Impact of greenhouse warming on mesoscale eddy characteristics in high-resolution climate simulations

Mesoscale eddies are prevalent throughout the global ocean and have significant implications on the exchange of heat, salt, volume, and biogeochemical properties. These small-scale features can potentially influence regional and global climate systems. However, the effects of climate change on ocean eddies remain uncertain due to limited long-term observational data. To address this knowledge gap, our study focuses on examining the impact of greenhouse warming on surface mesoscale eddy characteristics, utilizing a high-resolution climate simulation project. Our model experiments provided valuable insights into the potential effects of greenhouse warming on mesoscale eddies, suggesting that mesoscale eddies will likely become more frequent under greenhouse warming conditions and exhibit larger amplitudes and radii, especially in regions characterized by strong ocean currents such as the Antarctic Circumpolar Current and western boundary currents. However, a distinctive pattern emerged in the Gulf Stream, with increases in eddy occurrence and radius and significant decreases in eddy amplitude. This phenomenon can be attributed to the relationship between eddy lifespans and their properties. Specifically, in the Kuroshio Current, the amplitude of eddies increased due to the increased occurrence of long-lived eddies. In contrast, in the Gulf Stream, the amplitude of eddies decreased significantly due to the decreased occurrence of long-lived eddies. This distinction arises from the fact that long-lived eddies can accumulate more energy than shorter-lived eddies throughout their lifetime. These findings provide valuable insights into the complex dynamics of mesoscale eddies in a warming world.


Introduction
Mesoscale eddies are coherent rotating water vortices found across the global ocean with spatial scales ranging from tens to hundreds of kilometers and temporal scales ranging from days to years (Radko and Marshall 2004, Chelton et al 2011b, Mason et al 2014).They are formed through processes of barotropic and baroclinic instability (von Storch et al 2012, Kang and Curchitser 2015, Yan et al 2019, Li et al 2021, 2022).These eddies serve as important reservoirs of ocean kinetic energy, accounting for a significant portion of the total kinetic energy of the ocean (Wunsch andStammer 1995, Martínez-Moreno et al 2022).In addition to their energetic nature, mesoscale eddies are vital in transporting and mixing oceanic biogeochemical tracers and other physical properties (Ryan et al 2001, Zhang et al 2018, Liu et al 2020).This, in turn, influences the distribution of nutrients, heat, and carbon dioxide in the ocean, ultimately impacting ocean dynamics, marine primary production, air-sea interactions, regional weather systems, and climate patterns (Young and Sikora 2003, Heo et al 2012, Small et al 2019, Grist et al 2021).Furthermore, the interaction between eddies and the atmosphere varies depending on the eddy characteristics (Sweet et al 1981, Businger and Shaw 1984, Lin and Wang 2021).Lin and Wang (2021) demonstrated that larger eddies with a greater radius can induce more significant anomalies in surface wind speed and surface heat fluxes than smaller eddies.Despite its significance, many studies have traditionally relied on eddy kinetic energy (EKE) as a metric to gauge eddy activity.However, recent advancements in eddy detection algorithms have enabled a more comprehensive exploration of eddy characteristics.Recent studies have also focused on examining the long-term variations in other crucial attributes of eddies, including their quantity, radius, and amplitude (Oliver et al 2015, Liu et al 2021, Zhou et al 2021).Oliver et al (2015) observed an increase in anticyclonic eddies in the East Australian Current (EAC), which could contribute to a higher frequency of sudden extreme warming events.Likewise, Liu et al (2021) found an increase in both warm anticyclonic and cold cyclonic eddies on a global scale.However, it is essential to note that many of these studies heavily relied on short-term satellite data.This reliance poses challenges in distinguishing natural variability from the effects of global warming due to the limited observational period.This limitation hinders our ability to fully comprehend and differentiate the underlying factors that drive the changes in eddy characteristics.To overcome this limitation, we plan to leverage ultrahigh-resolution global warming simulations (Chu et al 2020, Wengel et al 2021, Nellikkattil et al 2023).By employing these simulations, we intend to gain a deeper understanding of the geographical statistics of eddy properties over the global ocean.We also explore the effect of greenhouse warming on these eddy characteristics.

Community Earth System Model (CESM) climate simulations
The CESM 1.2.2 ultra-high-resolution climate simulation project, known as CESM-UHR, aims to advance our understanding of multi-scale interactions and processes associated with extreme weather and climate in the context of greenhouse warming (Chu et al 2020, Huang et al 2021, Wengel et al 2021, Kad et al 2023, Liu et al 2023, Moon et al 2023, Nellikkattil et al 2023) Three century-long experiments were conducted using CESM-UHR to assess the impact of anthropogenic greenhouse warming on surface mesoscale eddy characteristics.Figure S1a shows a diagram of the CESM-UHR climate experiments used in this study.These experiments consisted of a present-day (PD) run with a fixed CO 2 concentration of 367 ppm, a doubling CO 2 (2 × CO 2 ) run with a concentration of 734 ppm, and a quadrupling CO 2 (4 × CO 2 ) run with a concentration of 1468 ppm.The concentrations of greenhouse gases and aerosols, except for CO 2 , were maintained at the PD levels.The PD simulation was initialized from a quasi-equilibrium state and integrated over 140 years.The 2 × CO 2 and 4 × CO 2 simulations were branched from the PD simulation at year 71 and run for 100 years.The data output frequency of the CESM-UHR is 6 hourly, daily, and monthly for the atmosphere, daily and monthly for the ocean, sea ice, and land and monthly for the riverrunoff.This study focuses on the daily model outputs from the last 30 years of each simulation, during which the system approached a near-equilibrium state.For more in-depth information on the CESM-UHR, please refer to Chu et al (2020) and the project website at https://ibsclimate.org/research/ultra-highresolution-climate-simulation-project/.
In figure S1(b), we present a snapshot of surface current velocity on 30 July, 0121, from the CESM-UHR PD run, effectively highlighting the presence of large-scale currents and mesoscale eddies within the Kuroshio Current and its extension.These features are depicted in the snapshot of surface relative vorticity, which is normalized by the Coriolis parameter (figure S1(c)).This collective evidence strongly demonstrates the CESM-UHR's exceptional capability to simulate and accurately represent mesoscale processes in the ocean, thereby affirming the model's effectiveness in capturing mesoscale eddies on a global scale.

Satellite altimetry data
To evaluate the model performance in reproducing surface mesoscale eddy characteristics such as eddy occurrence, amplitude, and radius, we employed the daily sea surface height (SSH) data from the Copernicus Marine Environment Monitoring Service (CMEMS) covering the period of 1993-2021.This CMEMS dataset has a horizontal resolution of 0.25 • × 0.25 • .

Eddy identification and tracking
Mesoscale eddies were identified and tracked using the py-eddy-tracker (PET), an open-source Python library (Mason et al 2014, Pegliasco et al 2022).The Mesoscale Eddy Trajectory Atlas version 3.2 DT (for Delayed-Time), distributed by the Archiving, Validation, and Interpretation of Satellite Oceanographic data, is built upon this library.A significant advantage of this approach is its parameterfree pattern mining method, which eliminates the need for predefined parameters.Instead, it automatically identifies and extracts inherent patterns from the data, resulting in more objective and generalized outcomes.The PET procedure begins by eliminating large-scale SSH variability from the daily SSH fields to isolate closed coherent eddy structures.This was achieved by applying a first-order Lanczos filter with a two-dimensional Bessel window.Following the removal of large-scale variability, the process entails scanning the SSH anomalies (SSHA) for closed contours within the range of −100-100 cm, utilizing a 0.2 cm interval.Closed contours that met the following criteria were then categorized as either cyclonic or anticyclonic eddies, while those that failed to meet the criteria were discarded.These criteria encompass shape error ⩽70%, amplitude ⩽0.4 cm, only a single extremum, pixel count ranging from 5 to 1000, and only pixels with SSH values below (under) the interval for anticyclones (cyclones).Here, 'shape error' denotes the ratio between the deviations in the total area of the contour from its best-fit circle and the area of this best-fit circle.A lower value of shape error indicates that the shape of the eddy is closer to a circle.To improve the accuracy, the contours were sampled in finer detail by increasing the number of points.The center of the eddy is determined by fitting a circle to the contour with the highest speed, providing a more precise estimate of its location.Additionally, the radius of the eddy was calculated based on the size of this fitted circle, allowing for a more accurate measurement of its extent.Subsequently, a tracking procedure was employed to establish the trajectories of the detected eddies over time.This tracking scheme involves searching for potential eddy candidates between two consecutive maps by identifying the maps with overlapping effective contours.An eddy candidate was selected for trajectory association if the overlap ratio, which compares the overlapping area to the combined area of the two eddies, exceeds 5%.This procedure ensures the reliable tracking and association of eddies throughout their temporal evolution.More details on the PET algorism are described in Pegliasco et al (2022).
Similar to previous studies (Patara et al 2016, Chen and Han 2019, Shi et al 2023), our analysis focused exclusively on eddy trajectories lasting more than 10 d.The analysis primarily focuses on several key characteristics of eddies, including their occurrence, amplitude, and radius.The eddy occurrence was determined by counting the number of eddy interiors within each 1 • × 1 • grid cell.The eddy amplitude was determined by calculating the difference in SSH between the extremum within the eddy and the surrounding area.This parameter is correlated with surface geostrophic eddy kinetic energy and signifies the strength of eddies.The eddy radius was determined by fitting circles to the contours with maximum circum-average geostrophic speed.In order to analyze the geographic statistics of eddy properties, eddy amplitude and radius were binned within 1 • × 1 • grid cells.

Delimitations of ocean basins and western boundary currents (WBCs)
Figure S2 outlines the various ocean basins and WBCs: the Southern Ocean, Pacific Ocean, Indian Ocean, and Atlantic Ocean.The Global Ocean encompasses the collective area of these ocean basins.

Rectangular boxes indicate the WBCs, including the
. The Antarctic Circumpolar Current (ACC) region is defined as the area between 40 • S and 65 • S, excluding the AC, EAC, and BMC.Equatorial regions within 5 • S to 5 • N, where the geostrophic approximation was not precise, were excluded.

Statistical characteristics of mesoscale eddies in the present climate
The PET algorithm identified an average of 2703 anticyclonic and 2882 cyclonic eddies per day in the CMEMS observation and 2327 anticyclonic and 2673 cyclonic eddies per day in the CESM-UHR PD simulation across the global ocean.These detections corresponded to a total of 572 432 anticyclonic and 619 005 cyclonic trajectories in the CMEMS and 488 490 anticyclonic and 575 763 cyclonic trajectories in the CESM-UHR PD simulation, as illustrated in figure 1.The eddy trajectories with longer lifetimes tended to be concentrated in the subtropical gyres between latitudes 20 • and 50 • .They commonly originate in the eastern boundary currents (EBCs)  S1 highlights the percentage of tracks and eddies within different lifetime by comparing the CMEMS observation with the CESM-UHR PD simulation.In the CMEMS observation, eddies with lifespans ranging from 90 to 180 d accounted for 24.1% of the eddies, whereas in the CESM-UHR PD simulation, this percentage was slightly higher at 24.9% of the eddies.Furthermore, eddies lasting 180 d or more constituted 14.2% of the eddies in the CMEMS observation, whereas, in the CESM-UHR PD simulation, this percentage was slightly higher at 15.4%.The eddies with lifespans of less than 90 d represented 61.7% of the eddies in the CMEMS observation and 59.7% in the CESM-UHR PD simulation.In summary, the CESM-UHR PD simulation demonstrated a greater occurrence of eddies with lifespans exceeding 90 d.In contrast, the CMEMS observation exhibited a higher proportion of eddies with lifespans shorter than 90 d.
In order to evaluate the geographic statistics of eddy properties, each property of the eddies was binned within 1 • × 1 • grid cells.Figure S3 presents the spatial distributions of eddy lifetime, mapped to the eddy genesis locations.The CESM-UHR PD simulation revealed similar patterns in eddy lifetime compared to the CMEMS observation, albeit with slightly longer lifetimes.These results are also demonstrated in figures 2(a) and (d).The global mean lifetime of eddies in the CESM-UHR PD simulation was estimated to be 65.9 d, somewhat higher than the global mean lifetime of 53.9 d observed in the CMEMS data.Figure S4 displays the spatial distributions of eddy genesis, which is determined by counting the occurrence of eddy interiors within each 1 • × 1 • grid cell when an eddy was initially identified.The CMEMS observation indicated higher genesis rates near strong WBCs and in the Southern Ocean.This observation aligns with the findings of Moreton et al (2020), which reported that eddy genesis rates in the open ocean are generally four times lower compared to these dynamic regions.The CESM-UHR PD simulation exhibited a similar pattern of eddy genesis distribution, although there was an overall underestimation, particularly for the EBCs.As shown in figure 1, the spatial distributions of eddy lifetime and genesis confirm that longerlived eddies predominantly originate within subtropical gyres and tend to propagate into the interior of the ocean.In contrast, shorter-lived eddies are more frequently generated near strong ocean current systems.These findings emphasize the significant role of these dynamic ocean currents in creating favorable conditions for eddy formation and development, resulting in shorter lifespans compared to other regions.
Mesoscale eddies are present throughout the global oceans, with higher concentrations observed in boundary currents and the ACC.The spatial pattern

Changes to eddy properties in a warmer climate
This study investigated the potential impacts of global warming, specifically increased atmospheric CO 2 , on the characteristics of eddies in different ocean basins.The focus was on changes in eddy occurrence, amplitude, and radius.Figures 3 and 4 illustrate the differences in eddy occurrence between the PD and the 2 × CO 2 and 4 × CO 2 simulations.In warmer climates, there is a general increase in eddy occurrence, mainly in the mid-latitudes.Notably, the Atlantic and Southern Oceans witnessed a significant increase in eddy occurrence.Conversely, the Pacific Ocean, particularly along the Kuroshio Current, and the Indian Ocean exhibited relatively modest increases, constituting less than 10% of the PD climate.Furthermore, there was a rise in eddy occurrence within the WBCs.However, it is important to note that this increase in eddy occurrence within the WBCs was not found to be statistically significant.
Under a warmer climate, there were significant changes in eddy amplitude, specifically in mid-latitudes and regions influenced by the WBCs and ACC (figures 5 and 6).The amplitude of eddies increased significantly, except for the Gulf Stream.In the Gulf Stream, the amplitude of eddies decreased significantly.Notably, the amplitude in the EAC shows the most significant increase, reaching approximately 40% compared to the PD under quadrupling CO 2 conditions.Furthermore, the spatial Regarding changes in eddy radius under a warmer climate, the study found a general increase in eddy radius across the global ocean, except for some low-latitude regions (figures 7 and 8).The increase in eddy radius suggests that eddies in most areas tend to become larger due to global warming.
In summary, the spatial patterns of changes in eddy occurrence, amplitude, and radius are nonuniform across all ocean basins.While the Southern Ocean exhibited simultaneous increases in eddy occurrence, amplitude, and radius, the characteristics of eddies within the WBCs show different patterns.In the WBCs, the frequency of eddies all increased, although there was no statistical significance.However, except for the Gulf Stream, the eddy amplitude all showed an increasing trend in the WBC.Additionally, the eddy radius consistently increased across the WBCs.These findings emphasize the variability in the response of eddy characteristics to future climate change, with notable differences between the Southern Ocean and the WBCs.It highlights the need to consider regional dynamics and specific oceanic features when assessing the impacts of climate change on eddy properties.

Kuroshio Current and Gulf Stream
Differences in eddy amplitude between the Kuroshio Current and Gulf Stream can be understood through the influence of eddy lifetime.Previous studies have shown that long-lived eddies tend to have higher amplitudes in their mature phases.This is because as eddies age and evolve, they undergo processes such as merging and energy transfer that can increase in amplitude.Long-lived eddies have more time to interact and exchange momentum with the surrounding flow, resulting in enhanced amplitudes compared to shorter-lived eddies (Chelton et al 2011b, Huang et al 2017, Pegliasco et al 2021).Therefore, in this study, eddies were classified and analyzed into two groups according to their lifespan.The first group consists of short-lived eddies with lifetimes longer than 10 d and shorter than 90 d, while the second group consists of long-lived eddies with lifetimes equal to or longer than 90 d (Kang andCurchitser 2013, Shi et al 2023).This study further elucidated the relationship between eddy lifetime and amplitude by examining the differences in eddy amplitude between these two groups.This categorization allows for a more comprehensive analysis of the impacts of eddy lifetime on eddy properties in different regions, such as the Kuroshio Current and Gulf Stream.
Figure 9 illustrates the spatial distributions of eddy occurrence and eddy amplitude for short-lived eddies and long-lived eddies in the CESM-UHR PD simulation.This indicates that long-lived eddies are mainly concentrated in the eastern part of the ocean basins and exhibit larger amplitudes in the WBCs and ACC.This means that regions of higher eddy occurrence do not necessarily correspond to higher eddy amplitude.Table 1 provides information on the changes in eddy occurrence and eddy amplitude, specifically for short-lived and long-lived eddies within the WBCs.Under 4 × CO 2 condition, in the Kuroshio Current, the occurrence of shortlived eddies decreased by 1.022 eddies/year/1 • × 1 • , while the occurrence of long-lived eddies increased by 0.171 eddies/year/1 • × 1 • .The eddy amplitude of the Kuroshio Current shows an increase of 0.561 cm for short-lived eddies and a larger increase of 4.033 cm for long-lived eddies.In contrast, the Gulf Stream exhibited different patterns.In the Gulf Stream, the occurrence of short-lived eddies increased by 1.596 eddies/year/1 • × 1 • , whereas that of long-lived eddies decreased by 2.891 eddies/year/1 • × 1 • .The amplitude of short-lived eddies in the Gulf Stream decreased by 1.130 cm, while the long-lived eddies exhibited a larger reduction of 4.257 cm in amplitude.These results lead to the conclusion that longlived eddies play a pivotal role in shaping amplitude changes, particularly in the Gulf Stream, where a decrease in long-lived eddies corresponds to a significant decrease in amplitude.Conversely, in the Southern Ocean, where the strong eastward flow of the ACC prevails, both short-lived and long-lived eddies exhibit increased occurrence and amplitude.Figure 10 describes the mean evolutions of eddy amplitude and eddy radius over the normalized lifetime, providing additional evidence that long-lived eddies tend to experience faster and more substantial growth in amplitude than their short-lived counterparts (figures 10(b) and (c)).This phenomenon can be attributed to the longer duration of longlived eddies, which allows them to accumulate more energy through interactions with their surroundings.Their prolonged existence enables continuous energy absorption, leading to an increase in amplitude.Moreover, the ability of long-lived eddies to store and sustain absorbed energy enhances their potential for amplitude growth (Shi et al 2023).Meanwhile, long-lived eddies exhibit more significant increases in both amplitude and size compared to shortlived ones (figures 10(e) and (f)).It is important to emphasize that as global warming progresses, long-lived eddies experience even more pronounced growth in amplitude and size.These results highlight the importance of factoring in eddy lifetime when assessing their influence on amplitude changes, particularly in dynamic regions such as the WBCs and ACC.

Conclusion and discussion
Mesoscale eddies, small-scale rotating ocean currents typically ranging from 10 to 500 km in diameter, play a vital role in various Earth systems (Kang and Curchitser 2015, Ha et al 2019, Yan et al 2019, Yun and Ha 2022).Understanding the characteristics of oceanic mesoscale eddies is essential for comprehending their influence on ocean dynamics, marine primary production, air-sea interactions, regional weather systems, and climate patterns.The impact of eddies can be contingent upon their characteristics, including size and amplitude (Sweet et al 1981, Businger and Shaw 1984, Lin and Wang 2021).Despite its significance, numerous studies have primarily employed EKE to measure the eddy activity.Recently, advancements in eddy detection algorithms have enabled a better understanding of eddy characteristics.Although there have been notable advancements in eddy-detection algorithms, a research gap remains concerning how global warming affects eddy characteristics, including intensity, frequency, size, and other properties.This study addresses this gap by investigating changes in eddy characteristics in response to greenhouse warming using mesoscaleresolving climate simulations, CESM-UHR.We quantified several key parameters of eddies using the PET algorithm, including their occurrence, amplitude, radius, and lifespan.Comparing the results of the PD simulation from CESM-UHR with satellite observations revealed interesting patterns.The model showed lower eddy occurrence rates and longer lifespans than satellite data.However, the geographical statistical features related to eddy lifespan, occurrence, amplitude, and radius were closely aligned with satellite observations.Crucially, our model experiments involving elevated CO 2 levels suggest that mesoscale eddies are likely to increase in frequency in mid-latitudes, accompanied by larger amplitudes and radii.However, regional variations were also observed.Within the Gulf Stream, the eddy occurrence and radius increased, whereas the amplitude decreased significantly.This pattern can be attributed to the decline of long-lived eddies, which typically store more energy throughout their lifetime.Conversely, in the Kuroshio Current, eddies increased in amplitude possibly due to the increased occurrence of long-lived eddies.These findings emphasize the crucial role of eddy lifespan in shaping their amplitude and energy storage characteristics.Figure 11 provides a visual representation of the anticipated changes in eddy occurrence, amplitude, and size under a warmer climate.
Although the CESM-UHR simulations provide valuable insights into the changes in eddy characteristics in response to greenhouse warming, a comprehensive discussion of the potential underlying mechanisms is still lacking.Oceanic mesoscale eddies originate primarily from barotropic and baroclinic instabilities, which are processes that transform mean energy into eddy energy within the ocean (Von Storch Additionally, the instability of Rossby waves can play a role in transferring wave energy to eddies through wave breaking (LaCasce and Pedlosky 2004).Consequently, the source of eddy energy involves complex processes.Numerous studies have investigated the trends and variations in eddy energy associated with global warming (Patara et al 2016, Liu et al 2021, Beech et al 2022, Li et al 2022, Shi et al 2023).Beech et al (2022) demonstrated that future changes in mesoscale eddy activity are interconnected with broader climate factors, including the decline of the Atlantic meridional overturning circulation, strengthening of Agulhas leakage, and shifting Southern Hemisphere westerlies.Li et al (2022) suggested that the poleward shifts of the WBCs in the Southern Ocean influenced mid-latitude easterly winds, leading to increased eddy generation.Shi et al (2023) showed that the increased amplitude of longlived eddies can be attributed to heightened baroclinic instabilities in the mean flows associated with topographical features.However, our results somewhat differ from other studies based on satellite observations.For instance, when it comes to changes in eddy amplitude, which are closely correlated with those in EKE, this study indicates contrasting changes between the Kuroshio Current and Gulf Stream.In contrast, Martínez-Moreno et al (2021), relying on satellite data, have shown a robust increase in mesoscale EKE in both current regions.This suggests that factors beyond greenhouse gas concentrations may have influenced observed long-term changes.Indeed, a comprehensive investigation of the dynamics responsible for changes in mesoscale eddy properties is warranted to gain a deeper understanding of the effects of greenhouse warming.
The changes in eddy radius may be linked to the increase in the first baroclinic Rossby radius with increasing oceanic stratification in the warmer climate (Saenko 2006, Fyfe andSaenko 2007).However, it is important to note that the Rossby deformation radius is not the sole determinant of eddy size, as other factors come into play.While an increase in the Rossby deformation radius generally tends to result in larger eddies, a more comprehensive analysis and modeling are required to precisely evaluate this relationship.
Mesoscale eddies significantly influence the distribution of biogeochemical properties and nearsurface atmospheric and oceanic conditions through complex air-sea interactions (Ryan et al 2001, Chelton et al 2011a, Carranza and Gille 2015, Huang et al 2017, Liu et al 2020, Wang et al 2021).However, it remains unclear how the physical and biogeochemical anomalies induced by eddies may change due to greenhouse warming.Therefore, further research on this topic is necessary to better understand the complex dynamics within the ocean-atmosphere system.

Figure 1 .
Figure 1.Trajectories of (a) anticyclonic and (b) cyclonic eddies from the CMEMS observation.(c) and (d) are the same as (a) and (b) but for the CESM-UHR PD simulation.In each panel, the color of each trajectory represents the lifetime of the respective eddy trajectory.

Figure 3 .
Figure 3. (a) Spatial distributions of eddy occurrence in the global ocean from the CESM-UHR PD simulation and the differences compared to (b) 2 × CO2 and (c) 4 × CO2 conditions.(d) Zonally averaged eddy occurrence from the CMEMS observation (grey line) and CESM-UHR PD simulation (black line) and the differences of zonally averaged occurrence compared to (e) 2 × CO2 and (f) 4 × CO2 conditions.Dotted areas indicate statistical significance at a 95% confidence level by Student's T-test in (b), (c).

Figure 4 .
Figure 4. Changes in eddy occurrence (%) for each basin and the western boundary current systems (WBCs).Pink (red) barplots represent changes in eddy occurrence under the 2 × CO2 (4 × CO2) condition compared to the PD condition.The grey error bars indicate the 95% confidence levels.Dotted patterns indicate that the differences between the 2×CO2 (4×CO) and PD conditions are significant at the 95% confidence level based on the Student's T-test.In (b), abbreviations KC, GS, AC, EAC, and BMC refer to the Kuroshio Current, Gulf Stream, Agulhas Current, East Australian Current, and Brazil-Malvinas Confluence, respectively.

Figure 6 .
Figure 6.Same as figure 4 but for eddy amplitude.

Figure 8 .
Figure 8. Same as figure 4 but for eddy radius.

Figure 9 .
Figure 9. Spatial distributions of (a) eddy occurrence (number of eddies per year per 1 • square) and (b) eddy amplitude (cm) for the short-lived eddies from the CESM-UHR PD simulation.(c) and (d) are the same as (a) and (b) but for the long-lived eddies.

Figure 10 .Figure 11 .
Figure 10.Mean evolutions of (a) eddy amplitude and (d) eddy radius throughout the normalized lifetime for all eddy tracks.(b) and (e) are the same as (a) and (d) but for the short-lived eddy tracks.(c) and (f) are the same as (a) and (d) but for the long-lived eddy tracks.The black, blue, and red lines represent the CESM-UHR PD, 2 × CO2, and 4 × CO2 simulations.
et al 2012, Kang and Curchitser 2015, Yan et al 2019, Li et al 2021, 2022).Barotropic instabilities, which generate eddies without vertical motion, stem from a misalignment between pressure and velocity fields (von Storch et al 2012).Conversely, baroclinic instabilities, producing eddies with vertical motion, result from density gradients in the ocean (von Storch et al 2012, Shi et al 2023).Multiple factors, including density gradients, wind stress, and bathymetry, contribute to initiating these instabilities (Yu and Metzger 2019, Fadida et al 2021, Shi et al 2023).
. The CESM 1.2.2 consists of various components: the Community Atmosphere Model version 5 for the atmosphere, the Parallel Ocean Program version 2 for the ocean, the Community Ice CodE version 4 for sea ice, and the Community Land Model version 4 for land.The atmospheric component features a horizontal resolution of approximately 25 km and 30 vertical layers, whereas the ocean component has a spatial resolution of about 10 km and 62 levels.

Table 1 .
in eddy occurrence (number of eddies per year per 1 • square) and eddy amplitude (cm) for the short-lived eddies and long-lived eddies in the western boundary currents (WBCs) under the 2×CO2 (4×CO2) conditions compared to the PD condition, respectively.Abbreviations KC, GS, AC, EAC, and BMC refer to the Kuroshio Current, Gulf Stream, Agulhas Current, East Australian Current, and Brazil-Malvinas Confluence, respectively.