An eddy-permitting numerical ocean model is used to test to what extent the Atlantic meridional overturning circulation (MOC) can be reconstructed from sea water densities at the ocean margins. By gradually reducing the number of locations where the densities are known and by adding systematic and random errors comparable to those expected in paleoreconstructions of sea water densities, we test if a reliable picture of the MOC can still be obtained. Our results show that even with only 0.07% of the boundary densities the mean state of the MOC as well as its variability can be reconstructed. The addition of a systematic error results in an overestimation or underestimation of the meridional transport. With a random error similar to the one expected for paleoestimates of the density the mean state of the MOC can still be reproduced, especially north of 40°N. However, the random noise largely masks the relatively modest MOC variability observed in the model run. For both systematic and random noise in the density field there is a larger sensitivity for MOC reconstructions the closer a location is from the equator. For a measuring campaign that aims to infer past states of the Atlantic MOC on the basis of boundary densities, the present study suggests that the best strategy is to collect data that allow estimation of the basin-wide vertical density structure between 40°N and 50°N. Information from only a few latitudes is sufficient for a reasonable representation of the mean MOC state.
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The variability of the Atlantic meridional overturning circulation (MOC) is a key element in understanding the past, present and future climate. Currently the Atlantic MOC transports about 1PW (1015W) of heat northward [Trenberth and Caron, 2001], thus contributing to Europe's characteristic mild climate. Paleoclimatic archives suggest that in the past the MOC has undergone large changes [Heinrich, 1988; Dansgaard et al., 1993]. During the last ice age abrupt changes associated with temperature variations of more than 10°C over Greenland were not uncommon [e.g., Lang et al., 1999] and one plausible mechanism is a changing strength of the MOC [e.g., Broecker et al., 1992]. Even though this view is widely accepted only little is known about the actual strength of the MOC and the amplitude of its variability during these past climatic events. This also holds true for the modern ocean. Despite many observations of MOC components such as the transport across the Florida Straits [Baringer and Larsen, 2001], the deep western boundary current [Lee et al., 1996] or the North Atlantic current system [e.g., Dickson and Brown, 1994] our knowledge about the variability of the MOC is incomplete. Inverse calculations provide estimates of cross basin transports [e.g., Ganachaud and Wunsch, 2000] but little can be said about the variability. On the basis of geostrophic estimates and Ekman transport, Talley et al.  provide a picture of the mean meridional overturning cell in the Atlantic, Pacific and Indian oceans, but the existing picture of MOC variability is largely based on numerical simulations [Delworth et al., 1993; Delworth and Dixon, 2000; Cubasch et al., 2001]. A recent study of Bryden et al.  indicates that the Atlantic MOC might have decreased by 30% since 1957. Whether this reduction is part of a long-term trend or of an oscillation is the subject of ongoing research. The recent deployment of an observing system for the Atlantic MOC at 26°N [Marotzke et al., 2002] means that much more knowledge about the short term variability, and the vertical structure of the MOC will become available very soon.
Most estimates of the past MOC are based on water mass properties such as δ13C, Cd/Ca [e.g., Duplessy et al., 1988; Curry et al., 1988; Curry and Oppo, 2005]. While these tracers give valuable clues about the behavior of the MOC in the past they do not provide direct estimates of the strength and structure of the meridional flow. Often, an observed tracer distribution obtained from measurements on sea sediments is consistent with very different circulation patterns [LeGrand and Wunsch, 1995]. A different approach based on a nonpassive tracer has been used by Lynch-Stieglitz et al. [1999a], who found a decrease of the vertical flow shear in the Florida Straits during the Last Glacial Maximum based on zonal density gradients obtained from δ18O in the calcite shells of foraminifera. The same approach was proposed to infer the cross basin transport [Lynch-Stieglitz, 2001]. However, it remains unclear to what extent the shear can be used to infer the MOC. For example it is difficult to say if the decrease in the shear found by Lynch-Stieglitz et al. [1999a] in the Florida Straits is linked to a weakening of the total transport through the Florida Straits and of the MOC. The reason for this is that nothing can be said about the strength of the barotropic (depth-averaged) flow. A smaller shear may have coincided with a stronger barotropic flow which leaves the total transport unchanged.
The aim of the present paper is to use a numerical model to investigate to what extent the past MOC might be reconstructed from measurements of sea water densities at the ocean margins and what sampling strategy should be used. A previous modeling study has shown that the total density field at ocean margins reflects main spatial and temporal features of the full MOC cell [Hirschi and Marotzke, 2006]. The robustness of these results is tested here by reducing the number of “measurements” and by including errors in the density field that simulate the errors one can expect in density reconstructions obtained from δ18O in the calcite shells of foraminifera.
The method used for the study is described in section 2, and the results are presented in section 3. A brief discussion and conclusions are given in sections 4 and 5.
2. Method and Experiments
This study is based on results from OCCAM an eddy-permitting ocean general circulation model described by Webb  and Marsh et al. [2005a, 2005b]. The version of OCCAM used here simulates the global ocean circulation between 1985 and 2003. The horizontal resolution is 1/4° and the vertical is divided into 66 vertical levels. The forcing consists of six-hourly NCEP fields for wind, heat and evaporation-precipitation. We only consider an Atlantic domain extending from the equator to 70°N and from 100°W to 40°E. The Atlantic domain has 277 and 561 grid cells in the meridional and zonal directions, respectively. In the following the indices j = 1, …, 277, i = 1, …, 561 and k = 1, …, 66 are used to denote the number of grid cells in y (latitude), x (longitude) and z (depth) directions, respectively.
Hirschi and Marotzke  assumed the complete density difference field Δρ(y, z) = ρe(y, z) − ρw(y, z) between the eastern and western margins to be known, where ρe and ρw are the densities at the eastern and western margins, respectively. Here we reduce the amount of density information used to estimate the meridional transports by assuming that Δρ is only known for the indices
where js + nΔj and ks + mΔk are the indices of the northernmost latitude and greatest depth where data are assumed to be known. The data density of Δρ can be reduced by increasing the values for Δj and Δk. For each value of Δρ there is a corresponding pair of boundary densities ρe and ρw. To simulate inaccuracies found in sea water densities obtained from measurements (CTD, sea sediments) a systematic or random error δρ is added to the boundary densities:
A linear interpolation is used in the vertical to fill the gaps between the depth levels k′ and k′ + Δk at which the density difference is known:
The zonal density differences Δ = e − w can now be used to estimate the meridional transport at each latitude y′. The method used in this study the same as that used by Hirschi and Marotzke , where the meridional transport ψtw related to zonal density gradients is computed according to
where v′ is the meridional velocity component related to zonal density differences and where xe and xw are the eastern and western limits of the basin, respectively. The velocity is a correction that ensures that there is no net mass transport across the section. The velocity v′ is based on the thermal wind relation and is defined as
where g, f, ρ*, L and H are the Earth acceleration, the Coriolis parameter, a reference density, the zonal basin width and the ocean depth, respectively. A linear interpolation of the transport ψtw is used to fill the gaps between the latitudes y′ where the transport is estimated from the zonal density difference:
where dy = yj′+Δj − yj′. According to equation (3), a density-based estimate of the meridional overturning circulation can be given between the southernmost and northernmost latitudes where “measurements” are available. On the basis of three sets of reconstructions we test the effects of reducing the amount of data used for the MOC estimates and of introducing systematic and random errors in the density values used in the calculations. An overview of all experiments is given in Table 1.
Table 1. Overview of Experiments Designed to Test if the Main Features of the MOC Can Be Captured by a Small Fraction of the Complete Boundary Density Fielda
Depth Range, m
% Margin Data
δρ, kg m−3
The second and third columns indicate how many latitudes or depths are used for the reconstructions (e.g., Δj = 5, Δk = 5 means that every fifth latitude and every fifth depth is used). The number in parentheses in the second column is the meridional spacing in ° latitude. For the depths the vertical spacing increases exponentially with depth; e.g., for the reconstructions R0C, R1A-R1C, and R2A-R2D, every fifth depth means that data are taken at 315 m, 545 m, 930 m, and 1505 m. The depth range indicates between what depths density data are “collected” at the margins. The percentage of the margin data quantifies by how much we have thinned out the full density field at the margins. Both the impact of systematic and random noise in the density field is tested in R2A-R2D. For the systematic error in R2A we assume that there is a change from σ(δ18O)atl to σ(δ18O)pac (see main text for details). For the random errors in R2B-R2D the numbers are the standard deviations of the noise fields δρ added to the densities at the margins.
The first set of reconstructions R0A-R0C allows a comparison between an MOC estimate based on the full density field (R0A) and two cases where the data are thinned out both in the meridional and vertical directions (R0B, R0C). For the reconstruction R0B we assume that density data are available between 300 and 4700 m, which corresponds to the depth range for which paleoestimates of seawater densities could be obtained in the real ocean. In general it is difficult to reconstruct paleodensities in the top 300 m and 4700 m corresponds to the carbon compensation depth in the Atlantic ocean, a depth below which the calcite shells of foraminifera needed for paleoestimates of density are not preserved. The depth range is further restricted to 300–2000 m for the reconstruction R0C on the basis of the assumption that most of the shear associated with the MOC is found in the top 2000 m of the ocean.
In the second set of reconstructions R1A-R1C the amount of data used for estimating the MOC is further reduced by using data from only a few latitudes. The reconstruction R1C is based on density information obtained from 4 latitudes only and is the scenario that comes closest to what would be feasible in the real ocean.
Experiment R1C is the basis for the third set of reconstructions R2A-R2D where we take into account inaccuracies in the density values. A systematic (R2A) as well as a random error (R2B-R2D) is used. A systematic error in density values derived from the δ18O of foraminifera can arise if σ(δ18O) (relation between density and δ18O) changes temporally. In the modern ocean different relationships σ(δ18O)atl and σ(δ18O)pac characterize the Atlantic and Pacific oceans [Lynch-Stieglitz et al., 1999b]:
where σ = (ρ − 1000 kg m−3) m3 kg−1 and where ρ is the potential density referenced to the surface and x denotes δ18O in ‰. The units for the first two coefficients on the right-hand side of equations (4) and (5) are ‰−2 and ‰−1, respectively. The third coefficient is nondimensional. The relations in equations (4) and (5) apply for temperatures warmer than 5°C. For past climates (e.g., during the last Ice Age) σ(δ18O) might have been different and the assumption of a constant σ(δ18O) can introduce an error in the strength of the MOC estimates. In the reconstruction R2A we assume a change from σ(δ18O)atl to σ(δ18O)pac. On the basis of equation (4) we calculate Atlantic δ18O values
Injecting those values into equation (5) yields the potential density σpac. The difference σpac − σatl is then added as a systematic error to the in situ densities used to compute the meridional transports.
The remaining reconstructions R2B-R2D illustrate the impact of adding a random noise to the in situ density field. Three different values are chosen for the standard deviation of the noise: 0.02, 0.1 and 0.2 kg m−3. Figure 1 shows the conversion from noise in density to δ18O units. Typically, the analytical error in δ18O from isotopic mass spectrometer measurements is 0.05‰. Additional uncertainties due to factors such as bioturbation or model mismatches mean that the corresponding error in δ18O and σ is larger. Therefore a noise in density of 0.1 and 0.2 kg m−3 mimics errors that can be expected in paleoestimates. The noise of 0.02 kg m−3 is representative of errors in density estimates obtained from in situ measurements in the modern ocean.
This section illustrates to what extent the reconstructions summarized in Table 1 can reproduce the spatial and temporal structure of the MOC.
3.1. Mean Circulation
First we concentrate on the mean circulation for the years 1985 to 2003. The reconstruction in experiment R0A has many similarities with the mean MOC obtained by zonally and vertically integrating the full three-dimensional meridional velocity field simulated in the numerical model (Figures 2a and 2b). The mean MOC in the North Atlantic for the years 1985 to 2003 consists of one clockwise overturning cell that is confined to the uppermost 2500 m (Figure 2a). Sinking occurs between 50°N and 67°N and about 15 Sv of deep water are exported to the southern hemisphere. Even if there are obvious differences the reconstruction R0 reproduces important features of the MOC (Figure 2b). The one cell structure is largely preserved and the depth at which the maximum transports occur is similar for both the MOC and the reconstruction. Compared to the MOC the reconstruction overestimates the strength of the MOC north of 35°N while the values are generally too small further south. The main reason for this is the absence of the Ekman circulation. Adding the Ekman circulation to the reconstruction R0A reduces the differences with the MOC since the mean values of the Ekman transports are negative and positive (clockwise and anticlockwise) at the locations where R0A overestimates and underestimates the MOC strength [Hirschi and Marotzke, 2006]. The Ekman contribution to the MOC is not considered here since there is no obvious way to reconstruct its past strength and variability. Of course one could include the Ekman contribution by making assumptions for the wind stress in the past, e.g., stronger wind stress related to larger meridional temperature gradients during the last Ice Age. However, in our model study this would not really allow us to quantify the effect of a changed wind stress on the MOC. A stronger or weaker wind stress not only modifies the Ekman contribution but also leaves its imprint on the density field and on the related geostrophic transport. This effect could only be estimated by running the numerical model with higher or lower winds. For computational reasons this cannot be done here. In the following we only concentrate on the density at the margins, a quantity that can be obtained for past oceanic states.
South of 36°N the reconstruction R0A is characterized by local maxima of meridional transport occurring in narrow bands of latitude. This area of increased noisiness which is not seen for the MOC coincides with latitudes where the contribution of the depth-averaged (barotropic) flow to the MOC is important. At locations where large velocities are found over sloping topography partly missing the barotropic flow can result in an underestimation or overestimation of the MOC [Hirschi and Marotzke, 2006]. In the model run considered here strong currents are found along the western boundary south of 36°N. Further north the western boundary current separates from the American continent and the strongest velocities move away from the boundaries which means that the currents are generally weaker over sloping topography north of 36°N. As a consequence the density-based reconstructions of the meridional flow are less likely to miss a significant barotropic contribution north of 36°N.
The main MOC features remain present in the reconstructions R0B and R0C (Figures 2c and 2d). Using only 2.24% and 1.42% of the boundary density has no major effect on the MOC reconstructions. For the reconstruction R0B the most visible difference is a reduced noisiness compared to R0A which is due to the data reduction in the meridional direction (data only every 1.25°). Using data from only every fifth depth and excluding data from the top 300 m and below 4700 m does not prevent the reconstruction R0B from reproducing the vertical MOC structure well. As for the MOC and R0A most meridional transports occur in the top 2500 m and the maximum northward transports are found around 1100 m. This shows that the northward surface branch as well as the compensating southward deep MOC branch are reproduced well. A further reduction of the density data to a depth range of 300–2000 m in R0C slightly modifies the vertical structure of the MOC (Figure 2d). The maximum transport is still found at a depth of 1100 m but the return flow now reaches down to depths of 3500 m to 4000 m. Because in R0C only data from the top 2000 m is used some of the shear related to the lower MOC branch is missed. As a consequence, using a spatially constant correction to ensure the mass balance across each longitude-depth section [Hirschi and Marotzke, 2006] means the lower MOC branch reaches to greater depths.
In the reconstructions R0A-R0C described so far we assume the availability of density data at a number of locations that is far beyond the quantity of data that could realistically be collected in the real ocean. The reconstructions R1A-R1C (Figure 3) rely on density data from much fewer locations and are therefore more representative of what we can expect if a similar approach is used to infer the MOC in the real North Atlantic. In the reconstructions R1A-R1C the meridional spacing is increased from 5° to 20°. The reconstruction R1C only relies on data obtained from 4 latitudes (7°N, 27°N, 47°N and 67°N). Despite the massive reduction of the number of density points used in R1A-R1C the main MOC features can still be reproduced (Figures 3a–3c). Even for the reconstruction R1C where only 0.07% of the boundary density points are used one would infer the presence of an overturning cell transporting about 20 Sv to high northern latitudes. Even if the spatial resolution of the meridional transports is much reduced in R1C compared to the reconstruction R0A similar states are inferred for the MOC.
Of course the reconstruction R1C is only one among many other possible realizations that use the same number of density values at the margins. The sensitivity of the MOC reconstructions to the sampling of the boundary densities is illustrated for experiment R1C by varying the values for js and ks. In total 10 different reconstructions are computed in order to highlight at what latitudes the MOC reconstruction is sensitive to changing the collection sites for the margin density. The standard deviation obtained from all reconstructions show that the largest sensitivity to the sampling is found south of 30°N (Figure 4). With values of up to 5 Sv the standard deviation is particularly large in this area. Much smaller values between 0 and 2 Sv are found north of 40°N. This result shows that for the northern part of the MOC cell the reconstruction is relatively insensitive to the choice of the sampling and choosing different latitudes and different depths only has a minor effect on the inferred meridional overturning cell. In contrast the sampling leads to substantially different transports south of 30°N. The reason for this is the noisiness of the MOC reconstruction that is seen south of 35°N in experiment R0A (Figure 2b). Only slightly shifting the meridional locations of where density data are used can lead to very different transport estimates.
Note that for a successful reconstruction of the MOC based on margin densities, it is crucial to have data from locations that allow estimation of the basin-wide shear. Only missing a small fraction of the total zonal extent of a section (e.g., the Florida Straits) can lead to large errors in the reconstructions. For example, in R1C the density is assumed to be known at 4 sites in the Florida Straits at 25°N (two at the eastern and western flanks), thus allowing an estimate of the transport across the Straits.
The other main assumption made so far is that the exact boundary densities are known. This is of course not true because density measurements obtained from sea sediments but also from in situ measurements of temperature, salinity and pressure are subject to inaccuracies.
The impact of systematic and random errors in the density field is tested in the reconstructions R2A-R2D (Figure 5). The effect of a systematic error is tested in R2A, where the assumption is made, that σ(δ18O)atl changes to σ(δ18O)pac. As a consequence the zonal density gradients are increased thus leading to a reconstruction showing a more vigorous MOC cell (Figure 5a). Compared to R1C the meridional transports increase by 10 to 30% north of about 30°N. A larger increase is found south of 25°N, where the estimated MOC is more than 50% stronger in R2A than in R1C.
Random errors are added to the boundary densities for the reconstructions R2B-R2D. For the smallest value of the random error (standard deviation of 0.02 kg m−3) the resulting MOC estimate is almost identical with the one obtained in R1C and clear differences can only be found south of 25°N (Figure 5b). Increasing the error to 0.1 and 0.2 kg m−3 in R2C and R2D leads to changes in the reconstructions that are particularly pronounced south of 35°N where they completely mask the MOC (Figures 5c and 5d). North of 35°N the main MOC cell is still reproduced reasonably well in R2C even if its strength is decreased by 20–30% compared to R1C. In R2D the MOC cell is still present but is shallower and weaker than in R2C. South of 40°N the reconstruction in R2D is no longer representative of the MOC. Here the noise leads to an anticlockwise overturning cell centered at 27°N which is not seen for the MOC.
The random errors added to the density field in R2B-R2D are based on the same noise field which is scaled in order have a standard deviation of 0.02, 0.1 and 0.2 kg m−3, respectively. The sensitivity of MOC reconstructions to different realizations of the random noise is shown in Figure 6, which depicts the standard deviation based on 19 reconstructions, each obtained using a different noise field. With a standard deviation of 0.02 kg m−3 different realizations of the noise field have only minor effect on the MOC reconstructions. Especially north of 40°N the effect is almost negligible with a standard deviation of less than 1 Sv and values between 1 and 4 Sv further south (Figure 6a). For an amplitude of the noise of 0.1 kg m−3 the values for the standard deviation are between 1 and 4 Sv north of 40°N (Figure 6b). Much larger values of up to 20 Sv are found at the southern end of the domain. A similar picture is seen for a noise amplitude of 0.2 kg m−3 (Figure 6c). Here the standard deviation is larger than 10 Sv south of 40°N and even further north the standard deviation is not negligible compared to the size of the MOC at that latitude.
For the addition of both a systematic or a random noise to the density field the MOC circulation shows a high sensitivity in the south of the domain which gradually decreases further north. The reason for this lies in the nature of the thermal wind balance which is at the center of our calculations [Hirschi and Marotzke, 2006]. The division by the Coriolis parameter means that the closer a location is from the equator the smaller the density gradients that are needed to support the same meridional transport. As a consequence the same error in the density field introduces a larger error in the meridional transport close to the equator than further north. In other words: the closer to the equator the greater the accuracy of the density measurements/estimates have to be.
For the reconstructions R1C and R2A-R2D the maximum MOC value is found at 47°N. In the reconstruction R1C the maximum northward transport is 20 Sv (as mentioned earlier this value overestimates the actual MOC because the reconstruction does not include the negative Ekman transport). With the systematic error in R2A the reconstructed transport increases to 27 Sv. The random noise of 0.02, 0.1 and 0.2 kg m−3 used in the reconstructions R2B-R2D introduces uncertainties of 0.5, 4 and 7 Sv for the maximum meridional mass transport at 47°N.
Ideally we should test if the different reconstructions can distinguish between “on” and “off” states of the MOC. Unfortunately, the model used in this study only simulates the years 1985–2003 during which the MOC does not show any major changes. For computational reasons it is not possible to run the model for very long periods such as the one that would be required if one would like to test the MOC reconstructions during the very variable North Atlantic climate of the last Ice Age.
Nevertheless, the MOC does exhibit variability in OCCAM between 1985 and 2003 [Marsh et al., 2005a; Hirschi and Marotzke, 2006] and a principal component analysis can show to what extent the reduced density fields are able to capture the spatial and temporal variability of the full MOC cell. The analysis of the variability is based on annual means for the years 1985 to 2003. We are aware that this temporal resolution is much higher than the one that can be expected from sea sediment data which is more likely to resolve centennial/millennial timescales. As mentioned earlier the short period of time covered by the OCCAM simulation does not allow investigation of these timescales. Nevertheless, it can be tested if some of the simulated MOC variability is reflected in the reduced density fields.
Especially north of 35°N the leading empirical orthogonal function (EOF) is similar for the MOC and experiment R0A (Figures 7a and 7b) and both indicate a similar spatial variability pattern with a coherent strengthening or weakening of the MOC cell (see [Hirschi and Marotzke, 2006] for details). For the reconstructions R0B, R1A and R1C the reduced boundary density information has only a small effect on the pattern of the leading EOF: all three reconstructions exhibit a variability center between 35°N and 60°N (Figures 7c–7e) which coincides with an area of high variability of the MOC. Even for the reconstruction R1C using only 0.07% of the boundary data points the main variability center can clearly be recognized. The temporal evolutions of the MOC and of its reconstructions are similar with a gradual decrease of the principal components during the years 1985 to 1994 and an increase in the second half of the simulation (Figure 7f). However, the details of the short term fluctuations are different for the MOC and the reconstructions. The percentage of variance explained by the leading EOF increases as the data resolution is decreased. For the MOC and R0A the first EOF explains 22% and 27% of the total variance. This number increases to 61% for the leading EOF of R1C. This increase is due to the fact that in R1C a small number of “measurements” determine the variability of the entire MOC cell. The linear interpolation used in equations (0) and (3) means that the smaller the number of locations where density data are assumed to be known, the larger the spatial coherence in the MOC reconstruction becomes.
As seen in section 3.1, MOC reconstructions are more sensitive to density errors the closer one gets to the equator. Concentrating the EOF analysis to latitudes north of 40°N leads to an even better agreement between the MOC and the reconstructions (Figure 8). Only a little information is lost for the main spatial variability pattern as the data density is reduced and all reconstructions exhibit a variability center which is very similar to the one seen for the MOC (Figures 8a–8e). The principal components show that for the temporal evolution as well the agreement between the MOC and the reconstructions is improved if the analysis is confined to latitudes north of 40°N. Confining the Atlantic domain to latitudes north of 40°N leads to an increase of the variance explained by the leading mode. Now the first EOFs explain between 33% (MOC) and 71% (R1C) of the total variance.
The impact of an error in the density field on the results of the EOF analysis is illustrated for the reconstructions R2B-R2D, where δρ is set to 0.02 kg m−3, 0.1 kg m−3 and 0.2 kg m−3, respectively (Figure 9). The addition of a random error has only a minor effect on the spatial variability pattern indicated by the EOFs (Figures 9a–9c). For all three values of δρ the pattern of the leading EOF is very similar to that seen for R1C (Figure 8e). There is a gradual decrease in the amplitude of the variability from north to south of the domain. This pattern that was already seen for R1C is not modified by the addition of δρ. As mentioned earlier the effect of errors in the density field are more pronounced the closer a location is from the equator. This explains why the first EOF is similar in R2B-R2D and R1C: the MOC variability introduced by adding δρ is larger in the southern than in the northern part of the domain considered in Figure 9. Whereas the spatial variability pattern is not affected by the noise, the temporal evolution clearly is. The evolution of the principal components for the reconstruction R2C and R2D is different from the one seen for the MOC and R2A and for δρ = 0.1, 0.2 kg m−3 the ability to reproduce the temporal behavior of the MOC is lost to a large extent (Figure 9f).
Without assuming errors in the density field both spatial structure and variability of the MOC are still reflected even if only 0.07% density information is used. Systematic errors due to a temporally changing σ(δ18O) affect the inferred MOC strength and can lead to an overestimation or underestimation of changes in overturning strength. In the real ocean, assuming a temporally constant σ(δ18O) to estimate paleodensities could wrongly lead to the conclusion that the MOC was weaker or stronger in the past, whereas in reality there was no change in the meridional transports but in σ(δ18O). On the bright side the 10 to 30% change in MOC strength seen in R2A for a change from Atlantic to Pacific conditions indicates that a shutdown or a massive decrease or increase of the MOC strength could still be detected even if σ(δ18O) is assumed to be temporally constant. For unknown changes of σ(δ18O) that are substantially larger than the differences we currently observe between different oceans in the real world even major changes of the MOC would become hard to detect. However, reconstruction of δ18O, salinity and temperature of seawater is possible for at least the Last Glacial Maximum using measurements from sediment pore waters [e.g., Adkins and Schrag, 2001]. This information could be used to determine the relationship between density and δ18O. In addition temperature reconstructions from Mg/Ca or Sr/Ca in benthic foraminifera can be used to look at changes in the relationship between δ18O and temperature in the past, helping to constrain the δ18O–density relationship to some degree.
A random error comparable to the one expected from in situ measurements (δρ = 0.02 kg m−3, R2B) has only a minor effect on estimates of the meridional transports. For errors similar to the one expected from paleoestimates (δρ = 0.1 kg m−3, R2C) large parts of the steady state MOC structure can be reproduced, especially north of about 40°N but the information about the temporal evolution is mostly lost. A better reproduction of the temporal variability could be obtained if the meridional resolution is increased. The reason for this is that the greater the number of locations where data are assumed to be known, the more likely the random noise is to cancel out. At each location the variability related to the noise is different and therefore the noise does not introduce coherent variability patterns in the MOC reconstructions. For a small data coverage (R1C, R2A-R2D) the overall variability is set by a small number of “measurements” and the noise related variability is much more likely to influence the overall variability pattern of an MOC estimate. It also has to be said that compared to the large MOC changes that are likely to have occurred in the past the variability in our numerical model is small. Therefore our results do not allow us to conclude to what extent large MOC changes can be reconstructed. In a situation where the MOC would exhibit a succession of “on”/“off” a strategy similar to the one used in experiment R2B might still be able to capture the main modes of variability. This should be tested in a model that exhibits larger fluctuations of the MOC.
MOC reconstructions are much more robust to a reduction of the density data in the meridional than in the vertical direction. This was the motivation for the reconstructions R1A-R1C where the resolution is only modified in the meridional direction, whereas the number of depths is kept constant. To decide which latitudes are most useful to infer the MOC from the densities at the margins we have to consider competing factors. Our results have shown that in general the MOC estimates are less sensitive to noise and the data sampling north of about 40°N, whereas both noise and sampling have a larger impact further south. On the other hand, it is known that Ekman transports are smallest at 30°N. Furthermore, this latitude is close to the Florida Straits through which the mass transport has been estimated for the Last Glacial Maximum [Lynch-Stieglitz et al., 1999a]. For those reasons the latitudes of the Florida Straits could appear as an ideal choice for reconstructing the past MOC strength. However, between 25°N and 30°N a density noise of 0.1 kg m−3 results in an uncertainty of 10–15 Sv for MOC reconstructions (Figure 6). In the Florida Straits itself even such a large error does not mask the large northward transport of about 30 Sv. However, the situation is different for the southward return flow in the Atlantic basin east of the Bahamas. In the top 1000 m there is a southward flow of about 15 Sv, a value which is similar to the uncertainty. With the current accuracy of reconstructions of paleodensities one is unlikely to obtain a reliable picture of the meridional mass transport and its vertical structure east of the Bahamas. However, a reliable estimate of this transport is crucial for an MOC reconstruction.
When moving northward it has to be considered that the uncertainty of the δ18O–density relationship increases at latitudes where sea ice becomes an important contributor to the freshwater balance. As a consequence it is unlikely that a reliable δ18O–density relationship can be obtained for high northern latitudes (e.g., 67°N in R1C, R2A-R2D). Therefore, if one is aiming for a measuring strategy able to reproduce the past MOC on the basis of margin densities, our results suggest that collecting data that allow estimation of the cross-basin vertical density structure at a few latitudes between 40°N–50°N gives the most robust results.
Using an eddy-permitting numerical ocean model we have tested to what extent the MOC can be reproduced based on densities at the margins. On the basis of our results we conclude the following:
1. The mean state of the MOC can be inferred from a small fraction of the total density information at the margins between depths 300–2000 m. Data from only a few latitudes are needed to infer the state of the MOC.
2. The addition of a systematic error to the density that mimics a shift from an Atlantic to a Pacific relationship of σ(δ18O) leads to a 10–30% change in the strength of the MOC reconstruction North of 40°N.
3. With the addition of a random error of 0.1 kg m−3 (similar to paleoestimates) the mean state of the MOC can still be reproduced north of 40°N but most of the MOC variability is masked. However, the variability in the numerical model used in this study is small.
4. The sensitivity of the MOC reconstructions to both systematic and random noise increases the closer a location is from the equator; i.e., the closer to the equator, the more accurate density estimates have to be.
5. With the current accuracy for estimates of paleodensities a measuring campaign that aims to reconstruct past states of the North Atlantic MOC based on densities at the margins should concentrate on latitudes between 40°N–50°N.
This work was supported by the National Environment Research Council as part of the RAPID programme and by NSF award OCE-9984989/OCE-0428803. This study was part of the activities of the SCOR/IMAGES Working Group on Past Ocean Circulation. The comments of two anonymous reviewers have helped to improve this paper.