Constraining oceanic sources and sinks of CO2 by
inverse modeling: A first step toward assimilation of
in situ and remote data
Final Report: June 2006
NAG5-12528
Nicolas Gruber (lead PI)
Department of Atmospheric Sciences
University of California, Los Angeles, Los Angeles, CA 90095
Sara Mikaloff Fletcher
University of California, Los Angeles, Los Angeles, CA 90095
Scott C. Doney
National Center for Atmospheric Research, Boulder, CO 80307
Mick Follows
Massachusetts Institute of Technology, Cambridge, MA 02139
Andrew R. Jacobson
AOS Program, Princeton University, Princeton, NJ 08540
Dimitris Menemenlis
Jet Propulsion Laboratory, Pasadena, CA
Jorge L. Sarmiento
AOS Program, Princeton University, Princeton, NJ 08540
1
1. Project Goals
The aim of this project was to address gaps in our understanding of CO2 exchange
across the air-sea interface using a Green's function-based inverse modeling approach
(Gloor et al., 2001, Gruber et al., 2001). This technique determines optimal estimates of
the time averaged pre-industrial and anthropogenic air-sea CO2 fluxes using ocean
interior observations and Green's functions representing the response of ocean interior
concentrations to CO2 fluxes at the surface. These Green's functions were calculated for a
discrete set of ocean regions using an ocean general circulation model (OGCM) by
injecting a unit flux of a dye tracer into each region, distributed spatially within the region
according to the climatology of Takahashi et al. (2002), and observing the response to this
flux throughout the oceans.
We proposed the following studies over a three-year period:
 Assess and quantify the robustness and uncertainties of the ocean inverse method by
using Green's functions from seven different OGCMs.
 Continue the development of the inversion method to incorporate additional
observations, such as surface ocean pCO2, wind speed, and atmospheric CO2, as
constraints.
 Improve the understanding of the mechanisms controlling the air-sea CO2 fluxes by
testing and optimizing gas exchange parameterizations and by determining the
relationship between the estimated fluxes and the processes governing pCO2.
2 Summary of Progress Towards Meeting Goals
We used the ocean inversion to estimate separately the natural air-sea CO2 fluxes that
existed in preindustrial times and the anthropogenic uptake of CO2, which is driven by
the perturbation of atmospheric CO2 by fossil fuel burning, cement production, and land
2
use change (Sarmiento et al., 1992, Murnane et al., 1999, Gruber et al., 2002). These
inverse air-sea fluxes were in good general agreement with previous estimates in most
regions, but they differed substantially from previous work in the Southern Ocean (south
of 44S). We found vigorous natural outgassing of natural CO2, which is counterbalanced by a slightly larger uptake of anthropogenic CO2, for a nearly neutral net flux.
Furthermore, we found a substantially greater natural CO2 uptake at southern mid
latitudes (18S to 44S) than previous studies. Since the mechanisms responsible for the
natural and anthropogenic carbon air-sea fluxes are expected to respond differently to
climate change, these results have considerable implications for the future of the carbon
cycle.
A suite of 10 OGCMs and a series of scenarios were used to quantify the sensitivity of
the inverse estimates to the modeled transport and the tracer-based methods used to
partition natural and anthropogenic air-sea fluxes. After extensive error analysis, we find
that the inverse estimates are remarkably robust with respect to the choice of OGCM and
most potential biases in the tracer-based methods. We also show that the inverse
estimates are driven by strong gradients in the gas exchange tracers used to constrain the
inversion. Therefore, we have a high degree of confidence in these results.
The natural and anthropogenic carbon estimates were then combined to determine the
contemporary air-sea fluxes, which were used in a joint ocean-atmosphere inversion for
both terrestrial and oceanic air-sea fluxes. Due to the overwhelming amount of ocean
interior data, the ocean inversion provided strong constraints for the air-land fluxes. In
particular, the well-constrained ocean fluxes combined with the atmospheric data imply
that the must be a large (~1 Pg C yr-1) land source in the terrestrial southern hemisphere.
In addition, the inverse flux estimates and basis functions were used to optimize
parameterizations in bulk formulas used to estimate air-sea gas exchange from
observations of wind speed and the difference in the partial pressure of CO2 in the
atmosphere and the surface ocean.
3
2.1 Natural Air-sea Flux Estimates
Globally, we find a nearly balanced exchange, with a mean flux of -0.03±08 Pg C yr-1.
Here and throughout the rest of this report, the inverse flux estimates are reported as the
mean of all 10 OGCMs and the error is reported as the standard deviation. These
quantities are weighted using a model skill score based on the observed and modeled
distributions of natural radiocarbon and CFCs (Mikaloff Fletcher et al., 2006a,b). This
nearly balanced global flux estimate emerges naturally from our inversion, since we did
not impose any constraints on the global integral of the flux. The finding of a near-zero
flux is interesting, because, in steady state, riverine carbon inputs are expected to lead to
Atlantic Ocean
an outgassing of natural0.4CO2 of about 0.6 Pg C yr-1 (Sarmiento and Sundquist, 1992).
0.3
We interpret the absence0.2of a significant net outgassing signal in our inversion results as
0.1
evidence that most of the0 river derived carbon outgasses back to the atmosphere near
- 0.1
coastal regions, and that- 0.2
therefore our inverse flux estimates of natural CO2 reflect open- 0.3
- 0.4
ocean fluxes without a significant
derived
Lo w- La t.N . Mi d.- La t.
N . Tro p. N .carbon.
Tro p.
S. Lo w- La t.ofS.river
S. Mi d.- La t.impact
Southern Ocean
0.5
N . H ighL at.
N. Ocean
Pacific Ocean
0.5as well
Spatially, we find natural
uptake of CO2 at mid-latitudes in both hemispheres
0.5
Ea ste rn Pa cific
0.4
0.4
0.2
0.2
We ste rn Pa cific
0.4
as0.3in the northern hemisphere
high latitudes, and outgassing in the tropics and in0.3the
0.3
0.2
Southern
Ocean (Figure 0.1
1). These results are generally in good agreement with0.1
forward
0.1
0
0
0
simulations
of OGCMs -coupled
with a biogeochemical model conducted as part
of the
- 0.1
0.1
- 0.1
- 0.2
- 0.2
- 0.2
Ocean
Carbon Model Intercomparison
Project-2 (OCMIP-2) in the northern hemisphere
- 0.3
- 0.3
- 0.3
- 0.4
- 0.4
- 0.4
(Figure
2). However, the
OCMIP-2 forward simulations and several other previous
- 0.5
- 0.5
Po lar S. S. Sub- P o l. S. Sub- Po l.
S. M id.-L at.
S. Tro p.
N . Trop.
N . Lo w- La t.
N . H igh- La t - 0.5 A rc tic Oc ea n
I nd. &
O ce an
studies
(Murnane
etAtl.al., 1999, Sarmiento et al., 2000, Wetzel et al., 2005) indicate little
P a c.
O cean Ocean, and substantially less at southern midIndian
or no natural air-sea flux in the
Southern
latitudes. More recent forward simulations using more complex biological models are in
better agreement with the inverse estimates in the southern hemisphere (Moore et al.,
2004, Doney et al., 2006).
4
Figure 2: Comparison between natural CO2 fluxes from forward model simulations undertaken as part
of OCMIP-2 and the inverse estimates (Pg C yr-1). The means and standard deviations for the forward
and inverse models have been weighted in exactly the same way and the results have been aggregated
to 11 regions for clarity.
The striking pattern of substantial natural outgassing in the Southern Ocean and
uptake at southern mid-latitudes in the inverse estimates is driven strong spatial gradients
in the data-based gas exchange tracer, Cgasex, (Gruber and Sarmiento, 2002) used to
constrain the inversion (Figure 3). Relatively high values of this tracer indicate that when
the water mass was last at the surface, it took up CO2 from the atmosphere and relatively
low values indicate that it has lost CO2 to the atmosphere.
Atlantic Ocean
Southern Ocean
Pacific Ocean
The inversion finds substantial outgassing in the Southern ocean. Cgasex shows high
values in the waters that upwell to the surface in this region, but has much lower values in
the waters downstream, particularly in Sub-Antarctic Mode Water (SAMW) (Figure 3).
This outgassing is likely driven by the upwelling of waters with high concentrations of
remineralized DIC, a substantial fraction of which can escape into the atmosphere since
the carbon uptake by biology in the surface ocean is slow and inefficient (Gruber and
5
Sarmiento, 2002). The inefficient biological pump in the Southern Ocean is thought to be
the result of a combination of light and iron limitation, and to a lesser extent grazing.
There is little net heat flux south of ~50S (DaSilva et al., 1994, Gloor et al., 2001), so
any solubility-driven CO2 flux is small.
In the mid-latitudes of the southern hemisphere (18S to 44S), we estimate a vigorous
uptake of natural CO2 (Figure 1). This strong uptake can also be traced back to the
Cgasex observations that constrain the inversion (Figure 3). In the southward flowing
surface waters of the southern hemisphere mid-latitudes, Cgasex is relatively low. As
these waters move southward, their Cgasex concentration increases substantially,
reflecting the uptake of CO2 from the atmosphere. This uptake is likely driven by a
combination of cooling and an efficient biological pump (Murnane et al., 1999, Gruber
and Sarmiento 2002).
The inversion estimates 0.94±0.17 Pg C yr-1 of outgassing in the tropics (18°N to
18°S), with approximately two thirds of this occurring in the Pacific Ocean (Figure 1).
The signal of equatorial outgassing can be identified in the Cgasex distribution, as the
upper thermocline waters that upwell in the tropics have high concentrations of Cgasex,
while the Cgasex values of the near-surface waters that are transported polewards by
Ekman transport are much lower. The outgassing in the tropics results from upwelling of
waters that are rich in remineralized DIC, which the biological pump is unable to fix
before it escapes to the atmosphere. Unlike the Southern Ocean, the upwelled waters
undergo substantial warming, resulting in a solubility pump contribution to the total
outgassing (Murnane et al., 1999, Gruber and Sarmiento, 2002).
In the mid- and high-latitudes of the northern hemisphere, we find uptake of natural
CO2 nearly everywhere, with the highest uptake fluxes occurring in the North Atlantic
(Figure 1). This is consistent with the high concentrations of Cgasex observed in the deep
Atlantic (Figure 3), which imply a substantial uptake of CO2 from the atmosphere.
6
Natural carbon transport in the interior ocean has played a major role in discussions
about the processes responsible for the northern hemisphere carbon sink that is implied by
the latitudinal gradient of atmospheric CO2 during the 1980's and 1990's, which is smaller
than expected based on the anthropogenic CO2 emission pattern, e.g. Keeling et al., 1989,
Tans et al., 1990. Keeling et al., 1989 suggested that this northern hemisphere carbon
sink is due to an uptake of about 1 Pg C yr-1 by the northern hemisphere ocean, and that
this carbon is then transported southward by the ocean currents across the equator into the
southern hemisphere, where it outgasses back into the atmosphere. Furthermore, they
argued that this transport existed in preindustrial times and that it is balanced by a
northward atmospheric transport of equal magnitude. Using an early, limited set of
surface ocean observations of the partial pressure of CO2 in the northern hemisphere
oceans, Tans et al., 1990 rejected this hypothesis, and argued that the northern
hemisphere sink was primarily due to the terrestrial biosphere. These hypotheses have
spawned a substantial number of investigations with conflicting conclusions, several of
which attempted to determine the interhemispheric transport of natural carbon by the
ocean based on analysis of hydrographic data and OGCM simulations, e.g. Broecker et
al., 1992, Keeling et al., 1995, Sarmiento et al., 2000.
The inverse estimates imply a relatively small southward cross-equatorial transport,
0.34±0.02 Pg C yr-1, which primarily occurs in the Atlantic Ocean. The uncertainty
estimate is based on the standard deviation between the models, which is taken after
the cross-equatorial transports for the Atlantic, Pacific, and Indian Oceans are summed.
Our small cross-equatorial transport estimate supports the hypothesis that there must be a
substantial terrestrial carbon sink in the northern hemisphere (Tans et al., 1990).
Nevertheless, our inversion gives a larger interhemispheric ocean carbon transport than
the three forward simulations used in the OGCM study of (Sarmiento et al., 2000), which
found a slight southward cross-equatorial transport of 0.12 Pg C yr-1. These differences
are because the forward models used in (Sarmiento et al., 2000) simulated less natural
7
carbon uptake at northern high- and mid-latitudes did not find substantial outgassing in
the Southern Ocean.
We employed a suite of 10 OGCMs and 9 scenarios for potential biases in Cgasex to
quantify the uncertainty associated with the inverse estimates (Mikaloff Fletcher et al.,
2006). We found that the results were generally remarkably robust with respect to choice
of OGCM (Figure 1). While the inverse estimates in the Southern Ocean are somewhat
sensitive to potential biases in the determination of Cgasex, the overall spatial structure of
outgassing between 59°S and 44°S and uptake between 44°S and 18°S persists in all of
the relatively extreme scenarios that we explored (Mikaloff Fletcher et al., 2006b). The
combination of the relatively low sensitivity to errors and the strong spatial gradients in
the observed Cgasex driving the flux estimates gives us a high degree of confidence in
these results.
2.2 Anthropogenic Air-sea Flux Estimates
The inversion finds a global anthropogenic CO2 uptake of 2.2 Pg C yr-1, with a
weighted standard deviation of 0.25 Pg C yr-1, scaled to a nominal year of 1995. The
range across all models is 1.85 to 2.81 Pg C yr-1 (Table 1). This substantial range is due
in part to differences between the effective vertical diffusivities in the models. Highly
diffusive models distribute
the dye over a larger
portion of the ocean. This
requires larger
anthropogenic CO2 fluxes
in order to match the high
observed anthropogenic
CO2 concentrations in the
upper ocean. The OGCMs
Table 1: Global total anthropogenic carbon uptake (Pg C yr -1)
estimated by the inverse and OCMIP-2 Forward Models. Errors
associated with the weighted mean are the skill score weighted
standard deviation between models.
Model
Inverse Estimates OCMIP Forward Estimates
Bern-3D
2.05
NA
ECCO
2.01
NA
MIT
2.22
NA
NCAR
2.17
2.36
PRINCE-LL
1.85
1.90
PRINCE-HH
2.33
2.44
PRINCE-LHS
1.99
2.04
PRINCE-2
2.16
2.24
8
PRINCE-2a
2.25
2.36
UL
2.81
2.95
Mean
2.2 ± 0.22
2.3±0.33
providing the high and low ends of this
Figure 4: Inverse air-sea flux estimates of anthropogenic CO2 (Pg C yr-1) for the 23 regions of the ocean
inversion. The gray bars represent the weighted mean and the error bars represent the weighted standard
deviation between models. Inverse estimates from individual models are show as symbols.
range (UL and PRINCE-LL) also have lower CFC-11 skill scores than the other OGCMs
used in this study (Mikaloff Fletcher et al.,2006a). This suggests that the cross-model
range can be considered an upper estimate of the uncertainty associated with the inversely
estimated global anthropogenic CO2 uptake.
The greatest anthropogenic CO2 uptake occurs in the Southern Ocean, particularly in
the sub-polar regions (44°S to 58°S), where the weighted mean anthropogenic CO2
uptake is 0.51±0.17 Pg C yr-1 (Figure 4). This flux represents 23% of the global total
anthropogenic CO2 uptake. In addition, the inversion finds considerable anthropogenic
CO2 uptake in the tropics. In contrast, anthropogenic CO2 uptake at mid latitudes is found
9
to be low, despite the fact that the greatest anthropogenic CO2 storage occurs there
(Sabine et al., 2004).
This uptake pattern is in good agreement with previous forward modeling studies. In
some of the first 3-D OGCM studies of the oceanic uptake of anthropogenic CO2,
Sarmiento et al., 1992 and Maier-Reimer et al., 1987 found a similar pattern of vigorous
anthropogenic CO2 uptake at high latitudes and at the equator, and low anthropogenic
CO2 uptake at mid-latitudes. They attributed the high uptake in the tropics and in the
high latitudes primarily to these regions being characterized by high rates of transport and
mixing of subsurface waters depleted in anthropogenic CO2 to the surface. Although
variations in gas transfer velocity were found by Sarmiento et al., 1992 to be of second
importance for the global uptake of anthropogenic CO2, the higher wind speeds in highlatitude regions were found to have some enhancing effect on greater anthropogenic CO2
uptake there. Due to the long residence of upper ocean waters near in the mid-latitudes,
anthropogenic CO2 in the surface waters of these regions generally follows the
atmospheric perturbation quite closely. This leads to low uptake.
While the overall spatial pattern is in good agreement with forward OGCM studies,
comparison between forward simulations using the same suite of models undertaken as
part of OCMIP-2 and the inverse estimates reveal considerable quantitative differences
(Figure 5). The forward model simulations for those models included both in this study
and in OCMIP-2 find a global anthropogenic CO2 uptake of 2.3±0.32 Pg C yr-1 when the
mean and standard deviation are weighted in the same way as the inverse estimates.
In comparison, the inverse estimates find 0.1 Pg C yr-1 less uptake than the forward
simulations and reduce the uncertainty estimate by 22%. For most of the models, the
inverse anthropogenic CO2 uptake estimates are substantially larger than those of the
forward model estimates in the Southern Ocean between 44°S and 58°S and in the Indian
10
Bern-3D
ECCO
MIT
NCAR
PRINCE-LL
PRINCE-HH
PRINCE-LHS
PRINCE-2
PRINCE-2a
UL
Latitude
Figure 5: The zonally and temporally integrated oceanic uptake of anthropogenic CO 2 estimated by the
ocean inversion (top) and by the OCMIP-2 forward models that also participated in this study (bottom).
Ocean south of 18°S. This is primarily driven by all of the forward models simulating a
smaller anthropogenic CO2 storage in the mid-latitudes of the Southern Hemisphere. In
order to match the data-based estimates, the inversion requires a more vigorous flux into
the sub-polar South Atlantic and sub-polar Indo-Pacific, whose signal is then transported
11
equatorward to mid-latitudes.
As was the case for the natural carbon fluxes, a suite of 10 OGCMs and potential
errors in the data-based anthropogenic carbon estimates were used to test the sensitivity
of the inverse estimates to errors in the method (Mikaloff Fletcher et al., 2006a). The
broad features in the spatial pattern of the fluxes are consistent across all of the models
that participated in this project. However, there are considerable model differences
between the anthropogenic flux estimates for some regions, leading to substantial
uncertainties in the weighted means (Figure 4). The greatest anthropogenic CO2
uncertainty occurs in the Southern Ocean, with a weighted standard deviation from the
weighted mean uptake of 0.10 Pg C yr-1 for the region south of 58°S and 0.17 Pg C yr-1
for the region between 44°S and 58°S. As a percentage of the total signal, the range in the
high-latitude North Atlantic is also very high. The inverse estimates are the most
consistent in the North Atlantic and North Pacific. We found the inverse estimates were
much less sensitive to scenarios for potential biases in the data-based anthropogenic
carbon estimates than to transport errors (Mikaloff Fletcher et al., 2006a).
2.1 Contemporary Air-sea Flux Estimates
The contemporary flux, the sum of the natural and anthropogenic fluxes (Figure 6),
resembles neither the natural fluxes nor the anthropogenic fluxes, illustrating the large
perturbation of the air-sea CO2 exchange imposed by the increase in atmospheric CO2. By
far the largest changes occur in the Southern Ocean south of 44°S, where the
anthropogenic CO2 uptake turns the strong natural CO2 outgassing into a small
12
Figure 6: Estimates of net air-sea CO2 exchange from the ocean inversion (top) compared with a variety of
independent estimates (top), and the components that comprise he contemporary air sea flux from the
ocean inversion (bottom).
contemporary CO2 sink.
This small contemporary sink in the Southern Ocean is the most dramatic difference in
13
our estimates of the source and sink distribution of atmospheric CO2 relative to
previously published estimates (Figure 6). These include estimates based on an earlier
compilation of oceanic pCO2 observations (Takahashi et al., 2002), those simulated by 13
ocean biogeochemistry models that participated in OCMIP-2 (Watson and Orr, 2003),
and those estimated from an atmospheric CO2 inversion intercomparison project
(TransCOM) (Gurney et al., 2002). As discussed in sections 2.1 and 2.2, based on our
detailed error analysis (Mikaloff Fletcher et al., 2006a,b) we have a high degree of
confidence in the inverse estimates despite their disagreement with previous estimates in
the Southern Ocean.
Strong support for this conclusion comes from the comparison of our inversely
estimated contemporary flux estimates with a new estimate of these fluxes based on a
vastly expanded and updated compilation of surface ocean pCO2 measurements. Figure 6
shows that this agreement exists regardless of whether the flux is computed using a
square dependence on the windspeed (Wanninkhof et al., 2002), or a recently proposed
linear dependence (Krakauer et al., 2006). Given the remarkable agreement between two
completely independently estimated data-based air-sea CO2 flux estimates, we conclude
that the long-term mean regionally integrated air-sea CO2 fluxes can now be estimated to
within less than 0.1 Pg C yr-1.
2.4 Joint Ocean-Atmosphere Inversion
14
The contemporary air-sea flux estimates from the ocean inversion were combined with
an atmospheric inversion to estimate fluxes from both ocean and land regions (Jacobson
et al., 2006a,b) using atmospheric observations from 74 surface stations
(GLOBALVIEW-CO2, 2000) and a suite of atmospheric transport simulations from the
TransCom model intercomparison (Gurney et al., 2002).
Atmospheric inversions are generally strongly limited by insufficient observational
coverage, requiring the use of a priori estimates of the regional fluxes using independent
methods or other regularization techniques (e.g. Enting et al., 1989, Gurney et al., 2002,
Bousquet et al., 2000). Conversely, the ocean inversion is well constrained due the
excellent spatial coverage of the observations (<60,000 observations) and the spatial
patterns due to air-sea exchange being relatively well-preserved in the interior ocean. As
a result, while the atmospheric data have little effect on the air-sea flux estimates from the
ocean only inversion, the ocean interior date indirectly constrain terrestrial fluxes in the
joint inversion by providing well-constrained estimates for many parameters in the joint
inversion. The joint inversion does not, therefore, require a priori estimates or similar
regularization techniques (Jacobson et al., 2006a).
The joint inversion has substantial implications for terrestrial fluxes. Our results
indicate that the combined tropical and southern land regions are a large source of carbon,
with a 77% probability that their aggregate source exceeds 1 Pg C yr-1. This value is of
15
similar magnitude to estimates of fluxes in the tropics due to land use change alone,
making the existence of a large tropical CO2 fertilization sink unlikely. This result is
strongly driven by the ocean inversion results in the Southern Hemisphere, which diverge
considerably from previous results from pCO2 climatologies and forward simulations,
as discussed in the previous two sections.
These results are highly robust with respect to the choice of atmospheric transport
model, the choice of OGCM, and potential biases in the gas exchange tracers used in the
ocean inversion (Jacobson et al., 2006a,b). Therefore, we have an unprecedented degree
of confidence in the total air-land fluxes over broad latitude bands.
2.1 Investigation of Air-Sea Gas Exchange Parameterizations
Air-sea fluxes of CO2 have traditionally been estimated from surface observations of
the partial pressure differences of CO2 in the atmosphere and surface ocean, pCO2, by
applying bulk formula for the gas transfer velocity (e.g. Takahashi et al., 2002). These
formulations attempt to represent the physical processes associated with gas transfer
across the air-sea interface by parameterizing the gas transfer velocity, which is generally
treated as a square or cubic function of the wind speeds (Wanninkhof et al., 1992 and
Wanninkhof and McGillis, 1999). The ocean inversion provides an independent method
of assessing air-sea gas exchange, and differences between the inverse estimates and
those using bulk formula can provide insights into possible errors in the pCO2
climatology and air sea gas exchange parameterizations.
16
Figure 7: Comparison between the observed pCO2 ( atm) climatology of Takahashi et al. (2005) and the
pCO2 implied by the ocean inversion assuming that NCEP winds and the parameterization of
Wanninkhof et al., 1992 are correct.
We found substantial differences between
pCO2 inferred from the inverse estimates and
NCEP reanalysis winds and those of the Takahashi
(2002) climatology (Figure 7). We find less tropical
disequilibrium between atmospheric and oceanic
CO2, stronger seasonality in northern mid latitudes
and a more neutral Southern Ocean than
Takhahashi. This may be partially due to errors in
the Takahashi (2002) climatology due to, for
example seasonal sampling bias in the Southern
Ocean. This hypothesis is supported by recent
updates to the Takahashi climatology that have not
yet been published (Figure 6).
If we assume the Takahashi (2002) climatology
Figure 8: Histogram of estimates of 
separated by latitude.  is estimated
from the square of the wind speed from
NCEP winds (center) and air-sea fluxes
from the ocean inversion (right). The
uncertainty associated with the inverse
estimates is represented using a Monte
Carlo simulation with 5,00 realizations
of the inverse fluxes.
and NCEP wind products are correct, we can
obtain optimal values of , the coefficient for the
quadratic gas transfer velocity of Wanninkhof
(1992). The inversion fluxes have a complex
uncertainty structure derived from an estimate of
17
model transport from 10 OGCMs, propagation of random errors, and from the assumed
spatial distribution of fluxes within estimation regions. We employ a Monte Carlo
technique to address this issue. 5,000 stochastic realizations of the global flux field were
generated from the inversion fluxes, and within each latitude band  was estimated using
least squares regression. The collection of  coefficients obtained is shown as a
histogram in Figure 8 as compared with the Wanninkhof (1992) estimate.
3. Conclusions
We have successfully completed all elements of the research we proposed to do. This
work has produced high-quality estimates of natural and anthropogenic air-sea flux
estimates with an unprecedented low uncertainty and insights into processes controlling
air-sea gas exchange. Furthermore, these air-sea flux estimates have major implications
for terrestrial fluxes. The project has produced eight peer reviewed articles, and a wide
array of presentations in conferences and professional meetings.
Publications and presentations resulting from this project
Refereed Journal Articles:
Gruber, N. M. Gloor, S. E. Mikaloff Fletcher, T. Takahashi, S. C. Doney, M. Gerber, A.
R. Jacobson, K. Lindsay, D. Menemenlis, A. Mouchet, and J. Sarmiento, Toward
consistent estimates of the oceanic sources and sinks for atmospheric CO2, Science,
submitted, 2006.
Krakauer, N.Y., J.T. Randerson, F.W. Primeau, N. Gruber, D. Menemenlis, Carbon
isotope evidence for the latitudinal distribution and wind speed dependence of the air-sea
gas transfer velocity, Tellus, submitted, 2006.
Mikaloff Fletcher, S.E., N. Gruber, A. R. Jacobson, M. Gloor, S. C. Doney, S.
Dutkiewicz, M. Gerber, M. Follows, F. Joos, K. Lindsay, D. Menemenlis, A. Mouchet, S.
Müller, and J. Sarmiento, Inverse estimates of the oceanic sources and sinks of natural
CO2 and their implied oceanic transport, Global Biogeochem. Cycles, submitted, 2006.
A. R. Jacobson, S. E. Mikaloff Fletcher, N. Gruber, J. L. Sarmiento, M. Gloor, and
TransCom Modelers, A joint atmosphere-ocean inversion for surface fluxes of carbon
18
dioxide, I: Methods, Global Biogeochem. Cycles, in revision, 2006a.
A. R. Jacobson, S. E. Mikaloff Fletcher, N. Gruber, J. L. Sarmiento, M. Gloor, and
TransCom Modelers, A joint atmosphere-ocean inversion for surface fluxes of carbon
dioxide, II: Results, Global Biogeochem. Cycles, in revision, 2006b.
Mikaloff Fletcher, S.E, N. Gruber, A. R. Jacobson, S. C. Doney, S. Dutkiewicz, M.
Gerber, M. Follows, F. Joos, K. Lindsay, D. Menemenlis, A. Mouchet, S. Müller, and J.
Sarmiento, Inverse Estimates of Anthropogenic CO2 Uptake, Transport, and
Storage by the Ocean, Global Biogeochem. Cycles, 20, doi:10.1029/2005GB002530,
2006.
Battle, M., S. E. Mikaloff Fletcher, M. L. Bender, R. F. Keeling, A. C. Manning, N.
Gruber, P. P. Tans, M. B. Hendricks, D. T. Ho, C. Simonds, R. Mika, and B. Paplawsky,
Atmospheric potential oxygen: New observations and their implications for some
atmospheric and oceanic models, Global Biogeochem. Cycles, 20,
doi:10.1029/2005GB002534, 2006.
Gloor, M., N. Gruber, J. Sarmiento, C. L. Sabine, R. A. Feely, and C. Rödenbeck, A first
estimate of present and preindustrial air-sea CO2 flux patterns based on ocean interior
carbon measurements and models, Geophys. Res. Lett., 30, 2003.
Other Publications:
Fletcher, S. E., N. P. Gruber, and A. R. Jacobson, Ocean Inversion Project How-To
Document Version 1.0, Internal Report, Institute of Geophysics and Planetary Physics,
University of California, Los Angeles, CA, 19 pp., 2003.
Available on the web at: http://quercus.igpp.ucla.edu/OceanInversion
Project Website:
http://quercus.igpp.ucla.edu/OceanInversion
Presentations at Conferences and Professional Meetings:
S. E. Mikaloff Fletcher et al., Towards robust estimates of preindustrial air–sea fluxes of
CO2 and ocean carbon transports, Seminar, Department of Chemistry, The University of
Otago, Dunedin, New Zealand, January 2006.
S. E. Mikaloff Fletcher et al., An ocean view on past and present air–sea fluxes of CO2,
Seminar, Department of Chemistry, The University of Otago, Dunedin, New Zealand,
January 2006.
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A. Jacobson et al., A Joint Atmosphere-Ocean Inversion for Surface Fluxes of CO2,
Seminar, Carbon Cycle Research Group, Penn State University, University Park, PA,
December 2005.
A. Jacobson et al., A Joint Atmosphere-Ocean Inversion for Surface Fluxes of CO2,
Seminar, Department of Geophysical Sciences, University of Chicago, Chicago, IL,
November 2005.
A. Jacobson et al., A Joint Atmosphere-Ocean Inversion for Surface Fluxes of CO2,
Seminar, Institute for Environmental Studies, University of Pennsylvania, Philadelphia,
PA, October 2005.
S. E. Mikaloff Fletcher et al., Preindustrial, Anthropogeinc, and Contemporary Air-sea
Carbon Flux, Seminar, Sarmiento group, Atmospheric and Oceanic Sciences, Princeton
University, Princeton, NJ, October 2005.
N. Gruber et al., Oceanic Sources and Sinks for Atmospheric CO2, Oral Presentation, 7th
International Carbon Dioxide Conference, Boulder CO, September 2005.
A. Jacobson et al., Oceanic Constraints on the Size of the Terrestrial CO2 Fertilization
Sink, Oral Presentation, 7th International Carbon Dioxide Conference, Boulder CO,
September 2005.
A. Jacobson et al., Implications of Ocean Interior CO2 For Air-sea Gas Exchange
Parameterizations and pCO2, Poster Presentation, 7th International Carbon Dioxide
Conference, Boulder, CO, September 2005.
S. E. Mikaloff Fletcher et al., Robust Estimates of Preindustrial and Athropogenic Air-sea
Carbon Dioxide Flux, Poster Presentation, 7th International Carbon Dioxide Conference,
Boulder, CO, September 2005.
S. E. Mikaloff Fletcher et al., Preindustrial, Anthropogeinc, and Contemporary Air-sea
Carbon Flux, Seminar, The Joint Global Change Research Institute, Pacific Northwest
National Laboratory, The University of Maryland, College Park, MD, September 2005.
A. Jacobson et al., Ocean Interior Data Suggest That There Is No CO2 Fertilization Sink,
Poster Presentation, Ocean Carbon and Climate Change Workshop, Woods Hole, MA,
August 2005.
S. E. Mikaloff Fletcher et al., Robust Estimates of Preindustrial Air-sea Carbon Dioxide
Flux and Ocean Carbon Transport, Ocean Carbon and Climate Change Workshop,
Woods Hole, MA, August 2005.
20
A. Jacobson et al., A Joint Atmosphere-Ocean Inversion for Surface Fluxes of CO2, Oral
Presentation, Cooperative Institute for Climate Science Meeting, Princeton, NJ, June
2005.
A. Jacobson et al., Estimating Surface Fluxes of Carbon Dioxide, Seminar, Socolow
group, Princeton University, Princeton, NJ, April 2005.
A. Jacobson et al., Determination of Carbon Fluxes by a Joint Inverse of Oceanic and
Atmospheric Observations, Poster Presentation, European Geosciences Union General
Assembly, Vienna, Austria, April 2005.
A. Jacobson et al., Estimating Surface Fluxes of Carbon Dioxide, Oral Presentation to Dr.
John Marburger, Presidential Science Advisor, Princeton, NJ, March 2005.
A. Jacobson et al., New Flux Estimates from a Joint Ocean- Atmosphere Inversion, Oral
Presentation, Carbon Mitigation Initiative Annual Meeting, Princeton, NJ, January 2005.
S. E. Mikaloff Fletcher et al., On the Robustness of Air-sea Flux Estimates of Carbon
Dioxide from Ocean Inversions, American Geophysical Union Fall Meeting, San
Francisco, CA, December 2004.
S. E. Mikaloff Fletcher et al., Estimating Oxygen Fluxes from Ocean Interior Data: A
Model Comparison Study, Atmospheric Potential Oxygen Workshop, Jena, Germany,
July 2004.
S. E. Mikaloff Fletcher et al., Estimates of air-sea anthropogenic carbon dioxide flux
from ocean interior carbon measurements and Ocean General Circulation Models, Poster
Presentation, Symposium on The Ocean in a High CO2 World, Paris, France, May 2004.
S. E. Mikaloff Fletcher et al., and the Ocean Inversion Project Modelers, Estimating airsea exchange of anthropogenic CO2: A comparison of inverse models and forward
models, Oral Presentation, Ocean Carbon Modeling Intercomparison Project Meeting,
Paris, France, May 2004.
N. Gruber et al., The Southern Ocean as a Sink for Atmospheric CO2, Oral Presentation,
American Geophysical Union Ocean Sciences Meeting, Portland, OR, January 2004.
S. E. Mikaloff Fletcher et al., Estimates of Air-Sea Anthropogenic Carbon Dioxide Flux
From Ocean Interior Measurements and Ocean General Circulation Models, Oral
Presentation, American Geophysical Union Ocean Sciences Meeting, Portland, OR,
January 2004.
21
A. R. Jacobson et al., A Joint Atmosphere-Ocean Inversion for Surface Fluxes of Carbon
Dioxide, Oral Presentation, American Geophysical Union Fall Meeting, December 2003.
S. E. Mikaloff Fletcher et al., Inverse Estimates of Air-Sea Anthropogenic Carbon
Dioxide From Ocean Interior Measurements and Ocean General Circulation Models, Oral
Presentation, American Geophysical Union Fall Meeting, December 2003.
A. R. Jacobson et al., On the Other Side of the Air/Sea interface, Oral Presentation,
TransCom Meeting, Jena, Germany, May 2003.
N. Gruber et al., Storage of Carbon in the Oceans: Observational Constraints, Oral
Presentation, Joint Global Ocean Flux Study Final Conference, Washington D. C., May
2003.
S. E. Mikaloff Fletcher et al., Carbon Fluxes and Propagation of Uncertainties in an
Ocean Inverse Model System, Poster Presentation, European Geophysical SocietyAmerican Geophysical Union Joint Assembly, Nice, France, April 2003.
A. R. Jacobson et al., Sensitivity of Inversion Estimates of Anthropogenic Carbon AirSea Fluxes to Transport Uncertainty, Oral Presentation, European Geophysical SocietyAmerican Geophysical Union Joint Assembly, Nice, France, April 2003.
C. LeQuere et al., Gaining Insight Into the Interannual Variability of Air-Sea CO2 Fluxes
Using Satellite Observations, European Geophysical Society-American Geophysical
Union Joint Assembly, Oral Presentation, Nice, France, April 2003.
C. LeQuere et al., Gaining Insight Into the Interannual Variability of Air-Sea CO2 Fluxes
Using Satellite Observations, OCEANS International Open Science Conference, Paris,
France, January 2003.
N.Gruber et al., Uptake, Transport, and Storage of Carbon by the Ocean: Implications for
the Global Carbon Cycle, World Ocean Circulation Experiment & Beyond Meeting, San
Antonio, TX, November, 2002.
Appendix II: Brief description of models
ECCO- In addition to circulation estimates from the prognostic models described above,
22
we also plan to use results from the Estimating the Circulation and Climate of the ocean
(ECCO) consortium Assimilation Model. Data constraints for the optimization include
absolute and time-varying TOPEX/POSEIDON sea-surface height (SSH) data, SSH
anomalies from the ERS-1 and ERS-2 satellites, monthly-mean sea-surface temperature
data (Reynolds and Smith, 1994), time-varying NCEP reanalysis fluxes of momentum,
heat, and freshwater, and NSCAT estimates of wind stress error. Monthly means of the
model state are required to remain within assigned bounds of the monthly mean Levitus
et al. (1994) climatology and a drift of the model over the 9-year period is penalized to
bring the model hydrography into a stable equilibrium with surface fluxes. To bring the
model into consistency with the observations, the initial potential temperature and salinity
fields and the surface forcing fields are modified. The resulting solution is a complete
description of the ocean flow fields, its transport properties, and surface fluxes that is
better than either model or observations alone. Detailed descriptions of this product, list
of related publications, and complete optimization outputs are available on the ECCO
consortium web site [http://ecco-group.org/]. The mean seasonal cycle of the nine-year
optimization will be used to drive an offline tracer model. The offline model is itself
based on the MIT GCM, described below, but instead of computing prognostic model
variables (temperature, salinity, velocity, and mixing coefficients), these variables are
read-in from previously generated files.
MIT- The Massachusetts Institute of Technology GCM solves the incompressible
Navier-Stokes equations on a C-grid, with optional hydrostatic approximation. For
coarse resolution global ocean circulation studies, mesoscale eddy transfer effects are
achieved using schemes related to the parameterization of Gent et al. (1990) with variable
mixing coefficients and reflecting the strong regional variability in ocean eddy activity
Visbeck et al., (1997). Vertical turbulent mixing in the surface mixed layer of the ocean is
parameterized using convective adjustment or the scheme of Large et al. (1994).
MOM- The Princeton Group employed several configurations of the Modular Ocean
Model that are improved versions of the LO-LO Model employed in the previous
inversion studies (Gloor et al., 2001, Gruber et al., 2001, Gloor et al., 2003). The
differences between these versions of MOM are described below. MOM is a global
seasonal model forced by seasonally varying wind-stress from Hellerman and
Rosenstein (1983). Surface temperature and salinity fields are forced with a hybrid
between restoring boundary conditions taken from the seasonally varying Levitus et al.,
(1994) sea-surface temperature and Levitus and Boyer (1994) salinity fields with a
restoring time-scale of 30 days, and flux boundary conditions on the basis of the
seasonally varying heat and freshwater fluxes of the DaSilva et al., (1994) climatology.
Lateral advection caused by sub-grid scale eddies is included following the
parameterization of Gent et al., (1995) and the implementation of Griffies (1998).
Configurations of MOM
23
LL- The standard version of the MOM3 model (KVLOW-AILOW of Gnanadesikan et
al., 2002) used in the earlier ocean inversion papers (Gloor et al, 2003, Gruber et al.,
2001, Gloor et al, 2001)
HH- A version of the model with high vertical mixing and high isopycnal diffusivity
LHS- The 'LL' model with enhanced vertical mixing of in the Southern Ocean south of
55º S
RDS- The 'LHS' model modified for moderate increased vertical mixing in the Southern
Ocean. In this version the model salinity is restored to observations at four selected
points in the Southern Ocean.
PSS- The 'RDS' model with the wind fields changed to ECMWF, narrowed topography
around the Drake Passage.
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