The role of eddy-wind interaction in the eddy kinetic energy budget of the Agulhas retroflection region

The Agulhas retroflection (AR) region possesses the highest eddy kinetic energy (EKE) level in the Indian Ocean. However, mechanisms regulating EKE of the AR remain uncertain. Here, by analyzing an eddy-resolving coupled model simulation with improved EKE representation, we show that the upper-ocean EKE of the AR is mainly generated through barotropic instability in its upstream and leakage zones and is by nonlocal transport in its downstream zone. The interaction between mesoscale eddies and local winds plays a key role in EKE dissipation. The lack of eddy-wind interaction results in flawed EKE budget in the leakage zone in ocean-alone models, leading to severe biases in EKE distribution with overestimation and over-strong penetration into the South Atlantic. Our results highlight the essence of mesoscale air-sea interaction in the dynamics of the AR, with implications for understanding the inter-basin transport of the Agulhas leakage.


Introduction
The Agulhas Current (AC) is the poleward-flowing western boundary current of the subtropical Southern Indian Ocean with a mean transport of 77 Sv (1 Sv = 10 6 m 3 s −1 ; Beal et al 2015).Upon reaching the southern tip of the African continent, it separates from the coast and retroflects east to feed the Agulhas return current (ARC) (Lutjeharms and Ansorge 2001), forming the Agulhas retroflection (AR) point (Lutjeharms and Van Ballegooyen 1988).The AR regime possesses the highest eddy kinetic energy (EKE) in the Indian Ocean (Zhu et al 2018).Rings and eddies generated from the AR serve as conveyors for the warm and salty Indian Ocean water to the Southern Atlantic Ocean, constituting the interbasin transport of the Agulhas leakage (Gordon 1985, Biastoch et al 2008).As a key feature of the AC system (Beal et al 2011), the AR is subjected to dynamic complexities and is worthy of in-depth investigation.
Mesoscale eddy activity (quantified by surface EKE) is crucial for the AR dynamics; it regulates zonal displacements of the AR point (Zhu et al 2021) and the formation of Agulhas leakage (Beal et al 2011).Eddy-resolving ocean model simulations are widely utilized in understanding the EKE budget of the AC system (Zhu et al 2018, Adeagbo et al 2022, Li et al 2023).Meanwhile, these studies also reveal common biases (although model-dependent in quantity) in these models, typically with over-strong penetration of EKE toward the South Atlantic (Maltrud and McClean 2005, Thoppil et al 2011, Renault et al 2017).These biases hinder the understanding of AR dynamics and lead to substantial uncertainties in the simulated Agulhas leakage in these ocean-alone models, with the transport ranging widely from 2 to 18 Sv (Biastoch et al 2008).
Existing studies suggest that the simulations of leakage transport and pathways of Agulhas rings are generally more realistic in coupled climate models, with mesoscale air-sea interaction is taken into consideration (Putrasahan et al 2015, Chen et al 2016).Notably, the interaction between eddies and winds represents a major contributor to EKE dissipation (10%-50%) in eddy-rich regions (Eden and Dietze 2009, Gaube et al 2015, Seo et al 2016) such as the AC system (Renault et al 2017).This damping effect is through eddy-induced wind stress anomalies (Renault et al 2016) and Ekman pumping (Gaube et al 2015).Moreover, neglecting the eddy-wind interaction may lead to an overestimation of the total wind work on the ocean and affect the simulated mean circulation (Pacanowski 1987, Luo et al 2005, Duhaut and Straub 2006, Scott and Xu 2009).
In this study, we aim to investigate the EKE budget in the upstream, downstream, and leakage zones of the AR by contrasting simulations of a coupled model and an ocean-alone model with similar resolutions.We show that the EKE distribution in the AR region is more realistically simulated by the coupled model, as referenced to satellite observations (figure 1).Further analysis confirms that mesoscale air-sea interaction play a crucial role in regulating EKE of the AR region and explains biases in ocean-alone models.

Datasets
Here we analyze the high-resolution simulation of the Community Earth System Model (CESM) version 1.2.2 (Small et al 2014, Chu et al 2020, Huang et al 2021).The ocean model component of CESM is the Parallel Ocean Program version 2 (POP2) (Smith et al 2010), with horizontal resolutions of 0.1 • × 0.1 • and 62 vertical levels and fully coupled to the 0.25 • atmospheric model (Community Atmospheric Model 5) (Neale et al 2012), the Community Ice Code version 4 (Hunke and Lipscomb 2008), and Community Land Model version 4 (Lawrence et al 2011).The simulations are conducted for about 140 years with a 14 year spinup run (Small et al 2014).In this study, we use the daily results of the last six model year simulations to analyze the EKE budget in the AR region due to the big data size of three-dimensional CESM data.In addition, the EKE in the AR region is concentrated in the upper 500 m, especially in the upper 200 m (figure S1(b)).
In addition to the CESM model, we also use the output of the eddy-resolving ocean general circulation model (OGCM) for the Earth Simulator (OFES) (Masumoto et al 2004, Sasaki et al 2008) in this study.The OFES data is based on the Modular Ocean Model, version 3 (MOM3; Pacanowski and Griffies 2000), which is a 3D, z-level, hydrostatic, Boussinesq ocean model.It has a horizontal resolution of 0.1 • and 54 vertical levels.Except for the different background viscosity and diffusivity coefficients of POP2 and MOM3 models, both of them use the KPP turbulent mixing closure scheme for mixing and biharmonic horizontal diffusion for vertical mixing in z-coordinate.There are three OFES simulations available (Climatological, NCEP-run, and QSCAT-run).The QSCAT-run simulation is used here due to the QSCAT wind is the highly spatiotemporal resolution observed wind that can resolve the mesoscale signals of wind.The QSCAT-run simulation is forced by the QSCAT winds from 20 July 1999 to 30 October 2009.As the AC has early retroflection in 2000-2001 (Dencausse et al 2010), the three day output of QSCAT-run OFES simulation from 2002 to 2007 (6 years like CESM data) is used in this study.It is note that the numbers of layers in the upper 500 m are similar in the OFES and CESM data, which are 29 and 32, respectively (figure S1(a)).
Daily satellite observational sea surface height and surface geostrophic velocity data used is the SSALTO/Data Unification and Altimeter Combination System (DUACS) multi-mission altimeter sea level product released in 2018 (DUACS-DT2018) with spatial resolution of 0.25 • for the 1993-2019period (Le Traon et al 1998, Taburet et al 2019).

Multiscale energy and vorticity analysis (MS-EVA) method
In this study, the EKE budget in the AR region is analyzed based on the MS-EVA method, which has been widely used in the energetic analysis in the Kuroshio extension (Yang and San Liang 2016) and the Gulf of Mexico (Yang et al 2020).For details of the MS-EVA method, see Liang and Robinson (2005) and Liang (2016).MS-EVA is based on a new functional analysis tool, namely, the multiscale window transform (MWT), which is developed for a physically faithful representation of multiscale energy (Liang and Anderson 2007).With the MWT, the original fields can be decomposed into several orthogonal scale windows (Liang 2016).Here, we decompose the variables into three windows: where A ∼0 , A ∼1 , and A ∼2 represents the reconstructions of mean flow, mesoscale eddies, and highfrequency processes, respectively.The high-frequency processes include submesoscale eddies, oceanic turbulence, and other unresolved subgrid processes (Yang and San Liang 2016).
The oceanic mesoscale eddy signals are associated with temporal scales of 30-270 d in the AC system (Zhu et al 2018(Zhu et al , 2021)).In this study, the cutoff period is set to 260 d between the mean flow and mesoscale eddies, and 30 d between mesoscale eddies and highfrequency processes, respectively.Note that changing the cutoff periods from 240 d (20 d) to 300 d (50 d) has no significant impact in the results.Within the MWT framework, the kinetic energy in the mesoscale eddy window is where ρ 0 is the reference density, u H = (u, v) is the horizontal velocity vector and the hat denotes the MWT operator.The detailed derivation of the kinetic energy equation is referred to Liang (2016).Here, the EKE budget equation is summarized in the following: where u = (u, v, w) is the three-dimensional velocity vector, and p is the dynamic pressure.The Γ K 1 term represents the cross-scale energy transfer to the mesoscale window, which mainly includes the mean kinetic energy (MKE) transfer to EKE (Γ K 0→1 ), and high-frequency kinetic energy (HKE) transfer to EKE (Γ K 2→1 ).A key difference between the MS-EVA and other existing energetics formalisms is that the crossscale energy transfer satisfies a conservation property, i.e, ϖ ,n Γ ϖ K = 0, where ϖ = 0, 1, 2 denote the windows and n denotes the discrete time steps.This important property indicates that Γ ϖ K is only redistribute energy among scale windows, without creating or consuming energy as a whole.The b 1 term is the conversion between EPE to EKE through baroclinic instability.The nonlocal transport process indicates the EKE is transported into (out of) the domain by energy flux convergence (divergence) through advection and pressure work.Note that the positive (negative) value of terms in the EKE budget indicates that it is the source (sink) of EKE.The F K 1 term is residual term, indicating the processes which are not explicitly calculated.It includes the external forcing, internal dissipation, and unresolved subgrid processes.As EKE is intensified in the upper 500 m layer in the AR region (figure S1 where u H ∼1 | surface and τ ∼1 are the horizontal surface velocity and surface wind stress in the mesoscale window, respectively.The negative value of W Wind indicates that the eddy-wind interaction serve as eddy killers that remove energy from eddies.We will estimate the contribution of eddy-wind interaction to the F K 1 term in this study.

EKE budget in the AR region
Before exploring the dynamics modulating EKE, it is necessary to verify the basin-scale oceanic circulation in the AC system based on model simulations (figure 1).Overall, the mean oceanic circulation and surface velocity estimated from CESM data (figure 1(c)) agree well with those based on altimeter data (figure 1(a)), except for a little difference in the Mozambique Channel, south of Madagascar, and the Antarctic Circumpolar Current regions.The linear spatial correlation between figures 1(a) and (c) is r = 0.89.In both data sets, the AC flows southwestward until it reaches the AR point (39 To elucidate the major sources and sinks of EKE in the AR region, the EKE budget integrated over the upper 500 m is diagnosed using CESM data (figure 2).Generally, the dynamic processes modulating EKE are spatially inhomogeneous, particularly in the upstream and downstream zones of the AR (the black boxes in figure 2(a)).Specifically, the Γ K 0→1 (figure 2(a)) exhibits maximum positive value in the upstream zone, indicating that the MKE transfer to EKE through barotropic instability.While the EKE transfer to MKE in the downstream zone with negative Γ K 0→1 spots.Compared to Γ K 0→1 , term (figure 2(b)) is one order of magnitude smaller than Γ K 0→1 , suggesting that the conversion between EPE and EKE through baroclinic instability is insignificant in generating EKE in the AR region.This is consistent with previous studies (Zhu et al 2018, Li et al 2023) that have suggested the significant role of barotropic instability in the AR region.Meanwhile, the high-frequency processes obtain energy from mesoscale eddies through forward energy cascade in the upstream zone, while the HKE releases back to EKE through inverse energy cascade in the downstream zone (figure 2(c)).In addition to the cross-scale energy transfer field, the nonlocal transport also exhibits different effects on the upstream and downstream zones of the AR (figure 2(d)).The EKE is generally transported out of the upstream zone by EKE divergence and accumulates in the downstream zone through EKE convergence.This is due to the mean flow carrying low (high) EKE water into the upstream (downstream) and high (low) EKE water out of the domain (figure 2(f)).The residual term F K 1 (figure 2(e)) reveals overall negative value with minimum in the AR region, suggesting that the F K 1 is mainly dominated by the dissipation processes associated with the most prominent dissipation in the AR region.
The distributions of processes in the EKE budget equation based on the OFES data (figure S3) are roughly consistent with that derived from CESM data in the upstream and downstream zones, while it exhibits a different pattern in the leakage zone.To find out the dominant mechanism modulating EKE in the three zones, we further quantified every term in the EKE budget equation based on the two datasets (figure 3).
In the upstream zone (figure 3 The principal distinction between the OFES and CESM models lies in the absence of mesoscale air-sea interaction in the OFES model, an element integral to the damping of EKE and the shaping of oceanic circulation (Seo et al 2016, Jullien et al 2020).However, in the AR region, thermal mesoscale air-sea interaction is not imperative for damping EKE, owing to the inconsequential conversion between EPE and EKE (figure 2(b); Ma et al 2016, Renault et al 2017).As a result, our investigation will pivot to assessing the role of eddy-wind interaction in moderating EKE in the AR region.

Potential role of eddy-wind interaction
The eddy-wind interaction acts as the eddy killer that remove energy from mesoscale eddies to the atmosphere (Renault et al 2016, Yang et al 2019).The CESM-derived W Wind reveals negative centers around the AR regime (figure 4(a)), indicative of pronounced wind stress, responsible for damping mesoscale eddies within the AR region.These zones correlate closely with eddy-shedding positions in the 10 • E-23 • E range (Zhu et al 2021), which are characterized by high EKE levels.Specifically, eddy-wind interaction in the upstream and downstream zones account for ∼12% and ∼36% of the total EKE dissipation, respectively.Compared to the mesoscale wind stress, mesoscale velocities are the primary factors controlling the eddy-wind interaction (figure S4).
While in the OFES simulations, the W Wind (figure 4(b)) is insignificant with a small magnitude in the AR region, indicating that the OFES model cannot accurately represent the eddy-wind interaction in damping EKE.It is worth noting that the W Wind shows positive spots stretching from the upstream zone to the leakage zone in OFES data, suggesting that wind stress is more conducive to eddy generation rather than eddy killer.Therefore, the lack of eddy-wind interaction leads to excessive eddies penetration into the South Atlantic Ocean with weak dissipation in the OFES data.
Meanwhile, the improper over-strong westward intrusion of mean current (figure 1  in the OFES data.As a result, the EKE in the leakage zone is mainly generated through nonlocal transport rather than locally cross-scale energy transfer in the OFES simulation.Therefore, the above results underline the critical role of eddy-wind interaction in modulating EKE in the AR region, and the lack of eddywind interaction in ocean-alone models can results in flawed EKE budget in the leakage zone, leading to severe biases in EKE distribution with overestimation and over-strong penetration into the South Atlantic.

Summary
In this study, an EKE budget analysis was performed utilizing CESM simulations, which provide an improved representation of EKE in both distribution and magnitude in the AR region.This study reveals different mechanisms regulating EKE in the upstream, downstream, and leakage zones of the AR.Specifically, in the upstream and leakage zones, the EKE is mainly generated from mean flow through barotropic instability.While in the downstream zone, the EKE reservoir is mainly dominated by nonlocal transport of EKE convergence.Eddy-wind interaction acts as eddy killers that remove energy from mesoscale eddies.Specifically, eddy-wind interaction is pronounced in the AR region, accounting for ∼12% (∼36%) of the total EKE dissipation in the upstream (downstream) zone of the AR in the upper 500 m layer.
However, previous studies reveal that the EKE distribution exhibits common biases (although modeldependent in quantity) in ocean-alone models, typically with overestimation and over-strong penetration of EKE toward the South Atlantic Ocean.
We found that the OFES simulation, with similar resolutions to CESM, can roughly capture the dominant mechanisms responsible for EKE generation in the upstream and downstream zones, while in the leakage zone, the EKE is generated through nonlocal transport of EKE convergence rather than locally cross-scale energy transfer field.The flawed EKE budget in the leakage zone is due to the lack of eddywind interaction in the OFES simulation, leading to insufficient EKE dissipation in the upstream zone and subsequent transport of excessive EKE to the leakage zone.In contrast, in the CESM simulation, the integral eddy-wind interaction dissipates EKE to the atmosphere, resulting in a concentration of EKE within the AR region, and the EKE is generated through locally cross-scale energy transfer in the leakage zone.
Overall, this study suggests the crucial role of eddy-wind interaction in EKE dissipation in the AR region and highlights that mesoscale air-sea interaction, such as eddy-wind interaction, should be taken into consideration in simulations to obtain a realistic representation of both the large-scale and mesoscale circulations in the AR region.It can further improve the estimation of the Agulhas leakage volume transport and contribute to the understanding of the interaction between the Indian and Atlantic Oceans.It is note that in the CESM and OFES models, the AC transport along 32 • in the upper 500 m is 50 Sv and 51 Sv, respectively, which are different from the observed mean AC transport of 77 Sv in the upper 3000 m (Beal et al 2015).Since the factors affecting the AC strength are complex, the reasons responsible for the underestimation of AC transport in the models needed to be further explored in future studies.In addition, our results present the potential reason responsible for the biases of Agulhas leakage in the ocean-alone models based on the comparison of two models.With the improvement of the eddy-resolving models, we will explore the other reasons in future studies.
(b),Zhu et al 2018, Li et al 2023), the EKE budget analysis is performed in the upper 500 m in this study.The eddy-wind interaction is the mesoscale wind stress work(Renault et al 2016, Seo et al 2016, Yang et al 2019, Jullien et al 2020), which can be estimated by

Figure 2 .
Figure 2. Spatial distribution of (a) ΓK 0→1 , (b) b 1 , (c) ΓK 2→1 , (d) nonlocal transport, (e) residual term, and (f) mean EKE and currents integrated over the upper 500 m derived from CESM data.The gray curve is the 0.6 m SSH contour.The three black boxes denote the upstream, downstream, and leakage zones, respectively.(f) shows the climatological EKE (color shading) and currents (vectors) averaged over the upper 500 m.
(a)), according to CESM simulations, EKE is mainly generated from MKE through barotropic instability (Γ K 0→1 ) with 0.25 W m −2 and dissipated through dissipation processes with −0.17 W m −2 .While in the downstream zone (figure 3(b)), the EKE reservoir dominant fueled by nonlocal transport by 0.06 W m −2 .Meanwhile, the destructions of EKE in the downstream zone are mainly through EKE inverse cascade to MKE by −0.04 W m −2 and dissipation processes by −0.03 W m −2 .The OFES data can roughly capture the dominant source and sink of EKE in the upstream and downstream zones, but the EKE budget in the leakage zone is incorrect.In the leakage zone, the CESM data shows that the EKE is mainly generated through barotropic instability and destructed by nonlocal transport (figure 3(c)).It is largely due to the mean flow does not extend to the leakage zone (figure 2(f)), where the EKE is mainly generated locally through the cross-scale energy transfer field.While in the OFES simulation, the EKE in the leakage zone is generated through nonlocal transport rather than locally.On the one hand, it is due to the eddies propagating westward into the South Atlantic Ocean with weak dissipation in the ocean-alone model (Maltrud and McClean 2005, Thoppil et al 2011).On the other hand, the improper over-strong westward intrusion of mean current (figure 1(e)) favors transporting EKE from the upstream zone to the leakage zone (figure S3(f)).
(e)) favors transporting EKE from the upstream zone to the leakage zone (figure S3(f)) in the OFES data.Compared to the CESM model, the wind stress in the OFES model is larger and more westward intrusion (figure S5), which result in an overestimation of total energy input to the ocean by wind work (figure S6; Scott and Xu 2009).It facilitates the mean current in the upstream zone transporting EKE to the leakage zone
(Biastoch et al 2008)zed by two remarkably stable meander troughs near 26 • E and 35 • E with a crest in between, which are topographically controlled by the existence of the Agulhas Plateau(Boebel et al 2003).In addition to oceanic circulation, The mean surface EKE pattern derived from CESM (figure 1(d)) resembles that from the satellite altimeter (figure 1(b)), with both characterized by the maximum EKE band aligned in the vicinity of AR at 15 • E-23 • E with a value of about 0.3 m 2 s −2 .The linear spatial correlation between figures 1(b) and d is r = 0.87.Hence, the oceanic circulation and EKE simulated in CESM data aligns markedly well with those derived from the satellite altimeter data in terms of spatial distribution and magnitude.In contrast, the OFES data is largely able to capture the background oceanic circulation in the AC system, but an over-strong mean current penetrate into the Southern Atlantic Ocean at around 10 • E (figure 1(e)), where is the Agulhas leakage zone(Biastoch et al 2008).
• S/15 • E), after which the majority of water retroflects, feeding the eastward ARC.