Introduction

Oceanic mesoscale activity, characterized by horizontal scales ranging from tens to hundreds of kilometers, accounts for almost 90% of the global ocean kinetic energy1, serving as principal regulators in the global energy budget and biogeochemical cycling2,3,4. In coastal transition zones, mesoscale fronts and eddies act as critical interfacial mediators, facilitating cross-shelf transport of momentum, heat, dissolved carbon, nutrients, and pollutants1,5,6,7,8,9,10,11,12. These processes exert cascading effects on environments and ecosystems13, as well as resource sustainability14,15 in coastal regions. Rapid ocean warming observed over the past few decades16, however, can alter these fundamental processes. Therefore, elucidating the zonal evolution of global mesoscale activity under global warming emerges as a scientific imperative for refining climate prediction, advancing sustainable ocean governance frameworks, and informing evidence-based coastal adaptation strategies.

Recent studies have investigated changes in global oceanic mesoscale activity via observations, reanalysis, and numerical simulation, but mainly focused on the meridional15,17,18,19,20,21,22,23,24. The poleward shift of oceanic mesoscale activity in the western boundary currents of the Southern Hemisphere15,19, as well as the increase of mesoscale activity near both poles are observed20,23,24. Based on eddy kinetic energy (EKE) and sea surface temperature gradient magnitudes (|∇SST | ), J. Martínez-Moreno et al.18 found that oceanic mesoscale eddies in eddy-rich regions, such as the western boundary currents and their extensions, have exhibited increased variability over the past several decades. From long-term observations, Beal and Elipot25 found that the increased mesoscale activity broadens the Agulhas Current via enhanced lateral viscous effects. Furthermore, recent observation25 and numerical26 studies indicated that the western boundary currents migrated shoreward over the past decades, implying a possible shoreward shift of oceanic mesoscale activity. However, little is known about the zonal evolution of mesoscale activity in global oceans under current and future warming.

To investigate the zonal evolution of ocean mesoscale activity, we examine EKE and |∇SST| from multiple data sources (see “Methods” for details), including one eddy-resolving reanalysis product (GLORYS), one eddy-resolving ocean hindcast (OFES), three satellite-derived datasets (AVISO, CMEMS and OISST), as well as two eddy-resolving climate models (FGOALS and HadGEM3) from Climate Model Inter-comparison Project phase 627 (CMIP6) models. A tracer-weighted average operator is applied to quantify the zonal distribution of EKE and |∇SST | , named as “zonal centroid” (enlightened by Yang et al.28, see “Methods” for details). The zonal centroids of EKE and |∇SST| are then calculated for 10 key regions29, including five western regions and five eastern regions (Fig. 1a and Table S1). The shift trends of zonal centroids are obtained by linear regression, and the significance is tested via the Student’s t-test. Significant shoreward intensification of oceanic mesoscale activity is found in most of the regions. The energy analysis reveals that both surface wind power and baroclinic energy conversion have also shifted onshore. Furthermore, we compute the zonal centroids of EKE and |∇SST| under the high-emission RCP8.5 scenario (2015–2050) from CMIP6 models to discuss the zonal evolution of oceanic mesoscale activity in response to global warming.

Fig. 1: Global trends of sea surface eddy kinetic energy (EKE) and their zonal centroid shifts from 1993 to 2022 from GLORYS.
Fig. 1: Global trends of sea surface eddy kinetic energy (EKE) and their zonal centroid shifts from 1993 to 2022 from GLORYS.
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a Distribution of surface EKE trends. b–k Time-series of zonal centroid anomalies (compared to the mean location over the time period) of EKE (gray) in west boundary regions including Western North Pacific (WNP, b), Western North Atlantic (WNA, c), Western South Indian Ocean (WSI, d), Western South Pacific (WSP, e) and Western South Atlantic (WSA, f), east boundary regions including Eastern South Atlantic (ESA, g), Eastern North Pacific (ENP, h), Eastern North Atlantic (ENA, i), Eastern South Indian Ocean (ESI, j), and Eastern South Pacific (ESP, k), and the global ocean l, superimposed with the linear trends. Gray shadings are the 95% confidence intervals for the linear fit based on the Student’s t-test. The plot labeled with * and ** indicates significance at the 90% and 95% confidence level, respectively. “V = ” on subplots “b–l” describes the shift speed in km per decade. The black dots indicate regions where the EKE trends are significant at 90%.

Results

Shoreward shift of oceanic mesoscale activity in past decades

Figure 1a shows the global trends of sea surface EKE from 1993 to 2022, derived from GLORYS. In the western boundary current regions, the EKE shows increased trends in the polar flank and decreased trends in the equatorial flank, implying the poleward shifts of EKE, consistent with previous studies15,17,19,28,30,31. In terms of the zonal distribution, the trend of EKE generally increases near the coasts, such as the China marginal seas, the California coast, and so on. Except for the western South Atlantic (WSA), all regions exhibit shoreward intensification of EKE (Fig. 1b–k). The global averaged zonal shift speed of sea surface EKE from GLORYS is 41.7 ± 14.4 km per decade (Fig. 1l). Notably, we select a wide region from the coast to the middle of the open ocean to calculate the zonal centroids of EKE. In this way, the overall changes in mesoscale activity distribution across the ocean basin over the recent three decades are quantified. To reveal changes of mesoscale activity from near-shelf to coast, we also select the nearshore region and calculate the shifts of the associated zonal centroids (Fig. S1). The shoreward shifts of EKE appear in most of the nearshore regions, consistent with the results obtained from the large domain (Fig. 1).

|∇SST | , a well-established proxy for oceanic mesoscale activity, also exhibit pronounced onshore intensification patterns. As shown in Fig. 2 and Fig. S2, the 1993–2022 period shows marked amplification of |∇SST| signatures within coastal regions. This spatial coherence aligns with observed asymmetries in regional SST warming, i.e., faster warming is observed near the coasts compared to adjacent open oceans (Fig. S3). The concurrent intensification of nearshore |∇SST| (Fig. 2a) and EKE centroid migration (Fig. 1a) suggests both momentum and temperature processes drive the coastal mesoscale activity over the recent three decades.

Fig. 2: Global trends of global sea surface temperature gradient magnitude (|∇SST | ) and their zonal centroid shifts from 1993 to 2022 from GLORYS.
Fig. 2: Global trends of global sea surface temperature gradient magnitude (|∇SST | ) and their zonal centroid shifts from 1993 to 2022 from GLORYS.
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a Distribution of global |∇SST| trends. b–k Time-series of zonal centroid anomalies (compared to the mean location over the time period) of |∇SST| (gray) in west boundary regions (b–f), east boundary regions (g–k), and the global ocean. l Superimposed with the linear trends. Gray shadings are the 95% confidence intervals for the linear fit based on the Student’s t-test. The figure labeled with * and ** indicates significance at the 90% and 95% confidence level, respectively. “V = ” on subplots “b–l” describes the shift speed in km per decade. The black dots indicate regions where the |∇SST| trends are significant at 90%.

Additionally, Figs. 1a and  2a show that approximately 40% and 30% of the grid points exhibit significant local trends in EKE and |∇SST | , respectively. However, these significant temporal trends in EKE and |∇SST| are distinct from the significance of the zonal centroid shifts. The former are local metrics, while the latter evaluates large-scale spatial redistribution. Consequently, the local trends cannot be used to directly determine the significance of changes in the zonal centroids.

Coherent shoreward shift of zonal centroids of EKE and |∇SST| appears in the global average across all observational, reanalysis and model hindcast products (Fig. 3a, b), with a multi-dataset mean displacement rate of 35.4 ± 22.5 km per decade and 34.4 ± 20.3 km per decade over the past three decades, respectively. Notably, reanalysis systems (GLORYS), model hindcast (OFES) and satellite-derived datasets demonstrate convergent trends (~ 35 km per decade).

Fig. 3: Summary of the shift trends of the zonal centroids of oceanic mesoscale activity.
Fig. 3: Summary of the shift trends of the zonal centroids of oceanic mesoscale activity.
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a, b Values of the shift trends of eddy kinetic energy (EKE) and sea surface temperature gradient magnitude (|∇SST | ) zonal centroids in different datasets. c Values of the shift trends of EKE and |∇SST| zonal centroids from CMIP6 HighResMIP historical and future experiments. d Schematic diagram of the shoreward shift of mesoscale activity, taking the western boundary current region as an example. Error bars are shown only for trends statistically significant at the 90% confidence level or higher.

Regionally, western basin regions exhibit robust patterns, showing statistically significant EKE/ | ∇SST| centroid shoreward shifts in the analysis (Fig. 3a, b). For EKE, the WNA, WNP, WSP, and WSI regions demonstrate cross-dataset consistency, whereas the WSA region presents paradoxical behavior, its zonal EKE centroid demonstrates an offshore displacement in all datasets except CMEMS. The offshore shift in WSA is potentially linked to South Atlantic SST front intensification and Brazil Current frontal variability32,33. For |∇SST | , shoreward shifts appear in all regions and all datasets, except OFES in the WNA.

Eastern basin regions display greater dynamical complexity. The zonal centroids of EKE |in all regions display shoreward shift trends in most of the datasets (Fig. 3a), while |∇SST| exhibits inter-dataset spread (Fig. 3b). The results from GLORYS and OFES are not all consistent with those from OISST, likely reflecting deficiencies in models. The offshore trends of |∇SST| in the eastern basin regions primarily resulted from the enhancement of SST in open oceans, evident in SST trends (Fig. S3). In contrast, the shoreward trends of |∇SST| in OISST are apparent in the nearshore regions (Fig. S2), consistent with the same regional significant shoreward EKE centroid shifts (Fig. S1).

Overall, there is a consistent shoreward shift of the zonal centroids of EKE and |∇SST| in approximately 77% regions, suggesting the redistribution of oceanic mesoscale activities over the past several decades. Observations from satellite observations are generally consistent with the results of GLORYS reanalysis, as well as the model hindcast (OFES).

Primary drivers

To investigate the potential dynamics driving the shoreward shift of the oceanic mesoscale activity over the past three decades, we analyze global trends of primary EKE source terms, including surface wind power (WP), baroclinic energy conversion (BC), and barotropic energy conversion (BT), derived from GLORYS34,35 (see “Methods” for details). The trend of these terms is spatially heterogeneous and obvious near the shore (Fig. 4a, c, e), implying the drastic changes of EKE over the recent decades. Note that surface wind power primarily acts as eddy-killing effects in regions with strong currents, while the wind work can be positive in coastal regions where the winds can drive small-scale currents36,37. The global mean distribution of WP38 shows that the mean WP is primarily negative along major ocean currents, while positive near the coasts. The zonal centroids of these energy terms are calculated to provide an integrated metric for evaluating whether the net energy forcing is shifting onshore. Since these energy terms contribute to the temporal evolution of EKE, the qualitative direction of these centroid movements indicates an onshore or offshore shifting in energy forcing. Figure 4b, d demonstrate significant shoreward shifts in the zonal centroids of WP (0.36 ± 0.28 km per decade) and BC (0.07 ± 0.04 km per decade), whereas the zonal centroid of BT (0.21 ± 0.32 km per decade) exhibits an insignificant offshore trend (Fig. 4f). The shifting directions of WP and BC are consistent with that of oceanic mesoscale activity, suggesting both WP and BC contribute to the onshore migration of EKE. Furthermore, the spatial trend distribution of the shoreward shift of WP is more consistent with that of EKE and |∇SST | , implying that the WP is more responsible for the onshore shift of mesoscale activity.

Fig. 4: Surface wind power and baroclinic instability contribute dominantly to the shoreward shifts of mesoscale activity.
Fig. 4: Surface wind power and baroclinic instability contribute dominantly to the shoreward shifts of mesoscale activity.
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a, c, e Global trends of surface wind power (WP), baroclinic instability (BC), and barotropic instability (BT) from 1993 to 2022 calculated using GLORYS. b, d, f Global-averaged time-series of zonal centroid anomalies (compared to the mean location over the time period) of WP, BC, and BT, respectively [Unit: km per decade].

The shoreward shift of WP is primarily attributed to intensified wind stress near coastal boundaries (Fig. S4). One possibility for intensified wind stress near coastal boundaries is amplified land-ocean thermal contrast under global warming35. The shoreward shift of BC may be associated with enhanced open-ocean stratification, primarily induced by temperature changes under global warming in the subtropics and mid-latitudes39,40. Zonal variations in mesoscale activity may also be linked to the shoreward shift of the western boundary currents25,26,41.

Furthermore, the increased nearshore |∇SST| may also be linked to the intensification of alongshore winds. According to the established hypothesis of Bukun42, intensified alongshore winds enhance upwelling in eastern boundary current systems, which inhibits nearshore SST rise and amplifies the cross-shelf gradient. In western boundary regions, which lack major upwelling systems, intensified alongshore winds may enhance mixing in the upper ocean, thereby suppressing the SST increasing rate and also strengthening the SST gradient. Concurrently, the enhanced stirring of mesoscale processes can also increase the nearshore SST gradient. Additionally, under global warming, enhanced ocean stratification can lead to onshore intensification of western boundary currents39, and thereby contribute to the |∇SST| shoreward shift. A more targeted analysis is required to quantitatively disentangle the relative contributions of these mechanisms to this trend.

Implications from high-resolution CMIP6 projections

To investigate zonal shift trends of oceanic mesoscale activity under global warming, we analyze two high-resolution simulations (HadGEM3 and FGOALS) from the CMIP6 HighResMIP future experiments under the RCP8.5 scenario (from 2015 to 2050). RCP8.5, representing the worst-case climate pathway in IPCC projections, projects 4.3–4.8 °C global warming by 2100 under unabated fossil fuel dependence.

HadGEM3 and FGOALS exhibit divergent zonal shift trends for EKE and |∇SST| (Fig. 3c). HadGEM3-historical simulates a significant shoreward EKE displacement, while FGOALS-historical shows an insignificant offshore trend. Although the future shift trend of EKE zonal centriod aligns with that of |∇SST | , the inter-model discrepancy reveals substantial uncertainties in projecting future mesoscale activity. These uncertainties emphasize the need to prioritize coastal monitoring. Furthermore, accurately simulating the zonal shift of mesoscale activities is critical for reducing air-sea flux biases and improving ocean circulation representation, an ongoing challenge for climate model development. Our findings provide a quantitative metric for evaluating eddy-resolving climate models.

Discussion

Our analysis reveals a consistent shoreward shift of sea surface EKE and |∇SST| across multiple ocean basins under global warming. Multi-dataset synthesis indicates global-averaged shift speeds of 35.4 ± 22.5 (EKE) and 34.4 ± 20.3 ( | ∇SST | ) km per decade with pronounced trends in the western basin regions (Fig. 3a, b). The shift speeds of EKE and |∇SST| zonal centroids are spatially correlated, a plausible explanation being that the shoreward shift of nearshore |∇SST| can increase the nearshore baroclinic instability, providing favorable conditions for the generation and maintenance of oceanic mesoscale activity.

EKE budget analysis reveals that both surface wind power and baroclinic energy conversion have also shifted onshore. Furthermore, the onshore intensification reported recently26 may be related to the shoreward shift of oceanic mesoscale activity. However, this phenomenon is not robust in CMIP6 models, likely due to insufficient horizontal resolution for resolving submesoscale and smaller-scale processes. Most of the CMIP6 simulations, with 0.25° horizontal resolution, are eddy-present43. This resolution is still too coarse to study mesoscale activity, particularly near high latitudes where the Rossby radius is only tens of kilometers44.

Here, we define “mesoscale activity” more comprehensively, using a high-pass filter to capture all mesoscale signals, which include but are not limited to eddies and fronts. The behavior of mesoscale eddies and fronts is a component of the overall signals; the extent to which their propagation changes accounts for the full zonal migration remains an open question worthy of further study.

The global warming-induced changes in oceanic mesoscale activity may alter coastal material exchange45 (Fig. 3d). For example, prolonged advection routes may reduce offshore nutrient transport by eastern boundary eddies, exacerbating subtropical ocean “desertification.” The observed shoreward shift of |∇SST| zonal centroids may extend to subsurface layers, influencing deeper mesoscale dynamics. Eddy-driven subduction pumps nutrients vertically via ageostrophic secondary circulation46,47, enhancing nearshore heat/carbon fluxes and biological productivity48. Thus, reconfigured coastal-open ocean exchanges may disrupt nutrient distribution, with cascading impacts on fisheries and biodiversity. It is urgent to integrate mesoscale dynamics into climate adaptation strategies to mitigate ecological and socioeconomic risks.

Methods

Datasets

For satellite observations, we use the daily Optimum Interpolation SST (OISST) sea surface temperature data from the National Oceanic and Atmospheric Administration, sea water velocity from the daily Global Ocean Gridded L4 Sea Surface Heights And Derived Variables Nrt of the Copernicus Marine Environment Monitoring Service (CMEMS), and the monthly Archiving, Validation and Interpretation of Satellite Oceanographic data (AVISO), with 0.25° horizontal resolution.

For eddy-resolving reanalysis product and ocean model simulation, we use the daily sea water velocity and SST from Global Ocean Physics Reanalysis (GLORYS) of CMEMS (1/12° horizontal resolution) and the monthly Ocean General Circulation Model for the Earth Simulator (OFES) developed at the Japan Agency for Marine-Earth Science and Technology (0.1° horizontal resolution). GLORYS is widely used in the study of oceanic mesoscale dynamics and has been proven to do well in regions such as the NW Atlantic shelf49. The time range of the above datasets is from 1993 to 2022.

For climate model simulations, we use the monthly sea water velocity and SST of the historical and future experiment from CMIP6 High Resolution Model Intercomparison Project (HighResMIP), including two models (10 km horizontal resolution), namely FGOALS-f3-H (FGOALS) and HadGEM3-GC31-HH (HadGEM3). Normally, the future experiment under the RCP 8.5 scenario and the historical experiment are on the 2015–2050 and 1950–2014 period, respectively. Due to the lack of data, however, only the historical experiments of HadGEM3 from 1955 to 2014 are obtained.

The wind stress data with 0.25° horizontal resolution is obtained directly from the monthly Ocean Reanalysis System 5 (ORAS5) prepared by the European Center for Medium-Range Weather Forecasts (ECMWF) ocean analysis-reanalysis system.

Zonal centroid calculation

The zonal centroid defined in this study serves as a metric to quantify the overall distribution of oceanic mesoscale activity across the entire region. It is essentially the regional average of the \(\lambda\)-direction arc length relative to a certain reference longitude (for ESA it is 180°and for other regions it is 0°), which is weighted by the variable field \(F({\rm{\lambda }},\varphi )\) and the spherical area element \({dS}\) at \(\left({\rm{\lambda }},\varphi \right)\). The unweighted arc length at the location \(({\rm{\lambda }},\varphi )\) relative to the reference longitude is:

$${lx}\left({\rm{\lambda }},\varphi \right)=\left({{R}}cos \varphi \right)\cdot \left({\rm{\lambda }}\frac{\pi }{180}\right)=\frac{\pi R}{180}\lambda \cos \varphi$$
(1)

dS at (λ, φ) is:

$${dS}=\left({Rd}\varphi \right)\cdot \left(R\cos \varphi d{\rm{\lambda }}\right)={R}^{2}\cos \varphi d{\rm{\lambda }}d\varphi$$
(2)

Therefore, the average of the weighted arc length over the whole region, namely the zonal centroid, is:

$$\bar{x}=\frac{\iint {lx}\cdot F\cdot {dS}}{\iint F\cdot {dS}}=\frac{\pi R}{180}\frac{\iint \,{\rm{\lambda }}{\rm{F}}{\cos }^{2}\varphi d{\rm{\lambda }}d\varphi }{\iint \, F\cos \varphi d{\rm{\lambda }}d\varphi }$$
(3)

where R is the radius of the Earth, R is 6371 km. λ and \(\varphi\) are longitude and latitude, respectively. F = F(λ, φ) is the variable field under latitude-longitude coordinates. In this study, F can be the field of variables. dλ and dφ are the elements of λ and φ in the spherical coordinate, respectively. Herein, dλ and dφ are the horizontal spatial resolutions of F in the zonal and meridional directions, respectively.

The calculation proceeds as follows. We first calculate annual mean fields from quality-controlled monthly data. For each year, we then compute the zonal centroid from these annual fields, creating a centroid time series. The shift speed is the linear trend of this time series, with a positive value indicating a shoreward shift. Finally, the global average shift speed is the area-weighted average of the regional speeds.

EKE calculation

EKE is defined as the kinetic energy of oceanic mesoscale activities. The calculation formula of EKE is as follows:

$${EKE}=\frac{1}{2}\left(\bar{{u}^{{\prime} 2}}+\bar{{v}^{{\prime} 2}}\right)$$
(4)

where \({u}^{{\prime} }\) and \({v}^{{\prime} }\) are the zonal and meridional components of perturbation sea surface velocity, respectively, which are obtained by applying 150 km spatial high-pass filtering to the GLORYS, AVISO, CMEMS, OFES and CMIP6 data at their respective minimum temporal resolutions. The overbar denotes a spatial average over 150 km. Additionally, we tested several cutoff wavelengths of filtering, including 50 km, 100 km, and 200 km. The results are consistent with each other. 150 km is applied for all spatial filtering in the study.

|∇SST| calculation

 | ∇SST| is defined as the magnitude of ∇SST,

$$|\nabla {\rm{SST}}|=\sqrt{{\left(\frac{\partial {{SST}}^{{\prime} }}{\partial x}\right)}^{2}+{\left(\frac{\partial {{SST}}^{{\prime} }}{\partial y}\right)}^{2}}$$
(5)

where \({{SST}}^{{\prime} }\) is the mesoscale sea surface temperature field, which is obtained by applying a 150 km high-pass filtering to OISST, GLORYS, OFES and CMIP6 sea surface temperature data at their minimum temporal resolution.

EKE source terms

We calculate the global trends of the primary source terms responsible for the temporal evolution of EKE, including surface wind power (WP), baroclinic energy conversion rates (BC), and barotropic energy conversion rates (BT) from monthly GLORYS34,35.

$${WP}=\frac{1}{{\rho }_{0}}\bar{{\tau }_{w}^{{\prime} }\cdot {u}_{s}^{{\prime} }}$$
(6)
$${BT}=-\left(\bar{{u}^{{\prime} }{u}^{{\prime} }}\frac{\partial \bar{u}}{\partial x}+\bar{{u}^{{\prime} }{v}^{{\prime} }}\left(\frac{\partial \bar{u}}{\partial y}+\frac{\partial \bar{v}}{\partial x}\right)+\bar{{v}^{{\prime} }{v}^{{\prime} }}\frac{\partial \bar{v}}{\partial y}\right)$$
(7)
$${BC}=-\frac{g}{{\rho }_{0}\frac{d\bar{\rho }}{{dz}}}\left(\bar{{u}^{{\prime} }{\rho }^{{\prime} }}\frac{\partial \bar{\rho }}{\partial x}+\bar{{v}^{{\prime} }{\rho }^{{\prime} }}\frac{\partial \bar{\rho }}{\partial y}\right)$$
(8)

where \({\tau }_{w}\) is the surface wind stress from ORAS5 and \({u}_{s}\) is the horizontal current at the sea surface. u and v are the components of the seawater velocity. Here, g is the acceleration of gravity, \({\rho }_{0}=1025{\rm{kg}}/{m}^{3}\) is the reference density. The overbar (prime) represents the low-pass (high-pass) filter.

Significance test

In this study, a unary linear regression model \(\hat{\bar{x}}=\hat{{\beta }_{0}}+\hat{\beta }T\) is used to analyze the linear trend of zonal centroids, where the superscript (hat) represents the estimated values. \(\hat{\beta }\) is the estimate of the slope, \(\hat{{\beta }_{0}}\) is the estimate of the intercept, \(\bar{x}\) and \(T\) represent the zonal centroid and time, respectively. The significance test for the linear trend (namely the slope \(\hat{\beta }\)) used in this study is based on the Student’s t-test, where the used t-statistic is:

$$t=\frac{\hat{\beta }\sqrt{{S}_{T}}}{\hat{\sigma }}$$
(9)

\({S}_{T}=\mathop{\sum }\nolimits_{i=1}^{n-2}{({T}_{i}-\hat{{T}_{i}})}^{2}.\hat{\bar{x}}\) and \(\hat{T}\) represent the estimated value of zonal centroid and time, respectively. n is the length of the time series. \(\hat{\sigma}\) is the unbiased estimate of the residual standard deviation. If,

$${|t|} > {t}_{\frac{\alpha }{2}}\left(n-2\right)$$
(10)

Then the trend is significant, else the trend is not significant. Where \({t}_{\frac{\alpha }{2}}\left(n-2\right)\) represents the upper \(\frac{\alpha }{2}\) quantile of the t-distribution with an effective degree of freedom of n-2, α is the significance level, in this paper, \(\alpha=\mathrm{0.05,0.1}\). To eliminate heteroscedasticity and autocorrelation in each time series, we implemented the Newey-West heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimator to correct standard errors and adjust confidence intervals.