To quantify mesoscale temperature fluxes and contributions to meridional HT, this analysis uses output from an eddy-permitting ocean general circulation model, the Parallel Ocean Program (POP) 2 . POP integrates the primitive equations with a z-depth coordinate and is configured in a tripole grid with two north poles over Canada and Siberia. The simulation was run on the Yellowstone computing cluster , with a 0.1∘ longitude grid spacing in the Mercator portion of the grid south of ∼28∘ N and progressively finer grid spacing approaching the two north poles. In physical distance, the grid spacing is approximately 11 km near the Equator, 5.5 km at 60∘ S, and 5–7.5 km at 60∘ N. Given this spacing relative to the baroclinic deformation radius e.g.,, it is expected that the model should at least permit mesoscale instability development equatorward of 50–60∘ latitude. The model simulation has 62 depth levels with 10 m vertical spacing in the upper 160 m. The ocean surface is forced with Coordinated Ocean-Ice Reference Experiments version 2 COREv2; fluxes based on National Centers for Environmental Prediction reanalysis with corrections from satellite data. The simulation was spun up during a 15-year period forced by CORE normal-year forcing , followed by a 33-year model integration with COREv2 interannually varying fluxes corresponding to the years 1977–2009. Our analysis covers the 32-year period of 1978–2009, the same span of time as in . For more details of the model simulation, see and .

As a proxy for the model's representation of mesoscale activity globally, the model time-mean surface EKE was compared with surface EKE from altimetry data. The altimetry dataset used is produced by Collecte Localisation Satellites and made available through the Copernicus Marine Environment Monitoring Service (CMEMS), with data merged from numerous altimetry missions onto a grid at 1/4∘ spatial and daily temporal resolution. The analysis demonstrates that the locations and EKE levels of the most energetic regions of the ocean are well represented in the POP simulation (Fig. ). However, it is also important to note that POP underrepresents EKE in many other regions of the ocean, including the subtropical eddy bands between 15 and 30∘ latitude in the North and South Pacific and South Indian oceans, and to a lesser extent the TIW region near the Equator. This underestimation of EKE in POP persists even if a different filter wavelength is applied to both model and altimetry datasets (e.g., 1∘), and indicates a consistent low bias of mesoscale activity in lower-energy parts of the ocean interior. One possible explanation is that the biharmonic viscosity ν0=-2.7×1010 m4s-1 and diffusivity κ0=-3×109 m4s-1 values used in this model simulation are well tuned for energetic regions such as western boundary currents but may suppress too much mesoscale activity in the less energetic ocean interiors. However, the low bias in time-mean EKE is not unique to this eddy-permitting model e.g.,. An attempt to estimate the impact of this bias on mesoscale contributions to meridional temperature fluxes and heat transport is discussed in Appendix .

The most common method of quantifying an “eddy” flux defines the eddy meridional velocity v′ and temperature T′ as deviations from a time mean (e.g., v=v‾+v′). The contributions to meridional HT are given by 1∫vT‾dx=∫v‾T‾+v′T′‾dx, and the second term on the right-hand side is the eddy contribution. In this paper, the temporal eddy flux is also referred to as the “all-time-varying” flux, encompassing the effects of transient/propagating phenomena at large scales as well as mesoscales. The time mean may also be implemented on shorter timescales (an example with 3-month time averages will be discussed in Sect. ), or another type of time averaging (e.g., seasonal climatological averages) may be used.

In contrast, the primary focus of this paper uses a decomposition that targets the mesoscale by explicitly separating spatial (rather than temporal) scales. This method was used by , following a similar application of spatial filters by but with the additional separation of the overturning contribution and corrections to the filtered v and T profiles near lateral boundaries. The meridional temperature flux is decomposed into three components (overturning, large scale, and mesoscale) by applying spatial filters to zonal profiles of v and T. The temperature flux is related to the heat flux by a factor of ρcρ, where ρ is the density and cρ the specific heat capacity of seawater; the heat flux integrated across a transect with near-zero net volume transport is a HT. In the spatial decomposition used in this study, the meridional temperature flux at each depth level is decomposed into zonal mean and zonal deviation components: 2∫vTdx=∫〈v〉〈T〉+v′′T′′dx, where 〈〉 indicates the zonal mean and ′′ indicates the deviation from the zonal mean. The first term on the right-hand side 〈v〉〈T〉 is the overturning component of the meridional temperature flux, consistent with earlier studies e.g.,. The overturning component, when multiplied by ρcρ and vertically integrated, gives the portion of meridional HT associated with basin-wide vertical gradients in meridional flow and temperature. The second term, variously referred to as the gyre or eddy temperature flux, contains all contributions from horizontally varying v and T. Our method further decomposes this term into contributions from large-scale and mesoscale variations in v and T: 3v′′=vL+vM4T′′=TL+TM5v′′T′′=vLTL+vLTM+vMTL+vMTM.

The first term on the right-hand side is the contribution from the large-scale circulation, while the remaining three terms constitute the meridional MTF (hereafter referred to as just the MTF). The cross terms vLTM+vMTL are considered part of the mesoscale contribution since these fluxes would not exist without mesoscale structures. In practice, vLTM is generally negligible compared to the other terms since zonal T profiles are red-shifted (have more large-scale structure) compared to zonal v profiles. However, vMTL can be the largest contributor to the MTF, especially near boundaries where large-scale temperature deviations from the zonal mean are often substantial.

In this analysis, transects are extracted from the model output along tracks corresponding to the nearest grid faces to integer lines of latitude. In the non-Mercator portions of the grid in the Northern Hemisphere, this results in a zig-zag of the transect through the model grid, but in this way the net volume transport through each transect is conserved. The spatial filters to compute the large-scale and mesoscale v and T are applied in the spectral (zonal wavenumber) domain, with v′′ weighted by Δx (the length of each grid face along the transect) to better conserve volume transport across the transect. The Fourier coefficients V′′(k) of v′′Δx and T′′ are filtered according to the transfer functions 6VL(k)=0.5+0.5erf-sln|k|k0V′′(k)7VM(k)=0.5+0.5erfslnkk0V′′(k).

The forms of the low-pass (Eq. ) and high-pass (Eq. ) filters are symmetric and contain a steepness factor s that affects the rate of signal roll-off near the cutoff wavenumber; a higher value approaches a boxcar filter with associated “ringing” effects, while a lower value avoids ringing but at the expense of cutoff precision. In filtering for large-scale and mesoscale v and T, a value of s=5 was selected as an optimal balance of roll-off between the physical coordinate and spectral wavenumber domains. The sets of Fourier coefficients VL and VM resulting from the two filters sum up to the original coefficients V′′. The threshold wavenumber k0=1/λ0 is the reciprocal of the threshold wavelength λ0, which defines the scale separation between large scale and mesoscale. Values of λ0 in this study were set to 10∘ longitude poleward of 20∘ latitude in both hemispheres, increasing to 20∘ longitude within 10∘ of the Equator. More details and a justification of these choices are given in Appendix .

To better preserve zero net volume/mass flux in the basin-integrated vL and vM components, our method incorporates boundary and channel corrections described in more detail in. These corrections also aim to improve local representation of the large-scale/mesoscale separation near boundaries and in narrow channels. Before filtering, (1) v profiles over land areas are set to zero, and (2) a buffer is applied to temperature profiles over land areas near boundaries to avoid sharp swings in TL. After filtering, (3) non-zero vL and vM that leaked onto land areas are returned to water areas, and (4) within channels bounded by bathymetry that are narrower than λ0/4, the meridional velocity profiles are set to vL=v and vM=0. Steps (1), (3), and (4) are taken in order to improve conservation of volume along the transect, while steps (2) and (3) improve the local representation of the large-scale and mesoscale separation. Regarding the rationale for step (4), at most latitudes mesoscale activity peaks near wavelength λ0/2 (e.g., Fig. ), so λ0/4 is approximately the diameter of a typical mesoscale eddy. Channels narrower than λ0/4 are therefore too narrow to support typical mesoscale instabilities, but transport in these channels can contribute substantially to the large-scale circulation (e.g., Indonesian Throughflow, Gulf Stream in the Florida Strait). Hence, all of the transport in these narrow channels has been assigned to the large-scale component.

Lastly, as with the total temperature flux, the time-mean MTF may contain contributions from the time-mean v and T, as well as time-varying v and T: 8MTF‾=MTFstat‾+MTFvary‾9MTFstat=vL‾TM‾+vM‾TL‾+vM‾TM‾10MTFvary=vL′TM′+vM′TL′+vM′TM′, with       ‾ indicating a time average. The mesoscale stationary flux MTFstat is the contribution of the time averages of v and T, and is often associated with boundary current recirculations and standing meanders. In this analysis, the time averages are applied over the full 32 years of model output used. The mesoscale time-varying flux MTFvary is associated with rectified fluxes from transient motions (e.g., instability-generated eddies).

Once computed, the distribution of the MTF in the global oceans highlights where mesoscale dynamics contribute most substantially to the lateral movement of heat in the oceans. There is however an important caveat when inferring the physical significance of the MTF. Flux vectors consist of rotational and divergent fluxes ; by definition, the rotational temperature (and heat) fluxes do not contribute to changes in ocean temperature or heat content and therefore are not generally of interest for climate studies. Our decomposition method is applied only in one horizontal dimension (zonally), so the divergent flux cannot be neatly separated from the rotational flux except in basin integrals (where the rotational flux is negligible). However, showed that rotational fluxes in mesoscale-active areas typically take on mesoscale structure (i.e., they recirculate at mesoscales), while divergent meridional fluxes tend to have larger-scale structure particularly in the zonal direction.

Hence, in this study, a zonal smoothing filter is applied to maps of temperature fluxes to reduce contamination from the “noise” of the rotational fluxes. This smoothing filter has the same form as the low-pass filter in Eq. (). However, for this smoothing, the threshold wavenumber k0 is chosen to be half the threshold wavenumber (twice the threshold wavelength) for the large-scale/mesoscale separation at that latitude. This larger value of the threshold wavelength is used to remove more of the rotational fluxes that occur at the mesoscale. In the smoothing filter, the steepness factor s is also set to 2 (rather than 5), because the smoothing effect is more important here than the precision of the wavelength cutoff. The smoothed MTF indicates the effect of the mesoscale circulation rectified to larger scales. It is the impact of mesoscale fluxes on large-scale temperature distributions that is most relevant when quantifying the fluxes that need to be parameterized in coarse-resolution models.

Maps of zonally smoothed time-mean MTF (Fig. ) show that the mesoscale contributions to meridional HT are generally concentrated near the western boundary. Even in the tropics, MTF contributions are mostly confined to the western boundaries, with the exception of the TIW band in the north-central equatorial Pacific and to a lesser extent in the eddy-rich region south of Indonesia. The impact of MTF contributions is generally to flux heat equatorward in the tropics and poleward at higher latitudes. However, there are exceptions where the MTF fluxes heat equatorward even at midlatitudes, most notably in the western boundary currents of the South Indian (Agulhas Current) and South Pacific (East Australian Current) oceans near 30∘ S (Fig. b). Equatorward MTF is also apparent in the Labrador Sea at the western edge of the North Atlantic subpolar gyre (Fig. a). We note that the significant low EKE bias in the more quiescent middle regions of the ocean (Fig. ) implies that MTF may be underestimated in these regions, especially at low latitudes. An assessment of the potential impact of this bias using composite averages is discussed in Appendix .

The stationary part of the MTF, excluded from temporal definitions of the eddy flux, comprises a substantial portion of the total MTF globally (Fig. ). At lower latitudes (equatorward of 40∘ in both hemispheres), contributions from MTFstat are overwhelmingly concentrated near the western boundaries of ocean basins. In the Southern Ocean, stationary contributions are found near meridional excursions in the Antarctic Circumpolar Current (ACC) at the Brazil–Malvinas Confluence and south of New Zealand. In the North Atlantic, MTFstat contributions are found in the Labrador Sea, Irminger Sea (between Greenland and Iceland), and near the coasts of the British Isles and Scandinavia. Because of the importance of the flow and temperature structure at mesoscales, all of these regions are areas where temperature fluxes are likely to be incorrectly represented in coarse-resolution climate models, unless these fluxes are properly parameterized.

The time-varying MTFvary is closer to the temporal eddy flux v′T′, but our definition excludes larger-scale temporal variability. As might be expected, MTFvary contributions are found mostly in regions where the model also has relatively high EKE (Fig. ): the Gulf Stream and North Atlantic Current, the Kuroshio Extension, the north equatorial Pacific, South Equatorial Current in the Indian Ocean, and the ACC. Many areas that have large MTFstat also have large MTFvary, including most western boundary regions and the ACC. However, ocean interior regions such as the North Atlantic Current and the north equatorial Pacific TIW area have large MTFvary without substantial MTFstat contributions, indicating that the flows driving these fluxes are both mesoscale and transient. In the Southern Ocean, the Agulhas Return Current (near 40∘ S, 0–60∘ E) and the lee of the Kerguelen Plateau (near 50∘ S, 80–90∘ E) are areas where the MTF is dominated by the transient rather than the stationary contribution. The distribution of MTFvary in Fig.  resembles the divergent component of the temporal eddy flux but with some distinctions; for instance, the near-equatorial fluxes are not as high amplitude in Fig. . This may be due to the dominance of long planetary waves at these latitudes, which are time-varying phenomena (temporal “eddy”) but our analysis considers them to be large scale, not mesoscale.

Some insight can be gained about the contributions of stationary vs. time-varying contributions to meridional HT by considering the cumulative zonal integral of each MTF component. Figure  shows this analysis for latitudes in the Indo-Pacific with relatively large MTF. It can be seen that stationary MTF contributions are typically associated with western boundaries (the western Pacific at 32∘ N, 4∘ N, and 13∘ S, and the western Indian at 32∘ S) and that the zonally integrated MTFstat contribution is much larger than MTFvary at the midlatitude locations. Time-varying MTFvary contributions are more substantial at the low-latitude locations (4∘ N and 13∘ S) and can be found both near the basin boundaries (Somali Current and Mozambique Channel/Mascarene Basin, respectively) and in the ocean interiors (Pacific TIWs and South Equatorial Current eddies, respectively).

Since stationary mesoscale contributions to meridional HT are substantial (Fig. ), it is important to understand the velocity and temperature structure that contributes to the flux. For example, the MTFstat contributions near midlatitude western boundaries are driven by a temperature difference between the poleward WBC jet and the equatorward recirculation (Fig. ). In the Gulf Stream, Kuroshio, and Brazil Current poleward of ∼30∘ latitude, the poleward jet is associated with a local maximum in temperature due to the advection of waters from lower latitudes (Fig. a–c). As a result, the water in the jet is warmer than the water in the recirculation, and the net MTF is poleward (Fig. a and b). In contrast, the jet axis of the Agulhas is coincident with a steep gradient in temperature instead of a local maximum in temperature (Fig. d); hence, the water in the jet is cooler than in the recirculation and the net MTF is equatorward. The sign of the MTF associated with WBCs therefore depends on whether the local temperature profile is determined more by the temperature advection of the WBC jet (poleward MTF) or the frontal gradient that the WBC is aligned with (equatorward MTF). Most WBCs have both characteristics, but the degree to which one is dominant can be the difference between a stationary flux that is 0.12 PW poleward (Fig. a) and 0.16 PW equatorward (Fig. d).

When integrated zonally across the global ocean or within ocean basins, the contribution of the MTF to time-mean meridional HT is largest at midlatitudes, with substantial contributions in the Indo-Pacific tropics as well (Fig. ). The largest magnitude mesoscale contribution to meridional HT at any latitude is at 40∘ S, with a poleward heat transport (-0.6 PW) powered by strong MTF in the Brazil–Malvinas Confluence and Agulhas Return Current regions (Fig. ). This exceeds the contribution of the large-scale meridional HT and nearly counters the equatorward meridional HT (+0.8 PW) associated with the overturning at that latitude. The Northern Hemisphere midlatitude meridional HT contributions are not as large; however, the mesoscale meridional HT contribution in the North Atlantic at 43–45∘ N is almost comparable to the overturning at those latitudes (in this case, both components are poleward). In the North Pacific, the mesoscale contributes to poleward meridional HT at ∼35–42∘ N where the overturning and large-scale contributions essentially vanish. Both the Southern and Northern Hemisphere midlatitude peaks in mesoscale meridional HT coincide with local minima in the magnitude of the large-scale meridional HT (Fig. a). This suggests that the mesoscale plays an important part in conveying poleward meridional HT from the subtropical to subpolar gyres in the Northern Hemisphere near 40∘ N and across the equatorward edges of the Southern Ocean near 40∘ S. Additional notable mesoscale contributions to time-mean meridional HT are found at the Indo-Pacific at 2–9∘ N (-0.3 PW) and at 15–11∘ S (+0.2 PW).

A key focus of this study is a better understanding of the interannual/decadal (ID) variability of the mesoscale contribution to meridional HT; accordingly, the time series of the spatial components at each latitude have been temporally low passed for periods longer than 14 months and the seasonal cycle explicitly removed. The standard deviations of the ID-filtered components (Fig. ) show that the overturning dominates meridional HT variability at most latitudes. This is not surprising since the overturning component of meridional HT highlights the effect of temperature differences between the shallow and deep ocean, and at lower latitudes these vertical differences are much larger than zonal temperature differences across ocean basins. However, mesoscale contributions to meridional HT variability can be comparable to the overturning and large-scale contributions at midlatitudes and high latitudes. Globally, the amplitude of mesoscale meridional HT variability at ID timescales is generally comparable to the large-scale variability poleward of 30∘ latitude and comparable to the overturning variability poleward of 40∘ latitude in both hemispheres (Fig. a). The largest peaks in ID mesoscale meridional HT variability occur at 43–40∘ S, 3–4∘ N, and 32∘ N, with the latter two peaks explained mostly by contributions from the Indo-Pacific (Fig. c). These latitudes correspond to the high EKE regions associated with the Agulhas Return Current, Pacific TIWs, and Kuroshio, respectively, implying that the very active mesoscale dynamics and interannual variability in these areas result in large MTF variability on ID timescales as well.

The mesoscale contribution to meridional HT using our method can also be compared to two definitions of the eddy contribution based on a temporal decomposition. The “all-time-varying” contribution consists of the residual eddy term on the right-hand side of Eq. () when the contributions from the 32-year time averages of v and T are removed. The “high-frequency” contribution, following , is the residual eddy term when time averages of v and T in each 3-month period are removed (i.e., consists of variability at timescales shorter than ∼3 months). When zonally integrated globally and across ocean basins, neither the all-time-varying nor high-frequency components are uniformly consistent with the mesoscale contribution (Fig. ). Generally, the mesoscale meridional HT is closer to the high-frequency contribution at low latitudes and closer to the all-time-varying contribution at midlatitudes. One possible inference from this is that mesoscale dynamics tend to have consistently high frequencies in the tropics (where planetary wave and eddy propagation speeds are higher), while mesoscale dynamics at higher latitudes tend to propagate more slowly and take on lower frequencies. The difference between all-time-varying and mesoscale meridional HT close to the Equator may also be associated with the impact of long Kelvin and Rossby waves, which are time varying with frequencies ranging from intraseasonal to interannual but with spatial wavelengths comparable to the size of an entire ocean basin e.g.,. Hence, the temporal eddy fluxes conflate the contributions of large-scale planetary wave activity and mesoscale eddy activity. In contrast, the mesoscale component isolates the contributions to meridional HT from fluxes that are not expected to be well represented in coarse-resolution climate models.

A comparison of the standard deviation associated with the ID time series of the three components (Fig. ) shows that all three components have spikes in temporal variability in the midlatitudes and near the Equator. As with the contributions to time-mean meridional HT, the ID variability of the mesoscale contribution more closely resembles the all-time-varying contribution at midlatitudes. In the tropics, the ID variability of the mesoscale does not resemble either component; in the tropical Indo-Pacific, the high-frequency and all-time-varying standard deviations are both larger than the mesoscale, implying substantial contributions from large-scale ID variability.

Mesoscale dynamics influence not only the time-mean meridional HT but also its variability on ID timescales (Fig. ), motivating a study of the regions where the mesoscale contributions to ID temperature flux variability are greatest. As with the time-mean MTF, the interannual and decadal variability of the MTF is mostly concentrated near western boundaries, the ACC, and the north equatorial Pacific and southern tropical Indian oceans (Fig. ). High levels of ID variability of the MTF also generally coincide with regions of high EKE in the POP model simulation (Fig. b). Notably, the subtropical eddy bands in the Pacific and Indian oceans seem to have a negligible impact on MTF ID variability. The POP model does underestimate EKE in these eddy bands relative to altimetry (Fig. ), but it still shows these bands as regions of elevated EKE; in contrast, there is almost no elevation in ID MTF variability associated with these eddy bands. This indicates that mesoscale fluxes are not particularly efficient at moving heat meridionally in subtropical eddy bands, at least in the POP simulation.

Another way to assess the contributions of MTF variability to basin-integrated meridional HT on ID timescales is to compute a linear regression or correlation between (1) the time series of meridional HT integrated across the basin at each latitude and (2) the local zonally smoothed MTF time series along the transect. This regression-based flux contribution can be expressed as 11RMTF=Rloctotσtot=C(loc,tot)σloc, where Rloctot is the linear regression coefficient of the local MTF given the time series of the total basin-integrated temperature flux, σloc and σtot are the standard deviations of the local and total basin-integrated time series, respectively, and C(loc,tot) is the correlation coefficient of the local and total basin-integrated time series. The regression flux contribution RMTF is the local temperature flux that would be expected to contribute to a basin-integrated value of 1 standard deviation above the mean; positive (negative) values of RMTF indicate a positive (negative) correlation of the two time series. RMTF can be expressed in units of temperature flux or heat flux, and the latter are used here. A similar analysis was shown in Figs. 7–8 of in profiles of longitude–depth, but the MTF is vertically coherent in most regions, so here the “local” time series are depth integrated.

In Fig. , RMTF is computed such that the local time series is the MTF and the total time series is the total meridional HT (sum of all components) at ID timescales with the mean and seasonal cycle removed. These maps show the regions where local MTF has substantial variability that is coherent with total meridional HT variability in a given basin. Overall, three areas emerge where the MTF variability contributes substantially (and positively) to basin-integrated meridional HT variability: the North Atlantic, the tropical Indo-Pacific, and the Southern Ocean between 0–100∘ E. In the North Atlantic, the positive contributions peak at ∼43∘ N, where the Grand Banks of Newfoundland protrude into the North Atlantic Current (Fig. a). In contrast, the “negative” contributions of the Gulf Stream and the Kuroshio south of their separations from the continental shelf imply that MTF variations compensate for other components (specifically large-scale temperature fluxes). For instance, if the large-scale flow is less efficient than usual at advecting heat poleward (perhaps due to the orientation or intensity of the main current), mesoscale variability may take up more of this flux instead. The tropical Indo-Pacific contributions are highest in the TIW bands (Fig. b), with a notable asymmetry across the Equator: north of the Equator, the MTF contributes directly to meridional HT variability, while south of the Equator, the MTF compensates meridional HT variability from other components. In the north equatorial TIW band, the mesoscale contribution to meridional HT contributes to the total meridional HT, often in phase with the much larger overturning contribution (Fig. ); this variability is also closely related to the El Niño–Southern Oscillation. The mesoscale contributions near 13∘ S (Fig. a and b) are focused in the Indian Ocean on both the western and eastern sides, though they are weaker than the near-equatorial contributions. In the Southern Ocean, the Agulhas Return Current (45–40∘ S, 10–20∘ E) and lee of the Kerguelen Plateau (55–45∘ S, 70–100∘ E) emerge as hotspots for mesoscale contributions to total meridional HT (Fig. c). Among the areas mentioned above, there are two regions where the local MTF and basin-integrated total meridional HT are also highly positively correlated with C(loc,tot)>0.5: the Pacific TIW region north of the Equator and the lee of the Kerguelen Plateau. The implication is that mesoscale processes in these two regions have a direct impact on the meridional HT at their respective latitudes, without much compensation from the overturning or large-scale contributions.

Local velocity variability and EKE have been considered in previous studies as possible observational proxies for lateral heat fluxes induced by mesoscale eddies e.g.,. explored the degree to which variations in surface EKE can account for MTF variability at ID timescales, along the 40∘ N transect in the North Atlantic. By applying mixing length theory e.g.,, the relationship can be expressed as 12MTF≈-κ∂T∂y13κ∝v′2Lmix≈EKELmix, where ∝ indicates proportionality (not equality), κ is the diffusivity (which is generally positive or downgradient), and Lmix is the mixing length. (The approximation in Eq.  assumes that u′2≈v′2, which is valid where dynamics are generally isotropic but not where flows are strongly asymmetric and nearly aligned with the zonal or meridional axis.) According to this construct, if the mixing length and meridional temperature gradient do not vary greatly, EKE should be correlated locally with the MTF. In this analysis, the zonal smoothing filter used on MTF in previous figures is applied to both EKE and MTF in order to reduce the impact of shifts in the location of currents and focus on the regional relationship between EKE and MTF.

Figure  shows the fraction of MTF variance at ID timescales explained by local variations in the surface EKE; the fraction of variance is equivalent to the squared correlation coefficient of the surface EKE and MTF. Many regions in the ocean have a significant correlation and fraction of variance explained. These areas include the southern excursions of the ACC, the subtropical bands of eddy activity in the Indo-Pacific at ∼20–25∘ latitude in both hemispheres, and the fringes of energetic western boundary currents. One characteristic shared by these areas is that they tend to have modest levels of time-mean EKE overall (Fig. ); in fact, many of these areas occur near the time-mean contour of 100 cm2s-2 in the POP model, which often separates energetic and quiescent regions in the ocean.

However, in the core of more energetic regions with high EKE, surface EKE is not a good proxy for the MTF. These energetic regions include the Gulf Stream and Kuroshio extensions as well as the Agulhas Return Current, which are annotated in Fig. . The lack of significant MTF variance associated with EKE in these high-energy regions may be attributed to several factors. EKE is a convenient and widely understood metric of mesoscale activity, but it is based on removing a temporal mean from the velocity field and it is not the most precise way to gauge the level of mesoscale energy present. Higher levels of EKE may be associated with an anomalous placement of the current jet and associated front, which does not necessarily change the cross-jet flux. Moreover, strong velocity jets tend to suppress diffusivity across fronts by reducing the mixing length ; the suppression effect of the flow is pronounced in many of the same energetic regions where EKE is a poor proxy for MTF . Ultimately, the MTF depends not only on the amplitude of mesoscale velocity and temperature variation but also on the local correlation between vM and TM , which in turn is a measure of the efficiency of mesoscale motions in producing a net directional flux. The factors affecting this vM–TM correlation locally need to be investigated more in future work. Figure  does however provide an indication of areas of the ocean where surface EKE might be a decent proxy for the MTF, in contrast with the more energetic regions where mixing length and gradient variability can interfere with the EKE–MTF relationship.