A new method to assess mesoscale contributions to meridional heat transport in the North Atlantic Ocean

. The meridional heat transport (MHT) in the North Atlantic is critically important to climate variability and the global overturning circulation. A wide range of ocean processes contribute to North Atlantic MHT, ranging from basin-scale overturning and gyre motions to mesoscale instabilities (such as eddies). However, previous analyses of “eddy” MHT in the region have mostly focused on the contributions of time-variable velocity and temperature, rather than considering the spatial scales that are more fundamental to the physics of ocean eddies. In this study, a zonal spatial-scale decomposition separates 5 large-scale from mesoscale velocity and temperature contributions to MHT, in order to characterize the physical processes driving MHT. Using this approach, we found that the mesoscale contributions to the time mean and interannual/decadal (ID) variability of MHT in the North Atlantic Ocean are larger than large-scale horizontal contributions, though smaller than the overturning contributions. Considering the 40 ◦ N transect as a case study, large-scale ID variability is mostly generated in the deeper part of the thermocline, while mesoscale ID variability has shallower origins. At this latitude, most ID MHT variabi- 10 lity associated with mesoscales originates in two regions: a western boundary region (70 ◦ –60 ◦ W) associated with 1–4 year interannual variations, and an interior region (50 ◦ –35 ◦ W) associated with decadal variations. Surface eddy kinetic energy is not a reliable indicator of high MHT episodes, but the large-scale meridional temperature gradient is an important factor, by inﬂuencing the local temperature variance as well as the local correlation of velocity and temperature. Most of the mesoscale contribution to MHT at 40 ◦ N is associated with transient and propagating processes, but stationary mesoscale dynamics con- 15 tribute substantially to MHT south of the Gulf Stream separation, highlighting the differences between the temporal and spatial decomposition of meridional temperature ﬂuxes. PW. The results of these studies imply that eddy heat ﬂuxes are dependent not just on model resolution, but on how “eddies” are deﬁned. A canonical eddy is typically a vortex that and temperature constituents. The regression of the basin-integrated onto local LTF reveals a substantial inﬂuence of variability

is no more than a few hundred kilometers in diameter (i.e., mesoscale), but model analyses have not yet (to our knowledge) quantified basin-integrated temperature fluxes according to the spatial scale of the processes driving the fluxes. Moreover, 60 observational estimates that use (remote sensing-based) eddy tracking methods to quantify eddy contributions to heat transport (e.g., Hausmann and Czaja, 2012;Dong et al., 2014;Sun et al., 2019) have reached divergent conclusions depending on the methodology and scope of what is considered part of the eddy transport. One way to address this ambiguity is to consider the impact of all mesoscale dynamics on meridional heat transport, whether or not these mesoscale fluxes are due to coherent vortices. 65 The focus of this study is to quantify the time-mean and time-variable contribution of mesoscale dynamics to meridional heat transport in the North Atlantic, with a particular focus at 40 • N where the Gulf Stream extension is nearly zonal and eddy kinetic energy (EKE) is near its maximum. Section 2 will discuss the eddy-permitting model simulation and the framework used to decompose the temperature fluxes into overturning, large-scale, and mesoscale components. Section 3 summarizes the results and the cross-basin structure of mesoscale temperature fluxes, while Section 4 relates the variability of mesoscale 70 temperature fluxes to other indicators of the ocean state such as EKE and meridional temperature gradient. Section 5 discusses novel aspects of the approach presented here and compared to earlier formulations of eddy fluxes, while Section 6 summarizes the conclusions of this study.

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Most of our analysis uses output from a numerical simulation of the Parallel Ocean Program (POP) 2, a primitive equation ocean model (Smith et al., 2010). 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 Johnson et al. (2016) and Delman et al. (2018). The simulation was run on the Yellowstone computing cluster (Computational and Information Systems Laboratory, 2016) with a resolution of 0.1 • at the equator, and approximately 8 80 km in the mid-Atlantic; it was forced with Coordinated Ocean-Ice Reference Experiments version 2 (CORE.v2; Large and Yeager, 2009), an interannually-varying flux dataset based on the National Centers for Environmental Prediction reanalysis with corrections from various satellite data. State variables (including velocity and temperature) and temperature fluxes have been archived from this simulation in 5-day averages, facilitating studies of mesoscale processes which frequently vary on intraseasonal timescales. 85 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 (Ducet et al., 2000) 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. 1), though there are several important 90 issues that have been previously noted in other model simulations (for a review of these issues see Chassignet and Marshall,3 https://doi.org/10.5194/os-2020-20 Preprint. Discussion started: 31 March 2020 c Author(s) 2020. CC BY 4.0 License. 2008). These include the Gulf Stream separating from the continental slope at 38 • -39 • N in the model (Fig. 1b) vs. ∼36 • N in observations (Fig. 1a), 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. 1c,d). These inaccuracies have been resolved in regional simulations of the North Atlantic at 1/10 • resolution (e.g., Bryan and Smith, 1998;Smith et al., 2000;Bryan et al., 2007), but persist in global simulations even 95 at the same resolution (e.g., Maltrud and McClean, 2005;Kirtman et al., 2012;Griffies et al., 2015). 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. 1c,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. 1e).
100 Figure 1. Comparison of mean dynamic topography from (a) CMEMS altimetry  and (b) POP simulation . The gray line indicates the 40 • N latitude transect, the focus of this study. (c, d) Same as (c, d) but for surface eddy kinetic energy (EKE); POP sea surface height is low-pass filtered to remove variability at scales smaller than 0.5 • , the Nyquist wavelength of the altimetry product. (e) Comparison of Atlantic zonally-averaged surface EKE from altimetry and POP.

Temperature flux decomposition
The meridional heat transport in the ocean is commonly regarded to consist of a mean and "eddy" component, where the "eddy" component is associated with velocity and temperature deviations from a temporal mean. Namely with ρ the reference density and c ρ the specific heat capacity of seawater, and the meridional velocity and temperature are 105 decomposed into time mean and deviation components v = v + v and T = T + T respectively. There are also cross-terms between the mean and deviation components in eq. (1), but these are zero by definition in time means. When the left-hand side is integrated zonally and vertically across a basin with zero net meridional flow ( vdxdz = 0), these heat fluxes are considered heat transports. The decomposition in eq. (1) is convenient for describing how much heat transport can be explained (and not explained) by the ocean's mean state, but it provides little information about the processes actually responsible for the heat 110 transport.
An alternative approach to the decomposition is to separate zonal mean and deviation components (e.g., Hall and Bryden, 1982); neglecting ρc ρ to focus on the temperature flux, this decomposition is where and indicate zonal mean and deviation respectively. While eq. (1) holds true only when the terms are time averaged, 115 eq. (2) involves zonal integration or averaging, and therefore holds true without any time averaging. Since the term v T varies in depth and time but not zonally, it quantifies the contribution to temperature transport from the overturning circulation, i.e., the meridional movement of warmer shallow waters over cooler deeper waters. The contributions of any lateral variations in the ocean are therefore contained in the v T term. However, these lateral variations include a wide range of processes that range in scale from subtropical and subpolar basin gyres, to instabilities at the smallest scales resolved by the model or 120 observing system.
In order to separate the contribution of large-scale processes (e.g., gyres, long planetary waves) from mesoscale processes (e.g. transient and standing eddies), we introduce a further decomposition of the v T term: in which the subscripts L and M denote large-scale and mesoscale components of meridional velocity and temperature. The 125 middle cross-terms on the right-hand side of eq. (3) are considered part of the mesoscale contribution since they would not exist without mesoscale processes; they are negligible when integrated or smoothed over a sufficiently large range in the interior, but near the boundaries the cross-terms may still make substantial contributions to basin-integrated transports. The separation 5 https://doi.org/10.5194/os-2020-20 Preprint. Discussion started: 31 March 2020 c Author(s) 2020. CC BY 4.0 License.
of large-scale and mesoscale components is carried out in the spectral (wavenumber) domain, with low-pass and high-pass transfer functions such that given the Fourier wavenumber coefficients for (zonally-detrended) meridional velocity V (k) and analogously for the decomposition of temperature. It can be readily seen that the sum of eq. (4) and eq. (5) is the original V (k). After filtering, the zonal trends are added back to the large-scale velocity and temperature, but not the mesoscale velocity 135 and temperature. Since the POP grid is not aligned with lines of latitude in the North Atlantic, velocities and temperatures are interpolated to regularly-spaced longitudes (0.1 • interval) before the computation of eq. (4) and eq. (5) and then interpolated back to the original model grid; this leads to a residual that is technically unassociated with either the large-scale or mesoscale, though given that it results from interpolation errors it is likely more associated with the mesoscale. Meridional velocity outside the basin boundaries and within interior land areas is set to zero; however, to minimize abrupt jumps in temperature and its 140 zonal derivative at the boundaries, a buffer is also included at the western and eastern boundaries after detrending but prior to the application of the filters in eq. (4)-(5). Given x b the western boundary position and x c the zonal decorrelation scale of temperature at a given latitude, depth, and time, the average values of temperature in the ranges x b < x < x b + x c and x b + x c < x < x b + 2x c (T 1 and T 2 respectively) are computed, and from these a boundary value T b = 1.5T 1 − 0.5T 2 and slope T s = (T 2 − T 1 )/x c . Then an error function is fitted outside the boundary that approximates the slope of the temperature profile 145 approaching the western boundary and the mirror opposite formulation is applied to the eastern boundary. For interior land areas, temperature is simply interpolated across the land gap for the purposes of filtering.
There are two parameters in the transfer functions in eq. (4)-(5) that need to be chosen: s the steepness factor at the wave-150 number cutoff, which is set to 5, and k 0 the cutoff wavenumber. To determine a sensible value for k 0 and the related cutoff wavelength λ 0 = 1/k 0 , spectral density estimates are computed from the POP meridional velocity v and temperature T fields at 40 • N (Fig. 2). With high levels of mesoscale activity at 40 • N, a clear mesoscale peak can be seen at wavenumbers corresponding to wavelengths between 4 • and 5 • longitude (Fig. 2a); there is a similar peak in wavenumber spectra of the Gulf Stream path through this region (e.g., Lee and Cornillon, 1996). The temperature spectral peak is less obvious, but is still visible rela-155 tive to the general downward slope with increasing wavenumber (Fig. 2b). Wavelengths corresponding to the mesoscale peak and large-scale/mesoscale transition were identified by smoothing the spectral density curves for v and T in logarithmic space and identifying the minimum and maximum of ∂ 2 (ln V ) /∂ (ln k) 2 within broad expected ranges (2 • -20 • wavelengths for the for the mesoscale peak and transition identified from the spectral curves of v and T are similar, providing confidence that the 160 mesoscale signal starts to emerge at wavelengths shorter than 10 • and peaks at approximately 5 • . Though a 5 • wavelength is much longer than the first baroclinic Rossby radius (∼20 km at this latitude), it does compare favorably with eddy radii of approximately 100 km observed at 40 • N in altimetry data (Chelton et al., 2011); the peak wavelength is expected to be approximately 4 times the typical eddy radius. Hence to obtain an optimal separation between mesoscale and large-scale processes, the cutoff wavenumber in eq. (4) and (5) is set to k 0 = 1/10 cycles/ • , corresponding to a 10 • wavelength.

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Applying this procedure, the contributions of the overturning, large-scale, and mesoscale components to heat transport can be computed for a range of latitudes in the North Atlantic (Fig. 3), along with the residual error that results from the interpolation to and from the regularly-spaced longitude grid. The time mean contribution to heat transport in the tropical North Atlantic is approximately 0.8 PW (Fig. 3a), which is weaker than observational (Johns et al., 2011) and model-based (e.g., Tréguier et al., 2012) estimates. The weaker Atlantic MHT in POP is likely associated with a weaker meridional overturning circulation of 12-170 13 Sv, which is towards the low end of model estimates (8-28 Sv, e.g., Danabasoglu et al., 2014). 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. 3a), in agreement with earlier findings (Bryan, 1982;Johns et al., 2011). Moving northward, the overturning contribution steadily decreases while the mesoscale contribution increases, reaching peaks at 39 • N and again at 45 • N. The time mean mesoscale contribution is larger than the contribution of large-scale (non-overturning) processes in the range 39 • -46 • 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 interpolation errors do not 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 cutoff period of 14 months (Fig. 3b). In the North Atlantic are larger than the large-scale temperature flux (LTF, blue curve). The LTF is not negligible however, and some peaks in the total non-overturning temperature flux (black curve) such as those in 1993 and 2008 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 195 both fluxes contribute substantially to a temperature flux peak (1979,1987). Yet several of the highest peaks in the total flux (1980,1996,2003) 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 and suggesting the overall validity of the LTF and MTF components. The only exception is in 2002 where the effect of interpolation errors likely results in one or both components being too high.  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. 5a, since they span a larger depth range (note the logarithmic depth scale of the figure). Integrated in depth, the deep LTF contributions are comparable to the shallow eastern boundary contribution, and their contribution to ID 210 variability is higher than the shallow eastern boundary, if not as high as the shallow western boundary (Fig. 5b). The time mean MTF structure is simpler to interpret than the LTF, as it is vertically coherent and mostly confined to the upper 700 meters (Fig. 5c). 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 also confined almost entirely to the upper 700 meters, and west of the Mid-Atlantic Ridge (Fig. 5d). The ID variability of the LTF can be explained in terms of the structure of its large-scale velocity and temperature constituents (Fig. 6). 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. 6a). Here the LTF is zonally-smoothed with a cutoff wavelength of 20 • , 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 a substantial influence of variability are in this depth range in the lower thermocline, with water temperatures of 5 • -12 • C (Fig. 6d). In this depth range the coldest waters are found at the western boundary, and the LTF contribution increases when the flow is southward (Fig. 6b), as the boundary temperature is cold relative to the zonal mean (Fig. 6e). Hence the contributions peak near the western boundary and at 40 • W (Fig. 6a) where there is a local minimum in temperature (Fig. 6e). The third area of contribution to the LTF 225 is associated with the near-surface maximum in temperature (Fig. 6e), and here northward flow increases the LTF. All of these contributions are associated with velocity variability advecting time-mean temperature structure (v L T L ). The time mean velocity field does also advect temperature variability (v L T L ), though the main contribution from this term ( Fig. 6a; dashed ellipse) is anticorrelated with the basin-integrated variability, and therefore acts to compensate the other contributions. This compensation occurs in the region of time-mean southward flow near 55 • W (Fig. 6f), where warmer flow (Fig. 6c) will cause 230 the total LTF to be more negative.
The structure of MTF variability on ID timescales (Fig. 7a) is similar to the structure of the time-mean MTF; however, the interior region (50 • -35 • W) which had a modest positive time-mean MTF becomes more important for ID variability. The focus of this interior MTF is also deeper than the boundary MTF, near 500 meters depth where the thermocline shoals (Fig.   6d). The western boundary remains significant for MTF variability; the middle region (60 • -50 • W, where there is negative 235 time-mean MTF) may have a compensating effect, but its magnitude is small compared to the western boundary and interior MTF contributions (Fig. 7a). It is worth noting that the structure of MTF variability is very similar to the deeper LTF variability contributions (Fig. 6a)   The eddy kinetic energy or 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., Holloway, 1986;Stammer, 1998) as where L mix is a mixing length parameter that is related to the width of the local frontal zone associated with the meridional 260 temperature gradient (Green, 1970 surface EKE variability is not a reliable indicator of time variations in the MTF (Fig. 8). High MTF occurs at times of at least moderately high transect-averaged EKE, and significant MTF peaks are all associated with surface EKE peaks. However, many of the highest values of surface EKE (1985-86, 1992, 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.

Constituents of MTF variability
To focus on what conditions permit high MTF across 40 • N, we consider the three highest peaks in the MTF time series, in 1980, 1996, and 2003 (Fig. 8). The spatial structure of MTF variations indicates that all of these peaks were associated with higher than usual MTF values in more than one region (Fig. 9a,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 275 is supplemented by a positive anomaly in the adjacent 60 • -50 • W (Fig. 9b), which corresponds to an abatement of the usually negative MTF in this region (Fig. 9a). Other positive anomalies in the 60 • -50 • W do not seem to influence basin-integrated MTF variability however (Fig. 9c), so 1996 may be an unusual episode. σ v M and σ T M are much larger in the western part of the basin than in the east (Fig. 10a-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 • -50 • W despite the fact that the large-scale meridional temperature gradient has the same sign here as elsewhere (Fig. 10d), implying 290 an upgradient diffusivity of temperature at 60 • -50 • W. When the time means are removed from the constituents in eq. (9), the sources of MTF variability can be attributed more clearly (Fig. 11). 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. 11c,d). By contrast, high MTF in 1996 is supported by slight positive anomalies in σ v M and R (and possibly σ T M ), while in 2003 has more robust positive anomalies in all of these contributions. The anomalies also 295 suggest a difference in behavior between the boundary and interior regions: the MTF is more responsive to σ v M (and likely EKE) variations west of 50 • W where time-mean σ v M is larger, while in the interior an increase in σ T M and/or R is necessary to increase MTF. Lastly, all three peak events (Fig. 9) are associated with an anomalously steep meridional temperature gradient in their source regions (Fig. 11d). Just as importantly, there was no robust positive (weaker) gradient anomaly during these three events, in contrast with 1990-95 when weaker gradients in the interior region may have contributed to negative (weak) 300 anomalies in all three constituents.

Large-scale temperature flux contributions
Having identified the influence of the meridional temperature gradient on MTF variability, we consider the role of the largescale 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 305 tends to be further north than usual at ∼66 • W (Fig. 12a). 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 Figure 11. Same as Fig. 10, but with the time means removed. Anomalies associated with peak MTF events are indicated by gray boxes.
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. 10d). 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. 12b-d). When the boundary 310 region contributes significantly to high MTF (1996 and2003), the steeper temperature gradient is associated with a positive temperature anomaly south of 40 • N. When the interior region contributes to high MTF (1979-80 and 2003), 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.

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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. 13). In particular, the higher-frequency interannual variability in MTF in the boundary region is closely associated with variations in the meridional temperature gradient (Fig.   13a). 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 320 MTF (Fig. 13b). However, two of the most significant maxima in meridional temperature gradient (1980 and 2003-04) are associated with elevated MTF, so steeper gradients at least make significant positive MTF events more likely.  This study also outlined 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 335 least one time mean component involved ( Figure 6). Mesoscale processes such as transient eddies produce rectified fluxes at spatial (and temporal) scales that are much larger (longer) than the original velocity and temperature anomalies. However, using spatial smoothing the MTF can be traced to specific locations (Fig. 5b,7), and supplemented by an analysis of the conditions that influence the MTF and instability in those regions ( Fig. 8-12).
In our analysis of MTF variability at 40 • N, we found that the influence of the meridional temperature gradient is modulated 340 by the velocity-temperature correlation, whose importance is emphasized by Fig. 10-11. In addition to its role in driving MTF temporal variability, the correlation explains the negative time-mean temperature flux at 60 • -50 • W, indicating that there is an upgradient flux across the (still-negative) meridional temperature gradient (Fig. 10c,d). Other studies of mesoscale eddy characteristics and heat fluxes (e.g., Hausmann and Czaja, 2012;Gaube et al., 2015;Frenger et al., 2015;Tréguier et al., 2017) have considered the displacement of temperature relative to velocity/pressure anomalies in eddies. Yet this work illustrates the 345 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.

Comparison of MTF with previous formulations of the eddy flux
It is helpful to compare how the mesoscale MHT we estimated compares to those based on previous methods, i.e., the co-350 variability of velocity and temperature (1) for all time scales ("time-varying"; e.g., Jayne and Marotzke, 2002;Tréguier et al., 2017) and (2) for deviations from 3 month-averages only ("high frequency"; Volkov et al., 2008). Because of the differences in models (including resolution and parameterization), a direct comparison of mesoscale MHT in our studies with "eddy" heat transports 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. 14). The time-varying v T term happens to be a decent Regarding the timescales of rectified 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. 14a). While mesoscale eddies are typically associated with intraseasonal frequencies, in the strong eastward flow of the Gulf Stream the 365 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, the mesoscale and time-varying MHT also have contributions of comparable magnitude in the 39 • -44 • N range, though with substantive differences at 38 • N near the Gulf Stream separation and north of 50 • N (Fig. 14b).
In this study a new decomposition method has been used to distinguish the contributions of mesoscale vs. larger-scale processes to meridional heat transport in the North Atlantic by using spatial scales (rather than temporal deviations) of velocity and temperature. This analysis technique can be applied to eddy-permitting ocean and coupled GCMs to better quantify the temperature flux produced by mesoscale ocean processes in the model. Applying this spatial-scale decomposition method in the North Atlantic, a substantial mesoscale contribution to time-mean, non-overturning MHT was found in the 32 • -47 • N la-375 titude range that exceeded the large-scale non-overturning contribution, while somewhat less than the overturning contribution ( Fig. 3a). North of the Gulf Stream separation the mesoscale contribution is associated with time-variable fluxes and so it is similar to the contribution of the traditional "eddy" temperature flux (Fig. 14a). However, south of the Gulf Stream separation there is a substantial mesoscale contribution to time mean MHT where the traditional "eddy" temperature flux is negligible, since stationary (not time-variable) mesoscale processes drive most of the MHT at these latitudes. Since the mixing effects of 380 mesoscale processes apply to both stationary and time-variable processes, the mesoscale temperature flux is a more meaningful estimate of the mesoscale contribution to MHT that should be represented by eddy parameterizations in non-eddying models (e.g., Gent and McWilliams, 1990).
This study has also considered the relationship of mesoscale temperature flux variability to variations of indicators such as the EKE and meridional temperature gradient. The first unexpected result is that eddy kinetic energy (or at least surface EKE) 385 is not a reliable indicator of MTF variability, with most of the highest instances of zonally-averaged surface EKE not being associated with an elevation in the MTF (Fig. 8). It is not surprising that meridional temperature gradients influence MTF variability, given that cross-frontal gradients are a part of classic theories of diffusivity and lateral mixing dating back at least to Taylor (1915). Yet the low magnitudes of the velocity-temperature correlation R imply that even small changes in R can have a large impact proportionally on the MTF. Hence an improved understanding of velocity and temperature structure within 390 mesoscale features is necessary to inform accurate representations of meridional temperature fluxes in models.
Data availability. The POP model output used in this study is stored on NCAR's High Performance Storage System (HPSS); the full model output (in 5-day averages) is available with a user account by logging into cheyenne.ucar.edu and accessing the following path on HPSS: /home/bryan/johnsonb/g.e01.GIAF.T62_t12.003/ocn/hist/. Source code to run the POP2 model is available at http://www.cesm.ucar.edu/ models/cesm1.0/pop2/. The CMEMS surface dynamic topography data used to produce the analysis in Figure 1