gmd 7 419 2014

gmd 7 419 2014
Geoscientific
Model Development
Open Access
Geosci. Model Dev., 7, 419–432, 2014
www.geosci-model-dev.net/7/419/2014/
doi:10.5194/gmd-7-419-2014
© Author(s) 2014. CC Attribution 3.0 License.
Can sparse proxy data constrain the strength of the Atlantic
meridional overturning circulation?
T. Kurahashi-Nakamura1 , M. Losch2 , and A. Paul1
1 MARUM
– Center for Marine Environmental Sciences and Faculty of Geosciences, University of Bremen,
Bremen, Germany
2 Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany
Correspondence to: T. Kurahashi-Nakamura ([email protected])
Received: 17 July 2013 – Published in Geosci. Model Dev. Discuss.: 20 August 2013
Revised: 10 January 2014 – Accepted: 24 January 2014 – Published: 26 February 2014
Abstract. In a feasibility study, the potential of proxy data
for the temperature and salinity during the Last Glacial Maximum (LGM, about 19 000 to 23 000 years before present)
in constraining the strength of the Atlantic meridional overturning circulation (AMOC) with a general ocean circulation model was explored. The proxy data were simulated
by drawing data from four different model simulations at
the ocean sediment core locations of the Multiproxy Approach for the Reconstruction of the Glacial Ocean surface
(MARGO) project, and perturbing these data with realistic noise estimates. The results suggest that our method has
the potential to provide estimates of the past strength of the
AMOC even from sparse data, but in general, paleo-seasurface temperature data without additional prior knowledge
about the ocean state during the LGM is not adequate to
constrain the model. On the one hand, additional data in the
deep-ocean and salinity data are shown to be highly important in estimating the LGM circulation. On the other hand, increasing the amount of surface data alone does not appear to
be enough for better estimates. Finally, better initial guesses
to start the state estimation procedure would greatly improve
the performance of the method. Indeed, with a sufficiently
good first guess, just the sea-surface temperature data from
the MARGO project promise to be sufficient for reliable estimates of the strength of the AMOC.
1
Introduction
The ocean is an important component of the climate system
because of its large storage and transport of heat as well as
its strong control on the atmospheric circulation. To understand the dynamics of climate change, it is essential to assess the role of the ocean. Proxy evidence (e.g., Keigwin and
Lehman, 1994; Clark et al., 2001; Epica Community Members, 2006) and climate models (e.g., Ganopolski and Rahmstorf, 2001; Stocker and Johnsen, 2003) suggest close links
between the temperature in the Atlantic region and variations
of the Atlantic meridional overturning circulation (AMOC)
and North Atlantic Deep Water (NADW) formation during past climate changes such as Dansgaard–Oeschger and
Heinrich events. Associated changes in the ventilation of the
deep ocean presumably affected the global climate by reorganizing the cycling of carbon and other nutrients, which in
turn led to different concentrations of carbon dioxide (CO2 )
in the atmosphere (e.g., Archer, 1991; Archer et al., 2000;
Gildor and Tziperman, 2001; Schulz et al., 2001; KurahashiNakamura et al., 2010). Therefore, proper reconstructions of
the AMOC is a key element in understanding the climate dynamics in the past.
The Last Glacial Maximum (LGM, 19 000–23 000 years
before present; Mix et al., 2001) is one of the most suitable time periods for studying a climate that is very different from the modern one, because the data coverage for
the LGM is comparatively good, and the radiative forcings,
boundary conditions and climate response are relatively well
known (Solomon et al., 2007). Nevertheless, the ocean circulation during the LGM is uncertain to the extent that even the
Published by Copernicus Publications on behalf of the European Geosciences Union.
420
T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
question of whether the strength of the AMOC was larger or
smaller in the LGM than in the modern day climate is still
open to debate.
On the one hand, the information on the past AMOC
strength is obtained from paleoceanographic proxy variables (Fischer and Wefer, 1999). For example, a weaker
AMOC is inferred by Lynch-Stieglitz et al. (1999a, b) and
Lynch-Stieglitz et al. (2006) based on a geostrophic transport estimate for the Florida Current from the oxygen isotope ratio (18 O/16 O) recorded in the fossil shells of benthic
foraminifera (often expressed as δ 18 O, that is, the deviation
from a standard ratio1 ), by Piotrowski et al. (2005) based on
neodymium isotope ratios (143 Nd/144 Nd), and by McManus
et al. (2004) and Negre et al. (2010) based on north-to-south
gradients of rate-sensitive radiogenic 231 Pa/230 Th isotope ratios (Negre et al. (2010) even argue for a reversal of the
abyssal flow during the LGM).
In contrast, a stronger AMOC is hypothesized by Yu et al.
(1996) and Lippold et al. (2012) also based on 231 Pa/230 Th
isotope ratios; by McCave et al. (1995), Manighetti and
McCave (1995), and McCave and Hall (2006) based on
the grain-size analysis of ocean sediments; and by Curry
and Oppo (2005) based on the stable carbon isotope ratios
(13 C/12 C, often expressed as δ 13 C2 ) of the dissolved inorganic carbon (DIC) in seawater, and cadmium/calcium trace
element ratios (Cd/Ca). Finally, Rutberg and Peacock (2006)
interpret glacial δ 13 C of DIC as consistent with a circulation
regime similar to today.
On the other hand, there are various estimates of the overturning strength during the LGM by different numerical climate models. In spite of the same forcing and boundary
conditions applied to the models, the estimates with coupled atmosphere–ocean models are not consistent (cf. OttoBliesner et al., 2007). Using inverse methods and data assimilation in the context of the LGM often required simplified
ocean models (e.g., Legrand and Wunsch, 1995; Gebbie and
Huybers, 2006; Huybers et al., 2007; Burke et al., 2011). For
example, Huybers et al. (2007) used a geostrophic model to
suggest that reliable estimates of the LGM AMOC requires
an accuracy of density data that exceeds that of available data
by one order of magnitude. Instead, Huybers et al. propose
using conservative tracers such as δ 13 C of DIC for constraining the circulation. There are, however, very few LGM-state
estimates based on general circulation models and the adjoint
technique. Winguth et al. (1999) and Winguth et al. (2000)
assimilated the δ 13 C of DIC and Cd/Ca data into a global
ocean model and suggested shallower and about 30 % weaker
AMOC strength with an adjoint ocean model (Winguth et al.,
2000). Dail (2012) used the sea-surface temperature (SST)
1 It
is
defined
(18 O/16 O)sample −(18 O/16 O)standard
× 103
(18 O/16 O)standard
2 It
is
defined
(13 C/12 C)sample −(13 C/12 C)standard
× 103
(13 C/12 C)standard
Geosci. Model Dev., 7, 419–432, 2014
as
δ 18 O(‰) =
as
δ 13 C(‰) =
data by the MARGO project (MARGO Project Members,
2009), δ 13 C of DIC, and δ 18 O of seawater for state estimation in the Atlantic domain, and inferred that the NADW in
the LGM was shallower but as strong as in the modern day.
More direct indicators of the past AMOC strength would
be the temperature and salinity of seawater. Since they drive
the ocean circulation through density differences, a numerical ocean model could be used to quantify an ocean circulation that is consistent with the temperature and salinity data.
To date, the most comprehensive compilation of SST estimates for the LGM ocean is provided by the MARGO
project (MARGO Project Members, 2009). A similar data
set for sea-surface salinity does not yet exist. Local estimates of the salinity of LGM bottom water may be obtained from measurements of the δ 18 O of the pore fluid in
sea-floor sediments (Adkins et al., 2002), but there is no direct proxy for salinity that could be applied generally. The
δ 18 O of calcite shells of planktonic foraminifera fossils depend on the local salinity as well as on temperature, and thus
it is possible to estimate the salinity if one can remove the
temperature effect with the help of an independent temperature proxy such as the Mg/Ca ratio (Gebbie and Huybers,
2006). However, error propagation yields large errors on the
reconstructed salinity (Schmidt, 1999; Rohling, 2000). The
MARGO project has also assessed the spatial distribution
of the available paleo-data for the deep ocean, such as the
δ 18 O of benthic foraminifera (Paul and Mulitza, 2009). By
all means, the paleo-data coverage is still very sparse compared to the present-day data coverage. Therefore, a powerful data assimilation technique is required to control the
model efficiently, given the limited amount of data (Paul and
Schäfer-Neth, 2005).
In this study, we adopted the constrained least-squares
technique for that purpose; namely, we seek a model ocean
that corresponds to the minimum value of a so-called objective function, which is mainly the sum of squared differences between data and corresponding model results. This
optimized model ocean provides the best estimate for the
AMOC strength. The adjoint method (e.g., Wunsch, 1996;
Errico, 1997) is a technique to find such an optimized state,
because it allows for the computation of the gradient of the
objective function with respect to selected control variables
(that may include initial and boundary conditions as well as
internal model parameters) and search for its minimum.
Our ultimate goal is to assimilate various paleo-data for the
LGM into a numerical ocean model (Paul and Schäfer-Neth,
2005; Schmittner et al., 2011), with the aim of estimating the
LGM ocean state as reliably as possible. As the first step,
the particular purpose of this paper is to examine whether
the spatial distribution and accuracy of the available compilation of paleo-temperature data is likely to be adequate
enough to constrain our model properly, and if not, what further data would be required. For this purpose, we used artificial pseudo-proxy data instead of the actual LGM data and
estimated the AMOC strength of a target model ocean from
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T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
which the pseudo-data was sampled. Thus, we could assess
the result of our state estimate exercise by comparing the estimated value with the known “true” value.
The artificial targets had a stronger or weaker AMOC
strength than the reference state to serve as potential analogues for the LGM ocean. The basic set of pseudo-proxy
data had the same spatial distribution and error estimates as
the MARGO data, in order to imitate the quality and quantity
of actual paleo-data. The experiments described in this paper
are not identical twin experiments where varied parameters
are part of the control vector and can be recovered by fitting
the model to data with a twin model. Instead, we chose to
generate targets with changed physics that were not part of
the control vector and that were held fixed in the estimation
process. As a consequence, the model cannot fit perfectly to
the pseudo-data. In this sense, model errors are included in
our experiments that need to be compensated for by adjusting
the control vector, which usually consists of surface forcing
fields. These “cousin” experiments are more difficult for the
numerical model, but they simulate the realistic situation of
imperfect models and inaccurate data.
2
Methods
We used the Massachusetts Institute of Technology general circulation model (MITgcm), a state-of-the-art model
suitable for ocean state estimation. Here, it was configured
to solve the Boussinesq, hydrostatic Navier–Stokes equations (Marshall et al., 1997). Subgrid-scale mixing was parameterized (Gent and McWilliams, 1990). A dynamic–
thermodynamic sea-ice model was coupled to the ocean
model (Losch et al., 2010). We used a cubed-sphere grid system that avoided converging grid lines and pole singularities
(Adcroft et al., 2004) and had six faces, each of which has
32 × 32 horizontal grid cells, and 15 vertical layers.
The MITgcm can be fitted to data by solving a leastsquares problem using the Lagrange multiplier method. For
this purpose, the computer code can be differentiated by automatic differentiation (AD) using the source-to-source compiler TAF (Giering and Kaminski, 1998; Heimbach et al.,
2005) to generate exact and efficient “adjoint” model code.
For the experiments with artificial pseudo-proxy data
(hereafter, referred as pseudo-proxy experiments), we ran the
MITgcm forward in time to generate five different model
ocean states. One of them was the reference state and at
the same time the starting point of all optimizations, and the
other four were divided into two sets: one set was very different from the reference state by changing the model physics
and the atmospheric boundary conditions (Targets 1 and 2),
while the other set was quite similar to the reference, but with
systematic biases due to modified internal model parameters
(Targets 3 and 4, see also Table 1 and Fig. 1).
For the reference state, the model was spun up from
present-day salinity and temperature (Levitus, 1982) for 800
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421
Reference
[m]
0
1000
2000
3000
4000
5000
Eq.
[m]
0
40 N
80 N
Target 1
Target 2
Target 3
Target 4
1000
2000
3000
4000
5000
[m]
0
1000
2000
3000
4000
5000
Eq.
40 N
-25
80 N
Eq.
0
40 N
80 N
25 [ Sv ]
Fig. 1. Stream function of the Atlantic meridional overturning circulation for the reference state and the four targets.
Figure 1
model years from the state of rest with the external forcings
based on the protocol of the Coordinated Ocean-ice Reference Experiments (COREs) project (Griffies et al., 2009). We
used a tracer acceleration method with a time step of 1 day
for the tracer equations and 20 min for the momentum equations. The maximum of the Atlantic meridional overturning
stream function of 18.3 Sv was taken as a measure of the
AMOC strength in the reference state.
The reference configuration was modified considerably to
generate Targets 1 and 2. In both runs the prescribed atmospheric fields were replaced by fields from a coupled atmospheric energy–moisture balance model (Ashkenazy et al.,
2013). These simulations corresponded to very different climates, mostly as a consequence of the dynamic interaction of
the ocean with the atmosphere, although some of the internal
ocean model parameters were also modified (Table 2). After another spin-up of 2000 years we added freshwater to the
North Atlantic Ocean uniformly between 20◦ N and 50◦ N at
a rate of 0.28 Sv for an additional 1000-year run. We calculated the Atlantic meridional overturning stream function and
took the maximum of 11.4 Sv as an indication of a reduced
AMOC strength for Target 1 as compared to the reference
state. The unmodified run with an increased rate of 23.7 Sv
became Target 2.
Targets 3 and 4 were generated by increasing or reducing
internal physical parameters that determine the lateral eddy
viscosity for additional 200-year runs from the reference.
These parameters for harmonic and bi-harmonic viscosity
(A∗h , A∗4 ) were not used as standard control variables in our
experiments. Increasing the eddy viscosity led to a smaller
overturning rate of 12.5 Sv (Target 3) as compared to the reference state, decreasing to a larger overturning rate of 22.9 Sv
(Target 4).
Targets 1 and 3 had similarly weak AMOC strengths and
Targets 2 and 4 similarly stronger AMOC strengths, but
Geosci. Model Dev., 7, 419–432, 2014
422
T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
Table 1. Summary of experiment settings and results. Used data are specified as follows. ST: surface temperature from MARGO data
locations, DT: Deep temperature from MARGO data locations, AST: surface temperature from all other grid cells, SS: surface salinity from
MARGO data locations, DS: deep salinity from MARGO data locations, and ASS: surface salinity from all other grid cells. Maximum values
of the AMOC stream function are shown in Sv (1 Sv = 106 m3 s−1 ). Reconstructed AMOC strength that is closer to the target than half of
the difference between the starting point (reference state) and target is shown in italics. The rightmost column shows the mean cost (i.e., the
value of objective function divided by the number of model-data comparisons). The unit of data error σ is K for temperature and psu for
salinity.
Used data
Experiment
ST
DT
AST
SS
DS
ASS
Maximum of AMOC
stream function (Sv)
Data errors
Reference state
Mean cost
(× 10−1 )
18.3
Target 1
E1-1
E1-2
E1-3
E1-4
E1-5
E1-6
E1-7
E1-8
x
x
x
x
x
x
x
x
Target 2
E2-1
E2-2
E2-3
E2-4
E2-5
E2-6
E2-7
E2-8
x
x
x
x
x
x
x
x
Target 3
E3-1
E3-2
E3-3
x
x
x
Target 4
E4-1
E4-2
E4-3
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Targets 1 and 2 were much colder than both the reference
and Targets 3 and 4 (Table 2).
The temperature and salinity distributions of each target
were sampled and averaged over the last 10 years of the simulations. Surface data (SST and SSS) were taken from the top
grid nodes, deep-ocean data from the bottom grid nodes. Normally distributed noise with a standard deviation of the prior
errors was added as a random error to obtain the pseudo-data.
Note that large uncertainties were associated with proxy data
so that the prior errors (see below) could be large. This led
to the realistic situation that the proxy data could be strongly
biased after adding large noise contributions on the order of,
for example, 1 ◦ C.
Starting from the reference run, the ocean model was fitted to the pseudo-proxy data by minimizing the following
Geosci. Model Dev., 7, 419–432, 2014
11.4
39.1
19.5
31.4
13.8
20.3
21.5
14.2
16.1
0.74
6.4
4.8
9.6
5.4
9.7
35
74
23.7
30.5
18.9
43.8
37.4
18.8
24.9
14.6
29.5
0.36
6.3
4.1
9.7
5.1
8.5
36
82
MARGO
σ = 0.1
MARGO
12.5
13.7
14.3
14.9
2.9
44
9.2
MARGO
σ = 0.1
MARGO
22.9
30.2
20.2
21.8
3.0
18
9.4
MARGO
MARGO/σ
MARGO
MARGO/σ
MARGO/σ
MARGO/σ
σ = 0.1
σ = 0.1
MARGO
MARGO/σ
MARGO
MARGO/σ
MARGO/σ
MARGO/σ
σ = 0.1
σ = 0.1
= 2.0
= 2.0
= 2.0
= 2.0
= 2.0
= 2.0
= 2.0
= 2.0
objective function J :
J = (Tmodel − Ttarget )T Wt (Tmodel − Ttarget )
+ (Smodel − Starget )T Ws (Smodel − Starget ) ,
(1)
where Tmodel and Smodel were the average over the last
10 years of a 20-year integration (for each iteration) of temperature and salinity, Ttarget and Starget were pseudo-proxy
data based on the artificial targets, Wt and Ws were weight
matrices that were the inverse of the error covariance matrices. All errors were assumed to be uncorrelated, so that
the inverse error covariances reduced to scalar weights. To
reconstruct the targets, we used the following control variables: the radiative and wind forcing at the sea surface, the air
temperature, the humidity above the sea surface, the precipitation, and the initial temperature and salinity. Every control
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T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
423
Table 2. Summary of model configurations for the reference state and the targets.
Parameters
Reference
Normalized lateral eddy viscosity A∗h (non-dim.)
Normalized biharmonic viscosity A∗4 (non-dim.)
Vertical eddy viscosity (r 2 /s)
1.2 × 10−2
Vertical diffusion coefficient (m2 /s)
Parameterization scheme for vertical mixing
Parameterization scheme for geostrophic eddies
Mean absolute deviation of sea-surface temperature
(SST) from the reference
Root mean square of SST difference from the
reference
Target 2
Target 3
Target 4
0
3.0 × 10−1
1.0 × 10−3
3.0 × 10−5
Nonlocal
K-profile
parameterization (KPP)
GM with
variable eddy
coefficientsb
2.9 K
1.0 × 10−3
3.0 × 10−5
implicit vertical diffusion
5.0 × 10−3
5.0 × 10−2
1.0 × 10−3
3.0 × 10−5
implicit vertical diffusion
Redi/GM
parameterizationa
–
0
3.0 × 10−1
1.0 × 10−3
3.0 × 10−5
Nonlocal
K-profile
parameterization (KPP)
GM with
variable eddy
coefficientsb
2.9 K
1.5 × 10−2
Redi/GM
parameterizationa
0.14 K
Redi/GM
parameterizationa
0.16 K
–
3.5 K
3.4 K
0.3 K
0.3 K
1.2 × 10−1
1.0 × 10−3
3.0 × 10−5
implicit vertical diffusion
Target 1
1.5 × 10−1
a Redi (1982); Gent and McWilliams (1990); Gent et al. (1995). b Visbeck et al. (1997).
variable was normalized according to the characteristic scale
of each variable, and was smoothed with a 9-point smoothing
scheme. A quasi-Newton algorithm (Gilbert and Lemaréchal,
1989) was used to iteratively find optimized control variables that minimized J . The essential gradient information
was provided by the adjoint model.
To explore the potential information content of the
MARGO data set, the first experiments with Targets 1 and 2
only used the model SST sampled at the MARGO core locations as pseudo-proxy data (Table 1). For these data, we used
prior data errors derived from the uncertainty estimated for
each individual data point by the MARGO project (MARGO
Project Members, 2009). MARGO uncertainty estimates are
conservative and meant to give an upper bound. If a model
grid cell contained more than one data point, the weighted
average of all data points was used.
Then we successively added hypothetical data sets to improve the data coverage and to assess its effect on the state
estimates. We assigned prior errors to the hypothetical data
points as specified in Table 1. We used the same prior errors
for temperature and salinity.
3
Results
Table 1 summarizes the experiments. A simple measure of
the quality of the model fit after the optimization is based on
the principles of a χ -squared test. The scaled contributions
to the cost function are assumed to be independent Gaussian variables with an expectation value of one, so that the
expectation value of a well-balanced problem is the number
of model–data comparisons. Therefore, the mean cost (i.e.,
cost function divided by the number of model-data comparisons) is of the order of one or less (Wunsch, 1996, 2006).
In all of our experiments with MARGO data errors the mean
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cost function value was less than one, so that we called the
model-fitting itself successful (rightmost column of Table 1).
For the other experiments with the much smaller data errors
of σ = 0.1, the values were larger than one. This implied
that the fit was not successful and the hypothesis that the
model was consistent with the data within prior errors had
to be rejected. Nevertheless, the stricter requirements for the
fit meant that the model was generally closer to observations
and thus better constrained than with the larger errors (also
see below).
Those experiments for which the AMOC strength was adjusted by the least-squares fit to be closer to the target than
half of the difference between the starting point (reference
state) and target were marked as successful in reconstructing
the overturning. These were experiments E1-4 and E1-7 for
Target 1 and E2-6 for Target 2. For Targets 3 and 4 all experiments except for E4-1 and E4-2 were successful by this
measure. The other experiments had either far too large an
overturning rate or the overturning rate was not affected by
the constraining observations.
For the two targets with a much colder climate (Targets 1
and 2) the results were incoherent. Surface data of temperature (E1-1 and E2-1) and salinity (E1-3 and E2-3) alone did
not appear to be sufficient to constrain the overturning rate.
Instead, assimilating these data led to much too strong an
overturning in all cases, even for Target 1 where the sampled surface data corresponded to a weaker overturning rate.
Temperature data alone at the surface and near the bottom
were also without effect. In these runs (E1-2 and E2-2), the
overturning rate hardly changed relative to the initial guess.
Temperature and salinity data near the bottom were required
to bring the overturning rate down to the target value in E14, or to enhance it in E2-4 (but here they led to too strong an
overturning). A large effect of salinity data on the overturning
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T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
E1-1
E1-3
E1-5
E1-6
E1-2
E1-4
E1-7
E1-8
50 N
30 N
50 N
30 N
60 w
30 w
60 w
30 w
-5
60 w
0
[K]
30 w
60 w
30 w
5
Fig. 2. Anomalies of temperature at the depth of 2000 m in E1-1–E1-8 compared to Target 1.
rate was clearly seen in the comparison between E1-2 and
E1-4, and between E2-2 and E2-4.
In runs E1-5, E1-6, E2-5, and E2-6 we assumed that the
data were available at all surface grid points. Even the complete data coverage of SST was insufficient to reconstruct the
AMOC properly for both targets. This may not come as a surprise, because even a current monitoring for modern AMOC
(e.g., Srokosz et al., 2012) needs more elaborate information including sea-surface height data to precisely constrain
AMOC behavior. With both temperature and salinity data at
all surface grid points, one experiment (E2-6) was successful
in reproducing the larger overturning rate of Target 2.
If we were able to increase the data accuracy, for example,
by increasing the number of observations within a grid cell
or by inventing new proxies that would yield a more accurate
reconstruction of temperature and salinity, we could hope
to improve the state estimates. In experiment E1-7 accurate
temperature data alone was sufficient for a good agreement
of the overturning rate to Target 1. The same configuration
led to an adjustment with the wrong sign in E2-7. Accurate
temperature and salinity data marginally improved the agreement with the targets’ overturning rates compared to other
experiments, but not sufficiently to be called successful.
The second set of targets (Targets 3 and 4) was created
with the same atmospheric forcing as for the reference state,
but internal model parameters were modified to mimic inherent model biases. Identical twin experiments, in which the
control parameters consisted of just these modified viscosity parameters, confirmed that the system was able to completely recover the original parameters. These experiments
only represent a (successful) zero-order test showing that the
system works with a perfect model. For the standard control
variables (initial conditions and atmospheric forcing fields,
see above), the first pair of experiments for Target 3 and
4 (E3-1 and E4-1) showed that, provided the targets were
close enough to the reference (i.e., the first guess) with regard to the temperature (Table 1), the same data distribution
Geosci. Model Dev., 7, 419–432, 2014
and errors as those for E1-1 and E2-1 were sufficient to guide
the AMOC strength to the right direction, even if the target strengths were much different from that of the reference
Figure
2 much smaller data prior errors (E4-2), the esstate.
With
timated AMOC strength for Target 4 was better estimated
compared to E4-1, although E3-2 was slightly worse than
E3-1. For the last two experiments (E3-3 and E4-3) we reduced the control space to the initial conditions, as well as
the surface wind stress and the incoming shortwave and longwave radiative fluxes (i.e., reducing the number of control
variables from nine to six, which made the model less flexible, see also Sect. 4.2). Even without the air temperature,
the humidity, and the precipitation as control variables, the
AMOC strength were successfully estimated.
4
4.1
Discussion
Analysis of the results for Targets 1 and 2
The experiments for Targets 1 and 2 showed that more data
or data with smaller errors did not necessarily lead to a better
AMOC reconstruction. However, the seemingly incoherent
tendency toward different solutions can be explained as follows.
In all experiments for both Targets 1 and 2, very strong
vertical mixing occurred in the high-latitude North Atlantic
at the beginning of each of the optimization runs, because
the model adjusted to the much colder target SST, implying
denser surface water.
For the experiments for Target 1 the further development
of the solution depended on whether the ocean could recover
from the “initial shock" of strong mixing or not. With no or
insufficient contribution of the deep-ocean data (E1-1, E13, E1-5, and E1-6) the lighter (i.e., warmer) deep water of
the reference ocean tended to remain (Fig. 2), so that mixing
continued. Note that temperature and salinity data of the deep
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T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
425
E2-1
E2-2
E2-5
E2-7
E2-3
E2-4
E2-6
E2-8
50 N
30 N
50 N
30 N
60 w
30 w
60 w
30 w
-3
60 w
0
[ psu ]
30 w
60 w
30 w
3
Fig. 3. Anomalies of the sea-surface salinity in E2-1–E2-8 compared to Target 2.
ocean were also used in E1-5 and E1-6, but their contribution
was very small, because the weight of the deep-ocean data
decreased relative to the surface-ocean data in proportion of
the number of data points. Among the other experiments (E12, E1-4, E1-7, and E1-8) only E1-2 failed completely, while
the other three were able to predict the direction of change of
the AMOC strength because of the deep-ocean data. Comparing it with E1-7 that had the same data locations, E1-2
still had a larger warm anomaly in the deep North Atlantic
that was poorly constrained by data with larger errors. The
warm water supported the relatively strong mixing.
For the experiments for Target 2, the warm deep water of
the reference state also helped to maintain the strong mixing. Without any salinity constraints, however, the surface
water became too light (too fresh), because there was less
evaporation with the colder SST and freshwater was also advected from the south (Fig. 3). This effect caused the overly
weak AMOC in E2-2, E2-5, and E2-7. Although the same
mechanism worked to some extent also in E2-1, strong warm
anomalies in the deep North Atlantic remained due to the
lack of deep-ocean data, which caused continuing strong
convection similar to the case of Target 1. By analogy with
E1-5 and E1-6, and because of the very small contribution of
the deep-ocean data, one might expect that E2-5 would have
a similar problem as E2-1, but the SST was adjusted in a
much larger area in E2-5 than in E2-1 so that more fresh surface water was created. The AMOC was weaker because the
excess of freshwater outweighed the effects of low abyssal
densities in the absence of deep-ocean data.
We further examined the mixed layer depth (MLD) and
the location of deep convection in the high-latitude North
Atlantic in some of the experiments (Figs. 4 and 6). Different AMOC strength during the LGM have been suggested to
be associated with a shift in the location of deep convection
(e.g., Rahmstorf, 1994; Ganopolski and Rahmstorf, 2001;
Oka et al., 2012). The reference state had its deepest convection site in the Labrador Sea, while Target 1 had one near
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Iceland. Although all four reconstructions shown in Fig. 4
shifted the convection sites roughly to the right place, the
Figure
3 not be recovered. In the experiments with a good
depth
could
AMOC strength estimate for Target 1 (e.g., E1-4), the MLD
shoaled from the reference state as for Target 1 (Fig. 4a).
Experiments that failed in reconstructing the weaker AMOC
strength had a deeper MLD (E1-1, 2, 6 in Fig. 4a). This
was consistent with an overly strong AMOC in the reconstructions; especially for the experiments with a very strong
AMOC strength (E1-1).
As before, the MLD of the state estimates was related
to the temperature in the deep ocean. While the temperature field at 1000 m depth for E1-4 was similar to the target
temperature (Fig. 4b), the deep ocean was too warm in the
other three experiments, especially in E1-1 and E1-6. Similarly, the deep-ocean salinity at 1000 m depth was too high
in the other experiments as compared to E1-4 (Fig. 4d). On
the other hand, the temperature field (Fig. 4c) and the salinity fields (Fig. 4e) at 3000 m clearly distinguished E1-4 and
E1-2 from E1-1 and E1-6. This was related by the vertical
distribution of the data in the North Atlantic Ocean (Fig. 5).
Because a relatively large number of deep-ocean data were
located around at 3000 m depth, the reconstructions at those
depths were greatly affected by whether the deep-ocean data
were used or not for the state estimation.
The availability of data also affected E1-7 and E1-8, because the difference between them was caused by different
temperature and salinity reconstructions in the ocean interior at depths shallower than 500 m, where there were almost no data points. This result emphasized the importance
of data at those depths, even though the convection of the
target could be roughly reconstructed from surface information. It was consistent with the sensitiveness of AMOC to the
temperature at those depths (Heimbach et al., 2011; Heslop
and Paul, 2012). Heslop and Paul (2012) showed that the
AMOC strength was more sensitive to ocean temperature at
depths shallower than 1000 m compared to the deeper ocean.
Geosci. Model Dev., 7, 419–432, 2014
426
T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
Target 1 - Ref.
E1-4 - Ref.
E1-2 - Ref.
E1-1 - Ref.
E1-6 - Ref.
2000 [m]
50 N
(a)
0
30 N
-2000
5 [K]
50 N
(b)
0
30 N
-5
3 [K]
50 N
(c)
0
30 N
-3
1 [psu]
50 N
(d)
0
30 N
-1
0.2 [psu]
50 N
(e)
0
30 N
60 w
30 w
60 w
30 w
60 w
30 w
60 w
30 w
60 w
30 w
-0.2
Figure 4
Fig. 4. Anomalies in Target 1, E1-4, E1-2, E1-1, and E1-6 compared to the reference state: the maximum monthly averaged mixed layer
depth (a), the temperature at the depth of 1000 m (b) and 3000 m (c), and the salinity at the depth of 1000 m (d) and 3000 m (e). In (a), the
deepest convection site is shown as a red ellipse for the reference state and as a blue ellipse for Target 1 and each experiment.
Geosci. Model Dev., 7, 419–432, 2014
0
Depth [m]
Huybers et al. (2007) also demonstrated that data in the ocean
interior is important for reliable circulation estimates. Along
with these studies our results explicitly suggested that there
are shortcomings in the vertical distribution of MARGO data
(Fig. 5).
For Target 2, experiments E2-6, which successfully reproduced the stronger AMOC, and E2-8 showed a similar MLD
anomaly with respect to the target (Fig. 6a; albeit the positive anomalies in E2-8 were too large, corresponding to the
overly high rate of overturning in this experiment). However,
in E2-7, the positive MLD anomaly was smaller, causing a
much weaker AMOC than in the target. As discussed above,
the sea-surface salinity (SSS) was very different for E2-7
compared to E2-6 and E2-8 (Fig. 6b). The low SSS of E27 caused low density of surface water which stabilized the
water column and reduced deep mixing.
The principal location of deep convection of Target 2 (to
the southeast of Iceland) was successfully predicted in every
experiment (i.e., irrespective of the AMOC strength). As for
Target 1, although the shifts in the location of deep convection were also observed in all experiments, only some experiments succeeded in predicting exactly the locations of the target. However, those experiments did not necessarily reconstruct the proper AMOC strength. These results suggested
that predicting the MLD was not equivalent to predicting the
location of deep convection. We note that the representation
0
-500
-500
-1000
-1000
-1500
-1500
-2000
-2000
-2500
-2500
-3000
-3000
-3500
-3500
-4000
-4000
-4500
-4500
-5000
0
5
10
15 20 40 60 80
-5000
The number of grid cells with data
Fig. 5. Vertical distribution of theFigure
data in5the North Atlantic Ocean.
The number of grid cells that contain any data in the domain illustrated in Fig. 4 is shown as a function of depth.
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T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
Target 2 - Ref.
E2-6 - Ref.
427
E2-8 - Ref.
E2-7 - Ref.
3000
50 N
(a)
0 [m]
30 N
-3000
-3
50 N
(b)
0 [ psu ]
30 N
60 w
30 w
60 w
30 w
60 w
30 w
60 w
3
30 w
Fig. 6. Anomalies in Target 2, E2-6, E2-8, and E2-7 compared to the reference state: the maximum monthly averaged mixed layer depth (a),
and the sea-surface salinity (b). In (a), the deepest convection site is shown as a red ellipse for the reference state and as a blue ellipse for
Target 2 and each experiment.
Target 3 - Ref.
The pseudo data with
MARGO errors - Ref.
E3-1 - Ref.
E3-2 - Ref.
E3-3 - Ref.
E4-2 - Ref.
E4-3 - Ref.
Figure 6
50 N
(a)
30 N
Target 4 - Ref.
The pseudo data with
MARGO errors - Ref.
E4-1 - Ref.
50 N
(b)
30 N
60 w
30 w
60 w
30 w
60 w
-4
30 w
0
[K]
60 w
30 w
60 w
30 w
4
Fig. 7. Anomalies of the sea-surface temperature compared to the reference state in Target 3, the pseudo-data with the MARGO errors, E3-1,
E3-2, and E3-3 (a), and Target 4, the pseudo-data, E4-1, E4-2, and E4-3 (b).
Figure 7
of the MLD may be affected by the low vertical resolution
of the model, but the targets and the model were sufficiently
similar (in fact the vertical resolution is the same) so that
the resolution did not affect our results. When fitting to real
proxy data, however, vertical resolution may become an issue
when data are mapped to model levels or MLD is estimated.
On the other hand, we emphasize that the coarse resolution
has the great advantage of low computational cost and relatively few degrees of freedom (especially given the apparently scarce data).
The shift of deep convection sites could be one factor that
complicated the reconstruction, because very different sinking locations represent non-linear “jumps" between the targets and the reference. Another difficulty for reconstruction
was that Targets 1 and 2 used entirely different parameterisations of mixing than the assimilation model (Table 2), which
meant that large model errors needed to be overcome. Large
model errors and non-linearities are anticipated when attempting to reconstruct the real LGM ocean, hence we deliberately chose such a diverse target for our tests. Other sources
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of non-linearity may be found in the sea-ice model. However, the reconstructed sea-ice distribution (not shown) was
getting better with more (or better) data even if the AMOC
was not. This implied that the sea ice can be reconstructed
more straightforwardly than the AMOC and can be interpreted more easily.
We did not find a coherent surface fingerprint of the
AMOC (e.g., Zhang, 2008) in our simulations. In comparison
to Zhang (2008), the large difference regarding the timescale
of phenomena need to be taken into account. Zhang (2008)
dealt with decadal variability, while our focus was on a quasisteady state including the deep ocean. Therefore, information
from the deep ocean was required to constrain the model.
Otherwise, a very long time period of assimilation would be
required so that the information at the surface could penetrate
the entire ocean.
4.2
Outlook for reconstructions with a better first guess
The experiments for Targets 1 and 2 demonstrated that the
targets were not consistently reconstructed, even when we
Geosci. Model Dev., 7, 419–432, 2014
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T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
(a)
(b)
(c)
Target 3 - Ref.
E3-3 - Ref.
Target 3 - Ref.
E3-3 - Ref.
Target 3 - Ref.
E3-3 - Ref.
Target 4 - Ref.
E4-3 - Ref.
Target 4 - Ref.
E4-3 - Ref.
Target 4 - Ref.
E4-3 - Ref.
50 N
30 N
50 N
30 N
60 w
30 w
-10-5
60 w
0
[kg/m2/s]
30 w
10-5
60 w
60 w
30 w
-0.5
30 w
0.5
0
[K]
60 w
30 w
-0.7
60 w
0
[ psu ]
30 w
0.7
Fig. 8. Anomalies in Target 3, E3-3, Target 4, and E4-3 compared to the reference state: the freshwater flux (a), the sea-surface temperature
Figure 8
(b), and the sea-surface salinity (c).
assumed very optimistic conditions for data quality and
quantity, and in spite of the fact that the atmospheric state that
was responsible for the differences was part of the control
vector and was adjusted in the optimization process. The results suggested that it was difficult with the available data to
guide the model properly towards targets that were very different from the first guess. Providing prior knowledge, that is,
a better first guess may alleviate the problem as illustrated in
the following. We remind the reader that for Targets 3 and 4
internal friction parameters were modified that were not part
of the control vector. This choice introduced a model bias
that could not be adjusted by the assimilation in the “correct” way, a situation that is definitely encountered in every
state estimation exercise.
In all three pairs of experiments for Target 3 and 4, the
AMOC corrections relative to the first guess had the correct
sign. However, there were large differences between the temperature fields of those experiments (Fig. 7). The SST fields
of E3-1 and E4-1 were very different from those of their respective target fields (third column in Fig. 7), because the
noisy pseudo-data to which the model adjusted was also very
different from the original targets due to the large associated
uncertainty (second column of Fig. 7). The experiments with
very small data errors and accordingly reduced noise in the
data (E3-2 and E4-2) did not have this problem and hence
the agreement between model and target was much better
(fourth column in Fig. 7). The experiments with fewer control variables (E3-3 and E4-3, fifth column in Fig. 7) avoided
the overfitting to data of poor quality (i.e., data with a low
signal-to-noise ratio) by using a less flexible model that restricted the departure from the first guess. This amounted to
providing even more prior knowledge, as we assumed implicitly that air temperature, humidity and precipitation were
well known.
The good NADW reconstruction in E3-3 and E4-3 was
connected to the modified freshwater flux in the high-latitude
North Atlantic (Fig. 8a). Note that the surface freshwater
flux was not part of the control vector in this case. Instead, changes in the surface freshwater flux were caused
Geosci. Model Dev., 7, 419–432, 2014
by adjustments of the incoming radiative fluxes that led to
changes in temperature and thus to changes in evaporation.
For E3-3, this positive freshwater flux anomaly, consistent
with the difference in freshwater flux between the target
and the reference state, stabilized the water column and inhibited NADW formation. In contrast, a negative freshwater anomaly destabilized the water column and led to increased NADW formation in E4-3. The difference between
the target and the reference state was also generally negative.
Similar patterns of the SST and freshwater flux anomalies
(Fig. 8b) show that the evaporation rate was strongly controlled by the SST. Consequently, adjusting the SST in the
high-latitude North Atlantic to the target values led to a successful reconstruction of the AMOC. By way of this freshwater flux anomaly, the SST adjustment roughly reproduced
the sea-surface salinity (SSS) without using SSS as a constraint (Fig. 8c), because the SSS anomalies in the targets
were also, in part, caused by the change in evaporation due
to SST changes.
5
Conclusions
Can we use sparse paleoceanographic proxy data to reconstruct the strength of the AMOC during the LGM, using the
MITgcm? Our answer is twofold: (1) with a sufficiently good
first guess, one can indeed reconstruct the strength of the
AMOC from sparse sea-surface temperature data such as the
existing MARGO data set. (2) Otherwise, however, it is important to obtain data from the deep-ocean and salinity data.
Although naturally small data uncertainties would help, sampling data at adequate locations seems to be a crucial factor
for proper estimation of the AMOC change.
Although a good first guess with a reasonable representation of past hydrographic conditions would be very helpful,
finding such a first guess is essentially part of the state estimation that we are aiming for. A further problem to be addressed is overfitting the model to data with a poor signal-tonoise ratio. Both issues could be addressed by adding either
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T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
more data (once available) or prior knowledge. One way of
adding prior knowledge would be re-considering the control
parameter space and adding more model physics.
In particular, the surface fluxes could be more physically
constrained by coupling the ocean model to an atmospheric
model, for example, an energy–moisture balance model (e.g.,
Ashkenazy et al., 2013). An advantage of this would be that
one would be able to remove a systematic bias (e.g., globally lower temperature) before the spatial patterns of smaller
scale are adjusted according to the local paleoceanographic
reconstruction based, for example, on MARGO. It should be
noted that Targets 1 and 2 were more difficult to reconstruct
than 3 and 4 because they had not only different spatial patterns (of temperature and salinity) but also a much different global mean temperature. After we remove the systematic bias of mean temperature for LGM as much as possible,
the adjustment of local patterns would become easier. Using such a coupled model could enable more control over the
global SST by changing, for example, the CO2 content of
the atmosphere, the planetary albedo or the atmospheric heat
transport efficiency (Paul and Losch, 2012). Note that the
CO2 content and the ice-sheet distribution during the LGM
are comparatively well known. At the same time, one could
decrease the degrees of freedom of the model by reducing
the control variables. Alternatively, one could imagine using
the results of LGM simulations with different coupled GCMs
(e.g., the PMIP project (Otto-Bliesner et al., 2007)) to improve the initial guess. A more direct but less physical way
to add prior knowledge is to enforce smoothness through a
Laplacian of some physical quantity (e.g., surface temperature) or to penalize deviations from the first guess; this, however, is only possible at the cost of introducing more biases.
From the viewpoint of paleo-ocean data, proxies for water
masses (δ 13 C), circulation rates (radiocarbon, 231 Pa/230 Th
ratios) and density (δ 18 O, possibly in combination with a
temperature proxy such as Mg/Ca) may also provide useful
additional constraints. This point, as well as the importance
of smaller data uncertainty, is also suggested by Huybers
et al. (2007). However, it should be noted that a simplified
model such as the one used by Huybers et al. (2007) involves
uncertainty due to a subjectively assumed level of no motion
(see also Burke et al., 2011). Besides, the model domain of
Huybers et al. (2007) excludes depths shallower than 1 km.
Therefore, they do not discuss the effectiveness of surface
data that are the main components of the currently available
data archive, such as the MARGO data. Our results showed
how important surface data are for predicting the convection.
The integration period in the state estimates (20 years)
was chosen for purely economical reasons, and our simulations were not long enough to guarantee stable steadystate solutions. Cost function terms that penalize inter-annual
variations could be used to enforce a steady state. Alternatively, longer integration periods for each iteration would
be required. Paleo-data from regions where Antarctic Bottom Water is formed may become more important on longer
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429
timescales, because the relative densities of the North Atlantic and Southern Ocean source waters are expected to play
a larger role for the meridional overturning circulation in the
steady-state problem (e.g., Paul and Schäfer-Neth, 2003; Weber et al., 2007). However, in our experiments the adjustment
of the AMOC was very fast; it typically occurred in the first
10 years of a 20-year experiment. This was also plausible
from the timescale of sensitivity propagation of the AMOC,
shown by Heimbach et al. (2011). Therefore, the time interval was assumed to be sufficient for estimating the change of
the AMOC strength.
Acknowledgements. This research was funded by the DFGResearch Center/Center of Excellence MARUM – “The Ocean in
the Earth System”. We thank two anonymous reviewers for their
insightful review and helpful comments. The adjoint model was
generated with TAF (Giering and Kaminski, 1998).
Edited by: J. Annan
References
Adcroft, A., Campin, J.-M., Hill, C., and Marshall, J.: Implementation of an Atmosphere Ocean General Circulation Model on
the Expanded Spherical Cube, Mon. Weather Rev., 132, 2845,
doi:10.1175/MWR2823.1, 2004.
Adkins, J. F., McIntyre, K., and Schrag, D. P.: The Salinity, Temperature, and δ 18 O of the Glacial Deep Ocean, Science, 298, 1769–
1773, doi:10.1126/science.1076252, 2002.
Archer, D.: Modeling the calcite Lysocline, J. Geophys. Res., 96,
17037, doi:10.1029/91JC01812, 1991.
Archer, D., Winguth, A., Lea, D., and Mahowald, N.: What caused
the glacial/interglacial atmospheric pCO2 cycles?, Rev. Geophys., 38, 159–189, doi:10.1029/1999RG000066, 2000.
Ashkenazy, Y., Losch, M., Gildor, H., Mirzayof, D., and Tziperman, E.: Multiple sea-ice states and abrupt MOC transitions in a
general circulation ocean model, Clim. Dyanm., 40, 1803–1817,
doi:10.1007/s00382-012-1546-2, 2013.
Burke, A., Marchal, O., Bradtmiller, L. I., McManus, J. F., and
François, R.: Application of an inverse method to interpret
231 Pa/230 Th observations from marine sediments, Paleoceanography, 26, PA1212, doi:10.1029/2010PA002022, 2011.
Clark, P. U., Marshall, S. J., Clarke, G. K. C., Hostetler, S. W., Licciardi, J. M., and Teller, J. T.: Freshwater Forcing of Abrupt Climate Change During the Last Glaciation, Science, 293, 283–287,
doi:10.1126/science.1062517, 2001.
Curry, W. B. and Oppo, D. W.: Glacial water mass geometry and the
distribution of δ 13 C of 6CO2 in the western Atlantic Ocean, Paleoceanography, 20, PA1017, doi:10.1029/2004PA001021, 2005.
Dail, H. J.: Atlantic Ocean Circulation at the Last Glacial Maximum: Inferences from Data and Models, Ph.D. thesis, Massachusetts Institute of Technology, Massachusetts and the Woods
Hole Oceanographic Institution, Massachusetts, 2012.
Epica Community Members, Barbante, C., Barnola, J.-M., Becagli,
S., Beer, J., Bigler, M., Boutron, C., Blunier, T., Castellano, E.,
Cattani, O., Chappellaz, J., Dahl-Jensen, D., Debret, M., Delmonte, B., Dick, D., Falourd, S., Faria, S., Federer, U., Fischer,
Geosci. Model Dev., 7, 419–432, 2014
430
T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
H., Freitag, J., Frenzel, A., Fritzsche, D., Fundel, F., Gabrielli,
P., Gaspari, V., Gersonde, R., Graf, W., Grigoriev, D., Hamann,
I., Hansson, M., Hoffmann, G., Hutterli, M. A., Huybrechts, P.,
Isaksson, E., Johnsen, S., Jouzel, J., Kaczmarska, M., Karlin, T.,
Kaufmann, P., Kipfstuhl, S., Kohno, M., Lambert, F., Lambrecht,
A., Lambrecht, A., Landais, A., Lawer, G., Leuenberger, M., Littot, G., Loulergue, L., Lüthi, D., Maggi, V., Marino, F., MassonDelmotte, V., Meyer, H., Miller, H., Mulvaney, R., Narcisi, B.,
Oerlemans, J., Oerter, H., Parrenin, F., Petit, J.-R., Raisbeck, G.,
Raynaud, D., Röthlisberger, R., Ruth, U., Rybak, O., Severi, M.,
Schmitt, J., Schwander, J., Siegenthaler, U., Siggaard-Andersen,
M.-L., Spahni, R., Steffensen, J. P., Stenni, B., Stocker, T. F., Tison, J.-L., Traversi, R., Udisti, R., Valero-Delgado, F., van den
Broeke, M. R., van de Wal, R. S. W., Wagenbach, D., Wegner, A., Weiler, K., Wilhelms, F., Winther, J.-G., and Wolff, E.:
One-to-one coupling of glacial climate variability in Greenland
and Antarctica, Nature, 444, 195–198, doi:10.1038/nature05301,
2006.
Errico, R. M.: What Is an Adjoint Model?, B. Am.
Meteorol.
Soc.,
78,
2577–2591,
doi:10.1175/15200477(1997)078<2577:WIAAM>2.0.CO;2, 1997.
Fischer, G. and Wefer, G.: Use of Proxies in Paleoceanography:
Examples from the South Atlantic, Springer Berlin Heidelberg,
available at: http://books.google.de/books?id=e8lIokyIG7gC,
1999.
Ganopolski, A. and Rahmstorf, S.: Rapid changes of glacial climate simulated in a coupled climate model, Nature, 409, 153–
158, doi:10.1038/35051500, 2001.
Gebbie, G. and Huybers, P.: Meridional circulation during
the Last Glacial Maximum explored through a combination of South Atlantic δ 18 O observations and a geostrophic
inverse model, Geochem. Geophy. Geosys., 7, Q11N07,
doi:10.1029/2006GC001383, 2006.
Gent, P. R. and McWilliams, J. C.: Isopycnal Mixing in
Ocean Circulation Models, J. Phys. Oceanogr., 20, 150–160,
doi:10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2,
1990.
Gent, P. R., Willebrand, J., McDougall, T. J., and McWilliams,
J. C.: Parameterizing Eddy-Induced Tracer Transports in
Ocean Circulation Models, J. Phys. Oceanogr., 25, 463–474,
doi:10.1175/1520-0485(1995)025<0463:PEITTI>2.0.CO;2,
1995.
Giering, R. and Kaminski, T.: Recipes for adjoint code
construction, ACM Trans. Math. Softw., 24, 437–474,
doi:10.1145/293686.293695, 1998.
Gilbert, J. C. and Lemaréchal, C.: Some numerical experiments
with variable-storage quasi-Newton algorithms, Math. Prog., 45,
407–435, doi:10.1007/BF01589113, 1989.
Gildor, H. and Tziperman, E.: Physical mechanisms behind biogeochemical glacial-interglacial CO 2 variations, Geophys. Res.
Lett., 28, 2421–2424, doi:10.1029/2000GL012571, 2001.
Griffies, S. M., Biastoch, A., Böning, C., Bryan, F., Danabasoglu,
G., Chassignet, E. P., England, M. H., Gerdes, R., Haak, H.,
Hallberg, R. W., Hazeleger, W., Jungclaus, J., Large, W. G.,
Madec, G., Pirani, A., Samuels, B. L., Scheinert, M., Gupta,
A. S., Severijns, C. A., Simmons, H. L., Treguier, A. M.,
Winton, M., Yeager, S., and Yin, J.: Coordinated Ocean-ice
Reference Experiments (COREs), Ocean Model., 26, 1–46,
doi:10.1016/j.ocemod.2008.08.007, 2009.
Geosci. Model Dev., 7, 419–432, 2014
Heimbach, P., Hill, C., and Giering, R.: An efficient exact adjoint of
the parallel MIT general circulation model, generated via automatic differentiation, Future Gener. Comput. Sy., 21, 1356–1371,
doi:10.1016/j.future.2004.11.010, 2005.
Heimbach, P., Wunsch, C., Ponte, R. M., Forget, G., Hill, C.,
and Utke, J.: Timescales and regions of the sensitivity of
Atlantic meridional volume and heat transport: Toward observing system design, Deep Sea Res.-Pt. II, 58, 1858–1879,
doi:10.1016/j.dsr2.2010.10.065, 2011.
Heslop, D. and Paul, A.: Fingerprinting of the Atlantic meridional overturning circulation in climate models to aid in the
design of proxy investigations, Clim. Dynam., 38, 1047–1064,
doi:10.1007/s00382-011-1042-0, 2012.
Huybers, P., Gebbie, G., and Marchal, O.: Can Paleoceanographic Tracers Constrain Meridional Circulation Rates?, J.
Phys. Oceanogr., 37, 394, doi:10.1175/JPO3018.1, 2007.
Keigwin, L. D. and Lehman, S. J.: Deep circulation change
linked to HEINRICH Event 1 and Younger Dryas in a middepth North Atlantic Core, Paleoceanography, 9, 185–194,
doi:10.1029/94PA00032, 1994.
Kurahashi-Nakamura, T., Abe-Ouchi, A., and Yamanaka, Y.: Effects of physical changes in the ocean on the atmospheric
pCO2 : glacial-interglacial cycles, Clim. Dynam., 35, 713–719,
doi:10.1007/s00382-009-0609-5, 2010.
Legrand, P. and Wunsch, C.: Constraints from paleotracer data on
the North Atlantic circulation during the Last Glacial Maximum,
Paleoceanography, 10, 1011–1045, doi:10.1029/95PA01455,
1995.
Levitus, S. E.: Climatological atlas of the world ocean, NOAA Professional Paper 13, US Government Printing Office, Washington
DC, 1982.
Lippold, J., Luo, Y., Francois, R., Allen, S. E., Gherardi, J.,
Pichat, S., Hickey, B., and Schulz, H.: Strength and geometry
of the glacial Atlantic Meridional Overturning Circulation, Nat.
Geosci., 5, 813–816, doi:10.1038/ngeo1608, 2012.
Losch, M., Menemenlis, D., Campin, J.-M., Heimbach, P., and Hill,
C.: On the formulation of sea-ice models. Part 1: Effects of
different solver implementations and parameterizations, Ocean
Model., 33, 129–144, doi:10.1016/j.ocemod.2009.12.008, 2010.
Lynch-Stieglitz, J., Curry, W. B., and Slowey, N.: A geostrophic
transport estimate for the Florida Current from the oxygen isotope composition of benthic foraminifera, Paleoceanography, 14,
360–373, doi:10.1029/1999PA900001, 1999a.
Lynch-Stieglitz, J., Curry, W. B., and Slowey, N.: Weaker Gulf
Stream in the Florida Straits during the Last Glacial Maximum,
Nature, 402, 644–648, doi:10.1038/45204, 1999b.
Lynch-Stieglitz, J., Curry, W. B., Oppo, D. W., Ninneman, U. S.,
Charles, C. D., and Munson, J.: Meridional overturning circulation in the South Atlantic at the last glacial maximum, Geochem.
Geophy. Geosys., 7, Q10N03, doi:10.1029/2005GC001226,
2006.
Manighetti, B. and McCave, I. N.: Late Glacial and Holocene
palaeocurrents around Rockall Bank, NE Atlantic Ocean, Paleoceanography, 10, 611–626, doi:10.1029/94PA03059, 1995.
MARGO Project Members, Waelbroeck, C., Paul, A., Kucera, M.,
Rosell-Melé, A., Weinelt, M., Schneider, R., Mix, A. C., Abelmann, A., Armand, L., Bard, E., Barker, S., Barrows, T. T., Benway, H., Cacho, I., Chen, M.-T., Cortijo, E., Crosta, X., de Vernal, A., Dokken, T., Duprat, J., Elderfield, H., Eynaud, F., Ger-
www.geosci-model-dev.net/7/419/2014/
T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
sonde, R., Hayes, A., Henry, M., Hillaire-Marcel, C., Huang, C.C., Jansen, E., Juggins, S., Kallel, N., Kiefer, T., Kienast, M.,
Labeyrie, L., Leclaire, H., Londeix, L., Mangin, S., Matthiessen,
J., Marret, F., Meland, M., Morey, A. E., Mulitza, S., Pflaumann,
U., Pisias, N. G., Radi, T., Rochon, A., Rohling, E. J., Sbaffi,
L., Schäfer-Neth, C., Solignac, S., Spero, H., Tachikawa, K., and
Turon, J.-L.: Constraints on the magnitude and patterns of ocean
cooling at the Last Glacial Maximum, Nat. Geosci., 2, 127–132,
doi:10.1038/ngeo411, 2009.
Marshall, J., Adcroft, A., Hill, C., Perelman, L., and Heisey, C.: A
finite-volume, incompressible Navier Stokes model for studies
of the ocean on parallel computers, J. Geophys. Res., 102, 5753–
5766, doi:10.1029/96JC02775, 1997.
McCave, I. N. and Hall, I. R.: Size sorting in marine
muds: Processes, pitfalls, and prospects for paleoflowspeed proxies, Geochem. Geophy. Geosys., 7, Q10N05,
doi:10.1029/2006GC001284, 2006.
McCave, I. N., Manighetti, B., and Beveridge, N. A. S.: Circulation
in the glacial North Atlantic inferred from grain-size measurements, Nature, 374, 149–152, doi:10.1038/374149a0, 1995.
McManus, J. F., Francois, R., Gherardi, J.-M., Keigwin, L. D.,
and Brown-Leger, S.: Collapse and rapid resumption of Atlantic
meridional circulation linked to deglacial climate changes, Nature, 428, 834–837, doi:10.1038/nature02494, 2004.
Mix, A., Bard, E., and Schneider, R.: Environmental processes of
the ice age: land, oceans, glaciers (EPILOG), Quaternary Sci.
Rev., 20, 627–657, doi:10.1016/S0277-3791(00)00145-1, 2001.
Negre, C., Zahn, R., Thomas, A. L., Masqué, P., Henderson, G. M.,
Martínez-Méndez, G., Hall, I. R., and Mas, J. L.: Reversed flow
of Atlantic deep water during the Last Glacial Maximum, Nature,
468, 84–89, doi:10.1038/nature09508, 2010.
Oka, A., Hasumi, H., and Abe-Ouchi, A.: The thermal threshold of
the Atlantic meridional overturning circulation and its control by
wind stress forcing during glacial climate, Geophys. Res. Lett.,
39, L09709, doi:10.1029/2012GL051421, 2012.
Otto-Bliesner, B. L., Hewitt, C. D., Marchitto, T. M., Brady, E.,
Abe-Ouchi, A., Crucifix, M., Murakami, S., and Weber, S. L.:
Last Glacial Maximum ocean thermohaline circulation: PMIP2
model intercomparisons and data constraints, Geophys. Res.
Lett., 34, L12706, doi:10.1029/2007GL029475, 2007.
Paul, A. and Losch, M.: Perspectives of parameter and state estimation in paleoclimatology, in: Climate Change, Proceedings of
the Milutin Milankovitch 130th Anniversary Symposium, Part
2, edited by: Berger, A., Mesinger, F., and Šijački, D., 93–105,
Springer, Heidelberg, 2012.
Paul, A. and Mulitza, S.: Challenges to Understanding Ocean Circulation During the Last Glacial Maximum, EOS Transactions,
90, 169–169, doi:10.1029/2009EO190004, 2009.
Paul, A. and Schäfer-Neth, C.: Modeling the water masses of the
Atlantic Ocean at the Last Glacial Maximum, Paleoceanography,
18, 1058, doi:10.1029/2002PA000783, 2003.
Paul, A. and Schäfer-Neth, C.: How to combine sparse proxy data
and coupled climate models, Quaternary Sci. Rev., 24, 1095–
1107, doi:10.1016/j.quascirev.2004.05.010, 2005.
Piotrowski, A. M., Goldstein, S. L., Hemming, S. R., and Fairbanks, R. G.: Temporal Relationships of Carbon Cycling and
Ocean Circulation at Glacial Boundaries, Science, 307, 1933–
1938, doi:10.1126/science.1104883, 2005.
www.geosci-model-dev.net/7/419/2014/
431
Rahmstorf, S.: Rapid climate transitions in a coupled oceanatmosphere model, Nature, 372, 82–85, doi:10.1038/372082a0,
1994.
Redi, M. H.: Oceanic Isopycnal Mixing by Coordinate Rotation, J. Phys. Oceanogr., 12, 1154–1158, doi:10.1175/15200485(1982)012<1154:OIMBCR>2.0.CO;2, 1982.
Rohling, E. J.: Paleosalinity: confidence limits and future applications, Marine Geology, 163, 1–11, doi:10.1016/S00253227(99)00097-3, 2000.
Rutberg, R. L. and Peacock, S. L.: High-latitude forcing
of interior ocean δ 13 C, Paleoceanography, 21, PA2012,
doi:10.1029/2005PA001226, 2006.
Schmidt, G. A.: Error analysis of paleosalinity calculations, Paleoceanography, 14, 422–429, doi:10.1029/1999PA900008, 1999.
Schmittner, A., Urban, N. M., Shakun, J. D., Mahowald, N. M.,
Clark, P. U., Bartlein, P. J., Mix, A. C., and Rosell-Melé, A.:
Climate Sensitivity Estimated from Temperature Reconstructions of the Last Glacial Maximum, Science, 334, 1385–1388,
doi:10.1126/science.1203513, 2011.
Schulz, M., Seidov, D., Sarnthein, M., and Stattegger, K.: Modeling ocean-atmosphere carbon budgets during the Last Glacial
Maximum-Heinrich 1 meltwater event-Bølling transition, International J. Earth Sci., 90, 412–425, doi:10.1007/s005310000136,
2001.
Solomon, S., Dahe, Q., and Manning, M.: Technical Summary, in:
Climate Change 2007, Contribution of Working Group I to the
Fourth Assessment Report of the Intergovernmental Panel on
Climate Change, edited by: Solomon, S., Qin, D., Manning, M.,
Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., and Miller, H.
L., 19–91, Cambridge Univ. Press, Cambridge, 2007.
Srokosz, M., Baringer, M., Bryden, H., Cunningham, S., Delworth,
T., Lozier, S., Marotzke, J., and Sutton, R.: Past, Present, and Future Changes in the Atlantic Meridional Overturning Circulation,
B. Am. Meteorol. Soc., 93, 1663–1676, doi:10.1175/BAMS-D11-00151.1, 2012.
Stocker, T. F. and Johnsen, S. J.: A minimum thermodynamic
model for the bipolar seesaw, Paleoceanography, 18, 1087,
doi:10.1029/2003PA000920, 2003.
Visbeck, M., Marshall, J., Haine, T., and Spall, M.: Specification of
eddy transfer coefficients in coarse-resolution ocean circulation
models, J. Phys. Oceanogr., 27, 381–401, 1997.
Weber, S. L., Drijfhout, S. S., Abe-Ouchi, A., Crucifix, M., Eby, M.,
Ganopolski, A., Murakami, S., Otto-Bliesner, B., and Peltier, W.
R.: The modern and glacial overturning circulation in the Atlantic
ocean in PMIP coupled model simulations, Clim. Past, 3, 51–64,
doi:10.5194/cp-3-51-2007, 2007.
Winguth, A. M. E., Archer, D., Duplessy, J.-C., Maier-Reimer, E.,
and Mikolajewicz, U.: Sensitivity of paleonutrient tracer distributions and deep-sea circulation to glacial boundary conditions,
Paleoceanography, 14, 304–323, doi:10.1029/1999PA900002,
1999.
Winguth, A. M. E., Archer, D., Maier-Reimer, E., and Mikolajewicz, U.: Paleonutrient data analysis of the glacial Atlantic using an adjoint ocean general circulation model, Washington DC
American Geophysical Union Geophysical Monograph Series,
114, 171–183, doi:10.1029/GM114p0171, 2000.
Wunsch, C.: The Ocean Circulation Inverse Problem, Cambridge
University Press, Cambridge, 1996.
Geosci. Model Dev., 7, 419–432, 2014
432
T. Kurahashi-Nakamura et al.: Ocean reconstruction from sparse data
Wunsch, C.: Discrete Inverse and State Estimation Problems, Cambridge University Press, Cambridge, doi:10.2277/0521854245,
2006.
Yu, E.-F., Francois, R., and Bacon, M. P.: Similar rates of modern
and last-glacial ocean thermohaline circulation inferred from radiochemical data, Nature, 379, 689–694, doi:10.1038/379689a0,
1996.
Geosci. Model Dev., 7, 419–432, 2014
Zhang, R.: Coherent surface-subsurface fingerprint of the Atlantic
meridional overturning circulation, Geophys. Res. Lett., 35,
L20705, doi:10.1029/2008GL035463, 2008.
www.geosci-model-dev.net/7/419/2014/
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