Most of our analysis uses output from a numerical simulation of the Parallel Ocean Program (POP) 2, a primitive equation ocean model . POP is the ocean component of the Community Earth System Model framework, and in this simulation it was configured on a tripole grid with two north poles over Canada and Siberia; more details of the simulation are found in and . The simulation was run on the Yellowstone computing cluster with a resolution of 0.1∘ at the Equator and approximately 8 km in the mid-Atlantic; it was forced with Coordinated Ocean-Ice Reference Experiments version 2 CORE.v2;, an interannually varying flux dataset based on the National Centers for Environmental Prediction reanalysis with corrections from various satellite data. The model integration was started from 15 years of spinup using CORE normal-year forcing and run over 33 years (corresponding to forcing for the years 1977–2009); our analysis encompasses 32 years and begins in 1978 to focus on the period after the post-spinup transition. State variables (including velocity and temperature) and temperature fluxes have been archived from this simulation in 5 d averages, facilitating studies of mesoscale processes which frequently vary on intraseasonal timescales.

In addition to the model simulation output, the ocean surface dynamic topography dataset merged from various altimeters is used to validate the model's mean state and its representation of ocean surface variability. This dataset is produced by Collecte Localisation Satellites and available through the Copernicus Marine Environment Monitoring Service (CMEMS) at 1/4∘ spatial and daily temporal resolution. Compared to the altimetry-based dynamic topography, the model reproduces most essential features of the circulation in the North Atlantic (Fig. ), though there are several important issues that have been previously noted in other model simulations for a review of these issues, see. These include the Gulf Stream separating from the continental slope at 38–39∘ N in the model (Fig. b) vs. ∼36∘ N in observations (Fig. a), and too-low eddy kinetic energy in the Northwest Corner region near 50∘ N, 40∘ W and in the Azores Current region near 34∘ N (Fig. c, d). These inaccuracies have been resolved in regional simulations of the North Atlantic at 1/10∘ resolution e.g., but persist in global simulations even at the same resolution e.g.,. Therefore, the focus of this study is on 40∘ N, in between the Gulf Stream separation and the Northwest Corner where the distribution of EKE in the model is qualitatively similar to observations (Fig. c, d). The zonally averaged values of EKE at 40∘ N are lower in POP than in the altimetry data, but this is true of much of the North Atlantic, and the zonally averaged EKE peaks in altimetry and in the model are both at latitudes near 40∘ N (Fig. e).

Applying the procedure described in Sect.  at several different latitudes, it is possible to obtain an understanding of the spatial scales associated with temperature flux contributions (Fig. ). For example, contrasts can be observed in the non-overturning MHT in the Atlantic at 28 and 34∘ N, both latitudes at which a strong northward western boundary current is compensating a broad interior southward Sverdrup flow (Fig. a–h). Most of the non-overturning temperature flux is associated with the large-scale component at both latitudes; however, the net mesoscale temperature flux (MTF) switches sign from negative at 28∘ N to positive at 34∘ N (Fig. d, h). The reason for this is the temperature difference between the core of the northward boundary current and the southward recirculation ∼2∘ to the east. At 351 m depth (a representative depth for lateral temperature gradients in the thermocline), the temperature at 28∘ N is lower in the boundary current than it is in the interior recirculation (Fig. b), as isopycnals tilt upward sharply approaching the Florida coast; this large-scale temperature gradient interacts with the mesoscale velocity structure, and therefore the vMTL term explains the negative MTF (Fig. d). However, at 34∘ N, the temperature peak along the zonal profile is coincident with the boundary current (Fig. f), and the temperature peak also has more of a mesoscale signature that explains why the vMTM contributes the most to the MTF (Fig. h). (The vLTM term is typically negligible due to the red-shifted spectra of temperature relative to velocity as shown in Fig. .) At 40∘ N, the angle of the grid combined with a large zonal current in the western part of the basin results in large spikes in the velocity field (Fig. i); fortunately, the decomposition method still retains the large-scale structure of the volume transport (barotropic streamfunction) in the large-scale velocity component (Fig. k). Notably, the time-mean contribution of the MTF is much larger at 40∘ N, though most of this contribution also occurs near the western side of the basin (Fig. l).

The contributions of the overturning, large-scale, and mesoscale components to basin-integrated heat transport can be computed for a range of latitudes in the North Atlantic (Fig. ). The time-mean contribution to heat transport in the tropical North Atlantic is approximately 0.8 PW (Fig. a), which is weaker than observational and model-based e.g., estimates. The weaker Atlantic MHT in POP is likely associated with a weaker meridional overturning circulation of 12–13 Sv, which is towards the low end of model estimates 8–28 Sv, e.g.,. Despite the probable low bias in the strength of the overturning, the overturning contribution to time-mean heat transport is much larger than non-overturning components at low latitudes (Fig. a), in agreement with earlier findings . North of the Gulf Stream separation near 38∘ N, the overturning contribution steadily decreases while the mesoscale contribution increases, reaching a peak at 43∘ N. The time-mean mesoscale contribution is larger than the contribution of large-scale (non-overturning) processes in the range 39–45∘ N, while to the north and south large-scale processes contribute more, likely driven by the strong subpolar and subtropical gyre circulations, respectively. The residual contribution is negligible at all latitudes in the North Atlantic, implying that short-timescale (<5 d) variability does not substantially impact our assessment of contributions to time-mean MHT.

The flux components have also been filtered to consider their contribution to interannual and decadal (ID) variability by removing the seasonal cycle and applying a low-pass filter with a half-power cutoff period of 14 months (Fig. b). While the higher-frequency (synoptic, intraseasonal, and seasonal) variability of MHT is substantial, we focus on ID variability in order to highlight the rectified impacts of mesoscale dynamics that may be of interest for climate studies. In the North Atlantic, the large-scale contribution to ID variability remains comparable to the mesoscale contribution, except at 40–41∘ N (where the mesoscale is larger) and poleward of 44∘ N (where the large scale is larger). The residual's contribution to ID variability is relatively small, if not as negligible as its contribution to time-mean MHT. The similarity in the ID standard deviations of large-scale and mesoscale MHT variability at 30–38∘ N may also indicate compensation between the large-scale and mesoscale due to mesoscale feedbacks on the large-scale circulation e.g., or large-scale preconditioning of flow variability and temperature gradients where mesoscale dynamics are active. Therefore, our method does not entirely disentangle the effects of the large-scale and mesoscale flow on temperature fluxes and transport. However, it provides a more precise diagnostic for the flux directly associated with mesoscale velocity and temperature anomalies; the spatial and temporal variability of these anomalies may then be studied in the context of variability in the background (large-scale) state.

In the rest of the analysis, we focus on 40∘ N to highlight how the spatial-scale decomposition can help diagnose the mechanisms of temperature flux variability across a transect. The 40∘ N latitude is an ideal location for this analysis, as the mesoscale contributions to time-mean and ID MHT are both substantial, and higher than large-scale contributions at the same latitude (Fig. ). Though the overturning contributions are still larger than the mesoscale at 40∘ N, we will disregard the overturning contributions in the remainder of this study to focus on the novel large-scale/mesoscale decomposition.

With the overturning contribution removed, the time series of the large-scale and mesoscale temperature flux components at 40∘ N (Fig. ) confirms that the ID variability of the MTF (red curve) is larger than the variability large-scale temperature flux (LTF, blue curve). The LTF variability is not negligible, however, and some peaks in the total non-overturning temperature flux (black curve) such as in 1993 can be attributed to the LTF more than the MTF. At some times, the LTF and MTF are anticorrelated and effectively cancel each other out (1990, 1995), and at other times both fluxes contribute substantially to a temperature flux peak (1979, 1996). Yet some of the highest peaks in the total flux (1980, 2003) are associated only with MTF variability, and the lowest total flux in the entire series (beginning of 2000) is also a result of low MTF. The sum of the two components (LTF and MTF) agrees very well with the total non-overturning temperature flux, implying a small residual from high-frequency (<5 d) v and T covariability.

We now turn our attention to the parts of the transect that contribute most to the time-mean and ID variability of the large-scale and mesoscale temperature fluxes. The time-mean LTF is the result of three areas of contribution in the upper ocean (<300 m), as well as two areas at depths of 400–1200 m (Fig. a). The upper ocean contributions to time-mean LTF are mostly found near the western boundary, where a positive LTF closest to the boundary is partially compensated by negative LTF further offshore near 50∘ W. A more modest positive LTF contribution is also located near the eastern boundary of the main ocean basin (20–10∘ W). The 400–1200 m contributions are between the western boundary and the Mid-Atlantic Ridge. These contributions of negative LTF at 65–45∘ W and positive LTF near the Mid-Atlantic Ridge are more substantial than they may appear in Fig. a, since they span a larger depth range (note the logarithmic depth scale of the figure); indeed, most of the mid-ocean structure in the LTF as seen in Fig. l is associated with this deeper minimum and maximum. The LTF contribution to ID variability is higher in the western part of the basin, especially near the western boundary where it is substantial to at least 3000 m (Fig. b). The time-mean MTF structure is simpler to interpret than the LTF, as it is vertically coherent and mostly confined to the upper 700 m (Fig. c). An area of positive MTF near the western boundary is stronger than the co-located positive LTF, the negative MTF at 60–50∘ W is weaker than its LTF counterpart, and there is an additional modest area of positive MTF near 40∘ W. The ID variability of the MTF is confined almost entirely to the upper 1500 m, and west of the Mid-Atlantic Ridge (Fig. d).

The ID variability of the LTF can be explained in terms of the structure of its large-scale velocity and temperature constituents (Fig. ). Using linear regression, we assess the local contributions of the LTF associated with a +1σ (1 standard deviation above the mean) basin-integrated LTF (Fig. a). In Fig. a, the LTF is zonally smoothed using the same filter as in Fig. , to facilitate interpretation and reduce the appearance of zonal LTF variability at wavenumbers up to twice that of the individual velocity and temperature constituents. The regression of the basin-integrated onto local LTF reveals most of the variability is found west of 50∘ W. Of the three main areas of contribution (positive regression values, indicated by solid ellipses), one extends to nearly 1000 m depth, with water temperatures of 5–12 ∘C (Fig. d). In this depth range, the coldest waters are found at the western boundary, and the LTF contribution increases when the flow is southward (Fig. b), as the boundary temperature is cold relative to the zonal mean (Fig. e). The other areas of contribution to LTF variability are near the surface, most notably the maximum near 60∘ W associated with the near-surface maximum in temperature (Fig. e), where northward flow increases the LTF (Fig. b). A third smaller area near the coast is associated with the advection of relatively cold surface waters, and there southward advection increases the LTF. All of these contributions are associated with velocity variability advecting time-mean temperature structure (vL′TL‾). The time-mean velocity field does also advect temperature variability (vL‾TL′), but the effects of this term (Fig. c, f) are too small to be represented in any of the maxima in Fig. a.

The structure of the zonally smoothed MTF variability on ID timescales (Fig. a) has some similarity to the structure of the time-mean MTF; however, the interior region (50–35∘ W) which had a modest positive time-mean MTF becomes much more important for ID variability. The focus of this interior MTF is also deeper than the boundary MTF, near 500 m depth where the thermocline shoals (Fig. d). The western boundary remains significant for MTF variability; the middle region (60–50∘ W) has a much smaller effect on ID variability compared to the western boundary and interior MTF contributions (Fig. a). Given the predominance of transient, propagating features in the oceanic mesoscale (e.g., eddies), much ID MTF variability at this latitude is not associated with the time-variable advection of time-mean TM‾ but with the rectification of intraseasonal vM′ and TM′ variability onto ID timescales. Therefore, the regression method used to explain the sources of LTF variability in Fig.  is insufficient to explain sources of the MTF, and different diagnostics are needed.

Figure a implies that two regions (a boundary and interior region) should account for most MTF variability on ID timescales. Time series of the MTF in each of these regions (Fig. b) confirm this while also illustrating differences in the timescales of variability present in each region. The variability of MTF in the boundary region (70–60∘ W) predominantly occurs on higher-frequency interannual timescales with peaks every 1–4 years, and many of these peaks are aligned with the basin-integrated MTF. The interior region (50–35∘ W) has some interannual variability, but there also appears to be an underlying decadal signal, and elevated interior MTF peaks in 1980 and 2003 align with some of the highest values of basin-integrated MTF during this period.

The EKE (defined as half the variance of the velocity vector with the time mean removed) is generally considered to be an indicator of the level of mesoscale activity in a given location and time; hence, we expect that EKE might influence MTF variability. This relationship can be expressed e.g., as 8vMTM=κ∂T∂y∝v′2Lmix-∂T∂y, where Lmix is a mixing length parameter that is related to the width of the local frontal zone associated with the meridional temperature gradient . Assuming fairly isotropic velocity variability, 9vMTM∝EKELmix-∂T∂y.

It would be convenient if EKE (specifically surface EKE) was the primary influence on MTF variability, since this can be diagnosed from satellite altimeters and would allow direct observational estimates of MTF variability. However, at 40∘ N, surface EKE variability is not a very reliable indicator of time variations in the MTF (Fig. ). High MTF generally occurs at times of high transect-averaged EKE, and significant MTF peaks are all associated with surface EKE peaks. However, many of the highest values of surface EKE (1985–1986, 1992, 2004, 2008) do not seem to drive an increased MTF; therefore, elevated EKE seems to be a necessary but not sufficient condition for high MTF along this transect. Local correlations of surface EKE and MTF in the eddy-active western part of the basin (not shown) are at best marginally significant at 95 % confidence levels, further suggesting that high levels of mesoscale energy do not imply elevated MTF.

To focus on what conditions permit high MTF across 40∘ N, we consider three episodes of high MTF, in 1980, 1996, and 2003 (Fig. ). The spatial structure of MTF variations indicates that all of these peaks are associated with higher than usual MTF values in more than one region (Fig. a,b). In 1980 and 2003 (the two highest peaks), the elevated MTF contributions clearly originate in the boundary and interior regions. In 1996, a positive MTF anomaly in the boundary region is supplemented by a broad (but not particularly strong) positive anomaly that extends eastward to ∼45∘ W (Fig. b), which corresponds to an abatement of the usually negative MTF in this region (Fig. a).

Typically, in the interior of the ocean, the dominant contribution to the MTF is associated with the vMTM term in Eq. (). Hence, in addition to the proportionality relationship in Eq. (), the MTF can be decomposed in terms of the contribution of the amplitude and covariability of vM and TM: 10vMTM=σvMσTMR, where σvM and σTM are the standard deviations of vM and TM and R is the correlation coefficient of vM and TM; the standard deviations and correlations are computed in windows that are localized in space and time to study spatiotemporal variability. In relation to Eq. (), EKE is most likely to influence σvM, while the meridional temperature gradient ∂T/∂y will likely influence σTM and potentially R. By computing the constituents on the right-hand side of Eq. () in moving windows spanning 10∘ longitude and 1-year ranges (in the upper 1000 m), the contributions of each constituent to MTF variability are evident (Fig. a–c). The basin-integrated MTF is the result almost entirely of fluxes west of the Mid-Atlantic Ridge (∼30∘ W) because σvM and σTM are much larger in the western part of the basin than in the east (Fig. a–b). However, R is responsible for the time-mean structure of the MTF within the western part of the basin; in fact, R is typically negative between 60 and 50∘ W, despite the fact that the large-scale meridional temperature gradient has the same sign here as elsewhere (Fig. d). This would imply an upgradient flux of temperature at 60–50∘ W, though it can not be determined solely from this zonal transect whether this apparent upgradient diffusivity is associated with a rotational component of the temperature flux e.g.,.

When the time means are removed from the constituents in Eq. (), the sources of MTF variability can be attributed more clearly (Fig. ). In 1980, high MTF is driven by a strongly positive R anomaly, coincident with a steeper-than-usual temperature gradient in the interior region (Fig. c, d). By contrast, high MTF in 1996 is supported by slight positive anomalies in σvM and R (and possibly σTM), while in 2003, it has more robust positive anomalies in all of these contributions. The anomalies also suggest a difference in behavior between the boundary and interior regions: the MTF is more responsive to σvM (and likely EKE) variations west of 50∘ W where time-mean σvM is larger, while in the interior an increase in σTM and/or R is necessary to increase MTF. Lastly, all three peak events (Fig. ) are associated with an anomalously steep meridional temperature gradient in their source regions (Fig. d). Just as importantly, there was no robust positive (weaker) gradient anomaly during these three events, in contrast with 1992–1995 when weaker gradients in the interior region may have contributed to negative (weak) anomalies in all three constituents.

Having identified the influence of the meridional temperature gradient on MTF variability, we consider the role of the large-scale current and temperature in generating anomalous meridional temperature gradients. The path of the Gulf Stream extension sets the location of strong temperature fronts in the western Atlantic at this latitude; notably, its path during high MTF events tends to be further north than usual at ∼66∘ W (Fig. a). This location is important because in the POP simulation it is where the mean path of the Gulf Stream first approaches 40∘ N. When there is a northward shift in the path at this region, the Gulf Stream's crossing of 40∘ N can happen hundreds of kilometers west of the usual location, and the meridional temperature gradient is steeper west of 65∘ W (Fig. d). Large-scale temperature anomalies in the upper ocean also show a difference in the mechanism for meridional temperature gradient anomalies at the boundary vs. the interior (Fig. b–d). When the boundary region contributes significantly to high MTF, the steeper temperature gradient is associated with a positive temperature anomaly south of 40∘ N. When the interior region contributes to high MTF, the steeper gradient is associated with a negative temperature anomaly north of 40∘ N. Since the mean path of the Gulf Stream is just south (north) of 40∘ N in the boundary (interior) region, each of these temperature anomaly patterns would nudge the path of the Gulf Stream closer to 40∘ N, intensifying the temperature gradient across the transect.

The importance of the meridional temperature gradients in both the boundary and interior regions is emphasized when comparing the time series of the gradients to the MTF in each region (Fig. ). In particular, the higher-frequency interannual variability in MTF in the boundary region is closely associated with variations in the meridional temperature gradient (Fig. a). In the interior region, decadal variability is not as pronounced in the meridional temperature gradient as it is in the MTF; there are a number of times when the meridional temperature gradient is steeper than the average, without a major effect on MTF (Fig. b). However, two of the most significant maxima in meridional temperature gradient (1979–1980 and 2003–2004) are associated with elevated MTF, so steeper gradients at least make significant positive MTF events more likely.

A key novel aspect of this study is the spatial decomposition method to separate the mesoscale and large-scale contributions to MHT, in contrast to the use of temporal covariability of velocity and temperature in many previous studies. As a diagnostic tool, the spatial-scale decomposition of MHT has important advantages over the more common approach of separating time mean and time deviation (often called “eddy”) fluxes. The mechanisms that drive large-scale processes such as gyres (wind forcing, boundary/topographic constraints) are often distinct from those driving mesoscale processes (e.g., baroclinic and barotropic instability, non-linear momentum/vorticity advection); quantifying the spatial scales of MHT contributions and their distribution is a first step towards understanding the processes that contribute to MHT. Moreover, rather than being defined relative to a time mean over an arbitrary time period (e.g., the post-spinup time span of the model simulation), the mesoscale MHT is defined as the deviation from a regional background state at each time. Since the integrated volume flux associated with the mesoscale velocity is small across zonal scales ≫10∘ longitude, the MTF smoothed over large zonal scales approximates a heat transport regionally and at each time.

Exploiting the advantages of the spatial decomposition method, this study outlines an approach for diagnosing the geographical origins of LTF and MTF variability. Large-scale temperature fluxes can generally be explained in terms of large-scale velocity and temperature components directly, with at least one time-mean component involved (Fig. ). Mesoscale processes such as transient eddies often produce rectified fluxes at spatial (and temporal) scales that are much larger (longer) than the original velocity and temperature anomalies. However, the MTF contributions can be traced to specific locations (Figs. b, ) and supplemented by an analysis of the conditions that influence the MTF and instability in those regions (Figs. –).

In our analysis of MTF variability at 40∘ N, we found that the influence of the meridional temperature gradient is modulated by the velocity–temperature correlation, whose importance is emphasized in Figs. –. In addition to its role in driving MTF temporal variability, the correlation explains the negative time-mean temperature flux at 60–50∘ W, suggesting that there is an upgradient flux across the meridional temperature gradient (Fig. c, d). Other studies of mesoscale eddy characteristics and heat fluxes e.g., have considered the displacement of temperature relative to velocity/pressure anomalies in eddies. Yet this work illustrates the impact of even subtle changes (of order 0.1) in the velocity–temperature correlation coefficient; hence, more comprehensive studies of the velocity–temperature correlation, its dependence on the structure of nearby fronts, and relationship to existing theories of diffusivity are needed.

It is helpful to compare how the mesoscale MHT we estimated compares to those based on previous methods, i.e., the covariability of velocity and temperature (1) for all timescales “time-varying”; e.g.,, (2) for deviations from 3-month averages only “high frequency”;, and (3) the baroclinic eddy contribution, which defined by removing first the depth-averaged (barotropic) and then the zonal average v and T. Because of the differences in models and observations used in these studies, a direct comparison of mesoscale MHT in our analysis with eddy heat transport from these previous studies is not suitable. We therefore compare our mesoscale MHT with the eddy MHT based on previous methods using the same POP model output (Fig. ). The time-varying v′T′ term happens to be a decent approximation of the mesoscale contribution to the time-mean MHT in the 39–43∘ N latitude range (Fig. a), corresponding to the region of highest MTF just north of the Gulf Stream separation. To the south and north of this active mesoscale region, all of the eddy formulations have much lower time-mean values, with the exception of the baroclinic eddy term which peaks as high as 0.35 PW at 36∘ N. However, the definition of the baroclinic eddy flux includes large-scale gyre flows that have a baroclinic component, and the baroclinic eddy contribution is generally comparable to or smaller than the large-scale contribution to time-mean MHT (Fig. a). The negative and positive mesoscale contributions to MHT at 28 and 34∘ N, respectively (Fig. ), can be seen in Fig. a, and since these contributions are not found in the time-varying MHT we can infer that this mesoscale MHT is associated with the time-mean (stationary) structure of the Gulf Stream and its tight southward recirculation.

Of the contributions to time-mean MHT, intraseasonal (high) frequencies account for about 30 %–40 % of the total time-varying contribution in the active eddy region north of the Gulf Stream separation (Fig. a). While mesoscale eddies are typically associated with intraseasonal frequencies, in the strong eastward flow of the Gulf Stream, the westward propagation of eddies and meanders is slowed and even in some cases reversed, resulting in more low-frequency (and stationary) mesoscale variability driving MHT. Regarding ID variability as a function of latitude, the time-varying flux has steep spikes in variability near the edges of the active mesoscale range at 38 and 44∘ N; the mesoscale contribution is again similar to the time-varying fluxes in the 39–43∘ N range but the mesoscale has more variability south of the Gulf Stream separation (Fig. b). The baroclinic eddy component has consistent variability across latitudes, generally lower than that of the time-varying and mesoscale fluxes at 35–45∘ N and higher outside of this range.