Research ArticleOCEANOGRAPHY

Ocean mesoscale mixing linked to climate variability

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Science Advances  23 Jan 2019:
Vol. 5, no. 1, eaav5014
DOI: 10.1126/sciadv.aav5014

Abstract

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 global dataset of lateral mesoscale eddy diffusivities at the ocean surface, obtained by applying the suppressed mixing length theory to satellite-observed velocities. We find interannual variability throughout the global ocean, regionally correlated with climate indices such as ENSO, NAO, DMI, and PDO. Changes in mixing length, driven by variations in the large-scale flow, often exceed the effect of variations in local eddy kinetic energy, previously thought of as the 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 as ecosystem dynamics and regional dynamics such as ENSO variance.

INTRODUCTION

Mesoscale turbulence (on scales from 50 to 200 km) is ubiquitous in the ocean 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 (47), as well as regional dynamics like El Niño–Southern Oscillation (ENSO) variance (8) and ecosystem dynamics.

Diffusion coefficients quantify the rate at which mixing processes transport tracers and are used in coarse-resolution climate models to represent unresolved transport processes. Previous work on mesoscale mixing has focused on estimating the long-term mean diffusivity and its spatial variability (913). The flanks of western boundary currents exhibit diffusivities up to 10,000 m2 s−1, while values on the order of 100 m2 s−1 are found in the subtropical gyres. The use of such spatially variable diffusivities, rather than constant values, in global climate models (7) or inverse methods (14) strongly affects the estimated ocean uptake of carbon and rates of water mass formation. It is thus critical to investigate whether and how mesoscale diffusivities change over time, a possibly missing element in future climate projections.

Persistent periods of increased/decreased mesoscale mixing could have a major impact on the transport of ocean tracers, particularly when these periods are connected to other fluctuating components of the climate system. This applies to both interannual to decadal climate variability and forced trends due to anthropogenic release of carbon dioxide. However, there have been very few studies of the interannual variability in the mesoscale mixing process (15). A recent study of the global sea surface salinity maxima found evidence for large-scale changes of surface diffusivities in the subtropical gyre of the South Pacific (16), but the methods used in that study are not suited to produce global maps of Eulerian diffusivity. In this study, we apply the suppressed mixing length theory (SMLT) to large-scale velocities derived from satellite altimetry to produce temporally variable global maps of surface diffusivities.

In earlier work (9), the Osborn-Cox diffusivity was applied to diagnose the mixing of numerically simulated passive tracers by the surface-geostrophic flow observed by satellite altimetry. These kinematic experiments provided an estimate of the time mean diffusivity over the entire satellite record. Our initial approach to estimating temporal variability 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 suitable for numerical tracer advection (removal of the divergence and adjustment to satisfy kinematic boundary conditions) introduced spurious basin-scale temporal variability in the flow (for details, see the Supplementary Materials). This spurious variability averages out for the long-term mean, but it does bias the temporal variability, such that we cannot rely on the tracer experiments to provide a realistic estimate. Instead, we use these experiments as a test bed to validate SMLT closure for diffusivity and then apply SMLT to the true, unbiased observations to infer to correct temporal variability in diffusivity.

The core concept of the mixing length theory (17) is that the eddy diffusivity (K) is proportional to the product of an eddy velocity Embedded Image (with the eddy kinetic energy Embedded Image; with u′ and v′ as zonal and meridional velocity anomalies), an O(1) constant mixing efficiency Γ, and a mixing length LEmbedded Image(1)

In isotropic turbulence without mean flow, L is assumed to be the eddy length scale (e.g., eddy diameter) Leddy. SMLT was developed to account for the role of large-scale mean flow and eddy propagation in modulating mixing rates. In the presence of a mean flow and eddy propagation, the mixing length is suppressed and is smaller than the eddy size Leddy, such thatEmbedded Image(2)where S ≤ 1 is a suppression factor (18, 19). In the original theory of Ferrari and Nikurashin (18), which applies to axisymmetric zonal jetsEmbedded Image(3)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 α = k22, with zonal wave number k = 2π/Leddy and decorrelation time scale γ. For the exact values used in this study, see below in Materials and Method.

Subsequent work suggested writing the diffusivity asEmbedded Image(4)where K0 = ΓLeddyurms is the unsuppressed diffusivity (19). An important conclusion from this formula is that both the small-scale (mesoscale) turbulent flow (represented by K0) and the large-scale background flow (related to S) conspire to determine the diffusivity.

This framework has been used to explain the spatial variability of mesoscale 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 tracer experiments (9) and Argo float data (12), all showing large spatial variability of eddy mixing in the ocean.

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

All of the above results hold for long-term mean estimates, but how big is the influence of variable surface flow on mixing rates? Can SMLT be used to diagnose interannual variability in mixing rates?

To investigate these questions, we first compared the estimate of SMLT to a direct calculation of cross-frontal mixing, using the Osborn-Cox diffusivity, in an idealized tracer experiment with interannual variability. The Osborn-Cox diffusivity is derived from the high-resolution numerical advection of simulated tracers and is thus independent from SMLT estimate. The appeal of SMLT is that it does not require high-resolution tracer fields but instead is based on the large-scale flow and mesoscale velocity statistics, without the need for any corrections to the velocity field. These velocity observations exist since the early 1990s and enable us to estimate surface diffusivities from a simple formula based on observational data for a time period of over 20 years. SMLT also offers a mechanistic interpretation for variations in diffusivity, which may form the basis for future parameterizations of lateral mixing in coarse-resolution ocean models.

The results (described in detail in Materials and Methods) indicate that both methods agree very well when describing relative temporal changes in surface mixing. Discrepancies exist mostly in the form of constant offsets and different amplitudes of temporal changes, with estimates from the Osborn-Cox method usually being larger with a stronger amplitude. This mirrors the findings of previous work (9, 12, 19), which show strong agreement in spatial patterns of mixing rates, while the absolute values are much less constrained. The strong correlation between our two independent estimates, however, indicates that SMLT is able to capture the underlying characteristics of interannual variability in mesoscale mixing.

RESULTS AND DISCUSSION

The surface diffusivity from SMLT (Kmix), derived from Aviso velocities, is shown in Fig. 1. The long-term mean (Fig. 1A) shows the familiar pattern of high diffusivities near the western boundary currents and low diffusivities within the subtropical gyres and the Antarctic Circumpolar current. The annual range (defined by the difference between the 10th and 90th percentiles of the annual means; Fig. 1B) shows a similar pattern. These results indicate that interannual variability in surface diffusivities is large, on the order of 100 to 1000 m2/s. This represents a large fraction of the mean value in most of the global ocean. The ratio of interannual range to mean diffusivity is larger than 25% in most of the global ocean and in some regions over 50% (Fig. 1C). The amplitude of variability suggests that capturing the temporal variability may be important for characterizing the effects of the mesoscale mixing process on the global ocean circulation. We now examine the mechanisms behind this variability and its relationship with large-scale climate.

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 (23 years) 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 to the large-scale velocity suppression over small-scale (EKE) contribution to the variability of surface diffusivity. The vertical lines in (C) and (D) show the median of the distribution.

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

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), the contribution 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 in panel 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 are smoothed with a 4-month Gaussian window.

In the western equatorial Pacific, Kmix values are substantially elevated during positive NINO3.4 periods. Increases up to 800 m2/s are diagnosed in the southwest subtropical Pacific; these increases are due almost entirely to variations in S caused by the large-scale flow. A recent climate modeling study concluded that larger lateral diffusivity leads to larger ENSO variance in the tropical Pacific (8). They showed that enhanced lateral diffusivity leads to stronger vertical and weaker lateral temperature gradients, both enhancing the coupling between ocean and atmosphere. Our results suggest that lateral diffusivity is positively correlated with ENSO events, particularly in parts of the subtropical Pacific (Fig. 2, A, D, and E), with amplitudes of changes similar or larger than the range of constant diffusivity values used in that study. We speculate that such interannual variations in lateral mixing may therefore play a role in modulating ENSO dynamics, particularly since the variability has a nonuniform (western intensified) pattern, which in the South Pacific even shows a change in correlation toward the East, however with smaller amplitude (Fig. 2E). Full investigation of the nature of this interaction would require the introduction of time-dependent SMLT in an eddy parameterization and a coupled climate model.

Temporally variable lateral diffusivities might matter for other regions as well. In the southern Indian Ocean, surface diffusivities are suppressed during increased NINO3.4 episodes (Fig. 2B). In this region as well, changes in large-scale velocity characteristics account for the majority of the observed variability, particularly with respect to the ENSO signal.

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

In the outflow region of the Indonesian throughflow (ITF), we observe a strong correlation between the surface diffusivities and the Dipole Mode Index [DMI; (24)] (seen in Fig. 2C). The region is critical for the exchange of water from the Pacific to the Indian Ocean. It has been shown that seasonal and large-scale climate fluctuations on the Pacific side and in the Indonesian seas modulate the characteristics of the outflow water (25). Lateral diffusion at shallow depth is essential for explaining the spreading of heat anomalies exiting the ITF into the Indian Ocean (26). Variations in how the water from the ITF is distributed into the Indian Ocean can have implications for ocean atmosphere interaction, including the Madden-Julian oscillation (27).

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

The examples above illustrate a key point of this study: The effects of variable large-scale flow are crucial in reproducing realistic changes in surface diffusivity. Suppression by the large-scale flow is not the sole mechanism for variability—the EKE still plays a major role, as should be expected—but regionally, the effect of mixing suppression by the large-scale flow can have a comparable or even larger effect on mixing variability as effects of EKE, which is related to local stratification via baroclinic instability (29). The latter is the only effect currently represented in some parameterizations for eddy transport in coarse-resolution ocean models.

Investigating in detail the regional effects of variable surface diffusivities will be the subject of future manuscripts; instead, here, we aim to illustrate how variable mixing processes could be crucial for a wide range of coupled climate phenomena.

CONCLUSIONS

In this study, we present a novel dataset of surface diffusivities based on long-term global velocity observations. We find strong evidence that mixing rates in the ocean vary on interannual and longer time scales in many regions of the global ocean. The observed mixing rates suggest a coupling between large-scale climate variability and eddy mixing rates due to small amplitude changes in the large-scale flow. To our knowledge, such large-scale, coherent temporal variability between mesoscale mixing and global climates modes has not been documented before. The vertical coherence of eddy velocities and transports over the upper 1000 m (30) implies that the near-surface lateral mixing variability described here corresponds with isopycnal mixing variability in the main thermocline (9). Because of the importance of lateral mesoscale mixing for the ocean uptake of heat and carbon (7, 31, 32), the distribution of oxygen and nutrients in the ocean (33, 34), ENSO dynamics (8), and water mass formation (3), we suggest that temporal variability in mesoscale mixing could be an important climate feedback mechanism.

This mechanism is not represented in eddy parameterizations for global climate and Earth system models, potentially biasing internal variability and long-term trends in circulation, water mass transformations, heat and tracer transport, ocean-atmosphere interaction, and global climate variability.

This becomes particularly important when looking at past and present climate states, where changes in circulation on the order of 1 cm/s seem very plausible in many parts of the ocean. The long-term diffusivity trend over the observed period (1993–2017) supports this point: The trend in Kmix seems to be a superposition of different trend patterns for the large-scale and small-scale contributions to Kmix (Fig. 3). Using only one component of the velocity field would lead to a quite different long-term evolution of the surface diffusivities. While these linear trends might not represent a purely anthropogenic (e.g., forced) signal, they illustrate 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.

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), the large-scale contribution (middle), and the small-scale contribution (lower).

Further research is needed to quantify the effects of variable mixing rates in coupled climate models, which will require more knowledge about the vertical structure of mixing rates and the suppression by large-scale flow. Although previous results suggest that increased surface diffusivity extends below the surface in the long-term mean (12, 20), the observed velocity data at depth are currently not sufficient to evaluate SMLT globally.

While the agreement in terms of relative change for different methods for estimating mixing rates is very good, large offsets and differences in amplitude remain and require further research and observational constraints. Our kinematic tracer experiments revealed that short-scale variations (seasonal to monthly) in EKE do not influence the diffusivity estimates, indicating that on those time scales, the fundamental assumption for a diffusive approach—the local balance between tracer variance creation and dissipation—might not be valid anymore. For the results presented here, on interannual time scales and longer, the assumption holds (details are discussed in the Supplementary Materials) but future work is needed to investigate the limits of a diffusive approach to parameterize the effect of mesoscale eddies in coarse-resolution general circulation models.

MATERIALS AND METHODS

Analysis tools

All analysis steps here were performed with Python (www.python.org); in particular, the two packages xarray (35) and xgcm (36) were used extensively.

Velocity data

All velocity data in this study are estimates of geostrophic surface velocity based on altimetry (AVISO DUACS2014; produced by Ssalto/Duacs and distributed 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 decomposition

To investigate the characteristics of the velocity field, we need to decompose velocities into a small-scale (mesoscale) and a large-scale component. We chose to use a combination of temporal and spatial filtering to reduce signals to “true” mesoscale eddy signals.

This separation approach is applied for both methods described below, and if not otherwise stated, overbars (primes) denote time averages (time deviations) over monthly intervals, which are additionally spatially lowpass filtered with a Gaussian kernel equivalent to 200 km. Since we focused on interannual variability in this study (see the main text), the resulting products are smoothed in time using a 4-month Gaussian window.

Tracer experiments

The kinematic tracer experiments are conducted in an idealized two-dimensional (2D) configuration of the MITgcm (37), with a horizontal resolution of 0.1° on a regular longitude/latitude grid. These experiments use prescribed velocities and several tracer initial conditions in “offline mode” (i.e., with no dynamics) to solve the 2D advection-diffusion equation without simulating additional processes (e.g., vertical processes or surface forcing), effectively isolating the effect of lateral eddy stirring. The advecting velocities are linearly interpolated from the Aviso 1/4° grid onto the finer model grid and then corrected to be nondivergent following the method described in (9). The effect of this correction is minimal at the mesoscale, but it does introduce small yet notable spurious variability of the basin-scale flow, which leads to biases in the diffusivity time series (see the Supplementary Materials for details). We therefore used these tracer experiments as an opportunity to validate SMLT closure, rather than as a direct estimate of realistic temporal variability in the diffusivity.

Osborn-Cox diffusivity

The Osborn-Cox diffusivity (38, 39), denoted as Koc, parameterizes the local down-gradient eddy flux associated with irreversible mixing across tracer fronts. We obtained a dataset of near-surface diffusivities by diagnosing Koc from the tracer fields of the experiments described above. These tracers are subjected to stirring by the offline velocity field until an equilibrium between the generation and dissipation of tracer variance was reached. Since this equilibrium was established rather rapidly (~2 months), this technique enabled us to resolve changes in mixing on interannual timescales. Koc was calculated asEmbedded Image(5)where q is a passive tracer (four realistic and synthetic tracer fields were used; for details, see the Supplementary Materials), κ is the grid-scale diffusivity, and the prime represents the mesoscale anomaly. The overbar and prime represent mean and deviations according to a 3-month time average 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 diffusivity κ by the creation of lateral tracer gradient variance due to eddy stirring. The small-scale diffusivity here is the result of explicit and numerical diffusivity diagnosed as 63 m2/s from the tracer variance budget (9). The ratio Embedded Image can be interpreted analogous to the length scales of the “effective diffusivity” (40), with large variance in the gradient of the lateral tracer anomaly representing a highly filamented tracer field. For the derivation of Koc and additional discussions, we refer to (9) and references therein. The quantity Koc is most useful for quantifying mixing when the tracer variance budget is characterized predominantly by a local balance between variance production and dissipation—which is the case for our experiments (see the Supplementary Materials for details on the tracer variance budget).

Diffusivity from SMLT

Here, we applied SMLT to attempt to reconstruct the temporal variability observed in Koc from simple physical principles. We hypothesize that the main aspects of the flow, which vary in time within Eqs. 4 and 3, are U and urms (derived from large scale and small scale components of the velocity according to the decomposition described earlier) and assume that Leddy, γ, Γ, and cw do not vary in time. In this case, the diffusivity formula Eq. 4 can be written asEmbedded Image(6)

For small amplitude variability, we can linearize this to findEmbedded Image(7)where the overbar indicates the long-term time mean and the Δ is a time fluctuation.

We find ΔK0 and ΔS by Taylor expansion. ΔK0 is trivialEmbedded Image(8)

The suppression factor requires a bit more algebraEmbedded Image(9)

If not otherwise noted, then the diffusivity variability and its contributions (e.g., ΔK, Embedded Image, and Embedded Image) are shown with the mean diffusivity Embedded Image (derived from long-term means of U and urms according to Eqs. 4 and 3) added.

In this study, we used constant values for Γ = 0.35, γ = 1/4 days [see (19)]. The Doppler shifted phase speed is calculated as Embedded Image, calculated using the depth- and time-averaged zonal flow Embedded Image and the first baroclinic Rossby radius LD, both estimated from an ocean state estimate [as in (19)]. The observed eddy length-scale was estimated from altimetry observations (41) [see also (19)].

Tracer experiment results

The time mean Koc over the 1993–2016 period (Fig. 4A) agrees well with previous studies (9), but our dataset also reveals strong interannual variability. The interannual range (the difference between the 10th and 90th percentiles) of Koc resembles the spatial structure of the mean (Fig. 4B). High variability, O(1000 m2 s−1), is found in the western boundary current extensions and parts of the Indian Ocean. The subtropical and subpolar basins show lower variability, O(100 m2 s−1). Most locations in the global ocean show interannual variability, with a magnitude on the same order of the mean diffusivity, suggesting that temporal variability is of high importance to characterize global surface diffusivities.

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 divergence corrected velocities (for details, see the main text).

For a more detailed analysis, we will focus on data averaged in space over two boxes in the subtropics of the North and South Pacific (see Fig. 5 for locations). Here, the large-scale velocities vary coherently over the region as a consequence of the divergence correction applied (see the Supplementary Materials). This property likely causes the temporal variability in Koc to be unrealistic, e.g., this is not how diffusivities behaved over the last 20 years, but it serves as a test bed to compare different methods of diagnosing diffusivities. In particular, we will focus on the effect of large-scale flow suppression on surface diffusivities. While the temporal evolution of the large-scale velocities in the tracer experiment might be unrealistic, the amplitude (±0.05 m/s; Fig. 5, A and B) is within changes observed from altimetry from interannual changes up to long-term trends (Fig. 5E). The resulting changes in surface diffusivity are large, up to 2000 m2/s in the chosen example boxes. This represents a large change compared to the approximate baseline diffusivity values of 1000 to 1500 m2/s.

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 the North and South Pacific subtropical boxes shown in map panels. (C) Correlation coefficient between surface diffusivity (Koc) and large-scale velocities. (D) Correlation coefficient between surface diffusivity (Koc) and small-scale velocity fluctuations. All quantities are lowpass filtered, with a 4-month Gaussian window to focus on interannual variability and points with significance level below 95% are masked. Note that all values are taken from the tracer experiments; hence, large-scale velocity fluctuations are influenced by the divergence correction (see the main text for details). (E) Normalized global histogram distribution of changes in surface velocities (from observed product) for various 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.

Notably, strong excursions of Koc are closely following episodes of increased westward velocity (Fig. 5 shows the velocities inverted to aid visual comparison), consistent with an increase in the suppression factor from SMLT (Eq. 3). The variations in small-scale velocities (Embedded Image) seem to have less relation to the diagnosed diffusivities, particularly for large diffusivity events. The pronounced seasonal cycle in urms (not shown) is not mirrored in the Koc values, possibly indicating that on time scales shorter than seasonal, variance advection becomes an important term in the variance budget and the concept of a diffusivity might break down. In this study, however, we will focus on interannual variability, and the subject of seasonal variability is left for future study. Analysis of the full tracer variance budget from the tracer experiment suggests that temporal variations on interannual and longer time scales can be represented by a diffusivity approach (for details, see Supplementary Materials), and thus in the remainder of this study, we will focus on interannual and longer signals, by lowpass filtering all monthly data with a 4-month Gaussian window.

The relationship between the large-scale velocity and Koc holds in many regions globally, as indicated by the large correlation coefficients shown in Fig. 5C. The negative correlation between large-scale zonal velocities and Koc is generally strongest in the subtropical Pacific, but values remain high throughout the world ocean. The correlation with urms (Fig. 5D) does not show values as high as the large-scale velocities, but most regions of the oceans show a moderate and significant correlation, suggesting that temporal variability caused by small-scale velocity fluctuations is not negligible.

Is this finding applicable to the real ocean? To answer this question, we will need to use SMLT-derived Kmix, since that can be applied directly to observed, uncorrected velocity fields. We thus compared the results from the tracer-based Osborn-Cox diffusivity (Koc) to Kmix, estimated from the divergence-corrected (unrealistic) velocity fields, to verify that the main features of variability are well captured.

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

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-scale velocity 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) Correlation map between Koc and Kmix. Both variables are lowpass filtered with a 4-month Gaussian window to focus on interannual variability and points with 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.

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

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/1/eaav5014/DC1

Supplementary Materials

Tracer variance budget

Fig. 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 (4245)

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

REFERENCES AND NOTES

Acknowledgments: Funding: J.J.M.B. acknowledges support from NASA award NNX14AP29H. R.P.A. acknowledges support from NSF OCE 1553593. We thank S. Groeskamp and the anonymous reviewers for comments that greatly improved the manuscript. Author contributions: All authors contributed to the interpretation of the results and writing of the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. The code to reproduce the results of this study is provided in a Zenodo archive (https://doi.org/10.5281/zenodo.1472889). The dataset presented (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, which was supported by NSF Award 1740648. Questions may be directed to the authors.
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