## 1. Introduction

The thermal physics of the ocean is of great interest in climate studies. This is mainly due to the ocean’s role in redistributing heat in the earth system. Meridional transport of heat by ocean currents contributes as much as one-third to the global poleward heat transport around 14°–24°N (Trenberth and Caron 2001; Ganachaud and Wunsch 2003). Divergences in ocean heat transport either can be stored locally within the ocean or exchanged with the atmosphere via radiative and turbulent fluxes. Sea surface temperatures mediate such air–sea energy fluxes, thus exerting a direct influence on climate, for example in the Atlantic sector (Marshall et al. 2001). Understanding and attributing the storage and transport of heat in the ocean is thus integral to fuller comprehension of climate system dynamics.

Thermal variability in the ocean can be due to direct forcing by the atmosphere, truly coupled ocean–atmosphere interactions, or intrinsic oceanic dynamics. Sea surface temperature variability has been studied extensively and related to various statistical indices of climate, as reviewed by Deser et al. (2010): interannual-to-decadal temperature variability in the extratropical ocean is related primarily to modes of atmospheric circulation (e.g., North Atlantic Oscillation); year-to-year tropical ocean temperature changes correspond to coupled atmosphere–ocean interactions (e.g., El Niño–Southern Oscillation); and on multidecadal time scales, surface temperature variability is supposed to reflect intrinsic modes of the ocean’s thermohaline circulation (e.g., Atlantic multidecadal oscillation). However, correlation with these statistical indices does not amount to causal explanation, and the dynamical relationship of sea surface temperature variability patterns to the storage and transport of heat in the ocean interior is not clear.

One time and repeat hydrographic occupations have allowed for the estimation of ocean meridional heat transports at a number of latitudes (MacDonald 1998; Bryden and Imawaki, 2001; Ganachaud and Wunsch 2003), and some estimates of the relative importance of various components of the circulation to the mean transports have been made from observations (Talley 1999, 2003) and models (Boccaletti et al. 2005). Shallow, intermediate, and deep overturning components can contribute importantly to the total meridional heat transport, for example, at 24°N in the Atlantic (Talley 1999, 2003). Regarding the temporal variability of heat transports, direct measurements are sparse (excepting 26°N in the Atlantic; see Johns et al. 2011), but coupled models have been used to estimate the seasonal-to-decadal variability and diagnose the underlying causes (e.g., Dong and Sutton 2001; Jayne and Marotzke 2001; Shaffrey and Sutton 2004). Variable Ekman fluxes generally make important contributions to seasonal and interannual heat transports, but other mechanisms (e.g., temperature variability, deeper overturning circulation changes) can also play a role depending on region and time scale (Dong and Sutton 2001; Jayne and Marotzke 2001). Subsequent attribution of ocean heat storage rates in terms of the factors known to underlie heat transport changes in large part has not been made, however.

Links between ocean circulation and heat transport variability, sea surface temperature changes, and ocean heat storage must be understood before the potential impacts of overturning circulation changes on Atlantic sector climate can be anticipated (Lozier 2010). The goal of this study is to elucidate how ocean heat storage rates are tied to changes in ocean circulation across various regions and time scales.^{1} To this end, variability in meridional heat transport and heat storage rates are examined across the Atlantic using an ocean state estimate produced by the Estimating the Circulation and Climate of the Ocean (ECCO) consortium (Wunsch et al. 2009). The ECCO estimates—generated by a general circulation model along with its adjoint and constrained to a multiplicity of observations through least squares—represent model–observation syntheses. The ECCO approach reduces some of the shortcomings characterizing model- or observation-only approaches (e.g., ill-known errors in the former case and data paucity in the latter) and thus, in a statistical sense, ECCO solutions arguably represent “best estimates” of the ocean state. The remainder of this paper is structured as follows: in section 2 the characteristics of both the state estimate and numerical model are discussed; for context, meridional heat transports and transport decompositions are presented in section 3; heat storage rate budgets are analyzed in section 4 to determine the importance of heat transport to heat storage rates as a function of region, depth, and time scale; and finally, a summary and discussion are offered in section 5.

## 2. General circulation model framework

An ocean state estimate produced by the ECCO group forms the basis of this study. The ECCO state estimates represent evolved, optimized solutions of the Massachusetts Institute of Technology general circulation model (MITgcm) (Marshall et al. 1997a,b; Adcroft et al. 2010) fit to a majority of the World Ocean Circulation Experiment (WOCE) era hydrography, Argo floats, satellite altimetry, and most other available ocean data in a weighted nonlinear least squares sense. Using the model’s adjoint (Heimbach et al. 2005; Heimbach 2008), a cost function weighing the model–data misfit is minimized via iterative adjustment of a high-dimensional control vector containing initial conditions and boundary conditions (Wunsch and Heimbach 2007; Wunsch et al. 2009). The optimization achieves both consonance with observations (to within specified uncertainties) as well as dynamical consistency with all model equations. The solution’s consistency allows for quantitative analysis of property budgets that close exactly. The various ECCO products, optimization procedures, as well as the data and data weights (i.e., uncertainties) used in the optimization are described in much more detail in several publications. Interested readers are referred to Wunsch and Heimbach (2007) as well as Wunsch et al. (2009) and the references therein. Refer to Adcroft et al. (2010) for a detailed description of parameterizations and numerics in the circulation model proper.

A brief description suffices for the present purposes. The solution is defined on a (nearly) global range, from 80°S to 80°N, with a 1° horizontal grid resolution and 23 vertical layers ranging in thickness from 10 m at the sea surface to 500 m in the abyssal ocean. The model uses the Boussinesq approximation with an implicit linear free surface and a virtual salt flux boundary condition. Hydrographic initial conditions are first taken from a blend of Gouretski and Koltermann (2004) and Boyer and Levitus (1998) climatologies; six-hourly products from the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis described by Kalnay et al. (1996) are used over the duration 1992–2004 as “first guess” atmospheric forcing fields; these initial conditions and boundary conditions constitute the ECCO control vector and are iteratively adjusted and optimized. Mixing fields generally have Laplacian, Gent–McWilliams (Gent and McWilliams 1990; Griffies 1998), Redi (1982), and nonlocal K-profile parameterization (Large et al. 1994) components. Surface heat fluxes comprise longwave, shortwave, sensible, and latent contributions; shortwave radiation is allowed to penetrate vertically as Jerlov Type IA water (Jerlov 1968; Paulson and Simpson 1977).

The present analysis makes use of ECCO solution v2.216 (version 2, iteration 216), which covers the years 1992–2004 and was produced at the Massachusetts Institute of Technology and Atmospheric and Environmental Research, Inc. (MIT–AER). This solution is described in detail in Wunsch et al. (2007) in the context of an analysis of decadal sea level trends. Though more recent 1° ECCO state estimates are now available, comparisons to the solution used here reveal similar qualitative results and suggest that contemporary versions are approaching a stable estimate (Wunsch and Heimbach 2009). Given the nonlinearity of the problem, however, one cannot categorically rule out the possibility of qualitatively distinct results in future ECCO estimates.

Monthly model output is the target of investigation here. Because of the observational data paucity and transients evident in the solution during 1992 (cf. Wunsch et al. 2007), the solution is analyzed only over 1993–2004. Our focus is mostly on transport and storage of heat in the subtropical and tropical Atlantic Ocean, though some higher-latitude regions in the North Atlantic are also considered. This study expands upon the work of Wunsch and Heimbach (2006), who computed heat fluxes at 26°N using an earlier ECCO integration.

## 3. Meridional heat transport

*c*is the specific heat capacity of seawater (J kg

_{p}^{−1}°C

^{−1}),

*ρ*

_{0}is a reference density (kg m

^{−3}),

*υ*is meridional velocity (m s

^{−1}), and

*θ*is potential temperature (°C). (A list of frequently used notation is given in Table 1.) Meridional heat transports computed from the ECCO state are presented in Fig. 1 alongside previously published observational estimates (Table 2).

^{2}Uncertainties in the literature values are standard errors while uncertainties in the ECCO estimates represent temporal variability. Although quantitatively ECCO values appear to underestimate the magnitude of the observationally derived heat transport at many latitudes, uncertainty ranges are mostly overlapping and the overall latitudinal pattern of the ECCO heat transports is qualitatively similar to the structure of the observation-based estimates.

Notation used in the text.

Heat transport estimates from the literature used in Fig. 1. Latitudinal sections given are nominal; see references for exact section location. Uncertainties are standard errors as provided. Where more than one value was given, mean values are presented here, and uncertainties are propagated standard errors plus the standard deviation of estimates. In the case of Talley (2003), no formal errors were given. Talley (2003) instead gives a general uncertainty of 10%–20% of the transport value, up to 0.2 PW. The upper bound of this range is used here.

Given our interest in temporal variability on seasonal and interannual time scales, heat transports are separated into time mean ^{−1}. We next examine what variables (mean and anomalous temperature and velocity) and components of the circulation (zonally symmetric barotropic, zonally symmetric baroclinic, and zonally asymmetric) contribute most to the behavior of

### a. Variable decomposition

^{−}) denotes the local time mean, and the prime (′) denotes deviation from the time mean, such that

Decompositions are presented in Fig. 2. Here, *σ*) is comparable to

Variable decomposition of heat transports. (a) Time-mean transports; (b) standard deviation of the 12-month seasonal cycle time series; (c) standard deviation of the 144-month interannual anomaly time series; (d) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Variable decomposition of heat transports. (a) Time-mean transports; (b) standard deviation of the 12-month seasonal cycle time series; (c) standard deviation of the 144-month interannual anomaly time series; (d) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Variable decomposition of heat transports. (a) Time-mean transports; (b) standard deviation of the 12-month seasonal cycle time series; (c) standard deviation of the 144-month interannual anomaly time series; (d) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

*σ*values in Figs. 2b–c do not contain information regarding signal phase. For a more thorough comparison, let the variance

*x*(

*t*) explained by another time series

*σ*

^{2}represents temporal variance. Thus defined

*x*are well explained by

*x*and

*σ*(

*x*). By way of example, a value of

*x*’s variance (i.e., removing

*x*amounts to a 50% decrease in variance relative to

*x*), while a value of

*increases*the variance of

*x*by 50% (i.e., removing

*x*amounts to a 50% variance increase). As shown in Figs. 2d–e, seasonal and interannual variance in

*θ*changes cannot be entirely neglected, however (Fig. 2d). At higher latitudes, variance in

*υ*and

*θ*variability as well as their covariability (Figs. 2d–e).

The dominant role of *υ*–*θ* covariation are relatively small at tropical and subtropical latitudes (Dong and Sutton 2002), they are in contrast to work done at higher grid resolutions suggesting that covariable contributions associated with mesoscale eddy processes (that cannot be resolved by coarse-resolution models) can explain up to 20% of the seasonal-to-interannual meridional heat transport variance in the tropics and along latitudes of strong western boundary currents (Jayne and Marotzke 2002; Volkov et al. 2008).

### b. Circulation component decomposition

Decompositions are presented in Fig. 3. While

Circulation decomposition of heat transports. (a) Time-mean transports; (b) standard deviation of the 12-month seasonal cycle time series; (c) standard deviation of the 144-month interannual anomaly time series; (d) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Circulation decomposition of heat transports. (a) Time-mean transports; (b) standard deviation of the 12-month seasonal cycle time series; (c) standard deviation of the 144-month interannual anomaly time series; (d) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Circulation decomposition of heat transports. (a) Time-mean transports; (b) standard deviation of the 12-month seasonal cycle time series; (c) standard deviation of the 144-month interannual anomaly time series; (d) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

These results are consistent with previous studies. In their inverse solution based on observations, Ganachaud and Wunsch (2003) find that

## 4. Heat storage rate budgets

*V*by means of the heat transport divergence

**u**is the three-dimensional velocity field (m s

^{−1}),

*A*is the surface area bordering the volume (m

^{2}), and

**n**is the normal unit vector. Here,

*V*can be defined as the volume integral of the forced advection–diffusion equation for local potential temperature conservation

^{−1}), and

^{−2}). Hereafter the (volume-integrated) four terms inside the brackets will be referred to as (from left to right) the heat storage rate

Oceanic study regions. Regions are named according to World Hydrographic Program (WHP) lines bounding the region to the north and south. Each region is bounded on the east and west by continents. See Fig. 4 for exact boundary locations.

Atlantic Ocean study regions. Regions are named according to bounding WHP transect lines.

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Atlantic Ocean study regions. Regions are named according to bounding WHP transect lines.

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Atlantic Ocean study regions. Regions are named according to bounding WHP transect lines.

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

### a. Near-surface budgets

Full time series of seasonal and interannual near-surface budget terms are shown in Fig. 5 and summarized statistically in Fig. 6. In most areas,

(left) Twelve-month seasonal (month 1 represents January) and (right) 144-month interannual time series of near-surface (0–100 m) budgets. All dependent axes are in Petawatts. Budget terms are denoted as heat storage rate

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

(left) Twelve-month seasonal (month 1 represents January) and (right) 144-month interannual time series of near-surface (0–100 m) budgets. All dependent axes are in Petawatts. Budget terms are denoted as heat storage rate

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

(left) Twelve-month seasonal (month 1 represents January) and (right) 144-month interannual time series of near-surface (0–100 m) budgets. All dependent axes are in Petawatts. Budget terms are denoted as heat storage rate

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Statistical summary of near-surface heat budgets. (a) Standard deviation of seasonal cycle time series of budget components; (b) standard deviation of interannual anomaly time series of budget components; (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Statistical summary of near-surface heat budgets. (a) Standard deviation of seasonal cycle time series of budget components; (b) standard deviation of interannual anomaly time series of budget components; (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Statistical summary of near-surface heat budgets. (a) Standard deviation of seasonal cycle time series of budget components; (b) standard deviation of interannual anomaly time series of budget components; (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Regarding interannual time scales,

### b. Upper-ocean budgets

Time series of upper-ocean budget terms are shown in Fig. 7 and summarized statistically in Fig. 8. In areas A0203 and A0305,

As in Fig. 5, but for the upper ocean (0–1000 m).

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

As in Fig. 5, but for the upper ocean (0–1000 m).

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

As in Fig. 5, but for the upper ocean (0–1000 m).

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

As in Fig. 6, but for the upper ocean.

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

As in Fig. 6, but for the upper ocean.

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

As in Fig. 6, but for the upper ocean.

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Substantial differences between interannual near-surface and upper-ocean budgets (cf. Figs. 5 and 7) indicate considerable interannual variability deeper than 100 m. Generally,

### c. Diagnosing the heat transport divergence

Because we are ultimately interested in attributing heat storage rates to changes in the general circulation, we now examine what variables and circulation components most contribute to the heat transport divergence in the study regions. By Gauss’s Theorem (see Eq. 6), the heat transport divergence over a full-depth, basinwide control volume can be computed as the difference in heat transport across the section’s northern and southern boundaries. Because the control volumes studied here are not bounded on the north and south by strict parallels (Fig. 4), decompositions of heat transport divergences over the study regions are estimated as the difference in the respective component of the meridional heat transport evaluated at the nominal latitudes bounding the control volume (Table 3). This yields a very good approximation to heat transport divergences computed over the control volumes proper (Table 4). Statistical summaries of decompositions of full-column heat transport divergence time series are presented in Figs. 9 and 10.

Variance in the heat divergence *r* ≥ 0.9; not shown); however, in some instances

Variable decomposition of heat transport divergences. (a) Standard deviation of seasonal cycle time series, (b) standard deviation of interannual anomaly time series, (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Variable decomposition of heat transport divergences. (a) Standard deviation of seasonal cycle time series, (b) standard deviation of interannual anomaly time series, (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Variable decomposition of heat transport divergences. (a) Standard deviation of seasonal cycle time series, (b) standard deviation of interannual anomaly time series, (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Circulation decomposition of heat transport divergences. (a) Standard deviation of seasonal cycle time series; (b) standard deviation of interannual anomaly time series; (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Circulation decomposition of heat transport divergences. (a) Standard deviation of seasonal cycle time series; (b) standard deviation of interannual anomaly time series; (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

Circulation decomposition of heat transport divergences. (a) Standard deviation of seasonal cycle time series; (b) standard deviation of interannual anomaly time series; (c) variance in 12-month

Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00123.1

The magnitude and timing of

Decompositions of

## 5. Summary and discussion

In this study we sought to relate heat storage rates in the Atlantic Ocean to changes in the general circulation. For this purpose we have employed an ocean state estimate produced by the ECCO project (Wunsch and Heimbach 2007; Wunsch et al. 2009). The state estimate utilizes most available ocean observations, fitting them to a state-of-the-art general circulation model using advanced optimization methods. The solution retains dynamical consistency and is ideally suited for closed budget analysis.

We contextualized our budget study by first presenting estimates of the time-mean and anomalous heat transports, decomposing the transports in terms of relevant variables and circulation components. Next, the role of heat transport divergence in determining heat storage rates as a function of region, depth, and time scale was studied. Last, it was determined what variables and components of the circulation contribute most to the behavior of the heat transport divergence. Viewed as a whole, these results provide insight on the role of circulation changes in determining Atlantic Ocean heat storage rates.

The relationship of meridional heat transport changes to velocity field changes or diagnostics of the overturning circulation depends strongly on latitude and time scale (Figs. 2–3). Seasonal heat storage changes are confined mostly to the top 100 m of the ocean, although contributions are evident at greater depths in low-latitude areas (Figs. 5–8). More than 90% of the interannual ocean heat storage rate variance is found at depths above 1000 m (not shown). Advection of heat is important in low-latitude regions, contributing to the magnitude and timing of the heat storage (Figs. 5–8). On interannual scales, advection is the primary contributor to heat budgets in the upper ocean; it is larger than the anomalous surface heat flux in all regions and alone it explains more than half of the heat storage rate variance in most regions (Figs. 7 and 8).

The above results are generally consistent with prior studies, yet further insight is gained by decomposing the advection in terms of velocity and temperature variations as well as components of the circulation (Figs. 9 and 10). Variance in heat advection is mostly accounted for by changes in the meridional velocity field (Fig. 9). Temperature changes are not always irrelevant, however, making important contributions to the heat transport divergence at higher latitudes (Fig. 9). In equatorial regions and at northern tropical and subtropical latitudes, changes in advection are attributable to heat transport carried by the zonally symmetric baroclinic flow (Fig. 10). Outside of this range, consideration of heat transport changes associated with zonally symmetric baroclinic and zonally asymmetric branches of the circulation becomes necessary to attribute the advection (Fig. 10).

Shallow, intermediate, and deep components of the general circulation are thought to contribute to time-mean heat budgets in the subtropical Atlantic (Talley 1999, 2003), but little is known about how heat storage is affected by overturning changes. Our results suggest that seasonal and interannual changes in the meridional overturning circulation can be important to large-scale heat storage rates. For the latitudes studied, Atlantic heat storage rate changes are confined mainly to the upper ocean. The zonally symmetric baroclinic flow generally comprises contributions from intermediate and deep overturning circulations as well as surface Ekman and deeper return flows and other shallow overturning circulations (Bryden and Imawaki 2001; Talley 2003). In our analysis, a combination of surface heat fluxes, shallow overturning (including Ekman flows), and overturning of intermediate waters (below c. 500 m) accounts for ocean heat storage rates near the equator as well as for interannual storage at most tropical and subtropical latitudes; overturning of deep waters (below c. 2000 m) probably is not important on these time scales.

Although overturning changes are believed to impact Atlantic sector climate via direct influence on sea surface temperatures, the details of this influence have not been established (Lozier 2010). Results presented here reveal instances in which changes in the zonally symmetric baroclinic circulation can be readily related to upper-ocean heat storage rates (Figs. 7, 8, and 10). Furthermore, within approximately 10° of the equator (i.e., region A0608), the timing of interannual near-surface and upper-ocean heat storage rate and advection fluctuations are all very similar (cf. Figs. 5 and 7); in this region, interannual near-surface heat storage rate variations can be related to changes in the full column heat transport divergence (correlation between

Some caveats of the present study should be acknowledged. In particular, the ECCO solution used in these analyses does not permit eddies, a sea ice model is lacking, and latitudes higher than 80° are not included. The sensitivity of our results to incorporation of any of these elements remains to be examined. As noted above, while our decomposition of meridional heat transports into circulation components (Fig. 3) agrees with a study based on a truly global, eddy-permitting model with a sea ice component (Grist et al. 2010), our assessment of the importance of covariable heat transports (Fig. 2) is lower than what one would expect based on eddy-permitting-model results (Volkov et al. 2008).^{3} The analysis period considered (1993–2004) also limits the range of time scales available for analysis. Once present shortcomings are resolved, future heat budget studies should allow us to explore, for example, how near-surface temperatures, sea ice cover, and circulation changes relate to one another in the high-latitude North Atlantic on decadal time scales (cf. Deser et al. 2002). Parallel efforts to incorporate elements mentioned above are being undertaken presently. (For a complete list of ECCO-related efforts and products, see http://www.ecco-group.org/).

## Acknowledgments

We acknowledge N. Vinogradova for producing the output needed in this study and assisting in the formulation of heat budgets. This work was supported by Grant NNX08AV89G from the National Oceanographic Partnership Program and Contract NA10OAR4310199 from the National Oceanographic and Atmospheric Administration’s Office of Global Programs. We sincerely thank the anonymous reviewers whose suggestions considerably improved the manuscript.

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^{1}

For clarity, the phrase “heat storage rate” is used throughout the manuscript as shorthand for “rate of change of ocean heat storage.”

^{2}

Because the ECCO state estimate is constrained by historical data, Fig. 1 should not be taken to represent a comparison to independent data; here, we mean simply to provide a context for ECCO heat transport values.

^{3}

To be clear, our assessment of *covariable* heat transports does not constitute an assessment of *eddy* heat transports; in this solution, subgrid-scale eddy processes are parameterized and contained in the mixing terms, and thus are not contained in our heat transport decompositions; further analysis is needed to examine how the effects of parameterized subgrid-scale processes compare to higher-resolution solutions where eddies are permitted or resolved.