Observations of thermosteric sea level (TSL) from hydrographic data, equivalent water thickness (EWT) from the Gravity Recovery and Climate Experiment (GRACE), and altimetric sea surface height (SSH) are used to infer meridional heat transport (MHT) anomalies for the Atlantic Ocean. An “unknown control” version of a Kalman filter in each of eight regions extracts smooth estimates of heat transport convergence (HTC) from discrepancies between the response to monthly surface heat and freshwater fluxes and observed mass and heat content. Two models are used: model A using only the heat budget for 1993–2010 and model B using both heat and mass budgets for 2003–10. Based on the small contributions of mass to SSH, model A is rerun using SSH in place of TSL to improve temporal resolution and data consistency. Estimates of MHT are derived by summing the HTC from north to south assuming either negligible anomalies at 67°N or setting MHT to observed values near 40°N. Both methods show that MHT is highly coherent between 35°S and 40°N. The former method gives a large drop in coherence north of 40°N while the latter method gives a less dramatic drop. Estimated anomalies in MHT comparable to or larger than that recently observed at the Rapid Climate Change and Meridional Overturning Circulation and Heatflux Array (RAPID/MOCHA) line at 26.5°N have occurred multiple times in this 18-yr period. Positive anomalies in coherent MHT correspond to increased heat loss in the North Atlantic subtropical gyre demonstrating the feedback of oceanic heat transport anomalies on air–sea fluxes. A correlation of MHT with the Antarctic Oscillation suggests a southern source for the coherent MHT anomalies.
Meridional heat transport (MHT) in the ocean and in the atmosphere removes excess heat from the tropics and redistributes it toward the poles. Unlike in the Pacific and Indian Oceans, where MHT is antisymmetric about the equator, the Atlantic Ocean transports heat from the Southern Hemisphere to the Northern Hemisphere across the equator, although there is considerable scatter in the direct measurements of MHT, particularly in the South Atlantic (Trenberth and Caron 2001; Ganachaud and Wunsch 2003). The Atlantic MHT reaches its maximum mean value near 25°N; poleward of this latitude the ocean fluxes this heat to the atmosphere, greatly reducing the oceanic component of MHT and increasing the atmospheric component. Changes in this transfer of heat may cause dynamical changes in the atmosphere, for example, in the location and intensity of storm tracks (Msadek et al. 2011). A study of the upper ocean heat budget in a region encompassing the Gulf Stream (GS) demonstrated the importance of ocean advection in creating the heat content anomalies that in turn cause air–sea flux anomalies (Dong and Kelly 2004; Kelly et al. 2010), although a direct link to MHT was not established.
The Atlantic MHT has a close relationship with the Atlantic meridional overturning circulation (AMOC) and climate models suggest that both the AMOC and the MHT will decrease in the coming decades in response to increasing greenhouse gases (Schneider et al. 2007). Numerous studies cite wind forcing as a contributing factor in MOC or MHT anomalies, with the wind anomalies centered in the North Atlantic, related to the North Atlantic Oscillation (NAO) (Cabanes et al. 2008; Zhang 2010; Häkkinen and Rhines 2004, 2009) or in the Southern Ocean (SO), related to meridional migration of the westerlies (Delworth and Zeng 2012; Kamenkovich and Radko 2011; Spence et al. 2010; Beal et al. 2011).
A joint U.S.–UK climate monitoring system, Rapid Climate Change (RAPID) and Meridional Overturning Circulation and Heatflux Array (MOCHA), was initiated in 2004 to directly measure changes in the AMOC and MHT near their peak values (Cunningham et al. 2007; Johns et al. 2011; Srokosz et al. 2012). A comparison of the AMOC and the non-Ekman component of MHT (Johns et al. 2011) found a nearly constant coefficient of 0.065 PW Sv−1 (1 Sv = 106 m3 s−1). A large anomaly occurred in 2009–10 in both the AMOC and in MHT (Srokosz et al. 2012; W. Johns 2012, personal communication). In response to several studies showing a lack of coherence in the AMOC across the northern subtropical/subpolar boundary (Bingham et al. 2007; Zheng and Giese 2009), additional monitoring has been proposed for both the South Atlantic and the high-latitude North Atlantic.
To estimate anomalies of MHT and examine their potential impact on the atmosphere, we combine the 18-yr record of altimetric sea surface height (SSH) anomalies with “thermosteric sea level” (TSL) down to 700 m and with the “equivalent water thickness” (EWT) anomalies from the Gravity Recovery and Climate Experiment (GRACE) satellite. Anomalies of SSH result from changes in ocean mass and changes in ocean density, forced by surface fluxes, changes in ocean circulation, and lateral inputs, such as river outflow or glacier melt. Changes in salinity contribute to SSH anomalies, “halosteric sea level” (HSL); however, salinity is not well observed and HSL is neglected here except as a source of error in the mass budget. The inclusion of bottom pressure to constrain heat content was tested using an ocean model by Jayne et al. (2003); their study concluded that mass measurements from GRACE could improve heat content estimates, particularly on shorter time scales.
For this study we use a simple heat budget or linked heat and mass budgets to predict sea level anomalies from surface fluxes. Surface forcing includes net surface heat fluxes and net freshwater fluxes. Heat transport convergence (HTC) and mass transport convergence (MTC) are inferred as a residual in the assimilation of the observations. MTC includes poorly observed contributions from glacier melt, river inflow, and runoff, as well as barotropic circulation.
Our approach here contrasts with estimating MHT from a full dynamical model that assimilates TSL or SSH in several ways. The advantage of these more complex assimilation schemes is the ability to analyze the three-dimensional fields of circulation and its contributions to heat transports. The disadvantages are the complexity of the model and of the assimilation scheme, extra constraints to make the model dynamically consistent, and the need to adjust the forcing or interior fields to agree with observations or sacrifice a closed heat budget (Zheng and Giese 2009; Heimbach et al. 2011). A recent comparison of assimilation products showed substantial differences in the interannual variability of AMOC between such products (Muñoz et al. 2011). Here we employ a box model and a simple assimilation scheme to infer convergences and MHT anomalies that are consistent with the observations within estimated errors. Our box model allows for errors in the forcing fields, but does not alter them, and the MHT is computed from residuals to this budget, which builds on the increased accuracy of new flux products, such as the Objectively Analyzed Air–Sea Heat Fluxes (OAFlux) products used here (Yu et al. 2007). Our approach complements other assimilation methods.
2. Observations and forcing fields
Observations of three sea level components are used here: SSH, TSL, and EWT (Table 1). The SSH anomaly is from the Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) merged altimeter gridded data, available weekly from October 1992 through early 2011. TSL is derived from in situ profiles of temperature down to a depth of 700 m and converted to sea level using a local coefficient of thermal expansion (Lyman and Johnson 2008). TSL is averaged yearly from 1993 to 2008; inclusion of Argo data greatly improved the TSL fields after about 2004. We supplemented the TSL fields for 2009 and 2010 using heat content derived from the same observations and converted to TSL using an empirical coefficient of thermal expansion α. The coefficient was derived by regressing estimates of TSL on ocean heat content in each of the eight regions used in the models. The EWT is derived from GRACE observations of gravity (Chambers 2006). Here we used the version of EWT that has been projected onto modes of model-derived bottom pressure (Chambers and Willis 2010).
Net surface heat flux consists of radiative fluxes (shortwave and longwave) and the turbulent fluxes (latent and sensible) as listed in Table 1. The turbulent fluxes used here are OAFlux products, which merge a variety of satellite-measured fields with numerical weather prediction fields to produce a climate quality record (Yu and Weller 2007). The radiative fluxes are from the International Satellite Cloud Climatology Project (ISCCP), which incorporates observed clouds (Schiffer and Rossow 1983); a monthly averaged version is available from 1992 through 2009. For 2010 we used radiative fluxes from the European Centre for Medium-Range Weather Forecasts (ECMWF), with anomalies reduced by a constant scaling factor to match the magnitudes of the ISCCP flux anomalies over a 7-yr overlap period.
Observed and forcing fields were converted to nonseasonal monthly anomalies spatially averaged over each of the regions described in section 3. The mean and seasonal cycle (first and second annual harmonics) were removed from all variables and forcing fields; higher temporal resolution fields were averaged monthly. Yearly TSL values were interpolated to monthly values. SSH and TSL anomalies are relative to the mean for 1993–2010, whereas the EWT anomalies are relative to the mean for 2003–10. To reconcile the EWT with TSL and SSH, the mean of the difference of the anomalies (SSH minus TSL) over 2003–10 was added to the EWT anomaly fields.
Recent observational estimates of MHT (or MOC) are available at 41°N, 26.5°N, and 34°S (courtesy of J. Willis, W. Johns, and S. Dong, respectively). The estimate at 41°N of the MOC was based on a regression between SSH and a more direct estimate and spans the entire altimetric record used in our study (Willis 2010). The MOC estimate was converted to an estimate of MHT using a coefficient of 0.06 PW Sv−1 of volume transport based on the regression coefficient at 26.5°N of about 0.07 PW Sv−1 and a somewhat smaller value (0.05 PW Sv−1) from a model at 34°S (Dong et al. 2011). The MHT estimate at 26.5°N is from the MOCHA program and begins in 2004. The estimates at 34°S are from repeated XBT surveys (Garzoli et al. 2013) and appear to underestimate MHT anomalies there, based on more recent estimates (C. Meinen 2013, personal communication) as discussed in section 4b.
Based primarily on the availability of observations and accurate forcing fields two separate models were run: model A, a heat budget only demo October 1992 to January 2011, and model B with combined heat and mass budgets from February 2003 to January 2011. The budgets are framed in terms of sea level to allow direct assimilation of satellite observations of SSH and of EWT.
a. Heat and mass budgets
The rate of change in SSH associated with changes in heat content ηH can be written as
where Qnet is the net surface heat flux into the ocean, α the coefficient of thermal expansion, and ρ the density and cp the heat capacity of seawater. The vertically weighted and spatially varying value of α/ρcp was derived by regressing estimates of TSL on ocean heat content derived from the same data.
The rate of change in SSH associated with changes in mass ηM is written as
where P is precipitation, E is evaporation, and the difference is the net freshwater flux into the ocean. The last term is the mass transport convergence, the net inflow of water into each region.
The modeled variables are denoted using η to distinguish them from the observed values: for example, ηH is the modeled contribution of heat to sea level and TSL is the observed thermosteric sea level. Small biases in the forcing fields result in unrealistic trends in η; therefore, we removed the mean forcing and the seasonal cycle and focused this analysis on the nonseasonal anomalies.
b. Selection of the regions
The models are run over boxes that span the Atlantic Ocean along latitude lines: 50°N, 40°N, 25°N, 10°N, 10°S, 20°S, and 35°S (Fig. 1). Lines at 40°N, 25°N, and 35°S were selected to be near direct observations of the MOC and MHT at 41°N, 26.5°N, and 34°S, respectively. The northern boundary at 67°N is the practical limit of usable observations. The Southern Ocean region is also defined by the extent of usable observations, but does not correspond entirely to a latitude line. The use of latitude lines insures that each region borders only two other regions, one to the north and one to the south, with the exception of the southernmost region, which exchanges heat with both the Indian and Pacific Oceans.
c. Unknown control
Heat and mass budgets were estimated using a predictor–corrector method, specifically the version of the Kalman filter known as the “unknown control” (UC; Wunsch 1996). The UC reconciles the various observations by assimilation, accounting for their errors, and estimates the residual to the model in combination with a Rauch-Tung-Striebel (RTS) smoother (Rauch et al. 1965; Wunsch 1996). Here the residual corresponds to lateral convergences in the budgets.
The predictor portion of the Kalman filter with UC is given by
where q is the vector of state variables (here η) at each time step j, F is the forcing, and U is the unknown term that is to be estimated. The matrix contains the model physics that depend on the state variables at the previous time step. The corrector of the Kalman filter adjusts the prediction to better match the observations (assimilation). The relationship between modeled and observed values is written
where y is the vector of observations and relates them to the modeled variables. If the modeled variables are directly observed, is an identity matrix.
for the jth time step dt. Here, is an identity matrix, UH is the contribution to ηH from HTC, and UM is the contribution to ηM from MTC.
For model A only ηH is stepped forward using (5). The predicted vector ηH(i, j) is adjusted toward the observations at each time step j for region i using
with a corresponding reduction in estimated errors. The residual between model and observations is saved and at the end of the 18-yr period, the RTS smoother is run (backward) on the model variables, the error estimates, and the residual to obtain a smoothed HTC and a smoothed estimate of ηH.
Three model runs are described here, two using model A and one using model B. Model A is run assimilating either TSL or SSH. Model B assimilates TSL, EWT, and SSH. Each run has errors associated with each type of data in the assimilation and with the neglected contributions. While TSL has the most direct relationship to the heat budget, the anomalies are yearly averages, which limit temporal resolution. In addition these estimates of TSL neglect anomalies below 700 m. Model B accounts for mass but neglects the halosteric contribution to sea level, which accounts for about one-third to one-half that of the thermosteric effect, typically with opposite sign (Church et al. 2010). The use of SSH in place of TSL in model A gives higher temporal resolution and a full water column measurement, but neglects the contributions of mass and salt. A study by Willis et al. (2004) showed high correlations between SSH and TSL except in the Labrador Sea and along 20°S and 20°N. Estimates of the missing contributions in each model run are quantified for the error estimates.
d. Error variance estimates
The Kalman filter retains a running estimate of model error. The relative sizes of the accumulated model and current observation errors determine how much the prediction will be adjusted to match the observations. For the UC the error of the model includes the error in the forcing fields, heat and freshwater fluxes, and an estimate of the size of the unknown terms, HTC or MTC.
1) Errors in observations
Errors in observations were derived from the product error estimates where possible and are given in terms of a fraction of the variance of the observed quantity. Errors in observations are reduced by averaging spatially over the model regions in Fig. 1; however, the variance is also reduced by the averaging. Therefore, we assumed that spatial averaging reduced the error fractions, the relative error, by only about 20%. For example, errors in the gridded SSH product have typical values of about 10% of the SSH variance (Ducet et al. 2000) and we assumed that errors for the region averages are 8% of the spatially averaged variance.
The TSL fields are mapped from in situ observations with an objective procedure that assigns a weight w to the mapped TSL at each point at each time, based on the amount of data available (Lyman and Johnson 2008). The TSL error fraction at location x is [1 − w(x, t)]2 and an estimate of the sampling error variance for region i is given by
where 〈w〉 and σ2(i) are the spatially averaged weight and variance of the TSL, respectively. The mean error fraction ranged from about 1% in the well-sampled North Atlantic to 8% of the variance of TSL in the southernmost region.
There are errors associated with the reduced (annual) temporal resolution and the limited depth of the TSL estimates. The omission of these terms means that the constraint (7) should actually be
where TSL (>700) is the contribution from the ocean deeper than 700 m and TSL′ is the missing higher-frequency anomaly. We used SSH statistics as a proxy to estimate the missing monthly variability, which was typically 9% of the annual variance. A recent study shows that warming of the deep ocean contributes as much as 0.4 mm yr−1 to sea level rise, mostly in the Southern Ocean (Purkey and Johnson 2010); to account for this missing signal we assumed an error of 10% of the annual TSL variance.
with a combined error variance from the errors in the SSH maps plus the variances of HSL and EWT. These errors can be smaller than those for TSL in (11) and the analysis benefits from better coverage and the higher temporal resolution of SSH.
GRACE EWT contains errors from several processes, notably gravity anomalies over land that leak into the ocean fields. Chambers and Willis (2010) achieve a large reduction in errors by expanding the gridded EWT in terms of a truncated set of empirical orthogonal functions (EOFs) of bottom pressure from an ocean model. They estimate the errors in the gridded fields as equal to one standard deviation, that is, an error fraction of 100%, which we reduce to 80% for the average over each region for constraint (8). The contribution of EWT to sea level is small: the standard deviation of the reconstructed EWT is only about 10%–15% of that of SSH; therefore, its contribution to errors in SSH is small also. However, the error variance for EWT in (8) is not small relative to ηM.
The model B constraint (9) should actually be
Therefore, it is necessary to add an estimate of the variance of HSL to the error estimate for SSH. Assuming a contribution of HSL to sea level of about one-half that of TSL, we added 25% of the TSL variance to the SSH error variance in (9).
2) Errors in the model
Errors in the models include errors in the forcing fields, as well as an estimate of the size of the missing convergence terms U. The forcing error is specified for a time step, so, for example, an error dQ in surface fluxes of 10 W m−2 would give an error in ηH of α dQ dt/(ρ cp) or about 0.001–0.002 m. A comparison of OAFlux turbulent fluxes with in situ fluxes derived from observations at a buoy in the GS from the Climate Variability and Predictability (CLIVAR) Mode Water Dynamic Experiment (CLIMODE) program (Marshall et al. 2009) showed correlations of about 0.85 for latent heat flux anomalies and 0.9 for the smaller sensible heat flux anomalies (http://faculty.washington.edu/kellyapl/, follow “Evaluation of Satellite Products” and then “Fluxes”). Based on these values we assumed an error variance of 30% of the flux variance. Heat budgets computed in the Atlantic (Dong and Kelly 2004; Piecuch and Ponte 2011) suggest that advection and surface forcing anomalies are of comparable size; therefore, we assumed that the variance of U for HTC is the same as the variance of the heat flux forcing. Combining the flux error variance with that of U gives a combined model error variance of 130% of the flux variance. We assumed that the MTC anomalies are similarly comparable to the forcing anomalies and that the relative errors in P − E are larger than for the heat flux, for a combined model error variance of 150% of the flux variance.
The goals of this anomaly analysis of the heat and mass budgets in the Atlantic are to estimate (a) the relative contributions of heat and mass to observed sea level anomalies, (b) the relative contributions of surface and lateral processes, (c) the extent to which anomalies in heat transport are correlated throughout the Atlantic, and (d) to investigate the impact of the MHT anomalies. In this section we present results that correspond to the first three goals of the analysis; the fourth goal is addressed in section 5.
Three runs are analyzed here: model A forced by heat fluxes and assimilating TSL or SSH (referred to as model A-SSH) and model B forced by heat and freshwater fluxes and assimilating TSL, EWT, and SSH. The heat transport convergence (HTC) was computed from the UC in all three runs and the mass transport convergence (MTC) was derived from the UC in model B.
a. Contributions to sea level
The heat budget (1) from model A shows comparable contributions from surface fluxes and HTC to thermosteric sea level ηH (Fig. 2). The heating contribution to sea level ηH increased in all eight regions shown from 1993 to 2010; however, except in regions 1 and 8, the heating contribution reached a maximum in 2001–02 and decreased afterward. This surface contribution was generally opposed by a heat transport divergence to leave a relatively small residual in thermosteric sea level (Fig. 2, thin line). In region 2, which contains part of the GS, there is less compensation especially during 1999–2000, when ηH increases along with surface heating, and again in 2004–09, when heat content increases along with HTC without compensating surface fluxes. The contributions from model B and model A-SSH showed similar magnitudes and relative contributions (not shown). The relationship between HTC (heat advection) and surface fluxes is discussed further in section 5.
Model B gives estimates of the contributions of lateral (MTC) and surface (P − E) processes to the tendency of EWT ∂ηM/∂t for 2003–10 (Fig. 3), converted to volume storage rate in Sv. Note that MTC in the model includes processes other than advection, as the freshwater forcing here is only from P − E. In the tropical Atlantic, in particular, there are large contributions from the Amazon and Congo Rivers. To an even greater extent than in the heat budgets, surface and lateral contributions cancel in the mass budget; that is, local mass anomalies are rapidly dispersed. Correlations between the forcing and the observed response ∂ηM/∂t (local balance) are not significant for any region; however, ∂ηM/∂tis significantly correlated between all adjacent regions, except in regions 7 and 8, reflecting large spatial scales of variability.
A comparison of the heat and mass contributions to total sea level shows the dominance of thermosteric effects (Fig. 4), which are nearly indistinguishable between model B (solid red line) and model A (dashed red line). A positive trend in SSH (thick black line) is apparent in all of the regions, with a small contribution from mass (solid blue line) and a larger contribution from heating, except in region 8 (Southern Ocean). Contributing factors to this weak trend in heating include larger errors in the heat flux anomalies, poor coverage for TSL, and errors in SSH associated with increasing wave heights (J. Willis 2011, personal communication). This discrepancy disappears in model A-SSH in which ηH is constrained by assimilation of SSH, so that SSH cannot be used as an independent check on the model.
The modeled mass component of SSH (solid blue line) can be compared with the residual (SSH minus ηH, dashed blue line) from model A, which contains contributions from both mass and salinity. The residual is substantially larger than the modeled mass contribution ηM, in part owing to the neglect of HSL. The use of the EOF reconstruction of EWT may also contribute to the residual; a regression of the residual onto ηM suggests that the EOF reconstruction underestimates EWT by as much as a factor of 2 in some regions. Underestimates of EWT are unlikely to qualitatively affect the mass budget because mass storage is a small residual between surface forcing and MTC (Fig. 3). However, an underestimate of the EWT magnitude may slightly alter the heat budget from model A-SSH.
b. Meridional heat transport
The models give estimates of HTC for each region, along with estimated errors (Fig. 5). In the South Atlantic (regions 6 and 7), heat storage results from a combination of surface fluxes and HTC. In the tropics (regions 4 and 5) large flux anomalies are offset primarily by HTC, an import (export) of heat from (to) an adjacent region. In the subtropical North Atlantic (region 3) the surface flux contributes more to heat storage and HTC is smaller than in the tropics (Fig. 2). The HTC does not directly determine the magnitude of the MHT anomalies through each region, only the change in MHT as it passes through the region.
We used two different methods for inferring MHT anomalies from HTC. We first summed HTC from north to south for all three runs, effectively setting the MHT anomalies to zero at 67°N. For model A-SSH we then computed the difference between the modeled MHT at 40°N and the smoothed nonseasonal MHT anomalies at 41°N derived using MOC estimates from Willis (2010). The time-varying difference was then added to the MHT estimates at each latitude (Fig. 10a); this adjustment leaves the HTC unchanged.
MHT anomaly estimates for all three models are shown: model A (Fig. 6), model B (Fig. 7), and model A-SSH (Fig. 8). Errors for the MHT were estimated as the root-mean-square (RMS) of the accumulated squared errors in HTC from the Kalman filter, except for model A-SSH at 40°N where both MHT anomaly and error estimates were taken from Willis (2010). MHT from model A and model B are similar except that model B has higher-frequency anomalies owing to the assimilation of monthly SSH anomalies; both these models share the assumption of negligible MHT anomalies at 67°N. The MHT from model A-SSH differs qualitatively from the others in that it has larger high-frequency anomalies in the North Atlantic (Fig. 8, top panel) that are apparent in all other regions.
a. Comparisons with other studies and observations
The model shows that lateral processes (HTC from advection and diffusion) make contributions to heat content anomalies that are comparable to surface forcing in all regions (Fig. 2). To quantify the contributions of these terms in the heat budget we compute the standard deviation of each term (converted to PW) in model A-SSH for each region (Fig. 9). The term magnitudes and their relative sizes are similar to those found by Piecuch and Ponte (2011; see their Fig. 8b) based on an analysis of the Estimating the Circulation and Climate of the Ocean (ECCO) consortium model output for the upper ocean down to 1000 m for nearly the same regions. Note that in their analysis, advection and diffusion (a small term) are computed separately. In both models the magnitude of the heat storage is largest, surface flux anomalies are slightly smaller and HTC (advection plus diffusion) anomalies are about ⅔ of the heat storage in both the ECCO model and in model A-SSH, except in the tropics where heat storage is the smallest term in our model. The similarity in term sizes suggests that computing HTC as a residual in our models does not produce excessively large values. There are numerous differences in the models including different surface heat flux products, greater depth for estimates from ECCO, and differences in the region definitions. The models share a reliance on observed upper ocean heat content and SSH (except for model A).
There are, however, differences in the term balances. In the analysis of Piecuch and Ponte (2011) the dominant balance is between HTC and heat storage rate on interannual time scales (their Fig. 7). In our analysis the dominant balance in regions 3–5 is between surface flux anomalies and HTC (advection) (Fig. 2). (Note that the term labeled “divergence” in Piecuch and Ponte is actually convergence and that the budgets shown are a temporal derivative of the results in Fig. 2). However, neither analysis shows a dominant balance between surface fluxes and heat storage, indicating that ocean heat transport is always important in the heat budget. The differences in the budgets may reflect the procedures made to balance the heat budget: in ECCO surface fluxes are adjusted (Heimbach et al. 2011) and in our analysis HTC is adjusted to produce the balance.
Anomalies in the South Atlantic are generally larger than those in the tropical or North Atlantic. The increase in magnitude from north to south results from coherent discrepancies between the time integral of surface fluxes and thermosteric sea level anomalies. Such a discrepancy is unlikely to be caused by SSH errors, which do not have a known bias (except in the Southern Ocean). The summation of HTC, if mean values were retained, would accumulate flux anomaly biases into MHT toward the south. However, because the mean fluxes over each region have been removed, the type of error that would accumulate is an over- or underestimate of the flux anomaly magnitudes that is correlated between regions. Errors that are uncorrelated between the regions tend to cancel. Although flux anomaly biases were not seen in the CLIMODE comparisons, such an overestimate in the tropics would account for the relatively large HTC there and the difference in the heat budget balance, compared to ECCO.
Estimates of MHT anomalies with which to evaluate the anomaly magnitudes have been problematic in the South Atlantic, at least until recently. Support for large MHT anomalies, despite small mean values, can be inferred from the large scatter of MHT estimates there (Ganachaud and Wunsch 2003). Estimates of MHT have been made from infrequent repeat hydrographic sections along 34°S: twice per year for 2002–03 and 4 times per year in 2004 through early 2007 and again in 2010 and 2011. For most of 2007 through 2009 an alternate line was used (Garzoli et al. 2012). MHT is likely aliased by the infrequent sampling; a smooth time series of MHT constructed from these estimates gives anomalies of only about 0.1 PW. A monitoring program for 34°S, the South Atlantic Meridional Overturning Circulation Initiative (SAMOC), is currently being implemented; preliminary results show monthly MOC anomalies of about 8 Sv from April 2009 to December 2010, which at 0.05 PW Sv−1 correspond to MHT anomalies of about 0.4 PW (C. Meinen 2013, personal communication), consistent with our results, and considerably larger than estimates based on the hydrographic surveys.
The direct measurements of MHT at 26.5°N since 2004 from MOCHA have a considerable overlap of time with our estimates (Fig. 10b) and give the most useful comparisons. A period of relatively small anomalies (2003–08) was followed by two sharp drops in MHT and an intervening recovery in early 2010. The peak-to-trough change in MHT in our smoothed nonseasonal version of the MOCHA MHT is about 1 PW. A corresponding change of 0.4 PW is seen in observations at 41°N from Willis (2010) (Fig. 10a). The poorly resolved change in model A at 25°N is about 0.2 PW (Fig. 6, center panel). The inclusion of SSH improves the resolution of these events in model B and in model A-SSH even before the adjustment to observations at 41°N (Fig. 10b, cyan and blue lines, respectively), giving changes of about 0.3 PW. The adjustment to match observed MHT at 41°N gives a much improved version of the MHT anomalies with a change of nearly 0.7 PW, which is consistent with the MOCHA estimates within our error bars. Based on these comparisons we believe that the model A-SSH MHT estimates give the best results of our three model runs, owing in part to the improved temporal resolution, but primarily from replacing the assumption of no MHT anomalies at 67°N with matching observations at 41°N.
b. Coherence in MHT
Considerable coherence of MHT is seen in all the runs, especially south of about 40°N. Correlations of MHT from model A or model A-SSH with model MHT at 10°N are high south of 10°N, but decrease substantially to the north (Fig. 11). The decrease in MHT coherence north of 10°N corresponds to a decrease in the magnitudes of the MHT anomalies. The adjustment of model A-SSH to the observations adds a coherent MHT component to all latitudes, which increases the coherence in the North Atlantic to above the significance level. The maximum correlations with 10°N (for both methods) occur for lags of 0 at all latitudes. For comparison with our models, observed MHT at 41°N leads MHT at 26.5°N by 3 months with a correlation of 0.50 (relative to a 95% significance level of 0.40).
Although it is not possible with our models to diagnose the oceanic components of HTC and MHT anomalies, as in the analyses of RAPID/MOCHA (Cunningham et al. 2007; Johns et al. 2011; Srokosz et al. 2012; McCarthy et al. 2012), our analysis can show the spatial extent of the coherent MHT anomalies, as well as the history of anomalies since 1993. Anomalies as large as those recently seen in MOCHA estimates, 0.7 PW in model A-SSH, are seen at other times and locations, the largest being in 1999 and again in early 2001, with coherent minima from 40°N to the Southern Ocean. The lack of a lag in the MHT anomalies and their meridional coherence are suggestive of an Ekman response to large-scale winds, consistent with results from RAPID/MOCHA (McCarthy et al. 2012).
A high level of coherence with a discontinuity near 40°N, the latitude of the separated GS, is consistent with results from several modeling studies. Using the Simple Ocean Data Assimilation (SODA) model, Zheng and Giese (2009) found high correlations between MHT anomalies from 40°N to the equator. This coherence can be seen (their Fig. 3) as far south as 30°S, but there is no apparent correlation with MHT north of 40°N. A similar discontinuity at 40°N was seen in the AMOC by Bingham et al. (2007), with anomalies to the south having a higher frequency than those to the north. A 1000-yr simulation by Zhang (2010) using Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model, version 2.1 (CM2.1), showed slow southward propagation between 50° and 35°N. Although MOC anomalies south of 35°N were correlated with anomalies to the north, there was a discontinuity at this latitude in the propagation speed. The nearly coherent anomalies for 0°–35°N are attributed by Zhang to the fast response of coastal Kelvin waves to forcing in the north. Anomalies in the South Atlantic are only weakly correlated with anomalies at 50°N and have shorter time scales in her study.
Significant coherence south of the GS is also found in MHT computed from a hindcast simulation of the GFDL Hallberg Isopycnal Model/Global Ocean Layer Dynamics Model (HIM/GOLD) (Fig. 14a). The vertical resolution includes two mixed layers, two buffer layers, and 45 isopycnal layers chosen to provide the highest resolution in the thermocline. The horizontal grid is 1° in longitude and latitude, decreasing to 0.5° latitude in the tropics. Circulation variability is forced by changes in surface winds and buoyancy fluxes from National Centers for Environmental Prediction (NCEP) reanalysis [Common Ocean Reference Experiment, version 2 (CORE-2)] from 1959 to 2005 (Large and Yeager 2009) after a spinup of several hundred years. Freshwater fluxes are applied together with a restoring of sea surface salinity using a variable time scale of 0.5 m day−1. This model run was also used in Deutsch et al. (2011) to investigate oxygen variability in the tropical Pacific. While coherence drops below the 95% significance level north of 40°N (Fig. 14a) as in model A (Fig. 11), the coherence also drops in the South Atlantic, suggesting that the coherence in the South Atlantic from our MHT estimates may be too high. An overestimate of the MHT anomalies in the South Atlantic arising from an overestimate of tropical flux anomalies would cause MHT coherence in the South Atlantic to be too high.
c. Atlantic Ocean heat budget
To understand the large-scale heat budget, we computed EOFs of surface heat fluxes, MHT, and heat storage from model A-SSH. The first mode of MHT accounts for 92% of the MHT variance (Fig. 12a), reflecting its high level of meridional coherence. The first three modes of surface fluxes (summed over the regions to give anomalies in PW) contained 33%, 23%, and 17% of the variance, respectively. Heat storage (derived from the tendency of heat content ∂ηH/∂t and converted to PW) contained 28%, 22%, and 17% of its variance in the first three modes. The distribution of variance over several modes suggests a relative lack of meridional coherence for either fluxes or heat storage.
The fields reconstructed from these modes are instructive (Fig. 12) in understanding the heat budget. The strongest relationship is between (the first mode of) surface heat flux forcing and MHT: an anticorrelation with MHT leading fluxes by 1 month (ρ = −0.78, compared with 0.6 for 95% significance). When MHT anomalies are positive (more heat is transported into the North Atlantic), more heat is lost from the ocean in the subtropical gyre (flux anomalies are more negative). This anticorrelation is consistent with the regional budgets (Fig. 2) and with previous analyses of the heat budget by Dong and Kelly (2004), which show that increased heat advection in a region that contains the GS increases the flux of heat to the atmosphere. The meridional decrease in MHT anomalies in regions 3 and 4 (10°–40°N) corresponds to the largest values of surface fluxes in the North Atlantic. The coherence of MHT decreases north of 40°N because so much of the heat transported by the ocean is fluxed to the atmosphere in the subtropical gyre.
On the other hand, heat storage (Fig. 12c) has no consistent relationship with surface fluxes (Fig. 12b). For example, during the recent drop in MHT (2009–10) at 26.5°N there is an expected decrease in surface heat loss (positive flux anomalies); however, heat storage decreases north of about 30°N, but increases south of 30°N. Heat storage anomalies frequently change sign across 30°N, whereas fluxes generally have the same sign.
The large-scale heat budget demonstrates the importance of ocean circulation anomalies in the climate system. As in the mean heat budget, anomalous heat storage is not a simple function of local surface flux anomalies. Heat absorbed by the ocean, rather than contributing to local heat storage anomalies, is transported by ocean circulation, specifically the MOC. An increase in the MOC corresponds to increased MHT; much of the anomalous heat transport by the ocean is fluxed to the atmosphere in the North Atlantic subtropical gyre (10°–40°N). This “baton pass” of heat from ocean to atmosphere increases the atmosphere’s heat transport, while potentially enhancing extratropical storms.
d. Relationship to climate indices
To help determine the origin of coherent MHT anomalies we lag correlated MHT with the dominant climate indices in the north and in the south. Neither the first nor the second MHT mode is significantly correlated with the NAO. Further, none of the MHT estimates across individual lines is correlated with the NAO. However, the first mode of MHT is significantly anticorrelated with the Antarctic Oscillation (AAO) (−0.34 [0.26]), with the AAO leading by 13 months, suggesting a southern origin (Fig. 13). A similar anticorrelation is found in HIM/GOLD (Fig. 14b), with AAO leading coherent MHT by 23 months. This relationship suggests that increasing westerlies in the Southern Ocean correspond to decreasing MHT in the South Atlantic more than one year later. An analysis of the OGCM for the Earth Simulator (OFES) model global simulations showed that MHT anomalies in the South Atlantic arise from convergences between flow through the Drake Passage and flow south of Africa, with the largest contributions from the Agulhas Current region (Dong et al. 2011).
A discussion of the mechanisms by which the Agulhas leakage and other southern processes would affect the AMOC focuses primarily on the decadal and longer time scales (Beal et al. 2011). The mechanisms are many, but one of the most direct mechanisms relates the winds in the Southern Ocean to the position of the subtropical front (STF). Southward excursions of the STF, corresponding to increasing westerlies (larger AAO anomalies) and a southward shift of the core of the winds, would increase the size of the window through which the Agulhas leakage occurs, increasing heat advection into the Atlantic. However, this would give a positive correlation between MHT and AAO and likely a longer temporal lag in MHT response. In particular the anomalously strong and southerly shift of the Southern Ocean westerlies that occurred in 1995–2004 does not clearly correspond to the coherent MHT anomalies (Fig. 8). A study that is consistent with our results is an analysis of an eddy-permitting model of the Southern Ocean that shows an increase in poleward eddy heat fluxes (a decrease in northward heat transport) in response to increasing winds (Spence et al. 2010).
e. Mass budget
Ocean mass anomalies do not show evidence of local forcing. A study by Ponte (2006) using a barotropic model demonstrated that local mass anomalies are much smaller than the large-scale forced response because open ocean mass anomalies are redistributed to achieve an equilibrium balance on the monthly time scales resolved by this model. Ponte noted that the ocean response to freshwater fluxes may be observable by GRACE, particularly at low latitudes; however, only region 7 had a significant correlation between freshwater flux forcing and mass tendency ∂ηM/∂t. To see whether the mass response to P − E was apparent on a larger scale, we computed EOFs of surface freshwater fluxes and ∂ηM/∂t. The first two modes of freshwater flux account for 33% and 22% of the variance and the first two modes of ∂ηM/∂t account for 75% and 18% of the variance (Fig. 15). Despite strong meridional gradients in freshwater forcing, the ocean mass response is highly coherent. The first modes of P − E and ∂ηM/∂t are not significantly correlated with each other, although both show a positive trend with time; thus, even on this large scale ocean mass is not responding locally to freshwater forcing at time scales longer than a month.
Freshwater forcing and response anomalies were examined in relation to ENSO. Precipitation in the western tropical Atlantic and over South America increases substantially during a La Niña (Dai and Wigley 2000). In an examination of hydrological conditions in the Amazon basin, Xavier et al. (2010) found that the rate of basin water storage, derived from GRACE gravity anomalies, was highly correlated with the Southern Oscillation index (SOI). Water storage rates from GRACE correspond well with estimates of Amazon River flow with rates as large as 0.01 Sv, comparable in size to the MTC anomalies in the model (Fig. 3). River outflow was not included explicitly in our models, owing to the difficulty in obtaining river flow records. However, assuming the river outflow would be dispersed as rapidly as precipitation, one would not expect to detect its contribution in this analysis. The only SOI signature appears in region 7 in both MTC and in P − E, which are highly anticorrelated; however, the source of this signature is likely the ENSO-related precipitation. The ENSO signature of Amazon River outflow is likely owing to an increase in precipitation over South America and it likely makes a more obvious contribution to the ocean salinity anomaly than to mass.
f. Model limitations
Salinity contributes to SSH through density and its neglect will affect the mass budget, as well as having implications for circulation; it will be included in a planned future analysis. We included estimates of the missing contribution of salinity in the error estimates for the Kalman filter that contributed to the error estimates of HTC in model B and model A-SSH.
A shortcoming of model A is the neglect of MHT anomalies below 700 m, owing to the depth limitations of TSL. An estimate of the error associated with this limitation is included in the error estimates, so that the error bars on HTC are not overly optimistic. The estimates of MHT at 41°N share this limitation to some extent; however, observations of MHT at 26.5°N do not (McCarthy et al. 2012). Several studies of the vertical structure of MHT suggest that the anomalies are surface intensified, although less so in the Atlantic than elsewhere. In an analysis from a coarse-resolution version of the Massachusetts Institute of Technology General Circulation Model (MITgcm), Boccaletti et al. (2005) argue that while the MOC depends greatly on the abyssal ocean, MHT does not, owing to weak temperature gradients there. Argo profiles that extend deeper into the ocean could greatly reduce this limitation.
Replacing TSL with SSH improved the temporal resolution of the heat budget in model A-SSH. The errors associated with neglecting mass and HSL in treating SSH as thermosteric sea level are no greater than the combined errors in TSL from sparse sampling, annual averaging, and neglect of anomalies below 700 m. However, using SSH in this way does not allow for an independent estimate of the contributions of mass to sea level.
6. Summary and conclusions
Using two versions of a box model and monthly observations with realistic error estimates, we computed the nonseasonal heat budget for the Atlantic Ocean over a period of 18 yr and both heat and mass budgets over 8 yr. We analyzed three model runs: the heat budget only, assimilating either TSL (model A) or SSH (model A-SSH), and a combined heat and mass budget assimilating TSL, EWT, and SSH (model B). Anomalies in heat content are the primary component of SSH anomalies, but mass anomalies contribute a small positive trend over the observation period (2003–10). In the North Atlantic subtropics and in the tropics surface heat flux anomalies are balanced by heat transport convergence (HTC), with heat storage making a smaller contribution. A similar, but more dominant balance between freshwater fluxes and mass transport convergence (MTC) occurs in the mass budgets, consistent with previous studies showing that mass anomalies are rapidly distributed throughout the ocean.
Using the HTC from three runs, estimates of meridional heat transport (MHT) were derived using two different assumptions. In all cases HTC was summed from north to south. For model A and model B, MHT anomalies were assumed negligible at the northern boundary (67°N); in model A-SSH MHT was adjusted everywhere, leaving HTC unchanged, so that MHT estimates at 40°N match an independent estimate of MHT at 41°N. MHT from model A-SSH at 25°N agrees well with independent estimates of MHT anomalies from the RAPID/MOCHA array at 26.5°N (McCarthy et al. 2012).
Modeled MHT is coherent from the Southern Ocean to 40°N with correlations dropping to the north, below the significance level for model A, but remaining significant for model A-SSH. This coherence pattern is similar to that seen in an ocean model; however, the comparison suggests that the coherence in the South Atlantic in our models may be too high. MHT coherence is a consequence of large South Atlantic MHT anomalies that are forced by HTC in the tropical Atlantic. Although direct observations of South Atlantic MHT are limited, the large anomalies suggest that the tropical heat flux anomalies used here are somewhat too large.
While not directly providing insight into the mechanisms, the MHT estimates demonstrate the magnitudes and timing of interannual MHT anomalies in the Atlantic over the 18-yr period. In particular, the model shows that anomalies in MHT comparable to or larger than that recently observed at the RAPID/MOCHA line occurred in 1999–2001; these anomalies extended throughout the Atlantic south of 40°N.
An analysis of the large-scale Atlantic Ocean heat budget reveals the role of the MOC in anomalies of atmospheric heat transport and in the fluxes that potentially enhance extratropical storms. During periods of large MHT anomalies (equivalent locally to large MOC anomalies) the ocean fluxes most of the excess heat to the atmosphere in the subtropical North Atlantic. The decrease in coherence of ocean MHT anomalies over the subtropical North Atlantic is caused by the flux of those heat anomalies to the atmosphere, parallel to the transfer of ocean MHT to the atmosphere in the mean. There is no consistent relationship between local surface fluxes and local heat storage, highlighting the importance of MHT in the heat budget.
The MHT anomalies are not correlated with the NAO; however, coherent MHT anomalies are correlated with the AAO, lagging it by more than one year. This suggests forcing in the South Atlantic or in the Southern Ocean. A similar relationship between coherent MHT and the AAO was found in an ocean model. We are currently conducting an exploration of the mechanisms for forcing by Southern Ocean or South Atlantic processes using additional data and climate models.
KAK and LT were supported by NASA through Grant 61-7449 (Ocean Surface Topography Science Team) with the University of Washington. JL was supported by the NOAA Climate Program Office and the NOAA Office of Oceanic and Atmospheric Research. The sea level product MSS_CNES_CLS10 was produced by CLS Space Oceanography Division and distributed by Aviso, with support from CNES (http://www.aviso.oceanobs.com/). The bulk of the in situ data was provided through the World Ocean Database 2005 and the Global Temperature-Salinity Profile Program (http://www.nodc.noaa.gov). Float data were collected and made freely available by the Argo Program (of the Global Ocean Observing System) and contributing national programs (http://www.argo.net/). GRACE gravity data were processed by Don P. Chambers, supported by the NASA MEASURES Program, and are available at http://grace.jpl.nasa.gov. The OAFlux project is located at the Woods Hole Oceanographic Institution and is supported by both the NOAA Climate Observations and Monitoring (COM) program and the NASA Ocean Vector Winds Science Team. The Global Precipitation Climatology Project (GPCP) and the International Satellite Cloud Climatology Program (ISCCP) were both established as part of the World Climate Research Programme (WCRP) to provide access to global products. We thank J. Willis, W. Johns, S. Dong, and C. Meinen for making their MOC/MHT estimates available for comparison. J. Zhang computed the MHT estimates from HIM. Anonymous reviewers contributed to an improved analysis and presentation.
Pacific Marine Environmental Laboratory Contribution Number 3950 and Joint Institute for Marine and Atmospheric Research Contribution Number 12-382.