Warm rings in mesoscale eddies in a cold straining ocean

Domain: earth_science
Published: 2025-10-20
Editorial outcome: major_revision

Abstract
The warm and saline Atlantic Water has long been recognized as being subjected to substantial heat loss during its transit towards the polar regions. In particular, the Lofoten Basin, a subpolar sea with energetic eddy activity and strong air-sea interactions, plays a crucial role in the transformation of Atlantic Water. Vertical heat transport at submesoscales (0.1-10 km) in the Lofoten Basin is potentially a key link in the heat transfer to the atmosphere. Here, based on multi-year Seaglider observations augmented by satellite altimeters, radiometers, and high-resolution numerical model results, we evaluate the oceanic vertical heat transport in the Lofoten Basin and demonstrate how geostrophic strain enhances heat transport. The enhancement is found to be associated with submesoscale ageostrophic motions along the mesoscale eddy edges, occurring on spatial scales smaller than 10 km and below the mixed layer depth. These strain-induced submesoscale vertical motions transport heat from the ocean interior to the surface, leading to a 0.4°C increase in sea surface temperature and the formation of “warm ring” structures in both cyclones and anticyclones. The dominant role of submesoscale heat transport likely represents the primary mechanism for substantial heat loss from Atlantic Water in the Lofoten Basin.

Introduction
The Lofoten Basin (LB) is the largest oceanic heat reservoir in the Nordic Seas and a region with strong air-sea interactions1,2. The North Atlantic Current is an important part of the oceanic conveyor belt that transports heat from the equator to the high latitudes3. As it flows through the Nordic Seas, especially the Lofoten Basin, the Atlantic Water undergoes transformation driven by both substantial heat loss to the atmosphere4,5 and lateral heat transport through mesoscale eddies6,7. This transformation significantly impacts the hydrographic environment, sea ice cover, and ecosystems in the region and ultimately the Arctic Ocean8. The LB (Fig. 1a) is characterized by a distinct shelf-slope-basin topography, which largely determines the general circulation pattern, water mass exchange, formation of eddies and transport of heat and nutrients in the region9,10. The LB hosts energetic mesoscale eddy fields, with a large number of eddies shedding from the most unstable area (near the Lofoten Islands)11,12 of the Norwegian Atlantic Slope Current and propagating westward, feeding the quasi-permanent Lofoten Basin Eddy (LBE), which subsequently is maintained by bottom topography1,13,14. Regional studies have demonstrated that mesoscale eddies and other lateral processes (e.g., advection and mixing) transport heat towards the LB, playing an important role in the transformation of Atlantic Water5,6,11. During winter, there is an increase in lateral exchanges and heat flux between the permanent anticyclonic LBE and its surroundings, primarily driven by instabilities and frequent eddy merging events4,6,15. Vertical heat exchange has also been reported to be significantly influenced by processes such as double-diffusive convection and internal-wave-driven mixing in polar regions16,17. Over the past decade, dynamical studies have increasingly highlighted the crucial role of submesoscale motions in facilitating vertical exchanges of heat and nutrients between the surface and the deep ocean18–20. However, their influence on the vertical heat transport (VHT) in the eddy-rich Atlantic Water transformation zone has received limited attention due to a lack of high-resolution observations.

To address this knowledge gap in the Lofoten Basin, the present study investigates how submesoscale dynamics enhance vertical heat transport in this eddy-rich region. Submesoscale motions, typically with lateral scales of order 0.1–10 km (the upper bound corresponding to the local deformation radius) and timescales of a few inertial periods (~days), are less constrained by Earth’s rotation than larger-scale motions and therefore often associated with ageostrophic secondary circulations, enhancing vertical transport19,21. In particular, the edges of mesoscale eddies are hotspots of submesoscale vertical transport, where the straining of mesoscale eddies can sharpen the lateral buoyancy gradients and drive ageostrophic secondary circulations – a submesoscale generation mechanism known as frontogenesis21,22. In eddy-rich regions such as the Kuroshio Extension, Gulf Stream, and Antarctic Circumpolar Current, submesoscale motions are found to be important contributors to vertical velocities (~10–100 m d−1) in the upper ocean20,23,24. They provide a pathway for vertical exchange of heat, nutrients and organisms between the surface and deep oceans19,20. In the Lofoten Basin, which is also eddy-rich, a recent study25 has focused on vertical transport mechanisms driven by mesoscale eddies, e.g., eddy pumping (1 m d−1) and eddy-induced Ekman pumping (0.1 m d−1), while the role of submesoscale vertical transport remains poorly documented and quantified due to the lack of extensive and long-term fine-scale in situ observations in this region.

We address this observational challenge by utilizing a fine-scale, Seaglider dataset over five years, which repeatedly traversed the mesoscale eddies in the Lofoten Basin. The motivation for focusing on the VHT associated with submesoscale motions is the frequent satellite-based detection of positive sea surface temperature anomalies (SST) along the edges of mesoscale eddies. Intriguingly, positive SST, forming “warm ring” structures of 1–10 km scale, were predominantly observed at the edges of both cyclones and anticyclones, with negative SST only rarely occurring. The combination of altimeter-based eddy dataset with Seaglider observations enables an exploration of whether these “warm rings” are driven by submesoscale ageostrophic motions occurring below the sea surface, and the role of geostrophic strain in meso-submesoscale interactions. Building on this intriguing observation, a key contribution of our study is the isolation and comparison of VHT in both cyclones and anticyclones. We investigate how deep-reaching submesoscale motions drive a systematic upward heat flux along their respective edges, providing a dynamical explanation for the “warm ring” phenomenon in a comparative context that has been largely overlooked.

Results
Submesoscale VHT revealed by Seaglider observations
Between July 2012 and August 2017, eight high-resolution Seaglider missions (M1–M8) amassed over 44,535 km of temperature and salinity data along profiles in the eddy-abundant regions of the LB (Fig. 1, Supplementary Tables S1, and Supplementary Fig. S1). A cross-basin example is the M1 mission conducted from 6 July 2012 to 16 August 2012 (Fig. 2). The sg559 glider was deployed near the continental slope and traversed over 600 km over one month on an nearly straight trajectory towards the west, recording data continuously from the continental slope to the center of the LB (70°N, 0-16°E). The glider passed numerous mesoscale eddies during the mission, and particularly it traversed two anticyclonic eddies and one cyclonic eddy on 13 July, 29 July, and 16 August, respectively (Fig. 2a–c and Supplementary Fig. S2). Frontal structures, characterized by large lateral buoyancy gradients (|bₓ|>2×10−7 s−2), were identified at the edges of these eddies along the glider track (approximately at 100, 400 and 500 km in Fig. 2e). These structures exhibit a strong spatial correspondence with the intense stretching identified in the altimetry-based finite-size Lyapunov exponent (FSLE) (Fig. 2a, d, e). FSLEs indicate the timescale of the stretching and compression induced by the strain field10,26,27 and, as such, strong FSLE are expected to be co-located with strong lateral gradients of buoyancy. This is indeed the case, as strong stretching FSLE characterized by large negative values (<−0.15 d−1), is distributed along the eddy edges, while the values inside and outside the eddy are much weaker, close to zero at the eddy center. The width of the frontal structure (Fig. 2e) ranges from 2 to 10 km, falling within the submesoscale range. To investigate the dynamical mechanism driving the formation of strong lateral buoyancy gradients, we compute the geostrophic Richardson number23,28 (Ri=f2N2/bₓ2). The small Ri values (Ri≤4, Fig. 2f) observed at the same locations indicate that energetic ageostrophic motions associated with intense vertical currents are occurring at the edges of eddies (see Methods for a full description).

The vertical section of variations in vertical velocity, ‘w’, can reach 60 m d−1 (Fig. 2g), indicating strong vertical transport. The w field inherits the same intermittency observed in FSLE and bₓ fields (Fig. 2a, e, g), with high magnitudes primarily found at the edges of the eddies. These strong vertical currents extend their influence well into the ocean interior—reaching depths of up to 500 m, which far exceeds the mixed layer (~20 m deep in summer). VHTs were further estimated by using the submesoscale components of vertical velocity and temperature (Fig. 2h). Although VHTs associated with mesoscale eddies are intensively distributed within the mixed layer, below the mixed layer the VHTs dominate at the locations of submesoscale fronts, consistent with a previous study23. Their local amplitude reaches 1600 W m−2 below the surface mixed layer and extends to at least 500 m. The intense VHTs located at the edges of the eddies are predominantly positive, indicating that these motions can drive heat transport from the ocean interior upward to the surface (see other transect cases in Supplementary Figs. S3, 4). These analyses of intense w and VHT are further supported by regional numerical simulations with a 2.4 km horizontal resolution (see details in Supplementary Notes). Model results from two representative cases in the same region similarly reveal strong vertical flows along both anticyclonic and cyclonic eddy edges, extending to depths exceeding 600 m (Supplementary Figs. S5, 6). These vertical velocities exhibit distinct paired structures of upward and downward flows, consistent with the observed patterns and indicative of strong secondary circulation at the eddy edges that facilitates heat transport from the ocean interior toward the surface.

Submesoscale VHT forms “warm rings” in both cyclones and anticyclones
While submesoscale signals can be obtained through Seaglider observations of individual eddies, the consistent features of the submesoscale emerge when compositing observations from a large number of section traverses through eddies (Fig. 3 and Supplementary Fig. S7). Figure 3a–d shows the composite distribution of absolute lateral buoyancy gradients (|bₓ|) and stretching induced by geostrophic strain in the normalized eddy-centered coordinates. An obvious feature is that the strong |bₓ| band is located within a ring-shaped area around the eddy with larger magnitudes in the anticyclonic eddy than the cyclonic case (Fig. 3a, b). The horizontal distribution of the strain field is almost identical to |bₓ| (Fig. 3a–d). This suggests the role of the strain in sharpening fronts27,29, i.e., stretching the fluid along the front (FSLE ridges) while compressing the fluid in the direction across the front. This front-sharpening mechanism explains why the gliders captured strong lateral buoyancy gradients when traversing these edges (fronts) (Figs. 2e, 3a, b and 4a, b). As the cross-front scale is compressed by the strain field, frontogenesis intensifies, increasing the buoyancy gradient and ultimately disrupting the thermal wind balance19,30. To restore this balance, an ageostrophic secondary circulation develops, characterized by surface convergence with downwelling on the dense side and upwelling on the lighter side of the front (Fig. 2g and Supplementary Figs. S3–6). This secondary circulation generates vertical velocities reaching up to 60 m day−1 below the surface mixed layer, nearly an order of magnitude greater than those associated with mesoscale motions (Fig. 2g, Supplementary Fig. S8, and Supplementary Notes).

A three-dimensional view of buoyancy anomalies measured by Seagliders reveals distinct vertical structures characteristic of mesoscale eddies at depth (Fig. 4). Anticyclonic eddies exhibit positive buoyancy anomalies forming a bowl-shaped structure, whereas cyclonic eddies display negative anomalies forming a doming structure. These patterns reflect different dynamics: anticyclonic eddies (high SSH) trap warm, saline waters driven by surface convergence and downwelling, whereas cyclonic eddies (low SSH) contain colder, fresher waters resulting from surface divergence and upwelling (Fig. 2c and Supplementary Fig. S2). The vertical distributions of temperature and salinity (Supplementary Figs. S1, 2) reveal the region’s typical hydrographic structure, with temperature variations (ΔT≈2–4°C) substantially exceeding salinity variations (ΔS<0.1–0.2). The dominant role of temperature in controlling density is quantified by the density ratio, Rρ=(αΔT)/(βΔS). Using representative values for thermal expansion (α≈2×10−4 °C−1) and haline contraction (β≈8×10−4 psu−1) pertinent to these waters, Rρ is approximately 5 for these observed variations. This high ratio indicates that, despite the high-latitude (69–72°N) Atlantic Water setting, temperature predominantly governs density structure below the mixed layer down to ~500 m depth. Complementary analyses of vertical velocity further highlight intense vertical motions predominantly driven by submesoscale processes along the edges of both anticyclonic and cyclonic eddies, extending downward to at least 400 m (Fig. 4c, d, Supplementary Fig. S8, and Supplementary Notes). The low geostrophic Richardson number (Ri≤4) are co-located with the strong geostrophic strain and the large magnitudes of |w|, further indicating an energetic ageostrophic regime characterized by intense vertical motions (Fig. 3c–h). These results are consistent with the expectation that geostrophic strain shrinks the frontal scale and intensifies lateral buoyancy gradients, disrupting thermal wind balance and thereby promoting cross-frontal secondary circulations in the frontal zone.

We explored the impact of deep-reaching submesoscale vertical currents on the domain-averaged VHT by constructing eddy-centered VHT composite fields. The composites (Fig. 3i, j and Supplementary Fig. S9) reveal upward VHT at the eddy edges where the geostrophic strain is enhanced, transporting heat from ocean interior to the surface. Remarkably, the magnitudes of the upward VHT in both cyclonic and anticyclonic eddies are comparable, reaching an average of ~400 W m−2 (Fig. 3i, j). This occurs because, irrespective of being cyclonic or anticyclonic, the submesoscale secondary circulations act to flatten sloping isopycnals at the fronts20,30, thus restoring stratification31. These secondary circulations are characterized by upwelling on the warmer (lighter) side and downwelling on the colder (denser) side of the front, resulting in consistently upward heat transport (w’T’>0), as further explained in the next section. A two-year composite analysis from numerical simulations also demonstrates the structure, depth range, and intensity of w and VHT, which are consistent with the observational results, further supporting our findings (Supplementary Fig. S10). To further examine whether the intense upward heat transport at the deep-reaching fronts affect the SST, we constructed composite averages of submesoscale SST. Prior to the composite analysis, SST fields were high-pass filtered spatially to remove large-scale circulation features. Results indicate that these deep-reaching submesoscale fronts indeed lead to an additional increase of ~0.4°C in SST along the edges of eddies (Fig. 3k, l).

Geostrophic strain-induced frontogenesis drives an intense ageostrophic secondary circulation and upward VHT
To identify the role of geostrophic strain in enhancing submesoscale VHT, the composite result of strain was organized into three categories based on strain intensity (Group 1: S ∈[P40, P60), Group 2: S ∈[P20, P40), Group 3: S ∈[P0, P20)) along the edge of eddies (Fig. 5a). The composite results for VHT and SST corresponding to these three groups of strain intensity are presented in Fig. 5b, c. As the intensity of the strain increases, the strength of the VHT also rises. Particularly, the group with the strongest strain (Group 3) is associated with the strongest upward heat transport in a ring-shaped region. This is attributed to frontogenesis, whereby strong geostrophic strain intensifies lateral buoyancy gradients along the eddy edges. An ageostrophic secondary circulation develops in response, acting to flatten these gradients and thereby enhances systematic upward heat transport. Further analyses of satellite SST composites (Fig. 5c) indicate that SST due to submesoscale motions are correlated with geostrophic strain, confirming that geostrophic strain is a crucial mechanism that facilitates the transfer of heat from the ocean interior to the surface.

Figure 6 illustrates how the development of submesoscale secondary circulation and upward VHT is driven by strain fields within hyperbolic regions. Specifically, these hyperbolic regions are located at the edges of mesoscale eddies, near areas of maximum azimuthal velocities, and can be identified by Lagrangian Coherent Structure (LCS)25,26,32. The most effective way to enhance ageostrophic front and trigger ageostrophic perturbations is by stretching along the front direction and compressing across the front direction30,31. As depicted in Fig. 6a, the strain field (black arrows) from t=0 to t=3 elongates the tracer patch in the y-direction (along the front) and compresses it in the x-direction (across the front). This process intensifies the buoyancy gradient while simultaneously reducing the tracer patch’s scales along the x-direction. The time-dependent LCS theory26 explains the fluid stretching mechanisms critical for forming submesoscale fronts. As strain fields compress the front, the cross-frontal buoyancy gradient intensifies and the cross-frontal scale decreases, driving frontogenesis and increasing the available potential energy at the front. When the local Rossby number (Ro=ζ/f) approaches O(1), thermal wind balance becomes disrupted, triggering ageostrophic secondary circulations that act to restore this balance. These circulations generate upwelling on the warm (light) side and downwelling on the cold (heavy) side of the front. This is accompanied by a cross-frontal surface flow moving from the warm to the cold side, and a cross-frontal deep flow moving from the cold to the warm side. The role of this cross-frontal ageostrophic secondary circulation (orange arrows in Fig. 6b) is to flatten the isopycnals and reduce the buoyancy gradient. Typically, warm, less dense waters occupy anticyclonic eddy interiors and cyclonic eddy exteriors, while cold, dense waters characterize cyclonic eddy interiors and anticyclonic eddy exteriors. As a consequence, the enhanced VHT associated with frontogenesis at the edges of both anticyclonic and cyclonic eddies is directed upward due to the positive correlation (w’T’>0) between temperature and vertical velocity anomalies (Fig. 6b). The combination of satellite-based FSLE with glider-based vertical measurements provides observational evidence for diagnosing how eddy strain fields drive strong buoyancy gradients and vertical transport at submesoscales in the ocean interior. The continuous upward VHT within strain-dominated regions transports heat from the ocean interior back to the surface, thereby elevating sea surface temperatures (SST) along the edges of eddies.

Methods
Satellite data
Daily Sea Level Anomaly (SLA) and geostrophic current velocity (ug, vg) product with a 0.25×0.25° resolution were utilized to identify mesoscale eddies in the Lofoten Basin area (0–16°E, 69–72.2°N). The Level-4 gridded altimetry products from Copernicus Marine Environment Monitoring Services (CMEMS, http://marine.copernicus.eu) were constructed by merging data from missions including TOPEX/Poseidon, Jason-1/2, ERS-1/2, GFO, CryoSat-2, HY-2A, Altika and ENVISAT. At our study latitude (~70°N), this gridded product yields a meridional resolution of ~27.8 km and a zonal resolution of ~9.5 km. For the mesoscale eddies with radii of 30–50 km that we focus on, the zonal resolution is sufficient to resolve their horizontal velocity structure given their quasi-circular nature. Our previous study45 quantitatively evaluated this dataset and found that altimeter-derived geostrophic velocities within eddies were ~25–30% lower than the geostrophic velocities concurrently measured by surface drifters within the eddies. This discrepancy was mainly attributed to the smoothing effect inherent in the gridding of altimeter data, along with additional influences on the drifter velocities from centrifugal acceleration and wind-slip effects.

Level-2 SST products from VIIRS Suomi-NPP and MODIS Aqua were taken from the NASA Ocean Color achive (https://oceancolor.gsfc.nasa.gov). The products from VIIRS and MODIS, with the spatial resolutions of 750 m and 1 km, respectively, were used to construct SST associated with the mesoscale eddies. Satellite altimetry and SST-based products were selected to be consistent with the data collected during the Seaglider operations from July 2012 through August 2017.

Stretching finite-size Lyapunov exponent (FSLE)
FSLEs, derived from satellite-based geostrophic velocities, were employed to characterize the properties of the strain field. The FSLEs are computed from the time interval τ, during which two fluid particles move from an initial separation distance δi to a final separation distance δf following their trajectories in the two-dimensional velocity field. At time t and position x, the Lyapunov exponent λ is defined as26,32,46:

λ(x,t,δi,δf) = 1/τ log(δf/δi) (1)

where the position vector x is the independent variable. The Lyapunov exponent λ quantifies the local exponential rate of separation between initially nearby trajectories starting at position x over the integration time τ. The separation distances (δi, δf) are expressed in degrees as angular distances on the Earth’s surface, and the ratio δf/δi becomes dimensionless after taking the logarithm, thus the units of FSLEs are d−1. Trajectories were extracted by applying a fourth-order Runge-Kutta scheme with a timestep of 3 h. Values of δi and δf were set at 0.02° and 0.4°, respectively, to capture meso- to submesoscale properties and to visualize structural details10,25.

We computed the daily FSLE field over the five-year period of Seaglider operations to quantify the stretching induced by geostrophic strain in the regions traversed by Seaglider. By combining these data with the altimetry-based eddy dataset, the strain characteristics at the edges and within the eddies were further extracted and analyzed. Negative (positive) FSLE values indicate that a tracer patch is stretched (compressed) in the x (y) direction of the background strain field (Fig. 6a). Consequently, greater negative (positive) FSLE values correspond to more intense stretching (compression). Here, negative FSLE values were computed back in time as detailed in Dong et al.10,25,46 and d’Ovidio et al.26,47.

Seaglider measurement
We analyzed in situ data collected between 4 July 2012 and 9 August 2017 through eight Seaglider missions (M1-8, see Fig. 1) in the Lofoten Basin48–50. The initial six glider deployments (M1-6) were part of the Norwegian Atlantic Current Observatory (NACO), dedicated to observing the variability of the North Atlantic Ocean Current48. The subsequent deployments (M7-8) were part of the ProVoLo project49. The Seaglider missions consisted of two main parts. The first part included 24 cross-basin transects (0–16°E) gliding in an east-west direction, primarily between the continental slope and LB, including some meandering paths. These transects covered a total length of 15,781 km, accounting for ~35% of the total distance and 45% of the total mission time. The second part involved repeated sampling on spiral and circular trajectories in the deepest areas of LB, covering 25,685 km, representing nearly 57% of the transects but only 44% of the time. These tracks covered the western side of the Norwegian Atlantic Slope Current and the LB region, where mesoscale eddy activity is most frequent and eddy intensity is strongest11,12,45. All Seaglider data have undergone quality control and post-deployment calibration (Supplementary Notes). Combined with satellite-derived eddy locations found that over the five-year time period, Seagliders collected vertical data on more than 1783 eddies, of which 760 were cyclones and 1023 were anticyclones. The glider collected data from 7031 sampling points associated with cyclonic eddies and 4270 sampling points associated with anticyclonic eddies (Supplementary Fig. S7). Over a total of 1543 days, these glider missions provided decent temporospatial coverage and resolution for studying the meso-submesoscale interactions in the LB.

Mixed layer depth
The MLD was defined as the level of density increase of 0.03 kg m−3 from the 15 m depth50,51.

Lateral buoyancy gradient
The along-track time series for buoyancy, defined as b= g(ρ0−ρ)/ρ0, where ρ is the potential density and ρ0=1025 kg m−3 as the reference density, demonstrates a variability encompassing both meso- and submesoscale processes. For further calculating the lateral buoyancy gradients, buoyancy (b) was first interpolated along the Seaglider’s paths onto a regular grid with a horizontal resolution of 2 km and a vertical resolution of 5 m. The front was identified by the buoyancy gradient along the Seaglider direction, defined as bs=∂b/∂s, where s is the along-track distance. Considering that the Seaglider’s trajectory typically inclines relative to the stretched FSLE streamlines, forming a certain angle with FSLE (streamlines rather than being perpendicular), and that the buoyancy front is assumed to align with the stretched FSLE, it became necessary to correct the Seaglider’s buoyancy gradients to accommodate the direction of the FSLE encountered23,52. To achieve this, it is assumed that θ represents the angle between a FSLE eigenvector and a Seaglider’s trajectory, and the normalized along-track lateral gradient of buoyancy (bₓ) was calculated as bₓ=bs/sinθ. To focus on the regions prone to submesoscale motions, we excluded data with θ<30°, which corresponds to a correction of more than a factor of 2, and only normalized bₓ associated with the large FSLE (>0.05 d−1): bs.

Richardson number
To quantify the occurrence of the energetic ageostrophic motions associated with intense vertical velocities, we estimated the non-dimensional geostrophic Richardson number (Ri) using Seaglider observation data19,23,28. The geostrophic Richardson number is defined as Ri=f2N2/bₓ2, where N2=∂b/∂z represents the Brunt-Väissälä frequency, and bₓ=bs/sinθ=∂b/(∂s sinθ)= ∂b/∂x represents the normalized along-track lateral gradient of buoyancy. Here, Ri quantifies the relative importance of stratification versus the lateral buoyancy gradient, effectively characterizing the dynamic regime by comparing the steepness of isopycnal slopes to N/f. When Ri≫1, stratification dominates and the flow remains close to quasi-geostrophic (QG) balance53,54; conversely, when Ri is on the order of unity (or Ri≤4), the weaker stratification relative to horizontal buoyancy gradient indicates an ageostrophic regime, characterized by intense vertical motions and active submesoscale dynamics19,23.

Vertical velocities and VHT
The ageostrophic vertical velocities (w) associated with mesoscale eddy fronts are diagnosed by numerically solving the adiabatic, two-dimensional (2D) version of the classical QG Omega equation (Supplementary Notes). The Omega equation was employed to solve for the gliding profile data of eight Seaglider missions within the 0–500 m depth range, aiming to obtain the variations of vertical velocities outside eddies, at eddy edges and within eddies. Buoyancy fronts are assumed to be elongated in the direction of stretching (Fig. 6), implying that the buoyancy gradient along the front (y-direction) is negligible compared to the gradient across the front (x-direction)21,23,30. Therefore, the 2D version (x, z) of the QG Omega equation can be expressed as19,20,23,53:

N2wxx + f2wzz = 2Q (2)

where the subscripts denote the derivatives. The variables N2 and bₓ were computed using Seaglider data. The mesoscale strain field, as illustrated by the black arrows in Fig. 6a, stretches the tracer patch in the y-direction and compresses it in the x-direction. This leads to the development of intense horizontal buoyancy gradients at the submesoscale, with a growth rate being associated with the strain rate uₓ=∂u/∂x. Therefore, we estimated the strain rate uₓ using the stretching FSLE derived from satellite altimetry data. Diverging from the traditional approach of directly estimating strain rate through ∂u/∂x, FSLEs have the advantage of utilizing both the spatial and temporal variability of the velocity field derived from SLA10,25. As such, this Lagrangian diagnostic method provides information about both the growth rate and orientation of elongated horizontal buoyancy gradients by measuring the largest separation rate (λ) of two neighboring particles in the flow field. Here, we considered the background flow field to be barotropic. In Eq. (2), Seaglider trajectories were assumed to be perpendicular to the eddy fronts, achieved by normalizing the buoyancy gradient as described above. The vertical heat flux23,40,41 is defined as:

VHT=ρ0 Cp w'T' (3)

where Cp is the specific heat capacity (Cp = 3985 J kg−1 K−1), and w' and T' are the anomalies of vertical velocity and temperature, respectively, after removing the sectional mean.

Identification of mesoscale eddies
To investigate the submesoscale motions at the edges of eddies in the Lofoten Basin, we constructed a mesoscale eddy dataset spanning over three decades using satellite altimetry data15,25. The dataset was constructed with an automated hybrid eddy detection algorithm that combines geometric (Sea Level Anomaly, SLA) and dynamical (Okubo-Weiss, OW parameter) properties of the flow field to identify eddies15,45,54–56. The eddy center is defined as the location of the SLA maximum within the identified closed contour45. The eddy area corresponds to the region enclosed by the SLA contour associated with the maximum azimuthal (geostrophic) velocity, and the eddy radius (Rₓ) is defined as the radius of a circle with an area equivalent to this enclosed region. To accurately delineate eddy boundaries and areas, our hybrid detection method15,25,45 employs the OW parameter (W) criterion to exclude spurious detections caused by noise or ambiguous, multipolar, or elongated contours, ensuring robust and consistent eddy boundaries. The OW parameter is defined as W=(Ss2+Sn2)−ς2, where Ss is the shearing deformation rate, Sn is the stretching deformation rate, and ς represents relative vorticity. The total strain rate S is calculated as S2=(Ss2+Sn2). Negative values of W indicate dominance of relative vorticity over strain, a fundamental dynamical feature of mesoscale eddies. This hybrid detection algorithm significantly reduces reliance on arbitrary thresholds, thereby minimizing subjectivity and enhancing accuracy15,25,45. The method has been successfully applied and validated in the Lofoten Basin region using Argo floats and surface drifters15,45,57. Additional details are provided in Dong et al.25 and Raj et al.15,45.

Eddy-centric collocations
To investigate the effects of submesoscale motions on VHT, we constructed eddy-centric composite fields18,36,58 based on five years of Seaglider observations and the mesoscale eddy dataset, focusing on five parameters: |bₓ|, strain field, Ri, |w|, and VHT. Composite fields were constructed using a normalized eddy-centric coordinate system, with R representing a dimensionless normalized radius. Rₓ represents the radius of an individual eddy. For each sampling point along the Seaglider transect, the radial distance (d) and azimuth angle (θ) relative to due east were computed from latitude and longitude coordinates (Supplementary Fig. S7a). These sampling points were subsequently collocated onto the normalized eddy-centric coordinate system according to their normalized radial distance (d/Rₓ) and azimuth θ (Supplementary Fig. S7b), then interpolated onto a 100×100 grid for compositing. Our analyses primarily focused on the region within two radii of the eddy center (d/Rₓ<2, Chelton et al.54), subdivided into three dynamical zones: eddy interior (d/Rₓ<0.8), eddy edges (0.8≤d/Rₓ≤1.2), and eddy exterior (d/Rₓ>1.2). This zone division was applied solely for descriptive and analytical clarity and was not employed in any data processing steps.

To provide a more intuitive demonstration of our composite analysis method, a case study figure is introduced to illustrate the single-eddy composite process (Supplementary Fig. S13). For this analysis, observational data from three specific eddies—ACE-02 and ACE-04 from the sg559-T2 transect, and ACE-01 from the sg561-T3 transect (Supplementary Figs. S3, 4)—were selected and then projected individually onto the normalized eddy-centric coordinate system after being averaged over the upper 500 m. The results clearly show that the strong signals of lateral buoyancy gradient (bₓ) and vertical heat transport (VHT) originating from the eddy edges are consistently mapped to the annular region at a normalized radius of r≈R. It is worth noting that our method does not perform any rotational alignment, thereby preserving the original azimuthal orientation of each feature.

To assess the impact of submesoscale VHT at the eddy edge on sea surface temperature, we constructed an eddy-centric composite analysis of SST during the period of Seaglider operations. Daily SST maps were interpolated onto a 0.02°×0.02° grid and high-pass filtered with 0.2° latitude×0.5° longitude half-power filter cutoffs to eliminate signals with length scales larger than the mesoscale variability25,35,36. This filtering process is denoted as SSTanom =HP(SST), where HP represents the high-pass filter. To reduce the influence of geographical locations and seasonal variabilities on the composite results, the long-term monthly averaged background fields at each longitude (x) and latitude (y) was subtracted from the SSTanom at the corresponding location. The SSTanom for the Seaglider transit were collocated to each identified eddy from the SLA for composite analysis. Eddies with over 70% coverage of available data within one radius of each identified eddy were included; those with less than 70% coverage were excluded. This minimizes the errors of the composites caused by cloud coverage within the eddy region25. Consistent with the coordinates of the Seaglider composites, the centers and radii of all eddies are normalized by the dimensionless radius R to conduct composite analysis of SSTanom for eddies with different sizes and polarities.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript describes the vertical heat transport at the skirts of mesoscale cyclones and anticyclones, suggesting a unified mechanism of upwelling-downwelling system. The mechanism suggested consists in an ageostrophic cross-front motion of fluid parcels of different direction at the upper and lower levels, which induces upwards/downwards vertical motions along the boundaries of the mesoscale eddies. These motions were suggested to be formed (or intensified?) episodically during the periods of an increased strain at the eddy boundaries, which, in turn, were a result of mesoscale eddy interactions with submesoscale structures. The resulting heat flux is speculated to be responsible for formation of the observed warm-core rings around both cyclones and anticyclones, as well as for enhancing the resulting heat flux from the ocean to the atmosphere.\nThe study is based on high-resolution Seaglider data in the Lofoten Basin, combined with the satellite altimetry data and high-resolution SST data. Eddies were derived by a threshold method using the value of Okubo-Weiss parameter in the closed SLA. Although this method is not optimal, it allows detecting strong mesoscale eddies at the sea-surface. The authors present a novel concept, which is supported with observations. The manuscript represents an interesting study and is well written. I recommend publication after minor modifications.\nThe explanation of the mechanism is vague. More details on how the sharpening of the front result in ageostrophic vertical motions would be beneficial. Are there any theoretical estimates on the intensity of such process? These can be compares with the derived vertical velocities.\nThere are also two additional points, which might be noted in the manuscript.\nThe authors should also mention, that the suggested mechanism is not the only one which can form such warm-ring structures. Another mechanism, acting in particular for undersurface anticyclones is trapping of a warmer water and wrapping it around the eddy center. In particular, this was observed for surface manifestation of meddies and the Lofoten Vortex – see Bashmachnikov et al., 2013. Manifestation of two meddies in altimetry and sea-surface temperature; Bashmachnikov et al., 2018. Pattern of vertical velocity in the Lofoten vortex (the Norwegian Sea. This forms far larger SST anomalies around eddies compared to 0.4oC (only slightly above on the limit of accuracy of the IK SST sensors) of the mechanism suggested by the authors.\nThe vertical velocities at the eddy boundaries, suggested by the authors (Figure 6b), do not fully merge with the vertical velocity structure in the Lofoten Vortex, derived using MIT model in the paper cited above. In the Lofoten Vortex the upwelling was dominating all the central part of the vortex and downwelling was observed at its outer skirt, but these motions were characteristics only at the level of the well mixed eddy core, intensifying towards the sea-surface. The driving mechanism was suggested to be also linked to a high strain at the eddy boundary, which increases towards the sea-surface. The resulting decay of kinetic energy form in the upper ocean an inverse secondary circulation, similar by nature to the one formed by the bottom Ekman boundary layer (see also Bosse et al., (2019) Dynamical controls on thelongevity of a non- linear vortex: The case of the Lofoten Basin Eddy,). This is another effect the strain, and the resulting vertical pattern should merge with the one suggested in the manuscript. Both mechanisms should form increase their intensity towards the sea- surface, where the largest energy (straining) of submesoscale is expected. This can be discussed and noted at the sketch in Figure 6b.\nMinor comments:\n49-50 “The North Atlantic Current is an important part of the oceanic conveyor belt that transports heat from the equator to the poles.” The NAC, as well as the Global Conveyor, does not reach the pols – please rephrase.\n51-53 “the Atlantic Water experiences substantial heat loss to the atmosphere, which is thought to be the main driver of the transformation of Atlantic Water” - one may also see Dugstad et al (218) “Lateral Heat Transport in the Lofoten Basin: Near-Surface Pathways and Subsurface Exchange” and Bashmachnikov et al., 2023 “Heat transport by mesoscale eddies in the Norwegian and Greenland seas” on the role of mesoscale eddies in regulating the AW transport across the Lofoten Basin.\n53-55 “This process significantly impacts the hydrographic environment, sea ice cover and ecosystems in the region and ultimately the Arctic Ocean” – What process from the mentioned above? The impact of AMOC on SST in the Nordic Seas is nonlinear and involves the atmospheric response to the ocean heating (Bengtson et al., 2004 “The Early Twentieth-Century Warming in the Arctic—A Possible Mechanism”, Shaffrey and Sutton, 2006 “Bjerknes Compensation and the Decadal Variability of the Energy Transports in a Coupled Climate Model”)\n165-166 “further indicating the presence of a cross-frontal secondary circulation” - Small Ri does necessarily mean enhanced vertical velocities. The facilitated Kelvin-Helmholtz instability does not require the cross-frontal exchange.\n212-216 “the scale across the front becomes small enough and the geostrophic balance can no longer be maintained” What do you mean by “small enough”? Less than Rossby radius of deformation? How this decreasing the cross-front scale affects the geostrophic balance?\n545-547 Ri characterizes stability of the vertically sheared flow. Ri>>1 means that Kelvin-Helmholtz instability cannot be generated. I do not see the direct relation between Ri and geostrophic-ageostrophic separation, which is basically linked to the Rossby number.", "reviewer_2": "As requested by the editor of Nature Communications, I reviewed the manuscript by Dong et al., titled “Warm rigs in mesoscale eddies in a cold straining ocean”. This study provides a thorough analysis of the vertical heat transport associated with submesoscale filaments around mesoscale eddies in the Lofoten Basin of the North Atlantic, and the resulting formation of surface warm ring structures, based on long-term SeaGlider observation data. I believe it is rare to find such a beautiful visualization of heat advection by submesoscale structures from actual ocean observations. Therefore, I support its publication in Nature Communications. However, there are several critical concerns described below. Please clarify these points.\nMajor concerns:\n1. TS Distribution & Salinity Contribution:\n- Request to see the TS distribution that determines the density of seawater.\n- Accurate quantification of salinity’s contribution to density and geostrophic flow is needed.\n- Figure 6b implies that temperature is dominant, but in high-latitude regions (70-72°N), salinity typically plays a more significant role in density-driven flows (e.g., Rudels et al. 2013, doi:10.1016/j.pocean.2013.11.006).\n2. Definition of \"Edge\" (L92, L98):\n- The definition of \"edge\" is unclear throughout the paper.\n- The use of \"r = R\" to describe the \"eddy edge\" is questionable. A clear definition of R is needed, possibly the location of maximum azimuthal velocity.\n3. Relative Vorticity & Rankine Vortex (L463):\n- Request to see the spatial distribution of relative vorticity (ζ) in eddy-centric coordinates.\n- Suggest assuming a Rankine vortex profile (ζ = constant for inner regions; zero for outer regions) to clarify the positioning of R.\n4. Geostrophic Velocity Resolution:\n- Questioning whether the geostrophic velocity (u_g, v_g) can be truly resolved from sea surface height (SLA).\n- Concern about whether the satellite data resolution (0.25 x 0.25 degrees, ~27 km latitudinal resolution) is sufficient to resolve the eddy’s horizontal structure, given the deformation radius (~10 km).\nSpecific comments:\nL31-32: having “poleward” appear twice in the same sentence feels repetitive. You should rephrase the sentence to avoid the redundancy. Like “heat loss during its transit towards the polar regions.”\nL60: Clarify if \"stabilized\" means the eddy disappears. Consider using \"weakened\" or \"dissipated.\"\nL67: Note that heat diffusion around polar eddies also involves mechanisms like double diffusion or mixing by internal waves (e.g., Kawaguchi et al. 2012, doi:10.1016/j.dsr.2012.04.006; Kawaguchi et al. 2016, doi:10.1175/JPO-D-15-0150.1).\nL71: The origin of the 0.1-10 km range is unclear. The upper bound should relate to the deformation radius.\nL78: \"frontgenesis\" should not be capitalized.\nL93: A description of the TS structure of cyclones and anticyclones below the mixed layer is necessary. Mention that salinity contributes minimally to density-driven GQ flow.\nL115: The term FSILE should be defined upon its first mention.\nL123: Provide a simplified definition of Ri or reference the relevant Methods section.\nL176: What is the relative contribution of temperature and salinity to restratification?\nL201: Clarify the \"hyperbolic region along the edges.\" Is it inside or outside?\nL209: Define \"LCS.\"\nL213: The statement \"frontgenesis develops by releasing the available potential energy of the front\" might be inaccurate. If internal density surfaces stand vertically, wouldn’t APE increase?\nL216: The \"warm side to cold side\" assumption only applies if the density profile is temperature-driven. In polar oceans, this could be reversed. Start by explaining the TS structure inside and outside the eddy.\nL220: Similar clarification is needed: \"Warm fluids are located within the anticyclonic eddy, whereas cold fluids are …\"\nL474: The dimensions of \"delta_i\" and \"delta_f\" (set at 0.02° and 0.4°) are unclear. Are these distances and assumed as constants? Also please clarify the independent variable in equation (1).\nL529: Clarify whether \"s is the along-track direction\" means distance instead of “direction.”\nL542: The use of \"N\" for buoyancy frequency and \"N\" for sampling number (Fig. 3) overlaps. Change one of the notations.\nL545: Ri’s formula should be presented separately and referenced earlier in the text.\nL577: \"anomalies\" should be clarified—anomalies relative to what?\nL579: Use consistent notation for '|bx|'—is it b_x or B_x?\nL587: Provide the definition of R_x.\nL590: Clarify \"position relative to the eddy\" as being either inside or outside relative to the eddy’s core.\nFigures and captions:\nFigure 1 (L288, L291, L295):\n- Blue dots on the blue background are hard to see; change the color of the background or the dots.\n- Provide full forms of SST, CHL, and FSLE for clarity.\n- Orange dots on the red background are difficult to see.\n- In panel c, showing a vertical section of temperature and salinity from the gliders (even in the supplementary material) would be helpful.\nFigure 2 (L306):\n- The notation for \"Bx\" seems inconsistent. Check whether \"Bx,\" \"B_x,\" \"b_x,\" and \"bx\" are mixed up.\nFigure 3 (L321):\n- The panel order in the caption is inconsistent. Either follow alphabetical order or change the panel layout for clarity.\n- Consider separating the left and right groups of panels with space and make the variables (Strain, Ri, SSTa) more prominent on the right.\n- The definition of \"R\" as the normalized radius of the eddy is unclear. Is R the point where azimuth velocity becomes maximal?\n- The notation for \"N\" and \"N*\" in panels a and b should be changed to avoid confusion with buoyancy frequency.", "reviewer_3": "The study uses glider observations near eddies to investigate vertical heat transport (VHT) driven by submesoscale processes down to 400 meters, with claims that this deep-reaching VHT warms the upper ocean and contributes to warm eddy rings. While the topic is promising, the manuscript currently suffers from significant issues in methodology, theoretical foundation, and dynamical interpretation. The authors seem to have limited experience with glider observations and an incomplete understanding of geophysical fluid dynamics, especially concerning high-frequency, small-scale ocean processes. Given these gaps, I believe that substantial portions of the study should be restructured, potentially with greater reliance on model results for a more reliable analysis.\nIn its first part, the study largely repeats findings from Siegelman et al. (2020), employing similar data but in a different region, with fewer mechanisms discussed. Scientific innovation diminishes when a concept is reiterated without substantial new insights; hence, this section lacks impact. The second part includes a composite analysis describing “warm rings” within eddies, a feature well-documented in previous literature. Although the authors attribute these rings to submesoscale VHT, there is no direct evidence linking the rings specifically to submesoscale rather than mesoscale dynamics, making the analysis questionable.\nA critical flaw of the method is the observing platforms. In the past two decades, observations using gliders do improve the observation skills especially about meso- and smaller-scale physics. Gliders may observe mesoscale features, but gliders, with a slow movement of approximately 10 km/day, cannot adequately resolve lateral submesoscale features. As established by Rudnick and Cole (2011, doi:10.1029/2010JC006849), the Doppler smearing and aliasing effects in glider data lead to significant errors in the submesoscale range, particularly in stratified layers. I think the author need to carefully go through this paper before working on this study. In fact, Studies typically use gliders for vertical profiles or along-isopycnal analyses, or in networked arrays to address resolution issues (e.g., Rudnick et al. 2022, doi:10.1175/JPO-D-21-0181.1). Consequently, I find the buoyancy gradients presented in Fig. 1e unreliable, which casts doubt on the Richardson number (Ri) and vertical velocity (w) estimates. The results of VHT are quite questionable unless the authors can demonstrate that the smearing and aliasing effects have limited impacts. As suggested in the recent several field campaigns these years, observations using onboard towed bodies (with ship speed >6 knots) are preferable to minimize such errors, although this is challenging.\nWhat do you mean by 3D view of vertical velocity (Line 161 and Fig. 4). The results are just presented without any clear interpretation. The results lack clear interpretation, and it’s unclear if they include submesoscale effects. If they do, this would be unexpected. If derived from composite fields, these vertical velocity estimates are likely inaccurate. Using composite eddy fields to infer ageostrophic processes is misleading, as this approach fails to capture true dynamics. It’s important to note that the composite field approach is essentially a method to illustrate the general features of the eddy and should not be used to quantify submesoscale characteristics. Composite fields average over time and space, which tends to smooth out smaller-scale variations and can misrepresent the true intensity and structure of submesoscale processes. Therefore, using composite fields to infer submesoscale dynamics is not methodologically sound and likely introduces significant inaccuracies.\nAdditionally, the role of mesoscale contributions to VHT is underrepresented. Mesoscale processes likely contribute substantially to VHT, especially in an averaged context, and should be acknowledged.\nMore calibration details on the glider data are needed, especially given the extended observation period.\nThe sentence on Line 157, “When the scale across the front is compressed to a critical point, geostrophic balance is no longer maintained. By breaking the geostrophic balance that suppresses vertical motions, the fronts support vertical velocities of up to 60 m day⁻¹ below the surface mixed layer,” is confusing. The breakdown of geostrophic balance typically increases vertical motions via non-geostrophic terms, rather than suppressing them.\nIn summary, the findings presented here are largely redundant with existing literature or are based on analysis and interpretation that lack sufficient rigor. The data-supported results largely replicate previously reported findings, while the remaining conclusions appear to stem from a lack of careful interpretation and logical coherence. This leaves an impression of incomplete novelty and unsound analytical approaches within the study."}, "author_response": ""}, {"round": 2, "reviewer_comments": {"reviewer_1": "I think the authors has done a perfect work in revising the manuscript and it is now ready for publication.", "reviewer_2": "Please refer to the separately uploaded letter for the comments.\n[Editorial Note: This letter has been appended to the end of this file]", "reviewer_3": "I appreciate the substantial revisions made in this version of the manuscript. The authors have addressed some of my previous concerns; however, several major issues remain unresolved. These concerns are critical and may introduce significant uncertainties in the results presented.\n1. On the novelty of the findings. While the authors continue to emphasize a connection between warm rings and mesoscale eddies, the core of the study essentially reflects enhanced vertical heat transport at oceanic fronts, as comprehensively addressed in Siegelman et al. (2020) and Cao et al. (2024) where similar dynamics and methodologies are presented. By the way, I think wrong citation for Cao et al. (2024) is listed in the reference. Upon revisiting these two references, I find that both the underlying dynamics and diagnostic methods have already been thoroughly explained in the existing literature. The current manuscript does not appear to introduce substantial new insights beyond these established findings. Although the authors attempt to highlight the elevated values of vertical heat transport (VHT), this alone does not convince me as a significant novelty, especially considering that these values may be overestimated, as discussed below.\n2. Concerns regarding data contamination. The issue of potential data contamination remains insufficiently addressed. While the authors have now described stricter data quality control procedures and implemented a 10-km smoothing filter to mitigate aliasing and smearing effects, there is no clear evidence demonstrating the effectiveness of this approach. A straightforward way to validate the impact of filtering may be to compare the wavenumber spectra before and after applying the filter. Based on my own experience with glider data, this method is unlikely to fully resolve contamination at submesoscales. It appears the authors may have misunderstood the findings of Rudnick et al. (2011): the primary limitation arises from the slow pace of gliders, not the quality of the sensors. Temporal and spatial glider motion can cause substantial aliasing from internal waves, limiting the reliable resolution of submesoscale variability. While gliders are valuable tools for oceanographic observations, their use in submesoscale studies carries inherent challenges that must be more carefully considered here.\n3. Concerns about composite analysis methodology. I continue to believe that the composite analysis employed is misleading. The mesoscale eddy structures included are highly variable, and their differences cannot be adequately captured by composite means. Critically, the strength and structure of fronts appear to be the primary drivers of VHT, as shown in Siegelman et al. (2020). These frontal characteristics are in turn influenced by external forcing, background flow, and possibly eddy–eddy interactions. The manuscript does not sufficiently define or justify how azimuthal variability is treated or interpreted across the ensemble of eddy cases. Given this heterogeneity, I strongly recommend that the authors instead present representative vertical sections from selected cases, which would offer a more physically meaningful and interpretable analysis."}, "author_response": "Response to Review Comments for\n“Warm Rings in Mesoscale Eddies in a Cold Straining Ocean”\nHuizi Dong, Meng Zhou, James C. McWilliams, Roshin P. Raj, Francesco d’Ovidio, Ilker Fer, Lixin\nQu, Bo Qiu, Lia Siegelman, Zhengguang Zhang, Walker O. Smith, Jr., Ann Kristin Sperrevik\nNote: Reviewer’ comments are in italic font; authors’ response comments are in normal font.\nRevisions in the revised manuscript are highlighted. Figs. 1–6 are presented in the revised main\nmanuscript; Figs. S1–S9 are included in the Supplementary Information; and Figs. R1–R2 are\nprovided in this response document.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nThe manuscript describes the vertical heat transport at the skirts of mesoscale cyclones and\nanticyclones, suggesting a unified mechanism of upwelling-downwelling system. The mechanism\nsuggested consists in an ageostrophic cross-front motion of fluid parcels of different direction at\nthe upper and lower levels, which induces upwards/downwards vertical motions along the\nboundaries of the mesoscale eddies. These motions were suggested to be formed (or intensified?)\nepisodically during the periods of an increased strain at the eddy boundaries, which, in turn, were\na result of mesoscale eddy interactions with submesoscale structures. The resulting heat flux is\nspeculated to be responsible for formation of the observed warm-core rings around both cyclones\nand anticyclones, as well as for enhancing the resulting heat flux from the ocean to the atmosphere.\nThe study is based on high-resolution Seaglider data in the Lofoten Basin, combined with the\nsatellite altimetry data and high-resolution SST data. Eddies were derived by a threshold method\nusing the value of Okubo-Weiss parameter in the closed SLA. Although this method is not optimal,\nit allows detecting strong mesoscale eddies at the sea-surface.\nThe authors present a novel concept, which is supported with observations. The manuscript\nrepresents an interesting study and is well written. I recommend publication after minor\nmodifications.\n1) The explanation of the mechanism is vague. More details on how the sharpening of the front\nresult in ageostrophic vertical motions would be beneficial. Are there any theoretical estimates on\nthe intensity of such process? These can be compares with the derived vertical velocities.\nResponse: We appreciate the comments and suggestions made by the reviewer. To address the\nconcern regarding the previously vague explanation of how frontal sharpening leads to ageostrophic\nvertical motions, we have made the following improvements:\n• The original unclear statements have been modified to “As the cross-front scale is compressed\nby the strain field, frontogenesis intensifies, increasing the buoyancy gradient and ultimately\ndisrupting the thermal wind balance. To restore this balance, an ageostrophic secondary\ncirculation develops, characterized by …” in Lines 171-176 of the revised manuscript.\n• We have been clarified the explanation “This occurs because, irrespective of being cyclonic or\nanticyclonic, the submesoscale secondary circulations act to flatten sloping isopycnals at the\nfronts, thus restoring stratification…” in Lines 207-210 of the revised manuscript.\n• The original sentences have been modified to “This is attributed to frontogenesis, whereby\nstrong geostrophic strain intensifies lateral buoyancy gradients along the eddy edges…” in\nLines 231-233 of the revised manuscript.\nIn response to the reviewer’s suggestion regarding theoretical estimates of this process and their\ncomparison with observed vertical velocities:\n• We have added a section \"Quasi-geostrophic frontogenesis theory and vertical velocity\" to the\nSupplementary Information (Lines 33–69).\nThere are also two additional points, which might be noted in the manuscript.\n2) The authors should also mention, that the suggested mechanism is not the only one which can\nform such warm-ring structures. Another mechanism, acting in particular for undersurface\nanticyclones is trapping of a warmer water and wrapping it around the eddy center. In particular,\nthis was observed for surface manifestation of meddies and the Lofoten Vortex – see Bashmachnikov\net al., 2013. Manifestation of two meddies in altimetry and sea-surface temperature;\nBashmachnikov et al., 2018. Pattern of vertical velocity in the Lofoten vortex (the Norwegian Sea.\nThis forms far larger SST anomalies around eddies compared to 0.4oC (only slightly above on the\nlimit of accuracy of the IK SST sensors) of the mechanism suggested by the authors.\nResponse: We agree with the reviewer that submesoscale motions are not the only mechanism for\nthe formation of warm ring structures. We have incorporated the suggested essential contents in\nLines 275-285 and Lines 292-300 of the revised version. Additional mechanisms related to warm\nrings and mesoscale vertical motions have also been supplemented in the main text and\nSupplementary Information.\nTo further clarify for the reviewer the critical role of submesoscale vertical motions at eddy edges\nin the northern Norwegian Sea, which is our area of interest, we would like to provide a\nsupplementary case analysis from an alternative perspective. Fig. R1 presents an additional case\nstudy based on Seaglider data from May 2017. This section was specifically chosen because the\nSeaglider crossed the edge of the same anticyclonic eddy three times during the one-month period\n(Fig. R1b). Corresponding nutrient and chlorophyll profile observations (Fig. R1a,b), obtained from\nthe NMDC database1 (https://doi.org/10.21335/NMDC-1271328906) during the same period,\nallowed us to analyze vertical transport patterns at both eddy-edge and non-edge regions.\nThe observations revealed pronounced lateral buoyancy gradients and strong vertical velocities at\nthe eddy edges, which facilitated enhanced upward transport of nutrients (e.g., nitrate, silicate)\ninto the surface layer. The increased surface nutrient concentrations subsequently led to elevated\nchlorophyll-a concentrations, providing indirect but compelling evidence of intensified\nsubmesoscale-driven vertical exchange at the eddy edges (Figs. R1g–i).\nSimilar results from additional cases involving both anticyclonic and cyclonic eddies (Fig. R2b–c)\nconsistently show that submesoscale vertical circulation at eddy edges significantly enhances\nnutrient availability and productivity relative to eddy interiors and external waters. This body of\nevidence collectively demonstrates that submesoscale-driven vertical transport mechanisms play a\ndominant role in the formation of warm-ring structures at eddy edges.\nFig. R1 | Characteristics of submesoscale motions of anticyclonic eddy edges and their impacts on\nvertical nutrient distribution. a SLA and b FSLE fields overlaid with the Seaglider track from 7 May\n2017 to 2 June 2017. The Seaglider traveled approximately 450 km from inside the anticyclonic eddy\n(point S1 in panel a) to outside the eddy (point S2), with measurements shown in panels c-g. The glider’s\nvertical sections show c buoyancy, d lateral buoyancy gradient (Bx), e vertical velocity (w) and f\nRichardson number (Ri). The mixed layer depth (MLD) is shown by a thick black line in c-f. Yellow and\ngreen stars in panels a and b represent BGC stations at the eddy edge and non-edge locations, respectively,\non 22 May 2017. g-i Vertical profiles of nitrate, silicate and chlorophyll-a (CHL-a) concentrations, where\nred lines represent profiles at the eddy edge station (yellow star in panel a) and black lines show profiles\nat the non-edge station (green star).\nFig. R2 | Vertical distribution of nutrients and chlorophyll in edge and non-edge regions of\ntwo anticyclonic eddies and one cyclonic eddy. a-c FSLE and SLA fields for three mesoscale eddy\ncases on a 22-May-2017, b 13-June-2022, and c 23-July-1995, overlaid with BGC stations at the\neddy edge (yellow stars) and non-edge locations (green stars). d-f Vertical profiles of nitrate, silicate\nand chlorophyll-a (CHL-a) concentrations, where red and blue lines represent profiles at the eddy\nedge station (yellow stars in panels a-c) and black lines show profiles at the non-edge station (green\nstars in panels a-c).\n3) The vertical velocities at the eddy boundaries, suggested by the authors (Figure 6b), do not fully\nmerge with the vertical velocity structure in the Lofoten Vortex, derived using MIT model in the\npaper cited above. In the Lofoten Vortex the upwelling was dominating all the central part of the\nvortex and downwelling was observed at its outer skirt, but these motions were characteristics only\nat the level of the well mixed eddy core, intensifying towards the sea-surface. The driving mechanism\nwas suggested to be also linked to a high strain at the eddy boundary, which increases towards the\nsea-surface. The resulting decay of kinetic energy form in the upper ocean an inverse secondary\ncirculation, similar by nature to the one formed by the bottom Ekman boundary layer (see also Bosse\net al., (2019) Dynamical controls on the longevity of a non-linear vortex: The case of the Lofoten\nBasin Eddy,). This is another effect the strain, and the resulting vertical pattern should merge with\nthe one suggested in the manuscript. Both mechanisms should form increase their intensity towards the sea-\nsurface, where the largest energy (straining) of submesoscale is expected. This can be discussed and noted at the sketch in Figure 6b.\nResponse: We agree with the reviewer that the circulation pattern of the LBE is indeed driven by\nmultiple mechanisms. As the reviewer noted, due to differences in model resolution, the vertical\nvelocity structure at the eddy edges in our study differs from that derived from the 4 km-resolution\nMITgcm model used by Bashmachnikov et al. (2018). Bashmachnikov et al. successfully\nreproduced the radius and depth of the LBE and described vertical velocity patterns both within and\naround the LBE. Our higher-resolution Seaglider observations (horizontal resolution of\napproximately 1–4 km, averaging ~2 km at eddy edges) build upon this work by providing a more\ndetailed view of finer-scale vertical dynamics, especially the strong lateral buoyancy gradients and\nintensified strain at the eddy edges. Specifically, the vertical velocities we observed within the eddy\ninteriors were consistent with those reported by Bashmachnikov et al., while the velocities at the\neddy edges were one to two orders of magnitude higher. Thus, while multiple mechanisms\ncontribute to the LBE circulation, our results suggest that submesoscale processes play a particularly\nprominent role in vertical transport.\nTo further clarify the relative contributions of submesoscale and mesoscale processes, we have\nadded a section titled “Comparison between mesoscale and submesoscale VHT” in the\nSupplementary Information (Lines 148–177 of the revised manuscript). Bosse et al. (2019) similarly\nhighlighted that the 4-km-resolution numerical model underestimated the maximum azimuthal\nvelocity and core vorticity, suggesting that submesoscale processes could be significant at eddy\nedges, thus requiring higher-resolution simulations. To address this, we have strengthened our\nanalysis using the high-resolution Norkyst-DA model (2.4 km horizontal resolution) in the revised\nversion. Two case studies from this model demonstrate similarly strong vertical velocities at eddy\nedges (Lines 152-158). Furthermore, composite analysis of model outputs (2017-2019) reveals that\nintense submesoscale VHT predominantly occurs at eddy edges, while mesoscale VHT, though\nmore widely distributed, is approximately an order of magnitude weaker. Even without accounting\nfor net heat fluxes, mesoscale VHT magnitude represents only about 1/6 to 1/5 of the submesoscale\ncontribution (see \"Numerical simulation verification\" section in the Supplementary Information).\nRegarding the reviewer's suggestion to add annotations to Fig. 6, considering that our study focuses\nnot only on the LBE but also on eddies across the eastern basin and continental slope regions (Fig.\n1a), we chose to include the suggested clarifications in the main text (Lines 277-286 and 292-300)\nrather than modifying Fig. 6. This approach preserves the schematic's broad applicability regarding\nsubmesoscale secondary circulations at eddy edges as presented in Fig. 6.\nMinor comments:\n49-50 “The North Atlantic Current is an important part of the oceanic conveyor belt that transports\nheat from the equator to the poles.” The NAC, as well as the Global Conveyor, does not reach the\npols – please rephrase.\nResponse: Following the reviewer’s suggestion, we have revised the text to ‘The North Atlantic\nCurrent is an important part of the oceanic conveyor belt that transports heat from the equator\nto the high latitudes’ in Lines 51-52 of the revised manuscript.\n51-53 “the Atlantic Water experiences substantial heat loss to the atmosphere, which is thought to\nbe the main driver of the transformation of Atlantic Water” - one may also see Dugstad et al (218)\n“Lateral Heat Transport in the Lofoten Basin: Near-Surface Pathways and Subsurface Exchange”\nand Bashmachnikov et al., 2023 “Heat transport by mesoscale eddies in the Norwegian and\nGreenland seas” on the role of mesoscale eddies in regulating the AW transport across the Lofoten\nBasin.\nResponse: We have revised the text to ‘the Atlantic Water undergoes transformation driven by both\nsubstantial heat loss to the atmosphere4,5 and lateral heat transport through mesoscale eddies6,7’ in\nLines 54-55 of the revised version. The suggested references have been added accordingly in the\nrevised version.\n53-55 “This process significantly impacts the hydrographic environment, sea ice cover and\necosystems in the region and ultimately the Arctic Ocean” – What process from the mentioned above?\nThe impact of AMOC on SST in the Nordic Seas is nonlinear and involves the atmospheric response\nto the ocean heating (Bengtson et al., 2004 “The Early Twentieth-Century Warming in the Arctic—\nA Possible Mechanism”, Shaffrey and Sutton, 2006 “Bjerknes Compensation and the Decadal\nVariability of the Energy Transports in a Coupled Climate Model”)\nResponse: We have revised the text to ‘This transformation of Atlantic Water significantly impacts\nthe hydrographic environment, sea ice cover, and ecosystems in the region and ultimately the Arctic\nOcean’ in Lines 55-57 of the revised version.\ncitations are Kohl 2007 “Generation and stability of a quasi-permanent vortex in the Lofoten\nBasin”, Bosse et al., (2019) Dynamical controls on the longevity of a non-linear vortex: The case\nof the Lofoten Basin Eddy, Santieva et al., 2021 “On the stability of the Lofoten Vortex in the\nNorwegian Sea”\nResponse: We have updated Line 64 with the more appropriate citations (Kohl et al., 2007; Bosse\net al., 2019; Santieva et al., 2021) in the revised version.\nResponse: We agree with the reviewer that the term ‘critical point’ was ambiguous. We have\nexpanded the paragraph as follows: “As strain fields compress the front, the cross-frontal buoyancy\ngradient intensifies and the cross-frontal scale decreases, driving frontogenesis and increasing the\navailable potential energy at the front. When the local Rossby number (R = ζ/f) approaches O(1),\no\nthermal wind balance becomes disrupted, triggering ageostrophic secondary circulations that act to\nrestore this balance. These circulations generate upwelling on the warm (light) side and\ndownwelling on the cold (heavy) side of the front.” in Lines 250-256 of the revised manuscript.\n165-166 “further indicating the presence of a cross-frontal secondary circulation” - Small Ri does\nnecessarily mean enhanced vertical velocities. The facilitated Kelvin-Helmholtz instability does not\nrequire the cross-frontal exchange.\nResponse: We appreciate the reviewer's comments, which highlight an important clarification. Here,\nwe calculated the geostrophic Richardson number (Ri= f 2N2/ b 2), which characterizes the stability\nx\nof the thermal wind balance under intensified buoyancy gradients (frontogenesis). A low\ngeostrophic Ri value indicates that the thermal wind balance is disrupted by strong lateral buoyancy\ngradients, thereby directly facilitating the development of cross-frontal ageostrophic secondary\ncirculations. We have clarified this in the manuscript (Lines 197-201) and included the formula\nwhen Ri is first mentioned (Line 133) in the revised manuscript.\nshear?\nResponse: The sentence has been revised in Lines 198-201 to read “These results are consistent\nwith the expectation that geostrophic strain shrinks the frontal scale and intensifies lateral buoyancy\ngradients, disrupting thermal wind balance and thereby promoting cross-frontal secondary\ncirculations in the frontal zone.”\nResponse: We have revised the text to use the full term “Lagrangian Coherent Structure” rather\nthan its abbreviation in Lines 242-243 of the revised version.\n212-216 “the scale across the front becomes small enough and the geostrophic balance can no\nlonger be maintained” What do you mean by “small enough”? Less than Rossby radius of\ndeformation? How this decreasing the cross-front scale affects the geostrophic balance?\nResponse: We thank the reviewer for point this out and have revised the original sentence “As strain\nfields compress the front, the cross-frontal buoyancy gradient intensifies and the cross-frontal scale\ndecreases, driving frontogenesis and increasing the available potential energy at the front. When the\nlocal Rossby number (Ro = ζ/f) approaches O(1), thermal wind balance becomes disrupted,\ntriggering ageostrophic secondary circulations that act to restore this balance” in Lines 250-255 of\nthe revised manuscript.\n545-547 Ri characterizes stability of the vertically sheared flow. Ri>>1 means that Kelvin-\nHelmholtz instability cannot be generated. I do not see the direct relation between Ri and\ngeostrophic-ageostrophic separation, which is basically linked to the Rossby number.\nResponse: We appreciate the reviewer’s comment. We clarify here that the Ri used in our study is\nthe geostrophic Richardson number (Ri = f 2N2/ b 2) , which is derived from the conventional stability\nx\nformulation for vertically sheared flows (Ri = N²/(∂v/∂z)²) through the thermal wind relation. Unlike\nthe traditional Ri, which characterizes vertical shear instability, this geostrophic Ri directly\ncharacterizes the disruption of thermal wind balance due to intensified lateral buoyancy gradients.\nTherefore, low geostrophic Ri values indicate conditions favorable for ageostrophic secondary\ncirculations associated with frontogenesis, closely linked to increased Rossby numbers.\nWe have clarified this distinction in the revised manuscript (Lines 610–622). Additionally, to avoid\nany confusion, we have consistently used the term \"geostrophic Richardson number\" throughout the\nmanuscript.\nReferences\n1. Ailin Brakstad, Kjetil Våge (University of Bergen, Norway), Sólveig Rósa Ólafsdóttir (Marine and\nFreshwater Research Institute, Iceland), Emil Jeansson (NORCE Norwegian Research Centre,\nNorway), and Geoffrey Gebbie (Woods Hole Oceanographic Institution, USA) (2023) Hydrographic\nand geochemical observations in the Nordic Seas between 1950 and 2019\n2. Bashmachnikov, I., Belonenko, T., Kuibin, P., Volkov, D., & Foux, V. Pattern of vertical velocity in\nthe Lofoten vortex (the Norwegian Sea). Ocean Dyn. 68, 1711–1725 (2018).\n3. Bashmachnikov, I.I., Boutov, D.D., & Dias, J.J. Manifestation of two meddies in altimetry and sea-\nsurface temperature. Ocean Sci. 9, 249–259 (2013)\n4. Bosse A., Fer I., Lilly J. M. & Søiland H. Dynamical controls on the longevity of a non-linear vortex:\nThe case of the Lofoten Basin Eddy. Sci. reports 9, 13448 (2019).\n5. Kohl, A. Generation and stability of a quasi-permanent vortex in the Lofoten Basin. J. Phys.\nOceanogr. 37, 2637–2651 (2007).\n6. Santeva, E.K., Bashmachnikov, I.L. & Sokolovskiy, M.A. On the Stability of the Lofoten Vortex in\nthe Norwegian Sea. Oceanology 61, 308–318 (2021)."}, {"round": 3, "reviewer_comments": {"reviewer_3": "Many of previous have examined vertical heat transport associated with submesoscale processes near the fronts using both models and observations. The topic is not new. As highlighted by the authors, the main novelty of this manuscript lies in the duration of the dataset and the quantification of VHT. However, the glider observations employed here are inherently limited in their ability to accurately resolve submesoscale dynamics, due to thier sampling technique. This limitation introduces substantial uncertainties in studying submesoscales, which are not adequately addressed in the current study. In addition, Many of the assumptions used in this study lack justification, significantly undermining the reliability of the conclusions.\nIn this revision, the authors have presented some additional analyses in response to my earlier concerns. However, these additions do not fully resolve the issues I raised. It is important for the authors to recognize that glider data have been available for over two decades, and yet they are seldom used to study submesoscale dynamics. Despite the apparent presence of submesoscale features, the slow sampling rate of gliders introduces significant contamination, particularly at scales below 30 km, often resulting in large errors, typically overestimations.\nI carefully reviewed the method proposed by the authors to mitigate this contamination, which involves smoothing the isopycnal depths. This approach is interesting and does reduce spectral variance substantially almost at all scales and especially at smaller scales. However, assuming the method is effective, the manuscript does not show any significant change in results. In this point, I seriously question the authors’ academic rigor. The response appears more focused on persuading the reviewer than on demonstrating robust, justified scientific results.\nMoreover, the application of a 10-km low-pass filter inevitably removes a substantial portion of the submesoscale signal. why a 10-km threshold is used? Reconstructing T and S fields based on smoothed isopycnal surfaces does not guarantee the removal of internal wave signals. The approach seems functionally similar to applying a 25-hour temporal smoothing, which also reduces internal wave influence but does not eliminate contamination from aliasing. This would also remove high-frequency submesoscale motions. In this way, the primary effect appears to alter the buoyancy gradient and T’, both of which are critical to the estimation of VHT. If the authors are confident in the validity of their approach, I recommend they simulate glider sampling using model output to test its reliability. From experience, such simulations often yield results that diverge considerably from expectations.\nOnce again, I insist that the composite-based quantification of submesoscale-driven VHT presented here is definitely misleading when based on glider data. In reality, gliders may move at speeds comparable to mesoscale eddies, capturing only a limited and potentially unrepresentative portion of the eddy structure, let alone the submesoscale variability. The analysis relies on the assumption that mesoscale eddies are stationary and steady, which is not entirely accurate. While such an assumption may be acceptable for identifying general eddy structures, it is not appropriate for quantifying specific variables like submesoscale-driven VHT. With the advent of new satellite missions like SWOT, we are beginning to observe significant asymmetries in mesoscale eddies, suggesting that many conventional assumptions may be ill-used and could lead to large errors in quantification. It is not a good time to go back.", "reviewer_4": "The manuscript titled “Warm Rings in Mesoscale Eddies in a Cold Straining Ocean” provides a well written report on submesoscale heat transport in the Lofoten Basin and reveals novel insights into the dynamical regimes present. The results have been presented in a clear and concise manner, and the analysis is of a sound standard. The primary purpose of my review is to provide additional guidance on the whether concerns raised by Reviewer 3 have been sufficiently addressed. I believe these points have been largely resolved, but minor deficiencies remain in the discussion of smearing and aliasing effects. My review reflects on the response to each of Reviewer 3’s points in turn, followed by two additional (minor) suggestions.\nPoint 1 – The authors raise valuable points in response to the assertion that the manuscript lacks novelty and I believe the paper is of significance to the field. However, the narrative in some places leads the reader to conclude that the present study is the first of its kind, when the headline result is building on that of Siegelman et al. (2020). Although not critical for publication, some minor changes to the text may help differentiate the manuscript’s novel findings from that of existing literature. My main recommendations are that (1) the study’s isolation of the cyclonic and anticyclonic contributions to submesoscale vertical heat transport is made clearer on lines 106-108 and (2) the framing of the text between lines 284-290 is refined to acknowledge that submesoscale heat fluxes in regions of strain has been identified in previous studies.\nPoint 2 – The authors have made considerable efforts to respond to the Reviewer 3’s concern on data contamination. In my view, their expansion of the analysis to compare spectral decompositions and analysis of the impact of isopycnal filtering sufficiently addresses the reviewers concern around the lack of transparency in qualifying the use of glider observations for the manuscript’s purposes. Results showing that fine-scale features remain in the buoyancy gradient and vertical velocity fields upon isopycnal filtering is sufficient indication that these are associated with submesoscale dynamics. The authors have taken on board the reviewer’s suggestions, but in the process have omitted a key distinction between smearing and aliasing that would aid their case. For example, line 305 quotes “Doppler aliasing” when this should be “Doppler smearing”. As outlined by Rudnick et al. (2011), aliasing is a function of sampling rate and Doppler smearing is associated with the speed that the observing platform travels through the water. As a minimum, I would recommend that a distinction is made in the text between the source of aliasing and smearing, and that the authors are careful not to use the terms interchangeably. Furthermore, though not necessary for publication, it could benefit the manuscript to cite the relevant length and spatial scales associated with these effects (e.g., Rudnick et al., 2011). It is possible to estimate the spatial- and temporal-scales upon which smearing and aliasing act, and the sampling intervals cited in the supplementary material indicate there may be limited aliasing at the submesoscale in the observations in question.\nPoint 3 – The authors have performed the additional analysis requested by Reviewer 3 regarding the composite analysis and their concerns have been addressed to a satisfactory level. Despite significant non-uniformity in eddy structure, the composite analysis appears to provide a robust measure of the alignment between vertical heat transport and strain.\nAdditional Suggestions\nThe sentence starting “The rotational flow…” on lines 279-282 is difficult to interpret. As far as I can tell, the intention is to convey that eddies can advect water masses. Since this is already stated in the previous sentence, I would suggest this sentence is removed. In addition, Reference 35 does not appear to have relevance to the claims made and, should the sentence remain, I would suggest reviewing whether this citation is appropriate.\nLine 287 currently reads “eddy eddies”. Should this be “eddy edges”?\nI hope this feedback is received as constructive and I look forward to seeing the work published, should that be the final decision.\nKind Regards,\nDr. R. D. Patmore (NOC, Liverpool, UK)"}, "author_response": "1 3rd Response to Review Comments for\n2 “Warm Rings in Mesoscale Eddies in a Cold Straining Ocean”\n6\n9\n10\n12\n14\n16 well written report on submesoscale heat transport in the Lofoten Basin and reveals novel insights\n17 into the dynamical regimes present. The results have been presented in a clear and concise\n18 manner, and the analysis is of a sound standard. The primary purpose of my review is to provide\n19 additional guidance on the whether concerns raised by Reviewer 3 have been sufficiently\n20 addressed. I believe these points have been largely resolved, but minor deficiencies remain in the\n21 discussion of smearing and aliasing effects. My review reflects on the response to each of\n23\n25 their assessment that the previous concerns have been largely resolved and appreciate the clear\n26 suggestions for the remaining minor but important issues. We have addressed all the points below.\n27\n29 novelty and I believe the paper is of significance to the field. However, the narrative in some\n30 places leads the reader to conclude that the present study is the first of its kind, when the headline\n31 result is building on that of Siegelman et al. (2020). Although not critical for publication, some\n32 minor changes to the text may help differentiate the manuscript’s novel findings from that of\n33 existing literature. My main recommendations are that (1) the study’s isolation of the cyclonic and\n34 anticyclonic contributions to submesoscale vertical heat transport is made clearer on lines\n35 106-108 and (2) the framing of the text between lines 284-290 is refined to acknowledge that\n36 submesoscale heat fluxes in regions of strain has been identified in previous studies.\n37\n1\n39 highlight the isolation and comparison of VHT in cyclonic and anticyclonic eddies. The revised\n40 text now reads (lines 106-111):\n41 “Building on this intriguing observation, a key novelty of our study is the isolation and\n42 comparison of VHT in both cyclones and anticyclones. We investigate how deep-reaching\n43 submesoscale motions drive a systematic upward heat flux along their respective edges, providing\n44 a dynamical explanation for the \"warm ring\" phenomenon in a comparative context that has been\n45 largely overlooked.”\n46\n48 heat fluxes. The new text is as follows (lines 284-292):\n49 “However, while these lateral transport processes remain important, previous work has identified\n50 enhanced submesoscale heat fluxes in strain-dominated regions23. Building upon this, our study\n51 reveals that within mesoscale eddies, vertical transport is largely governed by submesoscale\n52 ageostrophic motions along both cyclonic and anticyclonic edges (Supplementary Information and\n54 strain-dominated areas around eddies, serving as a crucial pathway for the vertical exchange of\n55 heat and energy between the ocean interior and the surface.”\n56\n58 data contamination. In my view, their expansion of the analysis to compare spectral\n59 decompositions and analysis of the impact of isopycnal filtering sufficiently addresses the\n60 reviewers concern around the lack of transparency in qualifying the use of glider observations for\n61 the manuscript’s purposes. Results showing that fine-scale features remain in the buoyancy\n62 gradient and vertical velocity fields upon isopycnal filtering is sufficient indication that these are\n63 associated with submesoscale dynamics. The authors have taken on board the reviewer’s\n64 suggestions, but in the process have omitted a key distinction between smearing and aliasing that\n65 would aid their case. For example, line 305 quotes “Doppler aliasing” when this should be\n66 “Doppler smearing”. As outlined by Rudnick et al. (2011), aliasing is a function of sampling rate\n67 and Doppler smearing is associated with the speed that the observing platform travels through the\n68 water. As a minimum, I would recommend that a distinction is made in the text between the source\n69 of aliasing and smearing, and that the authors are careful not to use the terms interchangeably.\n71 relevant length and spatial scales associated with these effects (e.g., Rudnick et al., 2011). It is\n72 possible to estimate the spatial- and temporal-scales upon which smearing and aliasing act, and\n73 the sampling intervals cited in the supplementary material indicate there may be limited aliasing\n74 at the submesoscale in the observations in question.\n75\n2\n77 smearing and aliasing. Accordingly, we have replaced the term “Doppler aliasing” with the correct\n78 “Doppler smearing” (lines 309–310 of the revised version).\n79\n82 (2011). The revised text now reads:\n83 “A key challenge in using glider data for submesoscale studies is potential contamination from\n84 high-frequency oceanic phenomena like internal waves, which manifests as two distinct effects:\n86 through the water (~0.2 m/s) and manifests as a smearing of the true wave number and\n87 frequency10. In contrast, aliasing is a function of the sampling rate, which causes variability from\n88 higher wave numbers to be folded into the resolved lower wave numbers10.”\n89\n91 the composite analysis and their concerns have been addressed to a satisfactory level. Despite\n92 significant non-uniformity in eddy structure, the composite analysis appears to provide a robust\n93 measure of the alignment between vertical heat transport and strain.\n94\n96\n98\n100 can tell, the intention is to convey that eddies can advect water masses. Since this is already stated\n101 in the previous sentence, I would suggest this sentence is removed. In addition, Reference 35 does\n102 not appear to have relevance to the claims made and, should the sentence remain, I would suggest\n103 reviewing whether this citation is appropriate.\n104\n106\n108\n110 version.\n111\n113 should that be the final decision.\n114\n3"}, {"round": 4, "reviewer_comments": {"reviewer_4": "My previous concerns have been addressed to a satisfactory level and I have no further feedback for the authors. I appreciate their efforts to improve the manuscript."}, "author_response": ""}]

Decision letter