A method developed recently by Grist et al. (2009) is used to obtain estimates of variability in the strength of the meridional overturning circulation (MOC) at various latitudes in the North Atlantic. The method employs water mass transformation theory to determine the surface buoyancy forced overturning circulation (SFOC) using surface density flux fields from both the Hadley Centre Coupled Model version 3 (HadCM3) and National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis observational data set. The previous application of the method was at 48°N using 100 years of model output, and here we show from a longer 400 year data set that it can be extended to provide useful estimates of the MOC variability in the range 35–65°N. The method relies on averaging of the SFOC over an interval prior to that at which the MOC estimate is required. The length of this interval increases as the latitude decreases from about 6 years at 65°N to 15 years at 36°N. Values for the correlation coefficient between the HadCM3 SFOC and MOC time series of 0.60, 0.64, and 0.39 are obtained at 60°N, 48°N, and 36°N. Thus, the SFOC approach may provide valuable complementary information about MOC variability in the middle-high-latitude North Atlantic to that determined from the Rapid array at 26°N but it becomes less useful as latitude decreases. The method is then applied using the NCEP/NCAR reanalysis to estimate MOC variability in the middle-high-latitude North Atlantic for the past 50 years.
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 The overturning circulation in the North Atlantic is a key component of the global climate system and the possibility that it may weaken with significant consequences for the climate of Europe is a major research issue [e.g., Srokosz, 2003; Vellinga and Wood, 2007]. A mooring based monitoring system, the rapid array, has been deployed at 26.5°N since March 2004 and is providing new insights into variability of the meridional overturning circulation (MOC) at this latitude [Cunningham et al., 2007; Kanzow et al., 2007]. At higher latitudes, indirect estimates of MOC variability based on surface forcing fields have the potential to provide valuable complementary estimates to the direct measurements further south.
 Within the water mass transformation framework, estimates of the amount of water formed in different density classes are obtained by calculating the convergence of the surface density gain (derived from the heat and freshwater fluxes) over the outcrop area of a given density range. The formation rates can be expressed as a stream function in latitude-density space, the maximum value of which, within a suitable latitude-density range can be compared with the MOC [Marsh, 2000; GMJ09]. In addition to these determinations of the surface buoyancy forced component of the overturning circulation, the transformation framework has been used more widely to investigate formation of different water masses. In particular, Gulev et al.  employed it with a sigma coordinate primitive equation model, forced by National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) fluxes, to investigate leading modes of surface water mass transformation in the T-S plane and identified decadal scale variability associated with the transformation of Labrador Sea Water and Subtropical Mode Water. As part of their study, they also linked the intensity of the meridional heat transport to both surface buoyancy and wind forcing, obtaining results which were consistent with the earlier study of Eden and Willebrand  regarding the dominance of the North Atlantic Oscillation at midlatitudes. In a separate ocean model study, Häkkinen  found significant variations in the meridional heat transport (MHT) at interdecadal time scales and related it to MOC variability. More generally, the importance of ocean heat transport within the climate system and its relationship with surface forcing has recently been reviewed by Rhines et al. .
 Returning to the Walin  formalism, it should be noted that when applied to ocean models this approach has potential uncertainties arising from model resolution. Gulev et al.  studied water mass transformation in coarse- (1°) and high- (1/6°) resolution versions of the same ocean model and found differences arising from variations in the lateral mixing procedures between the two versions. In particular, the coarse resolution model has the most effective representation of surface water mass transformation at high latitudes because the lateral mixing in the fine resolution model was too weak. A separate issue which has recently been noted with the Walin  approach is that it neglects the component of the shortwave flux which penetrates below the base of the mixed layer [Iudicone et al., 2008] as will be discussed further in section 2.
 With these caveats in mind we note that in GMJ09, which employed 100 years of output from each of three different coupled climate models, we found that if the SFOC is averaged over a prior time interval of appropriate length it provides useful estimates of the MOC variability at 48°N (this method is referred to as “past averaging” hereafter). As an example, for a past averaging interval of 10 years, the MOC value for the nominal year 1960 is compared with the mean of the 10 individual SFOC values in the 10 year window from 1951 to 1960. Averaging intervals of 3, 6, 10, and 15 years were considered in the earlier study and the best correlations were obtained for the 10 year interval (r = 0.66 with the Hadley Centre Coupled Model, version 3 (HadCM3)).
 Here, we extend our earlier analysis and address two main research issues. First, we employ output from the HadCM3 coupled model to explore the extent to which variability in the surface buoyancy forced overturning may be linked to the total overturning variability over the full latitude range of the North Atlantic. Second, on the basis of the results from the coupled model we attempt to reconstruct variability in the surface buoyancy forced component of the North Atlantic MOC over the period 1949–2007 using surface flux data from the NCEP/NCAR reanalysis [Kalnay et al., 1996]. For the coupled model analysis we make use of an additional 300 year data set extracted from a preindustrial control run with HadCM3. This enables us to test the robustness of our earlier results at 48°N and explore the latitude range in the North Atlantic over which the method may be usefully employed. The results to be presented will demonstrate the extent to which this technique has the potential to complement array based estimates of MOC variability in this basin.
 The layout of the paper is as follows. Details of the models, observations and method employed are presented in section 2. The main results are presented in sections 3 and 4 which cover the model and observation based analyses, respectively. Finally, some conclusions are reached in section 5.
2. Models, Observations, and Method
2.1. Model and Observational Data Sets
 The model output employed in our study consists of 400 years of data subsetted from a 1000 yearlong preindustrial control simulation with HadCM3. HadCM3 is a coupled ocean-atmosphere model developed at the UK Met Office with 19 levels in the atmosphere (horizontal resolution of 2.5° × 3.75°) and 20 levels in the ocean (resolution 1.25° × 1.25°), for full details see Gordon et al. . For GMJ09, we used output for the 100 year period from model year 2350 to 2450. Here, we have employed a further 300 years of output covering the earlier period 1850 to 2150. The MOC is in a stable state throughout the two periods selected and the model run is a preindustrial control simulation (i.e., fixed levels of atmospheric CO2). Thus the model years are simply used as identifiers and do not correspond to either historical or future periods.
 In addition to the HadCM3 analysis, surface heat and freshwater flux fields from the NCEP/NCAR reanalysis [Kalnay et al., 1996] and sea surface salinity from Boyer et al.  have been used to determine surface density flux fields and the surface-forced overturning stream function as described in section 2.2. The salinity data set consists of annual fields determined from pentadal averages for 1955–1959 to 1994–1998 and is available at http://www.nodc.noaa.gov/OC5/DATA_ANALYSIS/sal_intro.html. For the years before the start (after the end) of the salinity data set the mean for 1955–1959 (1994–1998) was used. The surface-forced overturning stream function forms the basis for a reconstruction of surface driven variability in the North Atlantic MOC for the period 1960–2007 over the latitude range 30–80°N. The NCEP/NCAR fluxes are known to overestimate the latent and sensible heat loss under certain conditions in high-latitude regions because of the choice of transfer coefficients in the bulk formula scheme [Renfrew et al., 2002]. However, as this is not a simple effect to correct for, we have used unmodified reanalysis fluxes while recognizing this potential problem which is likely to lead to a small bias but should not strongly influence our variability analysis.
2.2. Surface-Forced Overturning Stream Function Method
 The method for determining the surface-forced overturning stream function is described in detail by Marsh  and summarized in GMJ09. Here we simply note that when averaged over a region of ocean north of latitude θ, the volume flux, G(θ, ρ), across an isopycnal ρ, is related to the combined effects of surface density fluxes and mixing by the following equation:
where F(θ, ρ) is the surface-forced water mass transformation rate across ρ north of θ, the second term on the right hand side is the water mass transformation due to diapycnal divergence of the diffusive density flux, Ddiff(θ, ρ), and C(θ, ρ) is the density gain from isopycnal mixing along ρ, also termed cabbeling. With the assumptions of fluid incompressibility and a steady state, G(θ, ρ) is the same as the zonally integrated meridional overturning stream function or MOC (in density coordinates). Water mass transformation in the North Atlantic is predominantly due to surface forcing [Nurser et al., 1999]. Hence, we have neglected the contribution due to mixing in (1) and estimated the MOC, i.e., G(θ, ρ), directly from F(θ, ρ) determined as follows:
where Din is the surface density flux, Dflux, integrated over the region north of θ wherever the isopycnal ρ outcrops. Note that with this approach we are trying to capture the surface buoyancy forced component of the MOC variability. Mixing and entrainment south of the ridges separating the Nordic Seas may also have a significant influence on the strength of the MOC which will not be included in our analysis. In addition, we note that although the concept of a meridional overturning circulation works well over a range of latitudes there is a significant horizontal gyre component which becomes important at midlatitudes (as revealed by eddy resolving models [e.g., Marsh et al., 2009]) and is not represented in our analysis.
Dflux is calculated from the model surface heat and freshwater fluxes using the following formula of Schmitt et al. :
Where FT and FS, respectively, are thermal and haline contributions to the surface density flux. These are defined as follows:
Here ρ is the density of water at the sea surface, cP is the specific heat capacity of water, and S is the sea surface salinity, QNet is the net surface heat flux (positive for heat gain by the ocean from the atmosphere) and E – P is the net evaporation at the ocean surface (runoff and sea ice effects are ignored). The units of QNet used here are W m−2 while the units of E – P are m s−1; the surface density flux terms FT and FS have units of kg m−2 s−1. Iudicone et al.  have recently drawn attention to a potential source of error in calculations made using the above classical Walin  approach, arising from penetration of a proportion of the shortwave flux below the base of the mixed layer. They find that when this term is explicitly included within the transformation equations it can have a significant impact on water masses below the mixed layer with the greatest changes occurring in the tropics. In the middle-high-latitude range considered here, this term is likely to have a relatively small impact and we have not included it in our calculations at this stage but recognize it should be included in future analyses where possible.
 The terms α and β in (4) and (5) are the thermal expansion and haline contraction coefficients, respectively, determined using the following equations:
Values for ρ, CP, and in turn α and β have been calculated using the equation of state for seawater of Friedrich and Levitus . Note that time-dependent monthly values of T and S from HadCM3 are used throughout our calculations, thus variations in surface water properties have been properly taken into account. Because of the nonlinear nature of (4)–(7), the calculations should ideally be carried out with values at each model time step. This effect was explored using 5 day rather than monthly values for the analyses of Gulev et al.  and it gave rise to differences of up to 20–25% in places. With a 10 day storage strategy the differences were smaller (about 5–10% in winter) and even less in summer in the tropics [Gulev et al., 2003]. We have not been able to follow such an approach as we only have access to the monthly fields but this offers a potential improvement to our method in future studies. We also note that other recent work has shown varying results as regards the benefits of using daily rather than monthly forcing data to estimate the new transformation [Cerovečki and Marshall, 2008; Myers and Donnelly, 2008].
 In GMJ09, the maximum value of F(θ, ρ) for σ0 > 27.45 kg m−3 (where σ0 is the surface density, ρ0 – 1000) in the region 48–81°N was taken to be a measure of the total surface-forced overturning circulation (SFOC) at 48°N. Here, we extend this approach to other latitudes in the North Atlantic. Note, we have explored alternative values for the density threshold and find that our results are not overly sensitive to this choice. For simplicity, in the present analysis, we employ the fixed value stated above, however, in future refinements of this technique it may be worth investigating a latitude-dependent threshold density.
3. Surface-Forced Estimates of the MOC Variability in HadCM3
3.1. Model Meridional Overturning Circulation
 In this section, we compare stream functions of the MOC for the 300 year period from HadCM3 model year 1850–2150 with that for 2350–2450 employed in GMJ09. Note a detailed discussion of the MOC is given in GMJ09 and our main aim here is to establish whether there are any major differences in the earlier 300 year model output subset.
 The MOC stream functions for the two separate periods are shown in Figures 1a and 1b, positive values indicate clockwise circulation (i.e., northward flow in the upper branch of a cell with positive values and southward flow in the lower branch). In each case, the form of the MOC is broadly similar with a northward flowing overturning cell occupying the upper 2000 m up to a northern limit at about 65°N, and a weaker shallower cell extending to about 80°N. The first of these cells includes the main region in which Labrador Sea Water is formed in the model and the second weaker cell spans the Greenland Sea Deep Water formation site. Note that this is consistent with an analysis of maximum mixed layer depth in HadCM3 reported in an earlier study [Grist et al., 2007, Figure 1] which revealed deep convection in both the Labrador and Nordic Seas as well as the Irminger Sea. A counterclockwise cell is also apparent in the deeper layers, 3000–5000 m, with a narrower meridional extent, terminating at about 40°N.
 Comparison of Figures 1a and 1b indicates that the strength of the overturning in the earlier 300 year period is stronger than in the later 100 year interval. This is seen more clearly in a difference plot of the MOC for the two periods, Figure 1c, which reveals that both the upper and lower level overturning cells are somewhat stronger in the earlier period. The differences are not great (in the range 1–2 Sv) but they do provide the opportunity to test the method put forward by GMJ09 in a slightly stronger overturning regime.
3.2. SFOC and MOC Variability at 48°N
GMJ09 showed that the SFOC provides a useful estimate of MOC variability at 48°N when a past averaging interval for the SFOC of 10 years was employed. Here, the robustness of this result is tested using the additional 300 years of model output for the interval 1850–2150. Note the focus of the GMJ09 analysis was on 48°N, close to the latitude originally suggested by Marsh  as a suitable southern limit for most of the North Atlantic deep water formation.
 Time series of the MOC and SFOC variability at 48°N for the full 400 years (1850–2150 and 2350–2450 separated by a vertical dashed line) are plotted in Figure 2 for past averaging intervals of 6, 10, and 15 years; note that the vertical scale in Figure 2a spans a slightly greater range than those in Figures 2b and 2c. Correlation coefficients (r) between the SFOC and MOC anomalies and the standard deviation for each time series are listed in Tables 1 and 2, for both periods. All of the reported correlation coefficients (including those in subsequent Tables 3 and 4) are significant at the 95% level, where the number of effective degrees of freedom required for this calculation have been determined using the method of Bretherton et al. [1999, equation (31)], from the lag 1 autocorrelation values of both the SFOC and the MOC time series.
Table 1. Standard Deviation of the MOC and SFOC Anomaly Time Series at 48°N Shown in Figure 1 for the Two Model Periods Considereda
6 Year SFOC
10 Year SFOC
15 Year SFOC
Standard deviations are given in Sv.
Table 2. Values for the Correlation Coefficient Between the MOC and SFOC Anomaly Time Series at 48°N Shown in Figure 1 for the Two Model Periods Considered and the Three Values for the Past Averaging Interval
6 Year SFOC
10 Year SFOC
15 Year SFOC
Table 3. Values for the Standard Deviation and Correlation Coefficient Between the MOC and SFOC Anomaly Time Series at 60°N Shown in Figure 4 for the Full 400 Years of Model Outputa
6 Year SFOC
10 Year SFOC
15 Year SFOC
Here SD is the standard deviation and r is the correlation coefficient.
Table 4. Values for the Standard Deviation and Correlation Coefficient Between the MOC and SFOC Anomaly Time Series at 36°N Shown in Figure 5 for the Full 400 Years of Model Outputa
6 Year SFOC
10 Year SFOC
15 Year SFOC
Here SD is the standard deviation and r is the correlation coefficient.
 The MOC values show a similar level of variability in both the early and late model intervals with a standard deviation of 1.0 Sv in each case. Thus, the period 1850–2150 may be expected to prove suitable to test the conclusions reached in our earlier analysis. For all three past averaging intervals there is a reasonable level of agreement between the SFOC estimates of variations in the MOC and the actual values. A 6 year interval provides SFOC variability which is somewhat greater (standard deviation 1.5 Sv) than the model MOC value, with several extreme values in the period 2030–2080. The 10 and 15 year past averaging intervals each provide closer correspondence between the SFOC values and the MOC (r = 0.56 and r = 0.58, respectively) than is achieved with the 6 year interval (r = 0.47). If the shorter period 2350–2450 is considered, the 6 year interval provides a slightly higher SFOC-MOC correlation (r = 0.62) than the 15 year interval (r = 0.59) with the largest r value being found when the past-averaging interval is 10 years (r = 0.64). Thus, this analysis supports the main conclusion of GMJ09 that the SFOC is capable of providing a good estimate of MOC variability at 48°N. It also provides some indication that the choice of SFOC past averaging interval which provides the best estimate of the MOC may vary depending on the subset of model output considered. Having established the robustness of the method at 48°N, we explore the dependence on latitude in section 3.3.
3.3. Application of the Past Averaging Method at Other Latitudes
 We now investigate the extent to which the SFOC-based estimates provide a reliable measure of model MOC variability at other latitudes in the North Atlantic. The focus is on the range from about 35°N northward as it is here that we expect the strongest link to surface forcing variability in the high-latitude dense water formation regions. Results are first presented for the variation of the SFOC-MOC correlation with latitude, then we discuss in detail time series of the variability at 36 and 60°N in the context of the earlier results at 48°N.
 Values for the correlation coefficient between the SFOC and MOC annual anomalies have been determined from the full 400 year model output data set at each model latitude in the North Atlantic. The variation with latitude is shown in Figure 3 for the 6, 10, and 15 year past-averaging intervals discussed previously and also for a 3 year interval to demonstrate the reduced applicability of the method at short time scales. The same general variation is seen for the 6, 10, and 15 year curves with r values typically between 0.5 and 0.6 in the latitude range 40–65°N. The character of the MOC changes dramatically near 65°N (see Figure 1) because of the topographic constraint of the Greenland-Scotland Ridge; north of this latitude the r values fall away sharply. In the subtropics, from 40°N southward to about 30°N, the r values fall from about 0.45 to 0.25 indicating a reduced level of skill with decreasing latitude in this range. South of 30°N, r varies about 0.2 indicating that the method is of little use at these latitudes.
 Considering the individual curves, the 10 year averaging interval provides slightly higher correlation values than the 15 year interval over 55–65°N, the values are then almost identical from 43–55°N and south of 43°N the 15 year interval has the highest r values. This is consistent with the general idea that a longer time scale for integration of the effects of surface forcing variability on the circulation is more appropriate at decreasing latitudes, further from the source of deep sinking. The r values for the 6 year interval are noticeably smaller than those for the 10 and 15 year intervals except north of about 60°N again indicating that shorter integration time scales are appropriate close to the dense water formation regions. Similarly, the 3 year interval r values are much less than those for the other curves apart from at high latitudes. In their analysis of a 50 year surface forced ocean model simulation, Gulev et al.  found some evidence for a response of the meridional heat transport (which was closely linked with the meridional overturning) to changes in buoyancy fluxes at 3 and 7 year time scales. Our analysis, suggests that longer 10–15 year time scales may be more appropriate in the midlatitudes and further work is required to determine the reasons for these differences which may reflect variations in behavior between coupled and ocean only model runs. We also note that the reduction in correlation that we find south of 40°N is consistent with a recent analysis of the meridional coherence of MOC variability by Bingham et al. . They have analyzed a shorter 100 year section of HadCM3 output and conclude that MOC variations south of about 40°N are decoupled from those further north.
 The correlation analysis suggests that the GMJ09 past-averaging method for estimating MOC variability at 48°N from the surface forcing fields, according to the transformation theory of Walin , will also provide useful results at other latitudes within the approximate range 35–65°N. We now test whether this is the case by considering time series of the MOC and SFOC variability at 36 and 60°N, see Figures 4 and 5 which are presented in the same format as Figure 2, associated statistics are given in Tables 3 and 4.
 The time series at 60°N demonstrate that much of the variability of the MOC at this latitude can be captured using the SFOC estimates although individual events, in particular the high MOC value at 2040 may not be well represented. The highest correlation is obtained with the 10 year averaging interval (r = 0.60) but a better measure of the amplitude of the variability is provided by the 6 year estimate (standard deviation of 1.1 Sv which is the same as that for the MOC, compared with 0.9 Sv for the 10 year estimate). The 15 year averaging period produces quite weak variability (0.8 Sv) again indicating that shorter averaging time scales are best at high latitudes.
 In contrast, at 36°N the 6 year estimates are too high in amplitude (standard deviation of 1.7 Sv) when compared with the MOC (1.1 Sv) and the level of correlation is low (r = 0.29). The best correspondence here is found when a 15 year averaging time scale is employed (standard deviation is 1.1 Sv) although the correlation coefficient (r = 0.39) is smaller than that obtained at 48°N (r = 0.59 for a 15 year averaging time scale). To some extent, the reduced correlation at 36°N reflects the stronger interannual variability of the MOC (compare the black lines in Figures 4 and 5) at this latitude. This is to be expected given the stronger contribution from wind-driven variability in the Ekman component of the transport which of course is not estimated with this method.
 At latitudes south of about 30°N the method developed to date is unlikely to provide useful information. This probably reflects the stronger influence of wind forcing on MOC variability at lower latitudes. By including the wind-driven Ekman transport in our analysis and introducing a time lag to allow for the time required for the surface density flux forced signal to propagate from high latitudes, it may still be possible to obtain useful estimates of the MOC variability in this latitude range. A more physical basis for the latter improvement may be sought by combining deepwater advective time scales (to successively lower latitudes) with either canonical or meridionally varying values for isopycnal and diapycnal diffusivity, to represent the interior mixing of surface-forced transport anomalies. On this basis, we would account for the dispersal of layer thickness anomalies, and the associated implications for deepwater transport and hence MOC intensity.
 To summarize this section, the analysis presented here has demonstrated that the method developed in our earlier paper, GMJ09, is capable of providing useful estimates of the model MOC variability over a broad range of latitudes in the North Atlantic from about 35–65°N, with the highest correlations being found in the range 45–60°N. It is unlikely to be of much use south of 35°N but has the potential to give valuable information on the behavior of the MOC, complementary to that obtained with the Rapid array, when extended to observational data sets. We obtain observation-based estimates of variability over the last 50 years in section 4.
4. MOC Variability Over the Last 50 Years
4.1. Time Series at Key Latitudes (36, 48, and 60°N)
GMJ09 used surface heat and freshwater flux fields from the NCEP/NCAR reanalysis to determine SFOC based estimates of the MOC variability at 48°N with a 10 year past averaging interval. Here we extend their analysis to consider 36 and 60°N and use different combinations of past averaging intervals to provide some indication of the range of uncertainty in the reconstructed MOC variability at each latitude.
 Time series of the reconstructed MOC variability for the period 1960–2007 are shown in Figure 6. The variability at 60°N (Figure 6a) is estimated using both the 6 and 10 year past averaging intervals, the 15 year estimates being deemed unsuitable on the basis of the HadCM3 analysis presented earlier. At this latitude, both estimates show relatively little variability from 1960 through to about 1975, the estimated MOC then increases by 1.5–2.5 Sv in the early 1980s before leveling off in the early 1990s and increasing slightly around the year 2000. The variability that we find at 60°N can only be driven by variability in the surface density flux fields north of that latitude (i.e., in the Nordic seas) as that is the only source of information that feeds into the transformation analysis. In previous work we have shown that there is significant variability in the Nordic seas heat exchange [Grist et al., 2007, 2008] so we are not surprised by this result. The degree of variability in the Nordic Seas overflows remains an open question; although these overflows are now being measured more accurately than in the past [Dickson et al., 2008], the time period spanned by reliable observations remains relatively short and it is too early to obtain a clear picture of the strength of variability at interdecadal time scales from observations.
 At 48°N, the 10 year past averaged time series has already been discussed in detail by GMJ09 in the context of data assimilation analyses [Köhl and Stammer, 2008; Balmaseda et al., 2007]. Here, 6, 10, and 15 year interval estimates are presented and all show anomalously high MOC transport, by about 1–2.5 Sv, from 1980 to 1995 with a slight dip in the late 1980s; note that this period coincides with the prolonged positive phase of the North Atlantic Oscillation [e.g., Dickson et al., 1996] and may indicate that surface forcing associated with this mode plays a significant role in determining the strength of the MOC. From 2000 onward, the 6 and 10 year estimates indicate a slight weakening of the transport at 48°N and the 15 year estimate is close to zero. The time series for 60 and 48°N show noticeable differences in their time variability. This implies that variations in the air-sea heat and freshwater exchanges in the region between these latitudes must significantly modify the time dependence of the surface-forced overturning circulation. Indeed, in the zone 48–60°N, strong Labrador Sea Water formation during the early 1990s [Yashayaev et al., 2007] is likely to have contributed to an enhanced SFOC at that time.
 At 36°N, only the 10 and 15 year interval time series are shown as the HadCM3 analysis indicated that the 6 year interval was too short to estimate the MOC at this latitude. The MOC variability at 36°N is broadly similar to that at 48°N indicating meridional coherence of the MOC variability across this range that extends further south than the 40°N limit found by Bingham et al. .
4.2. Variation Across the Full Latitude Range 30–80°N
 Finally, we generalize the results at specific latitudes using a Hovmüller representation to show the time dependence of the SFOC based estimates of MOC variability over the latitude range 30–80°N. Here, we have chosen to use a 10 year past averaging interval as the HadCM3 analysis indicated that it had at least some applicability over a wide range of latitudes. Thus, for example, the value at a particular latitude for 1980 is the simple average of all values at that latitude in the 10 year interval 1971–1980. A more sophisticated analysis would use a latitude-dependent time interval but we are not yet in a position to specify this in detail.
 The time variation of the 10 year past average SFOC as a function of latitude is shown in Figure 7. Both the actual values for the SFOC (Figure 7a) and the anomalies when the mean over the full period at a given latitude is removed (Figure 7b) are shown. Figure 7 reveals a broad band from about 35–55°N where the SFOC varies coherently over the time period considered, note this is seen most clearly in Figure 7b. Anomalously low values occurred in the 1970s, followed by positive transport anomalies of up to 3 Sv from 1980 through to about 2000 (note the positive values are smaller in the 1990s than in the 1980s). In the period since 2000, there has been a reduction in the transport with largest negative anomalies of about −1.5 Sv reached in 2005 and slightly less negative values in 2006–2007. This corresponds to a reduction in the actual SFOC values from 16 to 14.5 Sv at 45°N. The recent weakening is interesting but is probably indicative of multidecadal variability of the MOC rather than signifying the start of a long-term decline. North of 55°N, the time dependence appears to have a higher frequency with five alternating episodes of positive and negative anomalies throughout the full period 1960 – 2007. Most noticeably in the mid-1990s the transport anomalies north and south of 60°N appear to be out of phase, while being in phase during the preceding decade. This change must be associated with the extent of coordination between dense water formation in the Labrador, Irminger and Nordic Seas. The reason for a change in coordination in the 1990s is not immediately evident, although changing characteristics of the North Atlantic Oscillation may have played a role, and we intend to pursue this further in a subsequent study.
 It is interesting to put these results in the context of earlier studies which have considered variability in the Atlantic MHT from surface forced ocean models [Häkkinen, 1999; Gulev et al., 2003]. Häkkinen  used the MHT as a proxy for the strength of the MOC and analyzed results from an ocean model forced with surface fluxes derived by combining information from various sources (ECMWF, COADS, NCEP) over the period 1951–1993 and latitude range 15°S–65°N. She found an abrupt increase in the MHT over a broad range of latitudes in the mid-1980s which persisted into the early 1990s. This is broadly consistent with the strengthening of the MOC that we find over the same period although the MOC strengthening in our analysis starts somewhat earlier around 1980 while Häkkinen  has weakened MHT from 1980 through to 1985. During the 1970s she finds weakened MHT in the first half of the decade, again consistent with our analysis but a subsequent strengthening up to about 1980 which is not seen in our MOC values. In the 1960s, the level of variability is weak in both studies.
Gulev et al.  also considered MHT variability in their analysis of an ocean model forced with NCEP/NCAR fluxes for 1958–1997. They found similar results to Häkkinen  as regards positive MHT anomalies in the midlatitudes in the 1990s and in the subtropics in the mid-1970s but found little agreement from the late 1970s to the late 1980s. They note that without a specific intercomparison of the two models it is not possible to establish the reason for these differences, possible causes being variations in model parameters, configuration and forcing. There are further caveats in any direct comparison of our MOC variability results with MHT variability, they are as follows: (1) the MHT does not simply map onto MOC variability, in particular north of about 45°N these two measures of the circulation are only weakly correlated [e.g., Biastoch et al., 2008]; (2) the SFOC computed here reflects changes in both heat and freshwater transport (as the implied circulation is density forced); (3) the model-derived MHT variability is further influenced by mixing and dynamical adjustment (missing in our analysis); and (4) the proportion of the full MOC variability which is surface buoyancy forced, and thus potentially captured by our approach, may vary between different decades. Hence, the results of any such comparisons should be treated with considerable caution. It is, however, worth noting that the strongest recent signal, midlatitude warming due to stronger MHT in the mid-1980s to early 1990s [Häkkinen, 1999] may be inferred from our analysis, if we assume that MHT is roughly proportional to MOC intensity.
Gulev et al.  included a comparison of their model variability against a limited number of hydrographic observations of the MHT at 48°N but noted various problems with this approach and had to normalize both the observational and model values before obtaining some qualitative comparability at a general level. With this in mind, we have not tried to make use of observation-based MHT (or MOC) estimates here but note they may well prove to be a useful source of information in subsequent studies.
 Given the reduction in the value of the MOC-SFOC correlation coefficient shown in Figure 3 we have not felt it worthwhile to extend the surface driven MOC reconstruction south of 30°N. However, it may be possible to increase the level of correlation at low latitudes by accounting for the wind-driven Ekman flow, which becomes more important at these latitudes. This may extend the latitudinal range over which it would be possible to estimate the MOC variability from surface observations; this is also an area for future research.
 In this paper, we have extended the earlier analysis of Grist et al.  and investigated the extent to which variability in the Atlantic MOC across a range of latitudes can be estimated from surface density flux fields using water mass transformation theory. Variations in the circulation, and in particular the potential for a significant reduction in the MOC, have become an area of major concern in recent years and have motivated the deployment of the Rapid monitoring array at 26°N [e.g., Cunningham et al., 2007]. This array is now providing accurate and continuous measurements of the transport variability at this latitude but it has been suggested that further estimates of MOC variability are required at higher latitudes because variability in the MOC north of 40°N is not strongly linked to that further south [Bingham et al., 2007]. Hence, if air-sea density flux fields can be used to estimate MOC variability at middle-high latitudes, they would provide valuable complementary data to the Rapid array measurements.
 In GMJ09, we focused on 48°N and developed a method for estimating MOC variability by averaging the transformation-based estimate of the surface-forced overturning circulation over a period of time prior to that at which the MOC estimate is required. Here, we have shown that this method is robust when tested using a further 300 years of model output from HadCM3, in addition to the 100 years originally employed. Furthermore, we have considered a range of latitudes and found that the method is capable of providing useful estimates of the model MOC variability in the North Atlantic from about 35–65°N. Interestingly, the best results are obtained using a time scale which increases from about 6 years at the northern limit of this range to 15 years at the southern limit, i.e., the time scale on which the Walin  approach is valid becomes longer as the distance from the dense water formation regions at high-latitudes increases. This may be expected as the overturning further from the regions of strong surface density gain is associated with increasingly time-integrated effects thereof.
 The method may be applied to observation-based surface density flux fields to estimate variability in the MOC over the last 50 years and GMJ09 carried out such an analysis with the 10 year past averaging technique at 48°N. We have developed this further using different averaging intervals to estimate in part the uncertainty in the reconstructed MOC at several key latitudes (60, 48, and 36°N). The results at 48°N support the conclusion of GMJ09 that the MOC varies appreciably (anomalies of up to 2.5 Sv) at multidecadal time scales while not showing a clear long-term trend. The time series at 36°N shows a similar time history to that at 48°N indicating a high degree of coherence in the MOC. However, at 60°N the time scale for variability appears to be somewhat shorter than further south and a broader analysis across a range of latitudes appears to indicate a transition zone at about 55°N. We have attempted to put our results in the context of earlier surface-forced ocean model analyses by Häkkinen  and Gulev et al. . It is difficult to draw firm conclusions from these comparisons but we note that midlatitude warming in the mid-1980s to early 1990s [Marsh et al., 2008] associated with enhanced MHT [Häkkinen, 1999] is consistent with positive SFOC anomalies during the same period.
 The variation of the MOC-SFOC correlation with latitude indicates that south of about 30°N the method is unlikely to provide useful information. However, to some extent this reflects the dominance of the Ekman transport in MOC variability at lower latitudes. By including the wind-driven transport in our analysis and introducing a lag to allow for the time required for the surface density flux forced signal to propagate from high latitudes, it may still be possible to obtain useful estimates of MOC variability south of 30°N. At present, the main application of our method is at middle-high latitudes (35–65°N) where we have shown that surface density flux based estimates of MOC variability provide a valuable complementary data set to direct measurements further south.
 This research has been carried out under Theme 1 of the UK Natural Environment Research Council Oceans 2025 program. We are grateful to the two reviewers for their many useful comments and acknowledge the British Atmospheric Data Centre for the supply of HadCM3 model output.