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1Princeton University, Princeton, NJ, USA. 2Lamont-Doherty Earth Observatory ofColumbia University, Palisades, NY, USA.*Corresponding author. Email: jbusecke@princeton.edu

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Ocean mesoscale mixing linked to climate variabilityJulius J. M. Busecke1* and Ryan P. Abernathey2

Mesoscale turbulence in the ocean strongly affects the circulation, water mass formation, and transport of tracers.Little is known, however, about how mixing varies on climate timescales. We present the first time-resolved globaldataset of lateralmesoscale eddydiffusivities at the ocean surface, obtainedby applying the suppressedmixing lengththeory to satellite-observed velocities. We find interannual variability throughout the global ocean, regionallycorrelated with climate indices such as ENSO, NAO, DMI, and PDO. Changes in mixing length, driven by variationsin the large-scale flow, often exceed the effect of variations in local eddy kinetic energy, previously thought of asthe primary driver of variability in eddy mixing. This mechanism, not currently represented in global climate models,could have far-reaching consequences for the distribution of heat, salt, and carbon in the global ocean, as well asecosystem dynamics and regional dynamics such as ENSO variance.

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INTRODUCTIONMesoscale turbulence (on scales from 50 to 200 km) is ubiquitous in theocean and strongly affects the meridional overturning circulation (1, 2),water mass formation (3), and the transport of tracers such as heat, salt,nutrients, oxygen, and anthropogenic carbon (4–7), as well as regionaldynamics like El Niño–Southern Oscillation (ENSO) variance (8) andecosystem dynamics.

Diffusion coefficients quantify the rate at which mixing processestransport tracers and are used in coarse-resolution climate models torepresent unresolved transport processes. Previous work on mesoscalemixing has focused on estimating the long-termmean diffusivity and itsspatial variability (9–13). The flanks of western boundary currentsexhibit diffusivities up to 10,000 m2 s−1, while values on the orderof 100 m2 s−1 are found in the subtropical gyres. The use of such spa-tially variable diffusivities, rather than constant values, in global climatemodels (7) or inverse methods (14) strongly affects the estimated oceanuptake of carbon and rates of water mass formation. It is thus critical toinvestigate whether and howmesoscale diffusivities change over time, apossibly missing element in future climate projections.

Persistent periods of increased/decreased mesoscale mixing couldhave amajor impact on the transport of ocean tracers, particularlywhenthese periods are connected to other fluctuating components of the cli-mate system. This applies to both interannual to decadal climate vari-ability and forced trends due to anthropogenic release of carbon dioxide.However, there havebeen very few studies of the interannual variability inthemesoscalemixing process (15). A recent study of the global sea surfacesalinitymaxima found evidence for large-scale changes of surface diffu-sivities in the subtropical gyre of the South Pacific (16), but themethodsused in that study are not suited to produce global maps of Euleriandiffusivity. In this study, we apply the suppressed mixing length theory(SMLT) to large-scale velocities derived from satellite altimetry toproduce temporally variable global maps of surface diffusivities.

In earlier work (9), the Osborn-Cox diffusivity was applied to diag-nose themixing of numerically simulated passive tracers by the surface-geostrophic flow observed by satellite altimetry. These kinematicexperiments provided an estimate of the time mean diffusivity overthe entire satellite record. Our initial approach to estimating temporalvariability was to use the Osborn-Cox diffusivity directly in a time-dependent way. However, we discovered that a subtle and unavoidable

artifact of the data processing necessary to produce velocities suitablefor numerical tracer advection (removal of the divergence and adjust-ment to satisfy kinematic boundary conditions) introduced spuriousbasin-scale temporal variability in the flow (for details, see the Supple-mentary Materials). This spurious variability averages out for the long-termmean, but it does bias the temporal variability, such thatwe cannotrely on the tracer experiments to provide a realistic estimate. Instead, weuse these experiments as a test bed to validate SMLT closure for diffu-sivity and then apply SMLT to the true, unbiased observations to infer tocorrect temporal variability in diffusivity.

The core concept of the mixing length theory (17) is that the eddydiffusivity (K) is proportional to the product of an eddy velocityurms ¼ffiffiffiffiffiffiffiffiffiffiffi

2EKEp

(with the eddy kinetic energyEKE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

u′2 þ v′2p

; withu′ and v′as zonal and meridional velocity anomalies), an O(1) constant mixingefficiency G, and a mixing length L

K ¼ GLurms ð1Þ

In isotropic turbulence without mean flow, L is assumed to be theeddy length scale (e.g., eddy diameter) Leddy. SMLT was developed toaccount for the role of large-scale mean flow and eddy propagation inmodulatingmixing rates. In the presence of amean flow and eddy prop-agation, the mixing length is suppressed and is smaller than the eddysize Leddy, such that

L ¼ LeddyS ð2Þ

where S ≤ 1 is a suppression factor (18, 19). In the original theory ofFerrari and Nikurashin (18), which applies to axisymmetric zonal jets

S ¼ 1

1þ aðcw � UÞ2 ð3Þ

where U is the zonal mean flow, cw is the zonal eddy phase speed[calculated as the absolute, i.e., Doppler shifted zonal phase speed(19)], and a = k2/g2, with zonal wave number k = 2p/Leddy and decorre-lation time scale g. For the exact values used in this study, see below inMaterials and Method.

Subsequent work suggested writing the diffusivity as

Kmix ¼ K0S ð4Þ

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whereK0 = GLeddyurms is the unsuppressed diffusivity (19). An impor-tant conclusion from this formula is that both the small-scale (meso-scale) turbulent flow (represented by K0) and the large-scale backgroundflow (related to S) conspire to determine the diffusivity.

This framework has been used to explain the spatial variability ofmesoscale mixing rates within the Antarctic Circumpolar Current(18), a broad sector of the Eastern Pacific, and for the global ocean(19). These results agree well with studies using idealized tracerexperiments (9) and Argo float data (12), all showing large spatial var-iability of eddy mixing in the ocean.

This body of research suggests that even small amplitude variabilityin the large-scale flow can have a major impact on the diffusive transportof tracers near the surface. Furthermore, several studies indicate that iso-pycnal diffusivity throughout the pycnocline is closely correlatedwith nearsurface mixing rates (12, 20). Together, this implies that small changes inthe large-scale flow, due to natural variability or a changing climate, couldhave strong effects on processes, which are sensitive to isopycnal tracertransport by mesoscale mixing, both at the surface and at depth.

All of the above results hold for long-termmean estimates, but howbig is the influence of variable surface flow onmixing rates? Can SMLTbe used to diagnose interannual variability in mixing rates?

To investigate these questions, we first compared the estimate ofSMLT to a direct calculation of cross-frontal mixing, using the Osborn-

Busecke and Abernathey, Sci. Adv. 2019;5 : eaav5014 23 January 2019

Cox diffusivity, in an idealized tracer experiment with interannual var-iability. The Osborn-Cox diffusivity is derived from the high-resolutionnumerical advection of simulated tracers and is thus independent fromSMLT estimate. The appeal of SMLT is that it does not require high-resolution tracer fields but instead is based on the large-scale flow andmesoscale velocity statistics, without the need for any corrections to thevelocity field. These velocity observations exist since the early 1990s andenable us to estimate surface diffusivities from a simple formula basedon observational data for a time period of over 20 years. SMLT alsooffers a mechanistic interpretation for variations in diffusivity, whichmay form the basis for future parameterizations of lateral mixing incoarse-resolution ocean models.

The results (described in detail in Materials and Methods) indicatethat both methods agree very well when describing relative temporalchanges in surface mixing. Discrepancies exist mostly in the form ofconstant offsets and different amplitudes of temporal changes, with es-timates from theOsborn-Coxmethod usually being larger with a stron-ger amplitude. This mirrors the findings of previous work (9, 12, 19),which show strong agreement in spatial patterns of mixing rates, whilethe absolute values are much less constrained. The strong correlationbetween our two independent estimates, however, indicates that SMLTis able to capture the underlying characteristics of interannual variabilityin mesoscale mixing.

Fig. 1. Kmix mean and annual range. The maps (A and B) show surface diffusivity (m2/s) from SMLT applied to observed surface velocities. (A) Full record (23years) average. (B) Annual range, defined as the difference between the 90th and 10th percentiles of annual averages. (C) Normalized histogram of the ratio of(B) over (A), indicating that in many parts of the ocean, interannual variability is a sizeable fraction of the mean. (D) Same as (C) but for the ratio of SDs due tothe large-scale velocity suppression over small-scale (EKE) contribution to the variability of surface diffusivity. The vertical lines in (C) and (D) show the medianof the distribution.

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RESULTS AND DISCUSSIONThe surface diffusivity from SMLT (Kmix), derived from Aviso veloci-ties, is shown in Fig. 1. The long-term mean (Fig. 1A) shows the fa-miliar pattern of high diffusivities near the western boundary currentsand low diffusivities within the subtropical gyres and the AntarcticCircumpolar current. The annual range (defined by the difference be-tween the 10th and 90th percentiles of the annualmeans; Fig. 1B) showsa similar pattern. These results indicate that interannual variability insurface diffusivities is large, on the order of 100 to 1000 m2/s. This re-presents a large fraction of the mean value inmost of the global ocean.The ratio of interannual range tomean diffusivity is larger than 25% inmost of the global ocean and in some regions over 50% (Fig. 1C). Theamplitude of variability suggests that capturing the temporal variabil-ity may be important for characterizing the effects of the mesoscale

Busecke and Abernathey, Sci. Adv. 2019;5 : eaav5014 23 January 2019

mixing process on the global ocean circulation. We now examinethe mechanisms behind this variability and its relationship withlarge-scale climate.

SMLT suggests that very small amplitude variations in large-scalevelocities, caused by, e.g., changes in thewind forcing, result in relativelylarge changes of diffusivity. It is hence very plausible that large-scale cli-mate fluctuations (21) and anthropogenic changes (22) lead to changesin both large-scale circulation and eddy activity, both of which affectsurface diffusivities. We find that in many regions of the world ocean,there is a strong relation between large-scale climate indices and the sur-face diffusivity, as shown in Fig. 2.

In the western equatorial Pacific, Kmix values are substantiallyelevated during positive NINO3.4 periods. Increases up to 800 m2/sare diagnosed in the southwest subtropical Pacific; these increases are

Fig. 2. Relation of Kmix to large-scale climate variability. Map shows simplified schematic of the relationship of several climate indices to the surface diffusivities.Red/blue indicates a positive/negative correlation with the respective index. (A to G) Show spatial averages (over boxes indicated on the map) of Kmix (black), thecontribution of large-scale velocity to Kmix (blue), the contribution of small-scale velocities to Kmix (orange), and a selected climate index (dashed gray; index indicated inpanel legend). The climate index is normalized with the mean and SD of the Kmix time series for visual comparison; thus, no units are given. All data shown aresmoothed with a 4-month Gaussian window.

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due almost entirely to variations in S caused by the large-scale flow. Arecent climate modeling study concluded that larger lateral diffusivityleads to larger ENSO variance in the tropical Pacific (8). They showedthat enhanced lateral diffusivity leads to stronger vertical and weakerlateral temperature gradients, both enhancing the coupling betweenocean and atmosphere. Our results suggest that lateral diffusivity is pos-itively correlated with ENSO events, particularly in parts of the sub-tropical Pacific (Fig. 2, A, D, and E), with amplitudes of changessimilar or larger than the range of constant diffusivity values used in thatstudy. We speculate that such interannual variations in lateral mixingmay therefore play a role in modulating ENSO dynamics, particularlysince the variability has a nonuniform (western intensified) pattern, whichin the South Pacific even shows a change in correlation toward the East,however with smaller amplitude (Fig. 2E). Full investigation of the natureof this interaction would require the introduction of time-dependentSMLT in an eddy parameterization and a coupled climate model.

Temporally variable lateral diffusivitiesmightmatter for other regionsas well. In the southern Indian Ocean, surface diffusivities are suppressed

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during increased NINO3.4 episodes (Fig. 2B). In this region as well,changes in large-scale velocity characteristics account for the majorityof the observed variability, particularly with respect to the ENSO signal.

Surface diffusivities respond not only to ENSO but also to a varietyof other climate indices, such as the North Atlantic oscillation (23),which correlates with diffusivities in the northeastern subtropical gyrein the Atlantic (Fig. 2F).

In the outflow region of the Indonesian throughflow (ITF), we ob-serve a strong correlation between the surface diffusivities and the Di-poleMode Index [DMI; (24)] (seen in Fig. 2C). The region is critical forthe exchange of water from the Pacific to the Indian Ocean. It has beenshown that seasonal and large-scale climate fluctuations on the Pacificside and in the Indonesian seas modulate the characteristics of theoutflow water (25). Lateral diffusion at shallow depth is essential for ex-plaining the spreading of heat anomalies exiting the ITF into the IndianOcean (26). Variations in how thewater from the ITF is distributed intothe Indian Ocean can have implications for ocean atmosphere interac-tion, including the Madden-Julian oscillation (27).

Fig. 3. The 23-year linear trend for Kmix and its components. The integrated linear trend in diffusivity over the 23-year period is shown for the full Kmix (upper), thelarge-scale contribution (middle), and the small-scale contribution (lower).

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In the North Pacific, surface diffusivities show a relation to thePacific Decadal Oscillation [PDO; (28)]. The large-scale component ofthe diffusivities shows a closer relation to the PDO than the small-scale(EKE-based) contribution (Fig. 2G). The resulting observed diffusivity inthis case is not dominatedby the large-scale contribution; instead, it seemsessential to capture both components to represent the full time series.

The examples above illustrate a key point of this study: The effects ofvariable large-scale flow are crucial in reproducing realistic changes insurface diffusivity. Suppression by the large-scale flow is not the solemechanism for variability—the EKE still plays a major role, as shouldbe expected—but regionally, the effect of mixing suppression by thelarge-scale flow can have a comparable or even larger effect onmixing var-iability as effects of EKE,which is related to local stratification via baroclin-ic instability (29). The latter is the only effect currently represented in someparameterizations for eddy transport in coarse-resolution ocean models.

Investigating in detail the regional effects of variable surface diffusiv-ities will be the subject of future manuscripts; instead, here, we aim toillustrate how variable mixing processes could be crucial for a widerange of coupled climate phenomena.

CONCLUSIONSIn this study, we present a novel dataset of surface diffusivities based onlong-term global velocity observations. We find strong evidence thatmixing rates in the ocean vary on interannual and longer time scalesin many regions of the global ocean. The observed mixing rates suggesta coupling between large-scale climate variability and eddymixing ratesdue to small amplitude changes in the large-scale flow. To our knowl-edge, such large-scale, coherent temporal variability between mesoscalemixing and global climates modes has not been documented before.The vertical coherence of eddy velocities and transports over the upper

Busecke and Abernathey, Sci. Adv. 2019;5 : eaav5014 23 January 2019

1000 m (30) implies that the near-surface lateral mixing variability de-scribed here corresponds with isopycnal mixing variability in the mainthermocline (9). Because of the importance of lateral mesoscale mixingfor the ocean uptake of heat and carbon (7, 31, 32), the distribution ofoxygen and nutrients in the ocean (33, 34), ENSO dynamics (8), andwater mass formation (3), we suggest that temporal variability in meso-scale mixing could be an important climate feedback mechanism.

This mechanism is not represented in eddy parameterizations forglobal climate andEarth systemmodels, potentially biasing internal var-iability and long-term trends in circulation, water mass transforma-tions, heat and tracer transport, ocean-atmosphere interaction, andglobal climate variability.

This becomes particularly important when looking at past and pre-sent climate states, where changes in circulation on the order of 1 cm/sseem very plausible in many parts of the ocean. The long-term diffusiv-ity trend over the observed period (1993–2017) supports this point: Thetrend in Kmix seems to be a superposition of different trend patterns forthe large-scale and small-scale contributions to Kmix (Fig. 3). Usingonly one component of the velocity field would lead to a quite differentlong-term evolution of the surface diffusivities. While these linear trendsmight not represent a purely anthropogenic (e.g., forced) signal, they illus-trate the need to account for the full interaction of large-scale and small-scale velocities to capture the effects of mesoscale mixing in the ocean.

Further research isneeded toquantify the effects of variablemixing ratesin coupled climate models, which will require more knowledge about thevertical structure of mixing rates and the suppression by large-scale flow.Although previous results suggest that increased surface diffusivity extendsbelow the surface in the long-term mean (12, 20), the observed velocitydata at depth are currently not sufficient to evaluate SMLT globally.

While the agreement in terms of relative change for different methodsfor estimating mixing rates is very good, large offsets and differences in

Fig. 4. Koc maps. Same maps as in Fig. 1, but for the surface diffusivities derived from the passive tracer experiment. Note that these were derived from the divergencecorrected velocities (for details, see the main text).

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amplitude remain and require further research and observational con-straints. Our kinematic tracer experiments revealed that short-scalevariations (seasonal to monthly) in EKE do not influence the diffusivityestimates, indicating that on those time scales, the fundamental assumptionfor adiffusive approach—the local balancebetween tracer variance creationand dissipation—might not be valid anymore. For the results presentedhere, on interannual time scales and longer, the assumption holds (detailsare discussed in the SupplementaryMaterials) but futurework is needed toinvestigate the limits of a diffusive approach to parameterize the effect ofmesoscale eddies in coarse-resolution general circulation models.

MATERIALS AND METHODSAnalysis toolsAll analysis steps here were performed with Python (www.python.org); inparticular, the twopackagesxarray (35) andxgcm(36)wereusedextensively.

Busecke and Abernathey, Sci. Adv. 2019;5 : eaav5014 23 January 2019

Velocity dataAll velocity data in this study are estimates of geostrophic surface velocitybased on altimetry (AVISODUACS2014; produced by Ssalto/Duacs anddistributed by Aviso, with support from Cnes, www.aviso.altimetry.fr/duacs/). The velocity record extends from January 1993 to January 2017(using the near real time product after May 2016).

Velocity decompositionTo investigate the characteristics of the velocity field, we need to decom-pose velocities into a small-scale (mesoscale) and a large-scalecomponent. We chose to use a combination of temporal and spatialfiltering to reduce signals to “true” mesoscale eddy signals.

This separation approach is applied for both methods described be-low, and if not otherwise stated, overbars (primes) denote time averages(time deviations) overmonthly intervals, which are additionally spatial-ly lowpass filtered with a Gaussian kernel equivalent to 200 km. Since

Fig. 5. Relationship of Koc to small- and large-scale velocities. (A and B) Time series of the Osborn-Cox diffusivity (Koc, black), large-scale velocity anomalies (U, red), and small-scale velocity anomalies (urms, gray) for theNorth and South Pacific subtropical boxes shown inmappanels. (C) Correlation coefficient between surface diffusivity (Koc) and large-scalevelocities. (D) Correlation coefficient between surface diffusivity (Koc) and small-scale velocity fluctuations. All quantities are lowpass filtered,with a 4-monthGaussianwindow to focuson interannual variability and points with significance level below 95% aremasked. Note that all values are taken from the tracer experiments; hence, large-scale velocity fluctuationsare influenced by the divergence correction (see the main text for details). (E) Normalized global histogram distribution of changes in surface velocities (from observed product) forvarious time-averaging intervals and the long-term trend integrated over the full time period of Aviso data. All data shown are smoothed with a 4-month Gaussian window.

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we focused on interannual variability in this study (see the main text),the resulting products are smoothed in time using a 4-month Gaussianwindow.

Tracer experimentsThe kinematic tracer experiments are conducted in an idealized two-dimensional (2D) configuration of the MITgcm (37), with a horizontalresolution of 0.1° on a regular longitude/latitude grid. These experimentsuse prescribed velocities and several tracer initial conditions in “offlinemode” (i.e., with no dynamics) to solve the 2D advection-diffusion equa-tion without simulating additional processes (e.g., vertical processes orsurface forcing), effectively isolating the effect of lateral eddy stirring.The advecting velocities are linearly interpolated from theAviso 1/4° gridonto the finer model grid and then corrected to be nondivergentfollowing the method described in (9). The effect of this correction isminimal at themesoscale, but it does introduce small yet notable spuriousvariability of the basin-scale flow, which leads to biases in the diffusivitytime series (see the Supplementary Materials for details). We thereforeused these tracer experiments as an opportunity to validate SMLTclosure, rather than as a direct estimate of realistic temporal variabilityin the diffusivity.

Osborn-Cox diffusivityThe Osborn-Cox diffusivity (38, 39), denoted as Koc, parameterizesthe local down-gradient eddy flux associated with irreversible mixingacross tracer fronts. We obtained a dataset of near-surface diffusivitiesby diagnosing Koc from the tracer fields of the experiments described

Busecke and Abernathey, Sci. Adv. 2019;5 : eaav5014 23 January 2019

above. These tracers are subjected to stirring by the offline velocity fielduntil an equilibrium between the generation and dissipation of tracervariance was reached. Since this equilibrium was established ratherrapidly (~2 months), this technique enabled us to resolve changesin mixing on interannual timescales. Koc was calculated as

Koc ¼ kj∇q′j2j∇�qj2 ð5Þ

where q is a passive tracer (four realistic and synthetic tracer fields wereused; for details, see the Supplementary Materials), k is the grid-scalediffusivity, and theprime represents themesoscale anomaly.The overbarand prime represent mean and deviations according to a 3-month timeaverage and spatial lowpass filtering with a 200-km Gaussian kernel.The Supplementary Materials show the derivation of the Osborn-Cox diffusivity for filtering operators.

Physically, Koc represents the local enhancement of a small-scale diffu-sivityk by thecreationof lateral tracergradient variancedue toeddystirring.The small-scale diffusivity here is the result of explicit and numerical diffu-sivity diagnosed as 63m2/s from the tracer variance budget (9). The ratio

j∇q′j2=j∇qj2 can be interpreted analogous to the length scales of the “ef-fectivediffusivity” (40),with large variance in the gradient of the lateral trac-er anomaly representing a highly filamented tracer field. For the derivationofKoc and additional discussions, we refer to (9) and references therein.The quantity Koc is most useful for quantifying mixing when the tracervariance budget is characterized predominantly by a local balance between

Fig. 6. Comparison between Koc and Kmix. (A and B) Time series of surface diffusivities, comparing Koc (gray-dashed), Kmix (black), the variability due to large-scalevelocity suppression (blue), and the variability due to small-scale velocity fluctuations (orange) averaged over the same boxes as Fig. 5. Note the different axes for the Koc values(left) and Kmix (right). (C) Correlationmap between Koc and Kmix. Both variables are lowpass filteredwith a 4-month Gaussian window to focus on interannual variability and pointswith significance level below 99% are masked. (D) Offset between the time average of Koc and Kmix. (E) Difference between the temporal SD of Koc and Kmix.

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variance production and dissipation—which is the case for our ex-periments (see the Supplementary Materials for details on the tracervariance budget).

Diffusivity from SMLTHere, we applied SMLT to attempt to reconstruct the temporal varia-bility observed in Koc from simple physical principles. We hypothesizethat themain aspects of the flow,which vary in timewithin Eqs. 4 and 3,areU and urms (derived from large scale and small scale components ofthe velocity according to the decomposition described earlier) and as-sume that Leddy, g, G, and cw do not vary in time. In this case, the dif-fusivity formula Eq. 4 can be written as

Kmixðurms;UÞ ¼ K0ðurmsÞSðUÞ ð6Þ

For small amplitude variability, we can linearize this to find

DKmix ¼ fK0DSLarge‐scale contribution

þ fSDK0Small‐scale contribution

ð7Þ

where the overbar indicates the long-term time mean and the D is atime fluctuation.

We find DK0 and DS by Taylor expansion. DK0 is trivial

DK0 ¼ ∂K0

∂urmsDurms ¼ GLeddyDurms ð8Þ

The suppression factor requires a bit more algebra

DS ¼ ∂S∂U

DU ¼ 2aðc� �UÞ�S2DU ð9Þ

If not otherwise noted, then the diffusivity variability and its con-tributions (e.g., DK, K0DS, and �SDK0) are shown with the mean dif-fusivityKmix (derived from long-termmeans ofU and urms accordingto Eqs. 4 and 3) added.

In this study, we used constant values for G = 0.35, g = 1/4 days [see(19)]. TheDoppler shifted phase speed is calculated ascw ¼ Uzt � bL2D,calculated using the depth- and time-averaged zonal flow Uzt and thefirst baroclinic Rossby radius LD, both estimated from an ocean stateestimate [as in (19)]. The observed eddy length-scale was estimatedfrom altimetry observations (41) [see also (19)].

Tracer experiment resultsThe time mean Koc over the 1993–2016 period (Fig. 4A) agrees wellwith previous studies (9), but our dataset also reveals strong interannualvariability. The interannual range (the difference between the 10th and90th percentiles) ofKoc resembles the spatial structure of themean (Fig.4B). High variability, O(1000m2 s−1), is found in the western boundarycurrent extensions and parts of the Indian Ocean. The subtropical andsubpolar basins show lower variability, O(100m2 s−1).Most locations inthe global ocean show interannual variability, with a magnitude on thesame order of themean diffusivity, suggesting that temporal variability isof high importance to characterize global surface diffusivities.

For amore detailed analysis, we will focus on data averaged in spaceover two boxes in the subtropics of theNorth and South Pacific (see Fig. 5for locations). Here, the large-scale velocities vary coherently over the

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region as a consequence of the divergence correction applied (see theSupplementary Materials). This property likely causes the temporalvariability in Koc to be unrealistic, e.g., this is not how diffusivities be-haved over the last 20 years, but it serves as a test bed to compare dif-ferent methods of diagnosing diffusivities. In particular, we will focuson the effect of large-scale flow suppression on surface diffusivities.While the temporal evolution of the large-scale velocities in the tracerexperiment might be unrealistic, the amplitude (±0.05 m/s; Fig. 5, Aand B) is within changes observed from altimetry from interannualchanges up to long-term trends (Fig. 5E). The resulting changes in sur-face diffusivity are large, up to 2000m2/s in the chosen example boxes.This represents a large change compared to the approximate baselinediffusivity values of 1000 to 1500 m2/s.

Notably, strong excursions of Koc are closely following episodes ofincreased westward velocity (Fig. 5 shows the velocities inverted to aidvisual comparison), consistent with an increase in the suppressionfactor from SMLT (Eq. 3). The variations in small-scale velocities(urms ¼

ffiffiffiffiffiffiffiffiffiffiffi

2EKEp

) seem to have less relation to the diagnosed diffu-sivities, particularly for large diffusivity events. The pronounced season-al cycle in urms (not shown) is not mirrored in the Koc values, possiblyindicating that on time scales shorter than seasonal, variance advectionbecomes an important term in the variance budget and the concept of adiffusivity might break down. In this study, however, we will focus oninterannual variability, and the subject of seasonal variability is left forfuture study. Analysis of the full tracer variance budget from the tracerexperiment suggests that temporal variations on interannual and longertime scales can be represented by a diffusivity approach (for details, seeSupplementary Materials), and thus in the remainder of this study, wewill focus on interannual and longer signals, by lowpass filtering allmonthly data with a 4-month Gaussian window.

The relationship between the large-scale velocity and Koc holds inmany regions globally, as indicated by the large correlation coefficientsshown in Fig. 5C. The negative correlation between large-scale zonalvelocities and Koc is generally strongest in the subtropical Pacific, butvalues remain high throughout the world ocean. The correlation withurms (Fig. 5D) does not show values as high as the large-scale velocities,but most regions of the oceans show a moderate and significant corre-lation, suggesting that temporal variability caused by small-scale veloc-ity fluctuations is not negligible.

Is this finding applicable to the real ocean? To answer this question,wewill need to use SMLT-derivedKmix, since that can be applied direct-ly to observed, uncorrected velocity fields.We thus compared the resultsfrom the tracer-based Osborn-Cox diffusivity (Koc) to Kmix, estimatedfrom the divergence-corrected (unrealistic) velocity fields, to verify thatthe main features of variability are well captured.

Figure 6 shows that the relative variability (e.g., the timing ofanomalies) in diffusivities is well captured, while the mean diffusivityand the amplitude of diffusivity anomalies are considerably differentbetween the two estimates of surface diffusivity. Figure 6 (A and B)shows the strong correlation between Koc and Kmix, in particular thevariability Kmix caused by the suppression of the large-scale flow.Globally, the correlation between the two estimates is high in mostregions (Fig. 6C), while time mean values of Koc are mostly higher,sometimes over 1000 m2/s (Fig. 6D, compare also the different y axesin A and B). In most regions, the amplitude of variability is larger forKoc, although there are exceptions (Fig. 6E). Overall, these results in-dicate that both methods agree well on the sign of anomalies, but theactual absolute values can differ substantially between estimates,most-ly with higher values and variability in the Koc.

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This result is highly encouraging, since it confirms that SMLT is ableto capture time variations in surface diffusivity, allowing the applicationof SMLT to realistic (uncorrected) velocities.

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/1/eaav5014/DC1Supplementary MaterialsTracer variance budgetFig. S1. Velocity bias introduced by divergence correction.Fig. S2. Comparison of Koc results for different initial conditions.Fig. S3. Validation of tracer variance budget.References (42–45)

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AcknowledgmentsFunding: J.J.M.B. acknowledges support from NASA award NNX14AP29H. R.P.A. acknowledgessupport from NSF OCE 1553593. We thank S. Groeskamp and the anonymous reviewers forcomments that greatly improved the manuscript. Author contributions: All authorscontributed to the interpretation of the results and writing of the manuscript. Competinginterests: The authors declare that they have no competing interests. Data and materialsavailability: All data needed to evaluate the conclusions in the paper are present in the paperand/or the Supplementary Materials. The code to reproduce the results of this study isprovided in a Zenodo archive (https://doi.org/10.5281/zenodo.1472889). The datasetpresented (and auxiliary data to reproduce results) are available under http://dx.doi.org/10.6084/m9.figshare.4928693. Data analysis was performed using the Pangeo platform, whichwas supported by NSF Award 1740648. Questions may be directed to the authors.

Submitted 21 September 2018Accepted 10 December 2018Published 23 January 201910.1126/sciadv.aav5014

Citation: J. J. M. Busecke, R. P. Abernathey, Ocean mesoscale mixing linked to climatevariability. Sci. Adv. 5, eaav5014 (2019).

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Ocean mesoscale mixing linked to climate variabilityJulius J. M. Busecke and Ryan P. Abernathey

DOI: 10.1126/sciadv.aav5014 (1), eaav5014.5Sci Adv 

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