Response of Ocean Mesoscale Coherent Eddies to Global Warming
Zhibin Yang1, Zhao Jing1, 2, and Xiaoming Zhai3
1Laoshan Laboratory, Qingdao, China.
2Frontier Science Center for Deep Ocean Multispheres and Earth System (FDOMES) and Physical Oceanography Laboratory, Ocean University of China, Qingdao, China. 3Centre for Ocean and Atmospheric Sciences, School of Environmental Sciences, University of East Anglia, Norwich, United Kingdom.
Corresponding author: Zhao Jing (jingzhao198763@sina.com)
Key Points:
•		The response of mesoscale coherent eddies to global warming is investigated using an eddy-resolving global climate model.
•		Eddies will have a larger radius, possess stronger density and salinity anomalies but reduced mechanical energy in the ocean interior.
•		Changes are linked to increased stratification and background gradients, implying altered eddy-induced transport in a warming climate.
Abstract
Mesoscale vertically coherent ocean eddies - defined here as eddies maintaining rotational coherence across depth - play a fundamental role in Earth's climate system by redistributing heat, salt, and other tracers. Yet it remains unclear how these eddies will respond to global warming. Here, we address this question using an eddy-resolving (0.1°) Community Earth System Model under a high-emission scenario. Between 60°S and 60°N, the eddy radius becomes larger in line with the increased baroclinic Rossby deformation radius caused by intensified stratification. The eddies exhibit larger density and salinity anomalies as a result of increased eddy radius and enhanced horizontal background density and salinity gradients. Both eddy kinetic and potential energy are reduced in the ocean interior due to a weakened baroclinic energy conversion pathway under intensified stratification. These findings highlight the significant anthropogenic impacts on mesoscale coherent eddies, with potential implications on their-induced heat and material transports in a warming climate.
Plain Language Summary
Ocean eddies—swirling currents hundreds of kilometers wide—play a key role in moving heat, nutrients and other properties across the seas. Using a high-resolution coupled global climate model, we find that under a high-emission scenario, these eddies are undergoing significant changes: they grow larger in size yet become less energetic in the ocean interior. At the same time, these eddies carry a stronger contrast in its density and salinity. These transformations will inevitably alter the eddies' crucial role in regulating the climate, impacting global heat and material transport in our warming world.
1		Introduction
Ocean mesoscale phenomena (e.g., fronts, filaments and eddies) are ubiquitous across the global ocean (Chelton et al., 2011a; Ferrari & Wunsch, 2009). They are primarily generated through baroclinic instability and play a fundamental role in Earth’s climate system and marine ecosystem (Benitez-Nelson et al., 2007; Chelton et al., 2011b; McGillicuddy et al., 1998; Zhang et al., 2014).
Global warming exerts significant impacts on the ocean mesoscale phenomena. Satellite observations reveal a positive trend in surface eddy kinetic energy (EKE) during recent decades, particularly in high-EKE regions such as the Antarctic Circumpolar Current (ACC) and mid-latitude western boundary currents as well as their extensions (WBCEs) (Martínez-Moreno et al., 2021). This observed enhancement aligns with high-resolution climate model simulations that explicitly resolve mesoscale phenomena in energetic regions (Beech et al., 2022). However, a recent study (Wang et al., 2024) indicates a paradoxical reduction in the vertically integrated EKE under global warming, despite the surface EKE increase. This reduction is attributed to deep-ocean EKE decrease that overwhelms the surface EKE increase in terms of their contribution to the vertically integrated EKE change (Wang et al., 2024).
Among the various kinds of mesoscale phenomena, vertically coherent mesoscale eddies (henceforth coherent eddies) - defined here as eddies maintaining rotational coherence across depth (different from the Lagrangian material coherence; e.g., Haller et al., 2016) - stand out due to their well-defined, long-lived structures, and strong nonlinear dynamics. They account for ~50% of surface kinetic energy, with trends in eddy number and amplitude already emerging in recent satellite observations (Martínez-Moreno et al., 2022). The nonlinear nature of coherent eddies (much faster rotational speed than translational speed) enables them to trap and transport water masses over long distances while maintaining core properties. This unique capability facilitates efficient redistribution of heat, salt, and other tracers, exerting substantial influence on Earth’s climate system and marine ecosystems (Roemmich and Gilson, 2001; Volkov et al., 2008). Previous studies based on Eulerian statistics (e.g., Wang et al., 2024) have documented the vertical redistribution of bulk eddy energy, encompassing all forms of mesoscale variability. Here, we go a step further by focusing specifically on vertically coherent eddies and diagnosing the changes in their core physical properties under global warming.
The paper is organized as follows. Section 2 describes the configurations of the numerical products and the eddy identification method. In Section 3, we present the changes in coherent eddies and their mechanisms. A summary is provided in Section 4.
2		Methodology
2.1		Numerical products
We employ a CESM with a nominal horizontal resolution of 0.1° for the ocean and 0.25° for the atmosphere to investigate the response of coherent eddies to global warming (Chang et al., 2020). The ocean component of CESM features 62 vertical levels, with grid spacing gradually increasing from the surface to a maximum of 250 m at 6000 m depth. The CESM includes a 500-year pre-industrial control and a transient simulation branched from year 250, using historical (1850-2005) and RCP8.5 (2006-2100) forcings following CMIP5 protocol (Taylor et al., 2012).
The daily mean three-dimensional velocity, temperature and salinity are available during two 15-year-long periods (1920-1934 vs. 2086-2100), enabling the identification of coherent eddies not only at the sea surface but also in the ocean interior.
2.2		Observational dataset
To validate the CESM simulation, we use satellite-derived geostrophic velocity data from the Copernicus Marine Service (Product ID: SEALEVEL_GLO_PHY_L4_MY_008_047), which has a spatial resolution of 0.125°×0.125°. This Level-4 product provides globally gridded sea level anomalies computed with respect to a twenty-year (1993-2012) mean, derived by merging along-track measurements from multiple altimeter missions through an optimal interpolation. For this study, we use the geostrophic velocity data during 2000-2024. The expansion of the altimeter constellation during this period significantly improves the effective spatio-temporal resolution and reliability of mesoscale feature detection, providing a robust observational benchmark for evaluating the representation of coherent eddies in the CESM simulation.
2.3		Eddy identification method
We employ a vector geometry-based eddy detection algorithm developed by Nencioli et al. (2010) to identify coherent eddies in both the CESM simulation and observational datasets. This algorithm detects eddies based on a series of geometrical constraints on the velocity fields. The eddy boundary is defined as the outermost closed streamline surrounding velocity minima (eddy center). The eddy radius is defined as the equivalent circular radius of the enclosed area. The eddy amplitude is defined as the difference in sea surface height (SSH) between the surface eddy center and the mean SSH along the surface eddy boundary. Daily eddy detection is performed throughout the upper 4000 m of the water column, limited to the latitudinal range of 60°S to 60°N and excluding the equatorial band 2°S–2°N. For the CESM data, the detection uses horizontal velocity fields, whereas for the satellite observational data, it relies on sea surface geostrophic velocity.
The strong coherence of coherent eddies, which allows for the construction of a vertically coherent structure, necessitates the use of a vertical tracking algorithm when computing eddy energy and eddy-possessed hydrographic anomalies. The algorithm applies the following criteria for establishing vertical coherence between adjacent layers: (1) horizontal separation between eddy centers must be less than a distance of max [R/2, R⋅dz/100], where R is the eddy radius in the upper layer and dz is the layer spacing, and (2) consistent rotational polarity across layers. The tracking proceeds downward from the surface layer until either condition fails. If no eddy is identified at the surface, the algorithm continues to probe subsequent layers sequentially, initiating downward tracking from the deepest layer at which an eddy is first detected. Only eddies maintaining vertical coherence across at least three consecutive layers with a minimum 50 m vertical extent are retained for analysis. This vertical tracking approach effectively excludes most algorithmically misidentified eddies. On average, this algorithm identifies 11,608 and 11,450 vertically coherent eddy tracks per day in CESM during 1920-1934 and 2086-2100, respectively.
The hydrographic anomaly possessed by an eddy is defined as the difference of hydrographic properties (temperature, salinity and density) averaged within the eddy from the far-field background values. To determine an appropriate far-field reference, we perform a radius-normalized composite analysis of density fields (Fig. S1). Both eddy types display similar spatial evolution in their density fields: tightly closed contours near the eddy center (<R) that undergo progressive deformation, transitioning to weakly curved contours at intermediate radii (R-3R), and eventually becoming essentially straight lines beyond 3R. Based on this transition, we define the far-field reference region as the annulus between 3R and 5R. Sensitivity tests using alternative far-field reference ranges (2R-4R or 4R-6R) do not alter the major conclusions of this study.
The EKE is defined as
EKE = (u2 +v2)/2(1)
where u and v are the zonal and meridional velocities within the eddies.
The eddy available potential energy (EAPE) is computed based on the quasi-geostrophic framework (Chen et al., 2014; Pedlosky 1987; VonStorch et al., 2012), expressed as:
2
EAPE = g	ρ′2 (2)
2ρ02N2
where g is the gravitational acceleration, ρ is the reference density, N 2 represents the time- and zonal- mean stratification, and ρ′ denotes eddy-possessed density
anomalies relative to the far-field background density. Other definitions of N 2 based on spatial Gaussian filtering and running-mean smoothing yield largely consistent results in the computed EAPE response pattern: an increase in the upper 400 m (by 3.7% to 10.9%), a decrease below 400 m (by 3.8% to 10.7%), and consequently, a net decrease in the total EAPE over the full water column (by 1.6% to 5.4%; Fig. S2).
2.4		Baroclinic Rossby deformation radius
The first baroclinic Rossby deformation radius (Rd) is calculated following Chelton et al. (1998):
0
R = 1	N(z)dz (3)
d πf ∫-H
where H is the water depth, f is the Coriolis frequency and N is the buoyancy
frequency.
2.5		Decomposition of background horizontal density gradient
The background horizontal density gradient is decomposed to quantify the relative contributions of temperature and salinity variations. Following the linear approximation of the equation of state, the decomposition is expressed as:
(∇Hρ)2 = (ρ0α∇HT)2 + (ρ0β∇HS)2 - 2ρ02αβ(∇HT⋅∇HS) . (4)
The thermal expansion coefficient α and saline contraction coefficient β are computed using the Gibbs-SeaWater (GSW) Oceanographic Toolbox, which provides accurate thermodynamic properties based on the TEOS-10 standard. The background density (ρ), temperature (T ), and salinity (S ) are calculated from 15-year averaged fields, which are then low-pass filtered with a Gaussian filter of 10 degrees. < > represents global average.
3		Results
3.1		Statistics of coherent eddies simulated by the CESM
The CESM simulates the statistics of coherent eddies across the global ocean reasonably well. The geographical distributions of amplitude, frequency, and radius of coherent eddies in the CESM are generally consistent with those estimated from gridded satellite products (Fig. 1). Both datasets show strong eddy activities in the mid-latitude WBCEs and the ACC (Figs. 1a,b). The observed coherent eddies occur more frequently along the boundary currents, the subtropical counter currents, the ACC and in the northeastern mid-latitude Atlantic basin (Fig. 1c). This geographical tendency is qualitatively reproduced by the CESM (Fig. 1d). As to the eddy radii in the observations and CESM, both decrease poleward (Figs. 1e,f).
Despite the qualitative consistence in the coherent eddy statistics between the observation and CESM, there are noticeable quantitative discrepancies. In particular, the CESM simulates more coherent eddies with smaller radii and amplitudes (Fig. S3; Figs. 1e,f). This bias may reflect the coarser effective resolution of gridded satellite products (Ducet et al., 2000; Le Traon et al., 1998) rather than CESM deficiencies.

Fig. 1. Geographical distribution of statistics of observed and simulated coherent eddies at the sea surface. a,b, Geographical distributions of eddy amplitude (sea surface height anomaly) estimated from satellite observations (a) and CESM during 1920-1934 (b). c-f, Same as a,b, but for eddy occurrence frequency (count per day on 1°×1° grid) (c,d) and radius (e,f), respectively. Only eddies with amplitudes greater than 2 cm are considered. Regions where no eddies with amplitudes greater than 2 cm are detected are filled in white. The equatorial region (2°S-2°N) is filled in grey.

3.2		Response of coherent eddies to global warming
Coherent eddies respond significantly to global warming yet their responses are geographically heterogeneous. For instance, the change of EKE under global warming shows patches of positive and negative values (Fig. S4). This pattern is a superposition of regional and global mean responses of coherent eddies to global warming. As the CESM-simulated regional response is governed by more complicated dynamics and less robust compared to the global mean response, we will focus mainly on the global mean response in the following analysis.
3.2.1		Eddy radius
The coherent eddies become generally larger in size under global warming. The increase of eddy radius is more pronounced at the mid latitudes in the upper 2000 m (Figs. 2a,b) where the absolute and relative increases reaching 5 km and 10%,

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respectively. This increased eddy radius likely results from the enhanced upper-ocean stratification that leads to a larger baroclinic Rossby deformation radius (Rd) under global warming (Chelton et al., 1998). As the eddy radius at the mid latitudes scales closely with the Rd, increased Rd would enlarge the eddy size. To test this conjecture, we compare Rd during 1920-1934 and 2086-2100 (Figs. 2c,d; Fig. S5). The value of Rd at mid latitudes is increased by about 10% under global warming (Fig. 2d). Such a percentage change is comparable to that of eddy radius. The percentage increase in Rd is larger toward higher latitudes (>30°N) but is not fully reflected in eddy radius changes. This is likely because Rd does not perfectly scale with eddy radius at high latitudes, where eddy size is modulated by background flow, topography, and nonlinear interactions (Chelton et al., 2011a). No such trend is detectable in satellite observations (Fig. S6), likely due to the short record and strong variability.
3.2.2		
Fig. 2. Response of eddy radius to global warming. a,b, Absolute and relative difference of zonally averaged eddy radius simulated by the CESM during 2086-2100 from that during 1920-1924. c,d, Same as a,b, but for the zonally averaged baroclinic Rossby deformation radius. Areas marked by '+' in a and b indicate significant difference at the 95% confidence level. The equatorial region (2°S-2°N) is filled in grey.

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Eddy-possessed hydrographic anomalies
The coherent eddies possess larger density anomaly under global warming. Fig. 3a compares the globally averaged squared density anomaly possessed by coherent eddies	ρ′2	during 1920-1934 and 2086-2100. During 1920-1934, ρ′2 peaks at 0.02 kg2 m-6 around 100 m and decays below with a 100 m e-folding scale. During 2086-2100, this maximum increases by 31.7% and shoals to 85 m. In addition, ρ′2	during 2086-2100 decays more slowly with depth (an e-folding scale of 120 m).
Accordingly,	ρ′2	in the upper 500 m is significantly enhanced under global
warming. The above conclusions also hold for anticyclonic eddies (AEs) and cyclonic eddies (CEs), respectively (Fig. S7).

Fig. 3. Response of eddy-possessed hydrographic anomalies to global warming. Vertical profile of eddy-possessed squared density anomaly (a), temperature anomaly (b) and salinity anomaly (c) averaged within 60°S-60°N excluding the equatorial band 2°S-2°N during 1920-1934 (blue) and 2086-2100 (red). Shadings denote the 95%-confidence interval. Only the upper 1000 m is shown.

The enhanced ρ′2	under global warming is likely due to the enlarged eddy radius and intensified background horizontal density gradient	(∇ ρ)2	(Fig. 4a)

2 (ρ0α∇HT)

that cause stronger density anomaly during eddy generation (Chelton et al., 2011b; Frenger et al., 2013; Yuan and Castelao, 2017). To shed light on the reasons for the enhanced (∇Hρ)2 under global warming, we decompose (∇Hρ)2 into
components related to the background horizontal temperature gradient
(temperature contribution), background horizontal salinity gradient	( ρβ∇
(salinity contribution), and the cross product between background horizontal temperature and salinity gradients	-2ρ02αβ∇HT ⋅∇HS	(cross contribution).
For the climatological mean state (1920-1934), the temperature contribution makes dominant contribution to	(∇ ρ)2	especially in the thermocline and deep
ocean with salinity contribution playing a minor role (Figs. 4b,c). Quantitatively, the
sum of temperature and salinity contributions is larger than	(∇ ρ)2	due to the
evident temperature-salinity (T-S) compensation manifesting as negative values of cross contribution (Fig. 4d). Under global warming, both temperature and salinity contributions to the increase of	(∇ ρ)2 , with the temperature contribution playing
a dominant role (Figs. 4b, c). The increase in temperature contribution arises primarily from the enhanced α which is an increasing function of temperature, while the background temperature gradient itself shows little change (Figs. S8a,c). The increase in salinity contribution, in contrast, is mainly driven by a stronger background salinity gradient, despite a slight decrease in β that partially offsets this effect (Figs. S8b,d). The enhanced salinity gradient is likely attributed to adjustments in surface freshwater fluxes and large-scale ocean circulations under global warming (Sathyanarayanan et al., 2011). Meanwhile, the cross contribution becomes more negative (T-S compensation becomes more evident), indicating enhanced temperature-salinity compensation that partially offsets the overall increase in the density gradient. In summary, it is the increase in α that primarily accounts for the increase in	(∇ ρ)2	under global warming.
The enhanced	ρ′2	implies anthropogenic changes in T′2 and S′2 :
S′2 peaks increase by 41.1% (Fig. 3c), while change of	T′2	is moderate (Fig.
22
3b). This is consistent with the enhanced ∇ S but less changed ∇ T HH
under global warming (Figs. S8a,b). It should be noted that the enhanced	ρ′2	is
not caused by the increased S′2	. Instead, it is the increased α that plays a
dominant role (Fig. S8c; Fig. S9). In other words, while S′2 become stronger due 2
to intensified ∇ S , their contribution to the overall	ρ′2	remains secondary
H
compared to the effect of increased α on the temperature contribution.

Fig. 4. Response of background horizontal density, temperature and salinity gradients to global warming. a, Vertical profiles of squared background horizontal density gradient	(∇ ρ)2	averaged within 60°S-60°N excluding the equatorial

band 2°S-2°N during 1920-1934 (blue) and 2086-2100 (red). b-d, Same as a, but for the decomposition of	(∇ ρ)2	into components related to the background

gradient	(ρ0β∇H

horizontal temperature gradient	(ρα∇ T )2 , background horizontal salinity
and the cross product between background horizontal temperature and salinity gradients -2ρ02αβ(∇HT ⋅∇HS) . Only the upper 1000 m is
shown.
3.2.3		Eddy energy
Anthropogenic changes of the EKE and EAPE are vertically incoherent (Fig. 5). There is a slight increase of EKE in the upper 200 m (0.13%; 0.3 PJ) but a more evident decrease of EKE below 200 m (-8.83%; -45.4 PJ). Accordingly, the total EKE over the full water column changes by -6.12% (-45.1 PJ). As to the EAPE, it increases by 9.9% (122.0 PJ) in the upper 400 m but decreases by 10.4% (259.7 PJ) below 400 m, leading to a net reduction of total EAPE (-3.4%; -137.7 PJ). Such vertically reversed trends of EKE and EAPE, which hold for both AEs and CEs (Fig. S10) and are also evident in the far-field region surrounding the eddies (Fig. S11), suggesting they reflect a nonlocal adjustment of the mesoscale energetic field under intensified stratification (Chen et al., 2014). Notably, the response exhibits marked spatial variability (Fig. S12): the Kuroshio Extension and ACC show intensified near-surface eddy energy coupled with a reduction at depth, consistent with the global mean, whereas the Gulf Stream exhibits weakening throughout the full water column. Changes in eddy-poor regions are generally weak. We also performed sensitivity tests using alternative thresholds for vertical coherence tracking (e.g., center-distance criteria, minimum vertical extents, and minimum number of linked layers) and full-field eddy statistics without vertical tracking. In all cases, the coherent eddies exhibit similar vertical energy structures—enhanced energy in the upper ocean but a

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net reduction over the full water column (Fig. S13). Notably, the integrated EAPE within 2°-60° is about 6 times that of EKE for the climatological mean state. Accordingly, the anthropogenic change of total eddy energy is dominated by that of EAPE, decreasing by 3.9% (182.8 PJ).
The enhancement of EKE and EAPE in the upper ocean and their overall reduction over the full water column can be understood based on the intensified stratification under global warming. On the one hand, the intensified stratification under global warming (Li et al., 2020; Sallée et al., 2021; Fig. S14) reduces the mean available potential energy (MAPE), suppressing the baroclinic energy conversion pathway and reducing the total EKE and EAPE (Wang et al., 2024). On the other hand, as the enhancement of stratification is more evident in the upper ocean, it tends to make the EKE and EAPE more concentrated in the upper ocean (Wunsch, 1997), accounting for the increased EKE and EAPE there.
4		
Fig. 5. Response of EKE and EAPE to global warming. Vertical profile of EKE (a) and EAPE (b) averaged within 60°S-60°N excluding the equatorial band 2°S-2°N during 1920-1934 (blue) and 2086-2100 (red). Shadings denote the 95%-confidence interval.

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Summary and Discussion
In this study, we assess the response of coherent eddies to global warming based on a high-resolution climate simulation under a high-emission scenario. The results reveal that these eddies in general will have a larger radius, possess stronger , density and salinity anomalies but their mechanical energy will be reduced. These responses exhibit notable regional and vertical dependence: the increase in eddy radius is most pronounced at mid-latitudes, the enhancement of density and salinity anomalies is confined to the upper ocean, and the reduction in mechanical energy 
occurs primarily below the thermocline while the upper ocean experiences a slight increase. CEs and AEs show qualitatively similar responses, though with minor differences in magnitude. While the observed reduction in eddy energy aligns with the mechanism that intensified stratification weakens baroclinic conversion (Wang et al., 2024), we do not directly diagnose these conversion pathways, as our algorithm captures mature eddies whose energy originates from nonlocal processes (Chen et al., 2014). These responses reflect the anthropogenic change of the mean state, including larger baroclinic Rossby deformation radius due to the intensified stratification, stronger horizontal background density gradient due to the increased thermal expansion coefficient, and stronger horizontal background salinity gradient due to adjustments in surface freshwater fluxes and large-scale ocean circulations (Sathyanarayanan et al., 2011).
Coherent eddies trap and transport water masses over long distances. Under warming, they likely translate faster due to intensified stratification (Chelton et al., 1998). Our results reveal that eddy-induced salt transport changes significantly under global warming (Figs. S15, S16), although this inference is based on Eulerian fluxes and geometrically defined eddy boundaries, which do not fully represent Lagrangian material trapping (Haller et al., 2016).
Acknowledgments
This work was supported by the National Natural Science Foundation of China (42306013 to Z.Y., 92358303 to Z.J.), and Marine S&T Fund of Shandong Province for Laoshan Laboratory (LSKJ202202501 to Z.J.). Computational resources were provided by Laoshan Laboratory (No. LSKJ202300302).
Conflict of Interest Statement
The authors have no conflicts of interest to disclose.
Open Research
The CESM-HR output can be downloaded from the website https://ihesp.github.io/archive/products/ds_archive/Sunway_Runs.html. The satellite-derived geostrophic velocity data can be obtained from Copernicus Marine Service (European Union-Copernicus Marine Service, 2017).
The mesoscale eddy automatic detection code is available to the public, and can be downloaded from Yang (2025). The Gibbs-SeaWater (GSW) Oceanographic Toolbox can be downloaded from http://www.TEOS-10.org/.
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