomputer. When well-formulated, idealized
models provide a practical method to analyze ocean
physical and biogeochemical dynamics and in some
cases to quantitatively constrain specific rates. Their
application is closely tied to ocean tracer observations, which are generally required for physical
calibration and evaluation. Idealized models remain
a valuable tool for estimating the oceanic uptake of
anthropogenic carbon and the long time-scale responses (centuries to millennia) of the natural carbon
cycle. Also, some of the more memorable and lasting
advances in tracer oceanography are directly linked
to simple conceptual models. Examples include
constraints on the deep-water large-scale vertical
diffusivity and demonstration of the dominance of
lateral over vertical ventilation of the subtropical
main thermocline.
Three-dimensional models offer more realism, at
least apparently, but with the cost of greater complexity, a more limited number of simulations, and a
higher probability of crucial regional errors in the
base solutions, which may compromise direct,
quantitative model-data comparisons. Ocean GCM
solutions, however, should be exploited to address
exactly those problems that are intractable for simpler conceptual and reduced dimensional models.
For example, two key assumptions of the 1-D advection–diffusion model presented in Figure 2 are
that the upwelling occurs uniformly in the horizontal
and vertical and that mid-depth horizontal advection
is not significant. Ocean GCMs and tracer data, by
contrast, show a rich three-dimensional circulation
pattern in the deep Pacific.
The behavior of idealized models and GCMs can
diverge, and it is not always clear that complexity
necessarily leads to more accurate results. In the end,
the choice of which model to use depends on the
scientific problem and the judgment of the researcher. Probably the best advice is to explore solutions from a hierarchy of models and to thoroughly
evaluate the skill of the models against a range of
tracers and other dynamical measures. Just because a
model does a good job reproducing the distribution
of one tracer field does not mean that it can be applied indiscriminately to another variable, especially
if the underlying dynamics or timescales differ.
Models can be quite alluring in the sense that they
provide concrete answers to questions that are often
difficult or nearly impossible to address from
sparsely sampled field data. However, one should not
forget that numerical models are simply a set of tools
for doing science. They are no better than the foundations upon which they are built and should not be
carried out in isolation from observations of the real
ocean. For ocean carbon cycle models, the two key
elements are the ocean physical circulation and
the biogeochemical processes. Even the best biogeochemical model will perform poorly in an illconstructed physical model. Conversely, if the
underlying biogeochemical mechanisms are poorly
known, a model may be able to correctly reproduce
the distributions of biogeochemical tracers but for
the wrong reasons. Mechanistic-based models are
critical in order to understand and predict natural
variability and the response of ocean biogeochemistry to perturbations such as climate change.
Glossary
Anthropogenic carbon The additional carbon that
has been released to the environment over the last
several centuries by human activities including
fossil-fuel combustion, agriculture, forestry, and
biomass burning.
Excess
3 He Computed as the
3 He in excess of gas
solubility equilibrium with the atmosphere.
Export production That part of the organic matter
formed in the surface layer by photosynthesis
that is transported out of the surface layer and into
the interior of the ocean by particle sinking,
mixing, and circulation, or active transport by
organisms.
Radiocarbon
14
C Either d
14 C or D
14 C where d
14
C ¼ [(
14
C/
12
C) sample /(
14 C/
12
C) standard – 1]Â 1000
(in parts per thousand or ‘per mil’); D
14 C is
similar but corrects the sample
14 C for biological
fractionation using the sample
13 C/
12 C ratio.
Transient tracers Chemical tracers that contain
time information either because they are
radioactive or because their source, usually
anthropogenic, has evolved with time.
Tritium–
3 He age An age is computed assuming
that all of the excess
3 He in a sample is due to the
radioactive decay of tritium, age ¼ ln[(
3
H þ
3 He)/
3
H ]/l, where l is the decay constant for tritium.
Ventilation The physical process by which surface
properties are transported into the ocean interior.
See also
Carbon Cycle. Carbon Dioxide (CO 2 ) Cycle. CFCs in
the Ocean. Nitrogen Cycle. Radiocarbon. Tritium–
Helium Dating.
Further Reading
Broecker WS and Peng T-H (1982) Tracers in the Sea.
Palisades, NY: Lamont-Doherty Geological Observatory, Columbia University.
OCEAN CARBON SYSTEM, MODELING OF 521
models provide a practical method to analyze ocean
physical and biogeochemical dynamics and in some
cases to quantitatively constrain specific rates. Their
application is closely tied to ocean tracer observations, which are generally required for physical
calibration and evaluation. Idealized models remain
a valuable tool for estimating the oceanic uptake of
anthropogenic carbon and the long time-scale responses (centuries to millennia) of the natural carbon
cycle. Also, some of the more memorable and lasting
advances in tracer oceanography are directly linked
to simple conceptual models. Examples include
constraints on the deep-water large-scale vertical
diffusivity and demonstration of the dominance of
lateral over vertical ventilation of the subtropical
main thermocline.
Three-dimensional models offer more realism, at
least apparently, but with the cost of greater complexity, a more limited number of simulations, and a
higher probability of crucial regional errors in the
base solutions, which may compromise direct,
quantitative model-data comparisons. Ocean GCM
solutions, however, should be exploited to address
exactly those problems that are intractable for simpler conceptual and reduced dimensional models.
For example, two key assumptions of the 1-D advection–diffusion model presented in Figure 2 are
that the upwelling occurs uniformly in the horizontal
and vertical and that mid-depth horizontal advection
is not significant. Ocean GCMs and tracer data, by
contrast, show a rich three-dimensional circulation
pattern in the deep Pacific.
The behavior of idealized models and GCMs can
diverge, and it is not always clear that complexity
necessarily leads to more accurate results. In the end,
the choice of which model to use depends on the
scientific problem and the judgment of the researcher. Probably the best advice is to explore solutions from a hierarchy of models and to thoroughly
evaluate the skill of the models against a range of
tracers and other dynamical measures. Just because a
model does a good job reproducing the distribution
of one tracer field does not mean that it can be applied indiscriminately to another variable, especially
if the underlying dynamics or timescales differ.
Models can be quite alluring in the sense that they
provide concrete answers to questions that are often
difficult or nearly impossible to address from
sparsely sampled field data. However, one should not
forget that numerical models are simply a set of tools
for doing science. They are no better than the foundations upon which they are built and should not be
carried out in isolation from observations of the real
ocean. For ocean carbon cycle models, the two key
elements are the ocean physical circulation and
the biogeochemical processes. Even the best biogeochemical model will perform poorly in an illconstructed physical model. Conversely, if the
underlying biogeochemical mechanisms are poorly
known, a model may be able to correctly reproduce
the distributions of biogeochemical tracers but for
the wrong reasons. Mechanistic-based models are
critical in order to understand and predict natural
variability and the response of ocean biogeochemistry to perturbations such as climate change.
Glossary
Anthropogenic carbon The additional carbon that
has been released to the environment over the last
several centuries by human activities including
fossil-fuel combustion, agriculture, forestry, and
biomass burning.
Excess
3 He Computed as the
3 He in excess of gas
solubility equilibrium with the atmosphere.
Export production That part of the organic matter
formed in the surface layer by photosynthesis
that is transported out of the surface layer and into
the interior of the ocean by particle sinking,
mixing, and circulation, or active transport by
organisms.
Radiocarbon
14
C Either d
14 C or D
14 C where d
14
C ¼ [(
14
C/
12
C) sample /(
14 C/
12
C) standard – 1]Â 1000
(in parts per thousand or ‘per mil’); D
14 C is
similar but corrects the sample
14 C for biological
fractionation using the sample
13 C/
12 C ratio.
Transient tracers Chemical tracers that contain
time information either because they are
radioactive or because their source, usually
anthropogenic, has evolved with time.
Tritium–
3 He age An age is computed assuming
that all of the excess
3 He in a sample is due to the
radioactive decay of tritium, age ¼ ln[(
3
H þ
3 He)/
3
H ]/l, where l is the decay constant for tritium.
Ventilation The physical process by which surface
properties are transported into the ocean interior.
See also
Carbon Cycle. Carbon Dioxide (CO 2 ) Cycle. CFCs in
the Ocean. Nitrogen Cycle. Radiocarbon. Tritium–
Helium Dating.
Further Reading
Broecker WS and Peng T-H (1982) Tracers in the Sea.
Palisades, NY: Lamont-Doherty Geological Observatory, Columbia University.
OCEAN CARBON SYSTEM, MODELING OF 521