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# Characteristics of Mesoscale-to-Submesoscale Eddies in the Labrador Sea: Insights from Ship Observations

Arne Bendinger, Ahmad Fehmi Dilmahamod, Aurélie Albert, Julien Le Sommer, Johannes Karstensen

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## To cite this version:

Arne Bendinger, Ahmad Fehmi Dilmahamod, Aurélie Albert, Julien Le Sommer, Johannes Karstensen. Characteristics of Mesoscale-to-Submesoscale Eddies in the Labrador Sea: Insights from Ship Observations. Journal of Physical Oceanography, 2025, 55 (11), pp.2037-2057. 10.1175/JPO-D-24-0216.1. hal-05412229

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Submitted on 14 Dec 2025

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Characteristics of Mesoscale-to-Submesoscale Eddies in the Labrador Sea: Insights from Ship Observations

ARNE BENDINGER<sup>a</sup>,<sup>a</sup> AHMAD FEHMI DILMAHAMOD<sup>b</sup>,<sup>a</sup> AURÉLIE ALBERT<sup>b</sup>,<sup>b</sup> JULIEN LE SOMMER<sup>b</sup>,<sup>b</sup>
AND JOHANNES KARSTENSEN<sup>a</sup>

<sup>a</sup> GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany

<sup>b</sup> Université Grenoble Alpes, CNRS, INRAE, IRD, Grenoble INP, Institut des Géosciences de l'Environnement, Grenoble, France

(Manuscript received 23 October 2024, in final form 28 July 2025, accepted 20 August 2025)

**ABSTRACT:** Characterization of coherent eddies is often based on gridded satellite altimetry products. In subpolar regions, these products face limitations due to their low spatial resolution and the decreasing Rossby radius of deformation at higher latitudes, making in situ observations indispensable for eddy characterization. Here, we present a census of mesoscale-to-submesoscale eddy characteristics in the Labrador Sea—a region where eddies play an important role in winter deep convection and subsequent restratification. Using ship-based observations, we fit an idealized eddy solution to horizontal velocity measurements acquired along ship tracks, determining an optimal eddy center and other key eddy properties. Based on three research cruises, we reconstructed 40 eddies ranging from 3 to 39 km in radius (mean 15 km) and azimuthal velocity between 7 and 58 cm s⁻¹ (mean 26 cm s⁻¹). The azimuthal velocity structure implies to a large extent solid-body rotation in the eddy’s inner core, while opposite signs of vorticity in the outer ring suggest strong vorticity shields. When compared to ship-based observations, the eddy field representation in gridded altimetry products is significantly distorted, with many eddies being underrepresented or undetected. This is even the case for larger-scale features despite having an eddy signature in the along-track altimetry product, which appears to be suppressed in the subsequent mapping methodology. Finally, comparisons with submesoscale-permitting numerical simulation output show favorable agreement giving confidence in both the ship-based reconstruction and the numerical model’s realism in representing high-latitude eddy dynamics.

**SIGNIFICANCE STATEMENT:** Oceanic eddies in the Labrador Sea play an important role in advecting heat, salt, and other properties to the interior basin with implications for winter deep convection and subsequent restratification of the homogenized water column. Using ship-based observations, our research provides a basinwide eddy characterization, capturing a broad range of spatial scales with radii from 3 to 39 km. We show that conventional satellite altimetry distorts eddy properties at high latitudes, where eddies are smaller in size and often remain undetected. By expanding the census of eddy characteristics in the Labrador Sea, our study offers a valuable dataset for assessing eddy dynamics in high-resolution numerical models, which often lack direct validation.

**KEYWORDS:** North Atlantic Ocean; Eddies; Small scale processes; Ship observations; Altimetry

# 1. Introduction

Coherent eddies occur everywhere in the global ocean and feature a broad range of amplitudes, radii, and lifetimes (Chelton et al. 2007, 2011). According to global ocean analyses, they contribute more than 90% of the surface kinetic energy and therefore account for much of the surface ocean variability (Chelton et al. 2007; Wunsch 2008; Ferrari and Wunsch 2009).

From an Eulerian statistical perspective, the term eddy is understood as a fluctuation about an Eulerian temporal or spatial mean state. Specific fluctuations are mesoscale and submesoscale

eddies (here summarized as coherent eddies), which are self-defined features and retain some element of coherence for relatively long periods, allowing them to be traced at great distance from their generation region (Yule 1978; Chigier 1979; McWilliams 1985). Coherent eddies are defined by increased nonlinearity, i.e., the ratio between relative and planetary vorticity advection exceeding unity, allowing them to trap fluid in their interior and contributing to the redistribution of heat, momentum, mass, and other properties (Early et al. 2011).

This study focuses on the characterization of coherent eddies in the northwestern subpolar North Atlantic, more precisely the Labrador Sea. The Labrador Sea is characterized by cyclonic surface circulation, i.e., a boundary current system composed of the East Greenland Current (EGC)/Irminger Current (IC), the West Greenland Current (WGC), and the Labrador Current (LC) (Fig. 1). Furthermore, it features elevated levels of eddy kinetic energy (EKE), which extend from north of 60°N southwestward into the interior of the basin. Eddies are argued to play a crucial role in the advection of heat and other properties from the boundary current to the central Labrador Sea. Hence, they are important for closing the heat budget of the Labrador Sea and also impact location,

Denotes content that is immediately available upon publication as open access.

Bendinger’s current affiliation: Laboratoire d’Océanographie Physique et Spatiale, Univ. Brest, CNRS, Ifremer, IRD, IUEM, Plouzané, France.

**Corresponding author:** Arne Bendinger, arne.bendinger@univ-brest.fr
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FIG. 1. Schematic of the cyclonic surface circulation in the Labrador Sea (blue arrows): (EGC)/IC, WGC, and LC. Surface geostrophic EKE (shading) including the 50 cm² s⁻² contour (dashed black line) derived from satellite altimetry (20-yr mean) is also shown. Known eddy types (red circular arrow) are 1) IRs, 2) convective eddies or CLs, and 3) BCEs. The thick black lines represent the 100-, 1000-, and 2000-m depth contours. Selected segments (white lines; la- beled 1–11) that were surveyed during one of the cruises analyzed in this study (MSM74).

extent, and strength of winter deep convection while driving the restratification of the homogenized water column after win- tertime convection (Straneo 2006; Hátún et al. 2007; Chanut et al. 2008; Saenko et al. 2014; Rieck et al. 2019).

Three types of surface-intensified eddies are known in the Labrador Sea from in situ observations: 1) Irminger rings (IRs), 2) convective eddies or convective lenses (CLs), and 3) boundary current eddies (BCEs; see Fig. 1). IRs form through either barotropic or baroclinic instabilities of the WGC and supported by the IC density field (Eden and Böning 2002; Lilly and Rhines 2002; Lilly et al. 2003; Brandt et al. 2004; Katsman et al. 2004; de Jong et al. 2014). They fea- ture radii and azimuthal velocities in the range of 11–35 km and 14–77 cm s⁻¹, respectively, as previously reported (Lilly and Rhines 2002; Lilly et al. 2003; Hátún et al. 2007; de Jong et al. 2014). CLs are generated through instability processes during the deep convection phase. These instability processes arise when deep density surfaces outcrop, creating quasi- vertical isopycnals and consequently small-scale eddies (Jones and Marshall 1993; Lilly et al. 1999; Marshall and Schott 1999; Pickart et al. 2002; Chanut et al. 2008). They are generally smaller in radius (5–18 km) and azimuthal velocity (9–32 cm s⁻¹) compared to IRs (Lilly and Rhines 2002; Lilly et al. 2003). BCEs are found at various locations along the boundary current (LC and WGC) and formed through baroclinic in- stabilities (Chanut et al. 2008; Thomsen et al. 2014; Pacini and Pickart 2022). Recent estimates suggest that BCEs along the WGC have a radius of around 10 km (Pacini and Pickart 2022). IRs are suggested to be predominantly anticyclones (Lilly et al. 2003; de Jong et al. 2014). In contrast, the classifi- cation of CLs and BCEs is less clear. The limited in situ ob- servations available indicate that they are typically either anticyclones or dipole pairs, with the latter consisting of an anticyclone immediately followed by a cyclone (Lilly et al. 2003; Pacini and Pickart 2022).

These in situ observations provide valuable insights into Labrador Sea eddy dynamics. However, they are sparse and mostly rely on moorings, restricting measurements to fixed lo- cations. Satellite altimetry products offer broad spatial cover- age and have been extensively used for several decades to study eddy dynamics in the global ocean (e.g., Chelton and Schlax 1996; Chelton et al. 2007, 2011; Pegliasco et al. 2022). These satellite altimetry products are obtained from gridding and optimal interpolation of available along-track absolute dynamic topography (ADT) or sea level anomaly (SLA) data projected typically onto a 1/4° × 1/4° horizontal grid (Pujol et al. 2016). The mapping methodology includes inter alia spa- tial and temporal correlation scales, which are described as function of latitude and longitude. In accordance with expec- tation, the mapping procedure represents a compromise be- tween the mesoscale eddy field characteristics (i.e., eddies with horizontal scales comparable to or larger than the first baroclinic Rossby radius of deformation *R*<sub>d</sub>) that are desired to be resolved and satellite sampling capabilities such as spatial and temporal coverage. As a direct consequence and in reality, the effective spatial resolution ranges between ~100-km wave- length at high latitudes and ~800-km wavelength near the equa- tor (Ballarotta et al. 2019).

This raises major concerns on the representation of meso- scale eddy dynamics in gridded altimetry products, particu- larly in high-latitude oceans with small *R*<sub>d</sub>. Amores et al. (2018) demonstrated that only 6% of eddies present in a high- resolution (1/60°) numerical model of the North Atlantic were captured in gridded altimetry-like SLA fields derived from full-resolution model data. Additionally, substantial discrep- ancies in eddy radius and amplitude were reported, with val- ues in gridded altimetry being up to 7–8 times larger than those in the numerical model. Eddies with radii < 100 km were especially affected by satellite undersampling, as they
were aliased into larger-scale structures up to 10 times their actual size. By combining satellite altimetry with space-borne synthetic aperture radar (SAR) data, submesoscale eddies as small as 1–2 km in radius have been detected in the north-ern Greenland Sea and Fram Strait (Bashmachnikov et al. 2020). The authors found that 80% of all eddies identified in SAR images had radii below 5 km, consistent with high-latitude $R_d$ estimates. In contrast, Bashmachnikov et al. (2020) reported that eddies detected in gridded altimetry products were limited to those with radii exceeding 40–50 km, although smaller-scale eddy signatures may still be present in along-track altimetry data. Similar limitations in resolving eddy characteristics are expected in the Labrador Sea, where $R_d < 10$ km—an order of magnitude smaller than the spatial scales resolved by satellite altimetry (Chelton et al. 1998; Funk et al. 2009).

Submesoscale-permitting numerical models help overcome the observational limitations by providing basinwide simulations with kilometer-scale resolution. Recent studies using such models have demonstrated the crucial role of mesoscale and submesoscale dynamics in regulating eddy-induced fluxes and winter deep convection (Pennelly and Myers 2020; Tagklis et al. 2020). In particular, submesoscale processes have been shown to reduce the convective water volume by over 80%, offering a plausible explanation for why climate and ocean general circulation models that do not resolve these smaller-scale processes tend to overestimate convection (Li et al. 2019). However, these simulations lack validation, highlighting the need for more in situ observations to assess their realism of mesoscale and submesoscale dynamics.

The primary objective of this study consists in providing a census of mesoscale-to-submesoscale eddy characteristics in the Labrador Sea while extending our present knowledge of these features. To achieve this, we use quasi-continuous horizontal velocity observations from ship acoustic Doppler current profilers (SADCPs). Our methodology follows the approach introduced by Castelão and Johns (2011) and further refined by Castelão et al. (2013) and is based on an eddy center optimization problem. It relies on an idealized eddy solution to obtain a robust eddy center estimate from horizontal velocity acquired along one-dimensional ship track sections that are suspected to partially intersect or cross coherent eddies. In cylindrical coordinates, the idealized eddy solution assumes solid-body rotation in the inner core, meaning that azimuthal velocity increases linearly with distance from the center, as in a Rankine vortex. Within this framework, a radial profile of azimuthal velocity can be analyzed, enabling estimates of estimates of key eddy properties such as radius and azimuthal velocity. This work has similarities with studies by Lilly and Rhines (2002), Lilly et al. (2003), and de Jong et al. (2014). However, these studies are based on moored velocity time series and, thus, constrained to fixed locations. Our methodology allows the eddy reconstruction for various locations in the Labrador Sea, wherever ship tracks are available.

The above analysis also highlights two important aspects, which are further addressed in this manuscript. First, a statistical comparison of the ship-based eddy reconstruction with their concurrent representation in satellite altimetry points out the

distortion of eddy characteristics in gridded data products. Second, an evaluation of a submesoscale-permitting numerical numerical model [North Atlantic simulation (NATL60), 1/60°] assesses the model's realism of mesoscale-to-submesoscale eddy characteristics, with valuable insight into how eddy properties are represented in subpolar regions—crucial for prospective studies focusing on accurately capturing eddy-driven heat transport and their influence on deep convection dynamics and climate.

The paper is organized as follows: Section 2 introduces the various datasets, including ship observations, satellite altimetry, and the numerical model. A description of the applied methodology to derive eddy properties from SADCP data, as well as the eddy detection and tracking algorithm applied to altimetry products and numerical model output, is provided in Section 3. The results are presented in three parts: ship-derived eddy characteristics in Section 4, quantitative and qualitative comparisons to gridded and along-track satellite altimetry in Section 5, and comparisons with numerical model output in Section 6. We finish with a brief summary and a final conclusion in Section 7.

## 2. Data

### a. Ship acoustic Doppler current profiler

Direct velocity observations used in this study were acquired during three research cruises, namely, MSM40 (6–24 August 2014) on the French Navire Océanographique (N/O) Thalassa and MSM54 (12 May–7 June 2016) and MSM74 (25 May–26 June 2018), both on the German R/V *Maria S Merian*. Both ships used a pair of Teledyne RD SADCPs. For MSM54 and MSM74, the devices operated with 38 and 75 kHz, respectively, with MSM40 a 38 and 150 kHz were used. Whenever available, the respective higher-resolution SADCP is used for the eddy reconstruction since it provides a higher sampling of the near-surface waters, which is essential for the comparison between ship-based and altimetric datasets. During MSM54, we chose the lower-resolution SADCP due to a malfunctioning of the 75 kHz. The SADCPs recorded data in an as-fast-as possible mode (about 1 s) while the processed data were averaged to 1-min intervals. Given the 1-min averaging interval and considering the varying ship speed between 6 and 12 kt (1 kt ≈ 0.51 m s⁻¹), the along-track spatial data resolution is between 180 and 360 m, respectively. A total of roughly 7900-km ship track length was analyzed. Technical details are summarized for each device in Table 1.

### b. Satellite altimetry

We used the global ocean gridded (https://doi.org/10.48670/moi-00148) multimission Data Unification and Altimeter Combination System (DUACS) product in delayed time and daily resolution produced and distributed by the Copernicus Marine Environment Monitoring Service (CMEMS). The sea level products are obtained by combining all available altimeter mission along-track data into a gridded product using optimal interpolation. The final product has a global Cartesian 1/4° × 1/4° horizontal resolution (Pujol et al. 2016). We also make explicit use of reprocessed along-track
<table><caption>TABLE 1. The total distance of analyzed ship transects, first bin, depth range as given by manufacturer specification, depth range used for optimization, bin size, bandwidth (NB—narrow band; BB—broad band), single ping precision $\sigma$, and standard error per bin ensemble ($\sigma_v = \sigma/\sqrt{N}$) for SADCPs operating throughout MSM40, MSM54, and MSM74. The standard error is calculated given the median amount of pings $N = 50$ (MSM40, 150 kHz), $N = 12$ (MSM54, 38 kHz), and $N = 25$ (MSM74, 75 kHz) per bin ensemble and averaging interval.</caption><thead><tr><th></th><th>MSM40<br>150 kHz</th><th>MSM54<br>38 kHz</th><th>MSM74<br>75 kHz</th></tr></thead><tbody><tr><td>Total distance of analyzed ship transects (km)</td><td>3135</td><td>2298</td><td>2441</td></tr><tr><td>First bin (m)</td><td>16</td><td>54</td><td>17.5</td></tr><tr><td>Depth range (m)</td><td>&gt;250</td><td>&gt;1000</td><td>&gt;425</td></tr><tr><td>Depth range for optimization (m)</td><td>16–104</td><td>54–118</td><td>17.5–105.5</td></tr><tr><td>Bin size (m)</td><td>8</td><td>32</td><td>8</td></tr><tr><td>Bandwidth (ping mode)</td><td>BB</td><td>NB</td><td>BB</td></tr><tr><td>Single ping precision (cm s<sup>-1</sup>)</td><td>8</td><td>10</td><td>15</td></tr><tr><td>Standard error $\sigma_v$ (cm s<sup>-1</sup>)</td><td>1.1</td><td>2.9</td><td>3</td></tr><tr><td>Gaussian influence (cutoff) radius (m)</td><td>16 (32)</td><td>64 (128)</td><td>16 (32)</td></tr></tbody></table>

data (https://doi.org/10.48670/moi-00146). The near-real-time (NRT) product is only considered for a case study in section 5b, focusing on the altimeter mission Ocean Surface Topography Mission (OSTM)/Jason-2 (J2G). It was used since the delayed product was not processed during the Jason-2 drifting phase (July 2017–2018) from the new long repeat orbit to the interleaved long repeat orbit.

### c. Numerical model

We make use of numerical model output from the submesoscale-permitting NATL60, a model configuration based on the Nucleus for European Modelling of the Ocean (NEMO; Madec and NEMO System Team 2024) code, version 3.6, provided by the multiscale ocean modeling (MEOM) research group at the Institut des Géosciences de l'Environnement in Grenoble, France. The model spans the North Atlantic from 26.5° to 65°N and from 80°W to 9.5°E with a horizontal grid of 1/60°, which corresponds to roughly 1 km in the Labrador Sea. It has 300 vertical levels with 1-m thickness at the surface and a maximum of 50 m in the deep ocean. The lateral advection of momentum and tracers is parameterized by a third-order upwind advection scheme. Initial and boundary conditions are provided by the eddy-permitting 1/4° resolution Global Ocean Reanalyses and Simulations version 3 (GLORYS2V3) oceanic reanalysis developed by Mercator Ocean (Ferry et al. 2012). Atmospheric forcing is taken from the Drakkar Forcing Set (DFS5.2; Dussin et al. 2016), which is based on the atmospheric reanalysis ERA-Interim (Dee et al. 2011) produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) with a 3-hourly temporal resolution and a spatial resolution of 0.75° for the period 1979–present. The model run used in this study originates from the second simulation CJM165 covering the period from June 2012 to October 2013 following a 6-month spinup (Molines 2018).

## 3. Methodology

### a. SADCP data processing

The eddy center optimization problem was first and foremost applied to the SADCP data from MSM40, MSM54, and

MSM74 (see section 2a). Prior to optimization, the velocity bins were filtered by percent good data, which defines the fraction of data that passed a variety of rejection criteria such as a low signal-to-noise (S/N) ratio, a low echo amplitude, and large error velocities (estimated from comparison of ADCP beam triplets) to suppress effects of noise. Velocity bins below the quality threshold of 75% were excluded from the data analysis. Furthermore, we decided to neglect velocity bins that were sampled at ship speeds below 5 kt to avoid velocity samples before and after as well as during a stationary ship. Velocity measurements during low ship speeds might interfere in the upper layers with the ship's bow thruster.

To reduce small-scale variability such as vertically propagating internal/inertial waves, the velocities are horizontally binned on a regular grid of 1-km resolution. Moreover, a Gaussian-weighted smoothing with 2-km influence and 4-km cutoff radii was applied. In the vertical, influence (cutoff) radii were set to 16 m (32 m) for the 150-kHz instrument during MSM40 and 64 m (128 m) and 16 m (32 m) for the 38- and 75-kHz instruments during MSM54 and MSM74, respectively (see Table 1). Whenever possible, the reconstruction was applied to the upper 100-m mean velocity data (see the depth ranges used for the optimization in Table 1). This allows to adequately represent the eddy surface signature, for comparison with satellite altimetry-derived eddy characteristics.

A processed SADCP section of zonal and meridional velocities along a partial ship track during MSM74 (see Fig. 1) is exemplarily shown in Fig. 2. Away from the boundary current, velocity maxima as high as 60 cm s⁻¹ are occasionally observed in the central Labrador Sea. The horizontal velocity fields suggest mesoscale eddy variability on spatial scales of O(10) km, corresponding to the local Rossby radius. Both barotropic and surface-intensified baroclinic features are evident when considering the vertical structure. As we will show later, smaller-scale variability, which we refer to as submesoscale, is also observed in the underlying data.

### b. Eddy center optimization problem

One central aim of this study is to estimate eddy characteristics from SADCP data obtained in areas that are suspected
<figure><img src="image_5.png" /><figcaption>FIG. 2. Gridded and smoothed (a) zonal and (b) meridional current velocities in the central Labrador Sea, measured along the ship track (subdivided into 11 segments) from MSM74 (see also the outlined white line in Fig. 1), from 1 to 13 Jun 2018, using the 75-kHz SADCP. The 0 cm s⁻¹ contour is shown in black. The yellow lines mark the 17.5–105.5-m depth range used for optimization.</figcaption></figure>

to intersect or cross coherent eddies. For such ship track segments, we applied a conversion from Cartesian into cylindrical coordinates. In brief, in cylindrical coordinates, every point in the x-y plane is defined by the radial distance r to the origin (eddy center) and the azimuthal angle θ. The azimuthal velocity v_θ and the radial velocity component v_r can be written as

$$v_r = u \cos(\theta) + v \sin(\theta), \quad (1)$$

$$v_{\theta} = -u \sin(\theta) + v \cos(\theta), \quad (2)$$

where u and v are the zonal and meridional velocities in Cartesian coordinates. For a vortex that is radially axisymmetric and nontranslating, it is expected that v_r = 0. Castelão and Johns (2011) and Castelão et al. (2013) introduced a method for estimating the center of a vortex by minimizing v_r (maximizing v_θ) through an optimal choice of a virtual eddy center via nonlinear optimization written as

$$|v| = -u \sin(\theta) + v \cos(\theta) + \epsilon, \quad (3)$$

$$\theta = \arctan(y_r/x_r), \quad (4)$$

$$y_r = y - y_c, \quad (5)$$

$$x_r = x - x_c, \quad (6)$$

where (x, y) are the position vectors of the horizontal velocity samples and (x_c, y_c) is the eddy center location. The residual ϵ represents the radial velocity to be minimized. This optimization problem assumes solid-body rotation in the inner core. This corresponds to a Rankine vortex, which is associated with v_r = 0 and a linear increase of v_θ = -u sin(θ) + v cos(θ) with increasing distance to the center. The basic principle of the applied method and the variables to be determined (in Cartesian coordinates) are visualized in Fig. 3a.

Following Castelão and Johns (2011) and Castelão et al. (2013), the optimization is performed by a nonlinear least squares Gauss–Newton algorithm, which minimizes an objective function in an iterative procedure,

$$\min_{\mathbf{x} \in \mathbb{R}^n} f(\mathbf{x}) = \sum_{j=1}^{m} \delta_j^2(\mathbf{x}), \quad (7)$$

where δ_j denotes the jth residual from the residual vector δ(\mathbf{x}) and \mathbf{x} is an n-dimensional parameter vector. Throughout this study, it is assured that m ≥ n, i.e., the number of samples is greater than or equal to the number of parameters to be determined. All input variables were scaled in the range [-1, 1] with preserving sign. The Gauss–Newton algorithm does not always guarantee convergence of the solution. Therefore, a damping factor α_k is implemented. It is chosen such that it fulfills the sufficient decrease condition known as the Armijo rule at the kth iteration:

$$f(\mathbf{x}_k + \alpha_k \mathbf{p}_k^{\mathrm{GN}})^T \le f(\mathbf{x}_k) + c_1 \alpha_k \nabla f(\mathbf{x}_k)^T \mathbf{p}_k^{\mathrm{GN}}, \quad (8)$$

where p_k^{GN} is the search direction, c_1 ∈ (0, 1), and T is the transpose (Armijo 1966). The Armijo rule prevents the line search from taking overly long steps and, hence, ensures a reasonable reduction of the objective function. To our knowledge, the damping factor is neither implemented in Castelão and Johns (2011) nor in Castelão et al. (2013) and, therefore, may help achieve convergence to a local or global minimum. Whether a local or global minimum is found within the optimization also depends on the initialization values. In our application, we initialized the algorithm with a cluster or array of starting values around the mean position along the ship track. The eddy center estimate associated with the lowest residual sum of squares can be considered the best guess and was further used in our analysis.

### c. Optimal eddy-center-derived eddy characteristics

The optimal eddy center allows us to derive key eddy characteristics such as an azimuthal velocity structure v_θ(r) as a function of radius r from the eddy center, the speed-based eddy radius R_max, and the corresponding azimuthal velocity V_max. Furthermore, v_θ(r) can be distinguished between the inner core (r ≤ R_max) and outer ring (r > R_max). We then assess the extent to which v_θ(r) resembles the theoretical velocity
<figure><img src="image_6.png" /><figcaption>FIG. 3. (a) Sketch visualizing the eddy center problem solved by the Gauss–Newton methodology. All velocity observations (white dots) across an eddy with maximum azimuthal velocity $V_{max}$ at radius $R_{max}$ are associated with an eastward $x_r$ and northward $y_r$ offset from the eddy center ($x_c, y_c$). (b) Plane view of the upper-mean (17.5–105.5 m) horizontal velocity represented by black arrows along segment 1 (for the location and vertical structure, see Figs. 1 and 2, respectively). The red dots connected by the red line correspond to (c) the optimized eddy center location at different iteration steps, which also shows the resulting residual sum of squares from the optimization. (d) Azimuthal velocity structure $v_\theta(r)$ for both radial sections, where $R_{max1}$ and $R_{max2}$ divide $v_\theta(r)$ into an inner core ($r < R_{max}$) and outer ring ($r > R_{max}$).</figcaption></figure>

structure of a simple model, such as the Rankine vortex, which is characterized by solid-body rotation in the inner core and hyperbolic decay in the outskirts, i.e.,

$$v_{\theta}(r) = \begin{cases} r \frac{V_{\max}}{R_{\max}}, & \text{for } r \le R_{\max} \text{ (solid-body rotation),} \\ V_{\max} \left( \frac{R_{\max}}{r} \right)^{n=1}, & \text{for } r > R_{\max} \text{ (hyperbolic decay),} \end{cases} \quad (9)$$

where $n$ is the inverse power-law exponent, which equals 1 for a Rankine vortex. Previously discussed in the literature, an exponential dependency $\exp[-(r - R_{max})/\lambda]$ for $r > R_{max}$ has also been considered for the outer ring (e.g., Olson 1980, 1991; Castelão and Johns 2011). The exponent $n$ and the outer ring decay scale $\lambda$ are determined by a one-term exponential and power series model fit, respectively. Further eddy characteristics are derived as follows.

Inserting the linear velocity model of Eq. (9) into the vertical component of the vorticity in cylindrical coordinates while neglecting the radial velocity component gives the inner-core relative vorticity:

$$\zeta_z = \frac{1}{r} \frac{\partial(rv_\theta)}{\partial r} = 2 \frac{V_{\max}}{R_{\max}}. \quad (10)$$

The nondimensional Rossby number of the gradient flow is $Ro = V_{max}/(f_0 R_{max})$, where $f_0$ is the inner-core Coriolis

parameter. Following Castelão and Johns (2011), the maximum sea surface height (SSH) signal $\eta_0$ is derived from the following equation while assuming cyclogeostrophic balance and neglecting the contribution of centrifugal acceleration to SSH in the outer ring:

$$\eta_0 = -\frac{V_{\max}}{2g} (V_{\max} + f_0 R_{\max} + 2\lambda f), \quad (11)$$

where $g$ is the gravitational acceleration and $f$ is the outer ring Coriolis parameter.

### d. Brief note on methodology assessment

The eddy characterization presented in this study stands out for its simplicity, as it determines the optimal eddy center using only a single ship track of horizontal current velocity data from SADCP data. Generally, the optimization was initiated after the visual inspection of alternating velocity signs. A solution was considered successful when convergence occurred within a few iterations with steadily decreasing residuals. A robust eddy reconstruction can be achieved as long as the ship crosses the eddy anywhere within its inner core. In such cases, the velocity profile will feature at least one maximum, which is associated with the eddy boundary. However, it is important to note that this methodological simplicity comes with certain constraints, as it relies on an idealized eddy solution.

The two main limitations are the assumptions of a radially axisymmetric and nontranslating vortex. The latter assumption
is justified by the relatively small sizes of eddies observed in the Labrador Sea. As shown below, for an average eddy with a diameter of approximately 30 km and a typical ship speed of 12 kt while in transit, crossing the eddy takes just over an hour—or even less if the track only partially intersects the eddy. This contrasts with the approach of Castelão and Johns (2011), who accounted for eddy translation speed. However, their study focused on North Brazil rings, where eddy center optimization was based on data collected over several days— long enough for the eddies to undergo significant propagation. Furthermore, eddy translation speed is generally higher at low latitudes due to the beta drift (~~$\beta R_d^2$, where $\beta = dfdy$; Cushman-Roisin et al. 1990). Since the beta effect weakens with increasing latitude, eddies at high latitudes—such as those in the Labrador Sea—typically exhibit slower translation speeds. This supports the assumption that translation can be neglected over the short time scales relevant to in situ sampling.

The validity of the assumption of a radially axisymmetric vortex may vary significantly among the surveyed eddies. Radial asymmetries can lead to nonconverging or oscillatory solutions, typically resulting in unreliable eddy center estimates, which were excluded from the analysis. Even when convergence was achieved, the derived eddy properties should be interpreted with caution, as many eddies were intersected only once. In such cases, estimated parameters like radius and azimuthal velocity may be distorted by asymmetries and depend strongly on the location and orientation of a ship track crossing.

A methodology assessment was conducted using the instantaneous NATL60 velocity field to evaluate this matter, with a brief summary provided below. A more detailed discussion can be found in the appendix. For a nearly axisymmetric vortex (ellipticity of 0.02), our analysis indicates that eddy radii and azimuthal velocities derived from various ship tracks deviate on average by only 2.3% and 1.5%, respectively, from their mean values. In the case of a more asymmetric vortex (ellipticity of 0.26), the deviations increase to 22.6% for radii and 7.7% for azimuthal velocities. Despite these variations, eddy radii and azimuthal velocities remain in good agreement with the corresponding reference values determined by an eddy detection algorithm (see section 3e) applied to the NATL60 output.

### e. AMEDA eddy detection and tracking algorithm

Apart from the ship-based eddy reconstruction, we identified eddies in the Labrador Sea using an eddy tracking algorithm, the angular momentum eddy detection and tracking algorithm (AMEDA; Le Vu et al. 2018). In brief, the AMEDA provides eddy location as well as eddy characteristics based on the physical parameters and the velocity field geometrical properties. The algorithm first identifies an eddy center, which corresponds to an extreme of the local normalized angular momentum (LNAM; +1 for cyclonic and -1 for anticyclonic). By default, the LNAM is computed over boxes scaled with $R_d$, excluding eddies for which $R_{max} < R_d$. Here, we use a constant radius, which is equivalent to the minimum resolvable radius of

2.5 km to avoid smoothing of submesoscale motion. Streamlines surrounding the LNAM extreme are then computed, and the mean radius and velocity for each streamline are evaluated. The radius of a circular disc with an area delimited by the closed streamline is analogous to the mean radius, while the circulation along the closed streamline is used to derive the mean velocity. The azimuthal speed increases toward the eddy boundary until maximum speed $V_{max}$ is reached, whose corresponding radius $R_{max}$ is equivalent to the speed-based radius (Chelton et al. 2011; Laxenaire et al. 2018; Le Vu et al. 2018). This closed contour of maximum speed is the characteristic contour of the detected eddy. Subsequently, the azimuthal speed decreases within the eddy's outer ring until the last closed streamline is reached. The relative vorticity and Rossby number are also computed from the characteristic eddy velocity $V_{max}$ and the corresponding radius $R_{max}$. AMEDA was applied to surface geostrophic velocity fields derived from gridded satellite altimetry to track the eddy field evolution during the time periods of MSM40, MSM54, and MSM74 (see the respective time periods in section 2a). It was also applied to three snapshots from the NATL60 model to detect eddies on given dates (15 May, 15 June, and 15 August 2013), using both the upper-mean (15–100 m) full-resolution velocity field and the surface geostrophic velocity field derived from resampled SLA (interpolated onto the nominal spatial resolution of $1/4^\circ \times 1/4^\circ$). These three dates were chosen to represent the approximate time periods of the year during which MSM40, MSM54, and MSM74 took place, respectively.

## 4. Ship-based eddy field reconstruction

### a. From optimization to characterization: An example of a surveyed eddy during MSM74

Mesoscale-to-submesoscale flow variability may be of a different origin and may indicate the existence of coherent eddies, fronts, or simply meandering currents. When radially axisymmetric vortices are crossed near their centers, the horizontal velocities along the ship track show alternating signs. For a zonal section, there are purely meridional velocities at the western and eastern flanks, and for a meridional section, these are purely zonal velocities at the northern and southern flanks. Since it is impossible to derive a two-dimensional velocity field from a single ship track, it is challenging to determine whether the observed velocities belong to an eddy. This is especially true when the ship track is well beyond the eddy center, near the eddy boundary. To identify flow features that can be attributed to the idealized eddy solution defined in section 3b, we applied in a manual procedure the Gauss–Newton optimization to sections of alternating signs of zonal and meridional velocity. By doing so, only certain flow features were identified and allowed optimization for a robust eddy center estimate. Further confidence for the presence of an eddy is given, when taking into account the barotropic or baroclinic velocity structure extending from the near-surface for several tens to hundreds of meters. An example for the reconstruction of a cyclonic eddy based on the upper-mean (17.5–105.5 m) horizontal velocity along segment 1 during MSM74 (see Figs. 1 and 2) is illustrated in Figs. 3b–d. We observed a rapid convergence
<figure><img src="image_7.png" /><figcaption>FIG. 4. All ship-based reconstructed eddies illustrated as solid circles (drawn to scale and representative of their location and size) in the central Labrador Sea along all analyzed ship tracks (MSM40, MSM54, MSM74; thin gray lines). The color coding refers to cyclonic (blue) and anti-cyclonic (red) rotation. Bathymetry contours as in Fig. 1. The first baroclinic Rossby radius of deformation $R_d$ (km) is also given (green contours). The inset shows the probability distribution of $R_{max}$ normalized by the local $R_d$.</figcaption></figure>

to a local or global minimum, which provided confidence in the success of the optimization (see Fig. 3c). For the example at the hand, the optimization revealed the cyclone was crossed on its eastern flank with a minimum distance of roughly 6 km to the eddy center.

Once the Gauss–Newton optimization converged and indicated an eddy center, the azimuthal velocity profile (Fig. 3d) is reconstructed and further analyzed (see section 3c). The speed-based radius $R_{max}$ and the corresponding azimuthal velocity $V_{max}$ are used to divide the azimuthal velocity $v_0(r)$ structure into the inner core ($r < R_{max}$) and outer ring ($r > R_{max}$). The inner core appears to be in solid-body rotation, supported by the linear regression coefficient of determination $r^2 = 0.98$ for both radial sections. The inverse power-law fit applied to radial sections 1 and 2 yields $n_1 = 1.5$ and $n_2 = 1.7$. In other words, the azimuthal velocity decays faster than defined by the Rankine vortex ($n = 1$). The exponential fit yields $\lambda_1 = 13.5$ km and $\lambda_2 = 10.2$ km. Based on two radial sections, we argue that the extracted cyclone is rather of radially symmetric nature since radii ($R_{max1} = 11.8$ km, $R_{max2} = 10.5$ km) and azimuthal velocities ($V_{max1} = 52$ cm s$^{-1}$, $V_{max2} = 45$ cm s$^{-1}$) are close to each other. However, the outer ring features some small-scale anomalies, which express inter alia in the variable decay rates.

b. Ship-based eddy characteristics

In total, we performed 40 eddy reconstructions, with 14, 9, and 17 eddies detected during MSM40, MSM54, and MSM74, respectively (Fig. 4 and Table 2). Fourteen of forty eddy signatures (35%) had a signature in SLA maps and were detected by AMEDA. Furthermore, according to SLA, at least two eddies were sampled twice during MSM74, making it a total of 38 surveyed eddies. For the remaining eddy

reconstructions without a corresponding SLA signature, it is unclear whether they were resampled. However, this seems unlikely, as most eddy reconstructions were conducted along the ship track during transit, with no return to previously surveyed regions. The mean eddy radius is 14.7 km, with a standard deviation of 9.8 km. The maximum azimuthal velocity averages 26 cm s$^{-1}$, with a standard deviation of 14.0 cm s$^{-1}$. Eddy radii range from 3 to 39 km and azimuthal velocities between 7 and 58 cm s$^{-1}$. The Rossby number $Ro$, computed using the respective $R_{max}$ and $V_{max}$ [see Eq. (10)], has an average value of 0.18 and a standard deviation of 0.09. With respect to the azimuthal velocity structure, the mean exponential and inverse power-law outer ring decay are $\lambda = 12.1 \pm 9.4$ km and $n = 1.7 \pm 0.8$, respectively. Note that we only calculate the outer ring decay scale for radial sections whose outer ring was sampled at least one radius $R_{max}$ beyond the eddy boundary. For reference, theory suggests $\lambda = 1/3R_{max}$ (Valcke and Verron 1997). Note that in the specific case of a Rankine vortex, $n$ equals 1 (see section 3c). Notably, the outer ring's azimuthal velocity structure exhibits large variability, as reflected by the standard deviation. The maximum SSH signal $\eta_0$ averages $8 \pm 9.6$ cm.

Among the 38 individual eddies detected in the ship observations, four have radii below the threshold $R_{max} < 2/3R_d$ and 14 have $R_{max} < R_d$. This corresponds to 11%–37% of eddies that could be classified as submesoscale (see the inset in Fig. 4). Given the smooth and poorly defined transition between submesoscale and mesoscale eddies, we do not differentiate between them in the following analyses. Unless otherwise specified, both mesoscale and submesoscale eddies are collectively referred to as coherent eddies or simply eddies.
<table><caption>TABLE 2. Mean eddy characteristics as derived from ship observations (SADCP), gridded altimetry (CMEMS), and submesoscale-permitting numerical model output (NATL60); SADCP, CMEMS, and NATL60 are presented in boldface for clarity. Speed-based radius $R_{max}$, maximum azimuthal velocity $V_{max}$, inner-core relative vorticity $\zeta_{in}$, Rossby number of the gradient flow Ro, outer ring exponential decay rate $\lambda$, inverse power-law exponent $n$, and maximum SSH signal $\eta_0$. The $\lambda$, $\eta$, and $\eta_0$ are only considered when the eddy outskirt was sampled at least one $R_{max}$ beyond the eddy boundary. The $\lambda$ and $n$ are not given for CMEMS and NATL60.</caption><thead><tr><th></th><th>R<sub>max</sub> (km)</th><th>V<sub>max</sub> (cm s<sup>-1</sup>)</th><th>ζ<sub>in</sub> (10<sup>-5</sup> s<sup>-1</sup>)</th><th>Ro</th><th>λ (km)</th><th>n</th><th>η<sub>0</sub> (cm)</th></tr></thead><tbody><tr><td><strong>SADCP</strong></td><td>14.7 ± 9.8</td><td>26.2 ± 14.0</td><td>4.4 ± 2.2</td><td>0.18 ± 0.09</td><td>12.1 ± 9.4</td><td>1.7 ± 0.8</td><td>8.1 ± 9.6</td></tr><tr><td>CE</td><td>15.2 ± 11.3</td><td>25.3 ± 10.5</td><td>4.7 ± 2.7</td><td>0.19 ± 0.11</td><td>12.1 ± 7.2</td><td>1.4 ± 0.5</td><td>-6.7 ± 6.1</td></tr><tr><td>AE</td><td>14.3 ± 8.5</td><td>26.8 ± 16.3</td><td>-4.1 ± 1.7</td><td>-0.17 ± 0.07</td><td>12.1 ± 11.3</td><td>2.0 ± 1.0</td><td>9.6 ± 12.1</td></tr><tr><td><strong>CMEMS</strong></td><td>42.6 ± 11.8</td><td>10.3 ± 5.5</td><td>0.89 ± 0.41</td><td>0.020 ± 0.009</td><td>—</td><td>—</td><td>10.3 ± 7.6</td></tr><tr><td>CE</td><td>42.5 ± 13.3</td><td>10.8 ± 7.4</td><td>0.92 ± 0.50</td><td>0.020 ± 0.009</td><td>—</td><td>—</td><td>-11.9 ± 10.5</td></tr><tr><td>AE</td><td>42.7 ± 10.7</td><td>9.9 ± 3.6</td><td>-0.86 ± 0.33</td><td>-0.020 ± 0.009</td><td>—</td><td>—</td><td>9.4 ± 4.1</td></tr><tr><td><strong>NATL60</strong></td><td>8.7 ± 5.2</td><td>14.1 ± 12.8</td><td>6.2 ± 2.9</td><td>0.13 ± 0.07</td><td>—</td><td>—</td><td>1.2 ± 2.1</td></tr><tr><td>CE</td><td>8.1 ± 4.5</td><td>11.4 ± 6.2</td><td>6.7 ± 3.2</td><td>0.13 ± 0.07</td><td>—</td><td>—</td><td>-0.7 ± 0.9</td></tr><tr><td>AE</td><td>9.4 ± 5.8</td><td>16.8 ± 16.7</td><td>-5.7 ± 2.4</td><td>-0.14 ± 0.07</td><td>—</td><td>—</td><td>1.7 ± 2.8</td></tr></tbody></table>

In total, 17 eddies were identified as cyclones (CEs) and 21 as anticyclones (AEs; see Fig. 4). We find that CEs are slightly larger in $R_{max}$, lower in $V_{max}$, and feature weaker magnitude in $\eta_0$ (see Table 2). The mean Ro disagrees with the findings for $R_{max}$ and $V_{max}$ because CEs have slightly larger Ro even though $R_{max}$ is larger and $V_{max}$ is smaller compared to AEs. However, this apparent inconsistency in Ro can be explained by the large number of smaller-scale CEs with radii as low as 5 km, also in agreement with the median Ro (0.17 for CEs and -0.16 for AEs). An interesting difference lies in the inverse power law, as the azimuthal velocity structure in the outer ring decays more rapidly for AEs ($n = 2.0$) compared to CEs ($n = 1.4$). This could be an indication of the anticyclones more isolated or coherent nature, discussed in more detail in section 7.

In contrast to the reported predominance of AEs in the literature (Lilly et al. 2003; de Jong et al. 2014; Pacini and Pickart 2022), our observations reveal a more balanced CE-AE distribution. However, due to the absence of high-resolution hydrographic data along the ship tracks, we cannot classify the different eddy types introduced in section 1. That said, the reported CE-AE asymmetry in previous studies may be biased, as they are often restricted to specific locations where certain eddy types—and their characteristic rotation—are expected to dominate.

### c. Ship-based azimuthal velocity structure

A broad range of $R_{max}$ and corresponding $V_{max}$ as well as high variability in the velocity decay in the eddies' outskirts are found (Fig. 5a). The speed-based radius is used to separate the radial velocity structure into an inner core ($r < R_{max}$; Fig. 5b) and an outer ring ($r > R_{max}$; Fig. 5c) for each considered eddy. To compare the azimuthal velocity structure of eddies with different radii, normalization with respect to $R_{max}$ in the inner core and additionally by their inverse power-law exponent $n$ in the outer ring was performed. Moreover, $V_{max}$ is normalized by the expected maximum azimuthal velocity of a Rankine vortex, which in turn is determined by a linear fit of the inner-core data and extracted at $R_{max}$. This approach allows us to quantify deviations from the theoretical Rankine vortex structure. We find that the velocity structure is predominantly

linear for at least half to two-thirds of the inner core, indicating solid-body rotation to a large extent (see Fig. 5b). Beyond this region, the azimuthal velocity profile transitions to a more Gaussian-like shape, flattening toward the eddy boundary before decaying exponentially in the outer ring (see Figs. 5a,b). The largest deviation from a Rankine vortex typically occurs at the eddy boundary ($r/R_{max} = 1$), where velocities are 5%-55% lower than those expected for solid-body rotation. The fact that the radial velocity structure of oceanic eddies is best described by a Gaussian-like model is well established in the literature as discussed in section 7.

We also inspected the radial vorticity structure computed by inserting the normalized linear and hyperbolic relationship [Eq. (9)] from Figs. 5b and 5c in $\zeta_z = (1/r)[\partial(rv_\theta)/\partial r]$ (Figs. 5d,e). By definition, Rankine vortex's vorticity is constant in the inner core and zero in the outskirts. The observations indicate a linear decrease of $\zeta_z$ toward the eddy boundary before changing sign in the outer ring and finally converging toward $\zeta_z = 0$. Negative vorticity in the outer ring generally suggests strong vorticity shields underlining the vortices' coherent nature.

### 5. Comparison to satellite altimetry

In high-latitude oceans, eddy dynamics are poorly resolved by satellite altimetry, leading to potential distortions in eddy properties. The ship-based observations provide a valuable dataset for quantifying the extent of these distortions and identifying the scales missed in altimetry-based estimates. To do so, we applied AMEDA to SLA maps corresponding to each ship cruise analyzed. For consistency, we considered only those eddies in the AMEDA dataset that were either directly crossed by or located in the immediate vicinity of the ship tracks. Eddies detected in ship data do not always appear in satellite data, and vice versa. Of the 40 eddy signals identified in ship observations, only 14 had a corresponding signature in SLA maps, limiting direct comparisons to a subset of eddies. Several factors contribute to these mismatches. On the one hand, if an eddy is detected in the gridded altimetry data but not in the ship data, it may indicate that the ship track is slightly beyond the eddy boundary, making a reliable
<figure><img src="image_8.png" /><figcaption>FIG. 5. (a) Azimuthal velocity structure $v_\theta(r)$ for all ship-based eddy reconstructions. The black triangles denote the eddy's characteristic $R_{max}$ and $V_{max}$. (b), (c) Normalized $v_\theta$, separately plotted for the inner core ($r < R_{max}$) and the outer ring ($r > R_{max}$) for eddies which were crossed near their center (19 eddies in total). The theoretical azimuthal velocity structure of a Rankine vortex is also shown (black line). (d), (e) As in (b) and (c), but for normalized relative vorticity $\zeta$. The inset in (e) serves as a zoom into the y axis for better visibility.</figcaption></figure>

reconstruction impossible. This may, in turn, imply that the eddy identified from gridded altimetry is overestimated in size. It is also possible that an eddy detected in gridded altimetry is very surface-intensified and, thus, not captured by the ship data, especially if the uppermost record from the ship is at 54-m depth. However, the latter case is rather unlikely since stratification in the Labrador Sea is weak and the velocity field is often of rather barotropic nature (see Fig. 2). Conversely, if an eddy is detected in ship observations but not in gridded altimetry, it likely represents a smaller-scale feature not captured by satellite altimetry due to the coarse spatial and temporal sampling of altimetry tracks as well as the underlying mapping procedure. This aspect is further elaborated in the following sections.

### a. How do eddy characteristics from gridded altimetry products compare to ship observations?

Along the ship tracks, eddies identified using AMEDA applied to gridded SLA have an average radius of $42.6 \pm 11.8$ km and a maximum azimuthal velocity of $10 \pm 5.5$ cm s⁻¹ (see Table 2). In comparison, eddies reconstructed from the ship observations are nearly three times smaller in radius and exhibit azimuthal velocities that are approximately 3 times higher (Table 2). This discrepancy is further evident in the probability distributions in Fig. 6. In particular, a significance fraction of the ship-based eddies have radii well below 10 km (Fig. 6a), while their azimuthal velocities can exceed 60 cm s⁻¹ (Fig. 6b). Subsequently, the ship-based eddies feature Rossby numbers roughly an order of magnitude higher
<figure><img src="image_9.png" /><figcaption>FIG. 6. Probability histograms of eddy properties: (a) $R_{max}$, (b) $V_{max}$, and (c) $R_o$ as derived from the ship observations (SADCP; green) and gridded altimetry (CMEMS; yellow). (d)–(f) As in (a)–(c), but for full-resolution (green) and resampled (yellow) NATL60 output.</figcaption></figure>

than those derived from gridded altimetry (0.18 compared to 0.02), indicating a stronger degree of nonlinearity (Table 2, Fig. 6c). An important point to consider when comparing velocities from in situ observations to gridded altimetry products is that for the latter, the geostrophic assumption becomes insufficient at scales where centrifugal acceleration is no longer negligible, and the balance shifts toward cyclogeostrophic (Ioannou et al. 2019; Cao et al. 2023). In such cases, when centrifugal acceleration is neglected, the geostrophic velocities derived from SLA tend to be overestimated for cyclones and underestimated for anticyclones. This imbalance may contribute to the substantial differences observed in the eddy velocities, particularly at scales where $R_o = 0.1–1$.

b. Complementary analysis of ship-based, gridded, and along-track satellite altimetry data

Unlike gridded SLA, along-track SLA may contain small-scale features that are otherwise smoothed out in the mapping procedure of gridded SLA. This is supported by the ship-based eddy reconstructions that we apply along the ship track on 1 June (Fig. 7) and 12 June 2018 (Fig. 8), elaborated in more detail in the following.

On 1 June, two distinct CEs (blue solid circular rings; denoted as CE1 and CE2) are identified along the ship track based on upper-mean (17.5–105.5 m) horizontal velocities as

measured by the SADCP (black arrows; Fig. 7a). CE1 and CE2 are centered around 53.9° and 54.4°N, with estimated radii of approximately 5 and 11 km and maximum azimuthal velocities of 20 and 48 cm s⁻¹, respectively. CE1 is well below the local $R_d$ and falls within the submesoscale range, whereas CE2, slightly exceeding the local $R_d$, can be classified as mesoscale. To put this into context, we also show the gridded SLA (shading), the derived surface geostrophic velocity (gray arrows), and corresponding eddies identified by AMEDA (black enclosed contours; SLA < 0: CE; SLA > 0: AE). This example explicitly shows how eddies can be missed in gridded SLA fields and AMEDA-based detections, particularly outside larger eddy cores. Here, the ship track lies between the AMEDA-identified CE–AE dipole but suggests the presence of small-scale features, such as filaments with cyclonic vorticity, likely resulting from the mesoscale stirring induced by the dipole interaction (Stegner et al. 2021).

While CE2 is not visible in the gridded SLA, along-track SLA from a nearby satellite pass (closest to the ship track) reveals a distinct negative signature in SLA, indicating its presence. This is further supported by the across-track geostrophic velocity component, calculated as $v_g = (g/f)(\Delta h/\Delta x)$, where $\Delta h$ and $\Delta x$ are the partial derivations of along-track SLA and distance, respectively. The resulting velocity profile along the highlighted satellite track suggests cyclonic rotation around
<figure><img src="image_10.png" /><figcaption>FIG. 7. (a) Ship-derived eddies (solid circular rings; denoted as CE1 and CE2) based on SADCP data collected along segment 1 on 1 Jun 2018 (see Fig. 1), shown over altimetry-derived eddies from AMEDA (black enclosed contours). Gridded SLA (color shading) for the given day and underlying along-track SLA (filled circles; track closest to ship track is highlighted/enlarged) from 30 May to 3 Jun from all available satellites are also shown. For reference, altimetry-derived surface geostrophic currents (gray arrows) and ship-based upper-mean (17.5–105.5 m) velocities (black arrows) are overlaid with identical scaling. (b) Along-track SLA (black) and across-track geostrophic velocity component $v_g$ (gray) for the highlighted satellite track in (a). Zonal and meridional velocity sections from SADCP, with CE1 and CE2 marked. (c)–(d) share the same latitude $x$ axis.</figcaption></figure>

the SLA minimum (Fig. 7b). This cyclonic rotation is evident throughout the upper water column as shown by the SADCP data (Figs. 7c,d). CE2 exhibits a baroclinic structure, being surface-intensified but potentially extending beyond 400-m

depth. CE1 also has a clear signature in the SADCP data but is likely too small to be resolved even if it were located near satellite passes, given the along-track sampling of 7 km (Pujol et al. 2016).

<figure><img src="image_11.png" /><figcaption>FIG. 8. As in Fig. 7, but for SADCP data collected along segment 10 on 12 Jun 2018 (see Fig. 1) focusing on AE1 and AE2.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>FIG. 9. NATL60 snapshots (15 Jun 2013) of the upper-mean (15–100 m) (a) horizontal current speed and (b) normalized relative vorticity. (c) Resampled, satellite-like SLA (shading) with geostrophic velocities (gray arrows) overlaid by solid enclosed contours in blue and red, which are representative of CEs and AEs, respectively, detected by AMEDA (see section 3e). CEs and AEs detected in the full-resolution snapshots are shown as blue and red patches, respectively. Bathymetry contours as in Fig. 1.</figcaption></figure>

On 12 June, numerous CEs and AEs (blue and red solid circular rings) were detected along the ship track, which are not properly represented in gridded SLA or detected by AMEDA (Fig. 8a). Here, we focus on two distinct AEs (denoted as AE1 and AE2). They are centered around 52° and 51°W, respectively, with estimated radii of approximately 25 and 23 km and maximum azimuthal velocities of 41 and 58 cm s⁻¹, respectively. Despite its relatively large-scale and clear velocity structure, AE1 is not apparent in gridded SLA, neither detected by AMEDA. Similar to the above example, we draw back on along-track SLA to support its presence. The satellite track closest to the ship track (J2G NRT; see section 2b) features a global maximum of SLA of almost 20 cm west of 51°W, which can be associated with AE2. Yet, a secondary SLA maximum occurs west around 52°W, which is associated with AE1. The resulting across-track geostrophic velocity component along the highlighted satellite track suggests indeed anticyclonic rotation around this secondary SLA maximum (Fig. 8b). This anticyclonic rotation persists throughout the upper water column as shown by the SADCP data (Figs. 8c,d).

Using ship-based observations, our analysis supports the findings of Amores et al. (2018) and Bashmachnikov et al. (2020), which demonstrated the limitations of conventional satellite altimetry in accurately representing the eddy field. Overall, eddy size tends to be overestimated and eddy density underestimated as multiple eddy-like signals may be merged into larger, spatially less frequent features. This distortion arises from the relatively sparse and uneven spatial and temporal sampling of conventional altimetry satellites, as well as the mapping techniques used to generate those gridded fields. This effect is particularly pronounced in high-latitude oceans like the Labrador Sea, where small $R_d$ and altimetry-induced aliasing further exacerbate the issue. Clearly, SADCP data are available at much higher spatial resolution and we showed that it allows for eddy detection well below $R_d$. However, the above examples demonstrate that even larger-scale features

(i.e., $R_{max} > R_d$) are missed by gridded altimetry products—even if they do have a signature in the along-track data. This effect is especially known for CEs, which are more dynamically unstable and evolve more rapidly than AEs (Arai and Yamagata 1994; Graves et al. 2006). Specifically, it was recently reported that their relatively fast evolution into smaller-scale CEs often is too challenging to be captured by available satellite tracks (Stegner et al. 2021).

## 6. Comparison to submesoscale-permitting numerical model output

### a. Distortion of eddy characteristics: Full-resolution versus resampled NATL60

Submesoscale-permitting numerical model output from NATL60 (see section 2c) allows us to further highlight the observed distortion of eddy properties in the Labrador Sea. The numerical model’s eddy field is exemplarily shown in Fig. 9 by instantaneous snapshots of the upper-mean (15–100 m) horizontal current speed (Fig. 9a) and normalized relative vorticity (Fig. 9b) on 15 June 2013. Enhanced mesoscale-to-submesoscale eddy activity away from the boundary currents is observed, expressed by large swirling velocities and circular patches of positive or negative relative vorticity.

The associated eddy field based on the upper (15–100 m) full-resolution velocity field for the given date as detected by AMEDA (see section 3e) is shown by the colored patches while distinguishing between CEs in blue and AEs in red (Fig. 9c). Following the approach of Amores et al. (2018), we also show resampled SLA alongside surface geostrophic velocities. The corresponding resampled eddy field as detected by AMEDA is shown by colored contours. Here, the full-resolution eddy field serves as an analog to the eddy field captured by ship observations, whereas the resampled eddy field is representative of gridded altimetry products. For the following comparison, we focus exclusively on eddies in the central Labrador Sea, where the bathymetry exceeds 2000 m.
This choice was primarily made to exclude regions where the boundary currents are overwhelmingly dominant.

The full-resolution and resampled NATL60 eddy fields exhibit a significant difference in the eddy density. Taking the full-resolution eddy field as reference truth, the example in Fig. 9c clearly illustrates that only a few eddies are accurately represented in terms of size and shape by the gridded altimetry-like product. The majority are either overestimated in size or not detected at all. In particular, the resampled product appears to merge two or three smaller-scale eddies into one larger one and therefore largely distorts eddy properties. In the full-resolution eddy field, in total, 260, 212, and 134 eddies are detected for three snapshots on 15 May, 15 June, and 15 August, respectively. This stands in contrast to only 35, 38, and 31 eddies in the resampled geostrophic velocity field. This would correspond to only 13%, 18%, and 23% of eddies, which are detected by the gridded altimetry-like product. This contrast is less pronounced than the 6% reported by Amores et al. (2018). However, their study covers the entire North Atlantic, whereas we focus specifically on the central Labrador Sea. Note that nearly twice as many eddies are detected in NATL60 on 15 May compared to 15 August. This increase is almost entirely due to an increasing amount of submesoscale eddies ($R_{max} < R_d$), while the number of mesoscale eddies remains largely unchanged. This pattern suggests that the submesoscale activity undergoes pronounced seasonal variations in accordance with midlatitude dynamics, driven by deeper mixed layers, stronger lateral buoyancy gradients, and an overall increase in available potential energy during the winter months (Callies et al. 2015). The absence of this seasonal variability in the ship data is likely due to limited spatial sampling along ship tracks.

Similarly to the analysis in section 5a, we compare the probability distributions of $R_{max}$, $V_{max}$, and Ro between the full-resolution and resampled eddy fields (Figs. 6d–f). The eddy properties largely differ from each other. The full-resolution $R_{max}$ averages $8.7 \pm 5.2$ km, whereas the resampled $R_{max}$ is significantly larger at $32 \pm 10.3$ km. Similarly, the full-resolution $V_{max}$ averages $14.1 \pm 12.8$ cm s⁻¹, compared to just $6.5 \pm 4.1$ cm s⁻¹ in the resampled field. The full-resolution Ro is also an order of magnitude higher than in the resampled dataset. We conclude that eddy properties derived from resampled NATL60 output exhibit similar discrepancies when compared to the full-resolution NATL60 output as gridded altimetry does to ship observations. Notably, ship observations and full-resolution NATL60 output reveal eddy radii more than three times smaller than their resampled counterparts, while azimuthal velocities are more than twice as large.

The choice of data product used for eddy property estimation also impacts the relationships between key eddy variables ($R_{max}$, $V_{max}$, and SSH signature) (Fig. 10). Full-resolution NATL60 output exhibits distinct linear relationships for $V_{max}$-$R_{max}$ (Fig. 10a), $R_{max}$-SSH (Fig. 10d), and $V_{max}$-SSH relationships (Fig. 10g). Furthermore, we note a clear rotational dependence in Figs. 10a and 10d. Although this rotational dependence is overall preserved in the resampled NATL60 output—with AEs exhibiting stronger positive $V_{max}$-$R_{max}$ relationships compared to CEs and CEs exhibiting stronger positive $R_{max}$-SSH relationships compared to AEs—it is

less distinct (Figs. 10b,e). Furthermore, the fitted linear slopes are notably altered in the resampled NATL60 output, indicating a distortion of the underlying relationships.

### b. How do eddy characteristics from full-resolution NATL60 compare with ship observations?

The realism of eddy characteristics derived from the full-resolution NATL60 output is assessed using the ship observations as a reference dataset. Compared to NATL60, ship-based eddies are, on average, almost 70% larger in $R_{max}$ and exhibit $V_{max}$ that are almost twice as high. Additionally, ship-based eddies have a ~40% larger Ro (see Table 2). The discrepancy in $R_{max}$ can be partially attributed to the broader range and the increasing number of larger eddy scales encountered during the research cruises (cf. Figs. 6a,d). In contrast to the model, $V_{max}$ observed in the ship data are more evenly distributed across the same range (cf. Figs. 6b,e). Furthermore, NATL60 features an increased number of submesoscale eddies (33%–60% compared to 11%–37%). Whatsoever, the relationship $V_{max}$-$R_{max}$ for CEs and AEs is surprisingly well captured by the ship observations, closely resembling the patterns seen in NATL60 (cf. Figs. 10a,c). There is little agreement when considering the relationships involving SSH.

Observational constraints likely contribute to the discrepancies between ship observations and NATL60 in both mean eddy statistics and the linear relationships for CEs and AEs. First, due to limited sampling along ship tracks, the number of eddies observed is relatively small (38 compared to 606 eddies). However, compared to mooring observations at fixed locations, ship-based measurements provide a significant improvement by capturing eddy properties over a broader spatial extent. Second, ship-based eddy properties may vary depending on eddy ellipticity and the specific location where the ship track crosses the eddy’s inner core (see section 3d and the appendix). The model’s tendency toward smaller eddy radii and azimuthal velocities could be related to the fact that smaller-scale eddies, which generally exhibit lower velocities, were less frequently captured in the ship observations. For a more representative comparison, we also computed eddy characteristics from the full-resolution NATL60 output, but only for eddies which lie along the three ship tracks. We count 51 individual eddies of which 23 are CEs and 28 are AEs. Probability distributions of $R_{max}$, $V_{max}$, and Ro (alongside their mean value) resemble those for the basinwide eddy characteristics (not shown). The discrepancy in SSH requires further investigation, as in ship observations, SSH is highly sensitive to the outer ring exponential decay scale [see Eq. (11)], which itself is influenced by the significant variability in the eddies’ outskirts (see Fig. 5c).

## 7. Summary and conclusions

This study focused on the objective reconstruction and characterization of surface-intensified coherent eddies in the Labrador Sea using quasi-continuously measuring current profiler data. By doing so, we aimed to contribute to the census of mesoscale-to-submesoscale eddy characteristics in the region, where few in situ studies exist. Assuming an axisymmetric and
<figure><img src="image_13.png" /><figcaption>FIG. 10. Relationship between $V_{max}$ and $R_{max}$ for (a) full-resolution NATL60 output, (b) resampled NATL60 output, and (c) ship-based observations (SADCP) distinguishing between CEs (blue) and AEs (red). The fitted regression line is included in each panel, along with the corresponding regression coefficient ($m$) and coefficient of determination ($r^2$). (d)–(f), (g)–(i) As in (a)–(c), but for the relationships $R_{max}$–SSH and $V_{max}$–SSH, respectively.</figcaption></figure>

nontranslating vortex, we derived eddy characteristics in cylindrical coordinates solving a nonlinear eddy center optimization problem following the approach of Castelão and Johns (2011) and Castelão et al. (2013).

Overall, we reconstructed 38 individual eddies with radii ranging from 3 to 39 km (mean 15 km) and maximum azimuthal velocities from 7 to 58 cm s⁻¹ (mean 26 cm s⁻¹). These values are in general agreement with mooring-based estimates from Lilly et al. (2003) and de Jong et al. (2014), which report eddy radii between 5 and 35 km and azimuthal velocities from

9 to 77 cm s⁻¹. More than one-third of these eddies feature radii below the local $R_d$, which could be considered submesoscale. Unlike previous studies, we did not classify the reconstructed eddies into specific eddy types (IRs, CL, and BCEs) due to the lack of high-resolution hydrographic data along the ship tracks. However, our approach enabled eddy characterization over an extended area of the central Labrador Sea, contrasting with the mooring observations at fixed locations.

The ship observations give detailed insights into the azimuthal velocity structure for both the eddy's inner core and
<figure><img src="image_14.png" /><figcaption>FIG. 11. Azimuthal velocity structure (shading; black solid/dashed contours) of an anticyclonic eddy surveyed during MSM40 with an 150-kHz and the 38-kHz SADCP operating in parallel. The inset shows observed velocities along the ship track and the optimized eddy center and boundary at 104-m depth. Depth-dependent radius $R_{max}(z)$ (white contour) obtained from the optimization to successive depth ranges (see the text for further details).</figcaption></figure>

outer ring. While the inner core exhibits to a large extent solid-body rotation, the overall velocity structure only partially resembles that of a Rankine vortex. The largest discrepancy to a Rankine vortex is observed at the eddy boundary, where the maximum azimuthal velocity is reduced by 5%–55%. Consistent with previous findings for vortices spanning a wide range of scales—from just a few centimeters (Meuel et al. 2013) to tens of meters (Kanak 2005), and up to planetary scales (Chelton et al. 2007, 2011)—we find that the azimuthal velocity structure more closely follows a Gaussian-like shape (Chelton et al. 2011; Wang et al. 2015; Yang et al. 2019).

The degree to which the azimuthal velocity structure deviates from that of a Rankine vortex may provide insights into the eddy’s coherent nature, its interaction with the surrounding flow, and its overall life cycle. The outer ring generally exhibits greater variability than the inner core, likely due to external strain fields from the background flow, nonlinear eddy–eddy interactions, and interactions between the mean flow and the eddy field (Zhang and Qiu 2018). Ageostrophic kinetic energy levels have also been shown to impact the azimuthal velocity structure and become increasingly important under enhanced geostrophic strain rates (Zhang and Qiu 2018). The developing perturbations are maximum around the eddy boundary. Moreover, they peak during the eddy’s formation and decay phases. Vortex stripping, first described by Legras and Dritschel (1993), is also considered to impact the azimuthal velocity structure by “stripping off” the most external layer of an isolated vortex and the associated penetration of the background velocity field. This process may drive outward advection of vorticity and eventually escaping filaments producing large vorticity gradients. Our study suggests the presence of strong vorticity shields, as indicated by opposite signs of vorticity just beyond the eddy boundary. This, in turn, implies a higher degree of isolation from the surrounding flow, with weak eddy–eddy interactions (Carton 1992; Verron and Valcke 1994; Valcke and

Verron 1997). Notably, anticyclones appear to be more isolated than cyclones, as shown by their more rapid decay of azimuthal velocity in the outer ring. This rotational dependence of eddy stability is well documented in the literature (Stegner and Dritschel 2000; Chelton et al. 2011; Stegner et al. 2021).

Ship-based eddy characteristics contrast with those derived from gridded altimetry products, with the latter exhibiting radii approximately three times larger and azimuthal velocities three times smaller. This distortion is primarily attributed to the presence of smaller-scale eddies ($R_{max} < R_d$) in the ship observations that remain undetected in altimetry. Additionally, even larger-scale eddies ($R_{max} > R_d$) may not be represented in the gridded product, despite having a detectable signature in the along-track data. This is likely due to the smoothing effect of the optimal interpolation applied in the generation of gridded altimetry products, which can diminish eddy signatures. Using ship observations, we arrive at the same conclusion as Amores et al. (2018) and Bashmachnikov et al. (2020): Eddy characteristics derived from gridded altimetry in high-latitude oceans should be interpreted with caution as they may be significantly distorted. Our objective is not to discourage the use of gridded altimetry products but rather to emphasize the importance of complementing them with additional (ship-based) datasets when available, to obtain a more accurate and comprehensive picture of local eddy dynamics.

That said, ship-based eddy reconstructions also have their limitations, as they are often based on a single eddy crossing. This can lead to distorted eddy properties, especially as eddy ellipticity increases, since a single transect may not fully capture the true eddy shape and dynamics. Nevertheless, we are confident that this methodology remains a valuable tool for characterizing eddies from an in situ perspective. Notably, it has proven effective in detecting eddies along the ship track that would otherwise remain undetected or be misrepresented
by conventional satellite altimetry. It may also be relevant for ship-based operations aiming to survey oceanic eddies to investigate their biogeochemical properties. Such operations often seek to cross eddies through their center to obtain a well-resolved representation of both the inner core and outer ring, which is crucial for accurately capturing their structure. An interesting application lies in the Surface Water Ocean Topography (SWOT) satellite altimetry mission, which has been shown to resolve submesoscale motion (Du and Jing 2024; Zhang et al. 2024; Archer et al. 2025). The here proposed ship-based eddy reconstruction may help interpret eddy signatures in SWOT SSH measurements and vice versa.

In this study, we focused solely on surface-intensified eddy reconstruction, applied to horizontal velocity data averaged over a defined depth range near the surface. Extending the reconstruction to successive depth ranges (discretized into depth layers) provides insights into the eddy's vertical structure. In the Labrador Sea, using SADCP data in the upper 1000 m is often insufficient to capture the first baroclinic mode eddy structure. However, a vertical reconstruction of such a baroclinic eddy, even when limited to the upper 1000 m, can still be partly achieved with this technique. This approach is demonstrated for an anticyclone encountered during MSM40, extending down to depths greater than 800 m (Fig. 11). Even though hydrography data along the ship track would be needed to verify, the eddy's anticyclonic rotation and radius are suggestive of an IR. IRs studied in Lilly et al. (2003), de Jong et al. (2014), and Hátún et al. (2007) feature similar vertical velocity structures, with a surface-intensified velocity core that can penetrate to great depths well beyond 1000-m depth. We note that by extending this technique to successive depth ranges, the analysis could also focus on deep subsurface velocity maxima as seen in Denmark Strait Overflow Water cyclones—a fourth eddy type in the Labrador Sea, which has recently been reported by Pacini et al. (2021) and Zou et al. (2021).

We hope to add to the census of mesoscale-to-submesoscale eddies in the Labrador Sea. The overall understanding of fine-scale dynamics is of increasing interest in this region. The here presented comprehensive and basinwide eddy field characterization aims to contribute to the assessment of high-latitude eddy dynamics in submesoscale-permitting numerical simulation output, with crucial knowledge for studies focusing on the impact of smaller-scale dynamics on larger-scale processes such as deep convection.

*Acknowledgments.* Part of this work was funded by the European Union under Grant Agreement 101094690 (EuroGO-SHIP). F. D. and J. K. acknowledge the funding from the European Union under Grant Agreement 101136548 (ObsSea4Clim; https://doi.org/10.3030/101136548). We thank Angel Amores for providing us with the resampled NATL60 SLA fields. We also thank Martin Storath for fruitful discussions on the Gauss-Newton optimization algorithm.

*Data availability statement.* The SADCP data are publicly available and can be downloaded for each research cruise via PANGAEA, the Data Publisher for Earth and Environmental

Science: MSM40 (Karstensen et al. 2023), MSM54 (Karstensen et al. 2020), and MSM74 (Karstensen and Czeschel 2021). This study has been conducted using EU Copernicus Marine Service Information CMEMS (https://doi.org/10.48670/moi-00147, https://doi.org/10.48670/moi-00146, https://doi.org/10.48670/moi-00148). The numerical simulation output from NATL60 to which we applied the eddy detection algorithm (AMEDA) can be found at https://zenodo.org/records/13975467. The resampled NATL60 SLA fields were made available by Angel Amores upon request. The software for the eddy center optimization problem is publicly available (https://github.com/arnebca/EddyCentre Toolbox). AMEDA is also publicly available (https://github.com/briaclevu/AMEDA; Le Vu et al. 2018).

# APPENDIX

## Methodology Assessment

The eddy characterization performed in this study relies on an eddy center optimization problem based on horizontal velocity data acquired along one-dimensional ship tracks, which crossed the eddy somewhere within its inner core. While a converging solution is suggestive of a robust eddy center estimate, derived characteristics such as radius and azimuthal velocity may be distorted for radially asymmetric eddies. This distortion can occur because these properties exhibit azimuthal variability—meaning that they can vary around the eddy particularly for elliptical-shaped eddies, making the derived characteristics sensitive to the specific location and orientation of the ship track crossing. Being aware of this dependency is crucial because the ship-based eddy reconstruction often relies on a single crossing.

The methodology assessment was performed for two exemplary eddies extracted from the instantaneous upper-mean (15–100 m) NATL60 horizontal velocity field on 15 June 2013: one nearly radially symmetric eddy (Fig. A1) and one more elliptical-shaped eddy (Fig. A2). We first interpolated the model horizontal velocities ($u_i, v_j$) along the model $i$ and $j$ axes and defined on a staggered Arakawa C grid onto a common set of grid points. Furthermore, $u_i$ and $v_j$ were rotated to eastward $u_{rot}$ and northward velocity $v_{rot}$ components as follows:

$$u_{\text{rot}} = u_i \cos\phi - v_j \sin\phi, \quad (A1)$$

$$v_{\text{rot}} = u_i \sin\phi + v_j \cos\phi, \quad (A2)$$

where $\phi$ is the angle between the line that spans two neighboring grid points and the positive $x$ axis (eastward). Note that $i$ and $j$ axes refer to the curvilinear computational grid, which may not align with geographic eastward and northward direction, respectively. A set of optimizations was conducted with virtual ship tracks crossing the eddy from the western to eastern flank (zonal crossings) and from the northern to southern flank (meridional crossings). In this way, the eddies were fully sampled in two-dimensional space, including sections that only partially intersect the inner core near the eddy boundary. Note that we consider eddy properties derived from AMEDA (see section 3e) as ground truth.
<figure><img src="image_15.png" /><figcaption>FIG. A1. Assessment of the Gauss–Newton eddy reconstruction for a radially symmetric vortex. (a) Upper-mean (15–100 m) NATL60 horizontal velocity field on 15 Jun 2013 (gray arrows), with zero relative vorticity contours (gray). Eddy center and boundary from AMEDA are shown in red; the black dot and solid circle indicate the Gauss–Newton mean eddy center and boundary across all virtual ship track crossings (inset), respectively. Dashed and dotted black circles show the mean boundaries from zonal and meridional crossings, respectively. Small dots show the individual center estimates. (b) Azimuthal velocity structure $v_\theta$ from the Gauss–Newton method, based on zonal (dashed) and meridional (dotted) crossings. Red lines mark $R_{max}$ and $V_{max}$ from AMEDA. (c) Azimuthal variability of $R_{max}$ (green) and $V_{max}$ (yellow) along the eddy boundary, binned in 20° increments counterclockwise from the x axis. Dashed lines denote the AMEDA estimates.</figcaption></figure>

We start the methodology assessment for a radially symmetric vortex (Fig. A1). The horizontal velocity field contour, alongside the enclosed zero relative vorticity contour, gives a first estimate of the eddy’s polarity, location, and extent. Note that in theory, the contour of zero relative vorticity coincides with the contour of maximum azimuthal velocity for a Rankine vortex (see section 4c). Eddy center and boundary as identified by the Gauss–Newton optimization, averaged over all virtual ship tracks, show strong agreement with AMEDA, with an almost perfect overlap (cf. black/red dots and circles in Fig. A1a). The estimated eddy radius is identical to one decimal place (19.1 ± 0.5 km for Gauss–Newton compared to 19.1 km for AMEDA). Both radii are underestimated when compared to

the contour of zero relative vorticity. However, this is not surprising as maximum azimuthal velocity and zero relative vorticity do not coincide in realistic vortices (see Fig. 5e). The maximum azimuthal velocity also agrees closely across methods (76.6 ± 1.4 cm s⁻¹ for Gauss–Newton compared to 75.2 cm s⁻¹ for AMEDA). The azimuthal velocity structure reconstructed from the Gauss–Newton eddy center optimization for each virtual ship track accurately captures the radial symmetry of the horizontal velocity field in both the inner core and outer ring (Fig. A1b). Considering all virtual ship tracks, the ellipticity defined as 1 – *b*/a (where *a* is the semimajor axis and *b* is the semiminor axis) is 0.03, closely matching the AMEDA-derived value of 0.02. Furthermore, the speed-

<figure><img src="image_16.png" /><figcaption>FIG. A2. As in Fig. A1, but for a radially asymmetric vortex.</figcaption></figure>
based eddy radius $R_{max}$ and corresponding maximum azimuthal velocity $V_{max}$ (binned in 20° increments along the eddy boundary and measured counterclockwise from the positive x axis) exhibit low azimuthal variability as they deviate on average by only 2.3% and 1.5%, respectively, from their mean values (Fig. A1c). We conclude for radially symmetric vortices that the Gauss–Newton optimization and derived properties show very little to no dependency on the location and orientation of the ship track crossing. In other words, a single ship track crossing—whether close to the eddy center or its boundary—is sufficient to obtain a representative eddy reconstruction.

A different conclusion emerges for a vortex with a more elliptical shape (Fig. A2). Although the eddy centers largely overlap and the average eddy radius ($22.4 \pm 5.5$ km for Gauss–Newton compared to $22.4$ km for AMEDA) and azimuthal velocity ($101.9 \pm 9.6$ cm s⁻¹ for Gauss–Newton compared to $96.3$ cm s⁻¹ for AMEDA) show good agreement when averaged over all virtual ship tracks, the reconstructed eddy properties are highly sensitive to the orientation and location of the ship track crossing (Fig. A2a). For example, the radius estimated from zonal crossings is significantly smaller ($18.2 \pm 1.5$ km, dashed black circle) than from meridional crossings ($28.7 \pm 2.1$ km, dotted black circle). Similarly, the azimuthal velocity differs between zonal and meridional transients ($105.4 \pm 8.0$ cm s⁻¹ compared to $96.8 \pm 9.4$ cm s⁻¹, respectively). Eddy center estimates from individual tracks also vary substantially (up to 10 km from the mean center), illustrated by the scattered dots connected by dashed and dotted lines representative of zonal and meridional crossings, respectively. This variability reflects the vortex's radial asymmetry and explains the higher standard deviations in radius and azimuthal velocity compared to the symmetric example in Fig. A1. The asymmetry is further evident in the reconstructed azimuthal velocity structure (Fig. A2b). Considering all virtual ship tracks, the ellipticity is 0.37, which approximates the AMEDA ellipticity values of 0.26. The $R_{max}$ and $V_{max}$ exhibit elevated azimuthal variability along the eddy boundary and deviate on average by 22.6% and 7.7% (with maximum values of 47.1% and 21.3%), respectively, from their mean values (Fig. A2c). We conclude for radially asymmetric vortices that the Gauss–Newton optimization and derived properties are largely dependent of the ship track's location and orientation. Depending on the degree of ellipticity, the eddy reconstruction from a single crossing can result in largely distorted eddy properties. To account for the two-dimensional shape, at least two sections along the major and minor eddy axes would be required. The degree to which our eddy characterization in section 4b is distorted remains unknown since most eddies were surveyed during transit and, hence, crossed only once.

The methodology was assessed using two large-scale AEs, illustrating how radial asymmetry influences eddy reconstruction along different ship transects. We extended this analysis to smaller-scale structures ($R_{max} = 5–10$ km) and eddies of both polarities (CEs and AEs), with consistent conclusions. In all cases, radially symmetric vortices—regardless of size or rotation direction—show little no dependency to the location or orientation of the ship transect. In contrast, most of the variability in reconstructed eddy properties such as $R_{max}$ and

$V_{max}$ is attributed to radial asymmetry, particularly elliptical eddy shapes.

REFERENCES

Amores, A., G. Jordà, T. Arsouze, and J. Le Sommer, 2018: Up to what extent can we characterize ocean eddies using present-day gridded altimetric products? *J. Geophys. Res. Oceans*, **123**, 7220–7236, https://doi.org/10.1029/2018JC014140.

Arai, M., and T. Yamagata, 1994: Asymmetric evolution of eddies in rotating shallow water. *Chaos*, **4**, 163–175, https://doi.org/10.1063/1.166001.

Archer, M., J. Wang, P. Klein, G. Dibarboure, and L.-L. Fu, 2025: Wide-swath satellite altimetry unveils global submesoscale ocean dynamics. *Nature*, **640**, 691–696, https://doi.org/10.1038/s41586-025-08722-8.

Armijo, L., 1966: Minimization of functions having Lipschitz continuous first partial derivatives. *Pac. J. Math.*, **16** (1), 1–3, https://doi.org/10.2140/pjm.1966.16.1.

Ballarotta, M., and Coauthors, 2019: On the resolutions of ocean altimetry maps. *Ocean Sci.*, **15**, 1091–1109, https://doi.org/10.5194/os-15-1091-2019.

Bashmachnikov, I. L., I. E. Kozlov, L. A. Petrenko, N. I. Glok, and C. Wekerle, 2020: Eddies in the North Greenland Sea and Fram Strait from satellite altimetry, SAR and high-resolution model data. *J. Geophys. Res. Oceans*, **125**, e2019JC015832, https://doi.org/10.1029/2019JC015832.

Brandt, P., F. A. Schott, A. Funk, and C. S. Martins, 2004: Seasonal to interannual variability of the eddy field in the Labrador Sea from satellite altimetry. *J. Geophys. Res.*, **109**, C02028, https://doi.org/10.1029/2002JC001551.

Callies, J., R. Ferrari, J. M. Klymak, and J. Gula, 2015: Seasonality in submesoscale turbulence. *Nat. Commun.*, **6**, 6862, https://doi.org/10.1038/ncomms7862.

Cao, Y., C. Dong, A. Stegner, B. J. Bethel, C. Li, J. Dong, H. Lü, and J. Yang, 2023: Global sea surface cyclogeostrophic currents derived from satellite altimetry data. *J. Geophys. Res. Oceans*, **128**, e0220JC019357, https://doi.org/10.1029/2022JC019357.

Carton, X. J., 1992: On the merger of shielded vortices. *Europhys. Lett.*, **18**, 697–703, https://doi.org/10.1209/0295-5075/18/8/006.

Castelão, G., and W. E. Johns, 2011: Sea surface structure of North Brazil Current Rings derived from shipboard and moored acoustic Doppler current profiler observations. *J. Geophys. Res.*, **116**, C01010, https://doi.org/10.1029/2010JC006575.

Castelão, G. P., L. C. Irber Jr., and A. B. V. Boas, 2013: An objective reference system for studying rings in the ocean. *Comput. Geosci.*, **61**, 43–49, https://doi.org/10.1016/j.cageo.2013.07.004.

Chanut, J., B. Barnier, W. Large, L. Debreu, T. Penduff, J. M. Molines, and P. Mathiot, 2008: Mesoscale eddies in the Labrador Sea and their contribution to convection and reستrafication. *J. Phys. Oceanogr.*, **38**, 1617–1643, https://doi.org/10.1175/2008JPO3485.1.

Chelton, D. B., and M. G. Schlax, 1996: Global observations of oceanic Rossby waves. *Science*, **272**, 234–238, https://doi.org/10.1126/science.272.5259.234.

—, R. A. DeSzoeke, M. G. Schlax, K. El Naggar, and N. Siwertz, 1998: Geographical variability of the first baroclinic Rossby radius of deformation. *J. Phys. Oceanogr.*, **28**, 433–460, https://doi.org/10.1175/1520-0485(1998)028<0433:GVOTFB>2.0.CO;2.

—, M. G. Schlax, R. M. Samelson, and R. A. de Szoeke, 2007: Global observations of large oceanic eddies. *Geophys. Res. Lett.*, **34**, L15606, https://doi.org/10.1029/2007GL030812.
—, —, and —, 2011: Global observations of nonlinear mesoscale eddies. *Prog. Oceanogr.*, **91**, 167–216, https://doi.org/10.1016/j.pocean.2011.01.002.

Chigier, N. A., 1979: Pollution formation and destruction in flames— Introduction. *Energy and Combustion Science*, Elsevier, 3–15, https://doi.org/10.1016/B978-0-08-024780-9.50005-8.

Cushman-Roisin, B., B. Tang, and E. P. Chassignet, 1990: Westward motion of mesoscale eddies. *J. Phys. Oceanogr.*, **20**, 758–768, https://doi.org/10.1175/1520-0485(1990)020<0758: WMOME>2.0.CO;2.

Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. *Quart. J. Roy. Meteor. Soc.*, **137**, 553–597, https://doi.org/10.1002/qj.828.

de Jong, M. F., A. S. Bower, and H. H. Furey, 2014: Two years of observations of warm-core anticyclones in the Labrador Sea and their seasonal cycle in heat and salt stratification. *J. Phys. Oceanogr.*, **44**, 427–444, https://doi.org/10.1175/JPO-D-13-0701.1.

Du, T., and Z. Jing, 2024: Fine-scale eddies detected by SWOT in the Kuroshio extension. *Remote Sens.*, **16**, 3488, https://doi.org/10.3390/rs16183488.

Dussin, R., B. Barnier, L. Brodeau, and J. M. Molines, 2016: The making of the Drakkar forcing set DFS5. DRAKKAR/ MyOcean Rep. 01-04-16, 34 pp., https://www.drakkar-ocean.eu/publications/reports/report_DFS5v3_April2016.pdf.

Early, J. J., R. M. Samelson, and D. B. Chelton, 2011: The evolution and propagation of quasigeostrophic ocean eddies. *J. Phys. Oceanogr.*, **41**, 1535–1555, https://doi.org/10.1175/2011JPO4601.1.

Eden, C., and C. Böning, 2002: Sources of eddy kinetic energy in the Labrador Sea. *J. Phys. Oceanogr.*, **32**, 3346–3363, https://doi.org/10.1175/1520-0485(2002)032<3346:SOEKEI>2.0.CO;2.

Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources, and sinks. *Annu. Rev. Fluid Mech.*, **41**, 253–282, https://doi.org/10.1146/annurev.fluid.40.111406.102139.

Ferry, N., and Coauthors, 2012: GLORYS2V1 global ocean reanalysis of the altimetric era 1992–2009 at mesoscale. *Mercator Ocean Quarterly Newsletter*, No. 44, Mercator Ocean Office, 29–39, https://www.mercator-ocean.eu/wp-content/uploads/2015/05/Mercator-Ocean-newsletter-2012_44.pdf#page=28.

Funk, A., P. Brandt, and T. Fischer, 2009: Eddy diffusivities estimated from observations in the Labrador Sea. *J. Geophys. Res.*, **114**, C04001, https://doi.org/10.1029/2008JC005098.

Graves, L. P., J. C. McWilliams, and M. T. Montgomery, 2006: Vortex evolution due to straining: A mechanism for dominance of strong, interior anticyclones. *Geophys. Astrophys. Fluid Dyn.*, **100**, 151–183, https://doi.org/10.1080/03091920600792041.

Hátún, H., C. C. Eriksen, and P. B. Rhines, 2007: Buoyant eddies entering the Labrador Sea observed with gliders and altimeter. *J. Phys. Oceanogr.*, **37**, 2838–2854, https://doi.org/10.1175/2007JPO3567.1.

Ioannou, A., A. Stegner, A. Tuel, B. LeVu, F. Dumas, and S. Speich, 2019: Cyclostrophic corrections of AVISO/DUACS surface velocities and its application to mesoscale eddies in the Mediterranean Sea. *J. Geophys. Res. Oceans*, **124**, 8913–8932, https://doi.org/10.1029/2019JC015031.

Jones, H., and J. Marshall, 1993: Convection with rotation in a neutral ocean: A study of open-ocean deep convection. *J. Phys. Oceanogr.*, **23**, 1009–1039, https://doi.org/10.1175/1520-0485(1993)023<1009:CWRIAN>2.0.CO;2.

Kanak, K. M., 2005: Numerical simulation of dust devil-scale vortices. *Quart. J. Roy. Meteor. Soc.*, **131**, 1271–1292, https://doi.org/10.1256/qj.03.172.

Karstensen, J., and R. Czeschel, 2021: ADCP current measurements (38 and 75 kHz) during Maria S. Merian cruise MSM74. PANGAEA, accessed 11 March 2021, https://doi.org/10.1594/PANGAEA.929000.

—, —, and G. Krahmann, 2020: ADCP current measurements during Maria S. Merian cruise MSM54. PANGAEA, accessed 4 February 2020, https://doi.org/10.1594/PANGAEA.911727.

—, —, and —, 2023: ADCP current measurements (38 and 150 kHz) during THALASSA cruise THA-MSM40. PANGAEA, accessed 12 September 2023, https://doi.org/10.1594/PANGAEA.962231.

Katsman, C. A., M. A. Spall, and R. S. Pickart, 2004: Boundary current eddies and their role in the restratification of the Labrador Sea. *J. Phys. Oceanogr.*, **34**, 1967–1983, https://doi.org/10.1175/1520-0485(2004)034<1967:BCEATR>2.0.CO;2.

Laxenaire, R., S. Speich, B. Blanke, A. Chaigneau, C. Pegliasco, and A. Stegner, 2018: Anticyclonic eddies connecting the western boundaries of Indian and Atlantic oceans. *J. Geophys. Res. Oceans*, **123**, 7651–7677, https://doi.org/10.1029/2018JC014270.

Legras, B., and D. Dritschel, 1993: Vortex stripping and the generation of high vorticity gradients in two-dimensional flows. *Advances in Turbulence IV*, F. T. M. Nieuwstadt, Ed., Fluid Mechanics and its Applications, Vol. 18, Springer, 445–455, https://doi.org/10.1007/978-94-011-1689-3_70.

Le Vu, B., A. Stegner, and T. Arsouze, 2018: Angular momentum eddy detection and tracking algorithm (AMEDA) and its application to coastal eddy formation. *J. Atmos. Oceanic Technology*, **35**, 739–762, https://doi.org/10.1175/JTECH-D-17-0010.1.

Li, F., M. S. Lozier, G. Danabasoglu, N. P. Holliday, Y.-O. Kwon, A. Romanou, S. G. Yeager, and R. Zhang, 2019: Local and downstream relationships between Labrador Sea water volume and North Atlantic meridional overturning circulation variability. *J. Climate*, **32**, 3883–3898, https://doi.org/10.1175/JCLI-D-18-0735.1.

Lilly, J. M., and P. B. Rhines, 2002: Coherent eddies in the Labrador Sea observed from a mooring. *J. Phys. Oceanogr.*, **32**, 585–598, https://doi.org/10.1175/1520-0485(2002)032<0585:CEITLS>2.0.CO;2.

—, —, M. Visbeck, R. Davis, J. R. N. Lazier, F. Schott, and D. Farmer, 1999: Observing deep convection in the Labrador Sea during winter 1994/95. *J. Phys. Oceanogr.*, **29**, 2065–2098, https://doi.org/10.1175/1520-0485(1999)029<2065:ODCITL>2.0.CO;2.

—, —, F. Schott, K. Lavender, J. Lazier, U. Send, and E. D'Asaro, 2003: Observations of the Labrador Sea eddy field. *Prog. Oceanogr.*, **59**, 75–176, https://doi.org/10.1016/j.pocean.2003.08.013.

Madec, G., and NEMO System Team, 2024: NEMO ocean engine Reference Manual Version 5.0. Zenodo, https://doi.org/10.5281/zenodo.1464816.

Marshall, J., and F. Schott, 1999: Open-ocean convection: Observations, theory, and models. *Rev. Geophys.*, **37** (1), 1–64, https://doi.org/10.1029/98RG02739.

McWilliams, J. C., 1985: Submesoscale, coherent vortices in the ocean. *Rev. Geophys.*, **23**, 165–182, https://doi.org/10.1029/RG023i002p00165.

Meuel, T., Y. L. Xiong, P. Fischer, C. H. Bruneau, M. Bessafi, and H. Kellay, 2013: Intensity of vortices: From soap bubbles
to hurricanes. *Sci. Rep.*, **3**, 3455, https://doi.org/10.1038/srep03455.

Molines, J.-M., 2018: Meom-configurations/NATL60-CJM165: NATL60 code used for CJM165 experiment Version 1.0.0. Zenodo, https://doi.org/10.5281/zenodo.1210116.

Olson, D. B., 1980: The physical oceanography of two rings observed by the cyclonic ring experiment. Part II: Dynamics. *J. Phys. Oceanogr.*, **10**, 514–528, https://doi.org/10.1175/1520-0485(1980)010%3C0514:TPOOTR%3E2.0.CO;2.

—, 1991: Rings in the ocean. *Annu. Rev. Earth Planet. Sci.*, **19**, 283–311, https://doi.org/10.1146/annurev.ea.19.050191.001435.

Pacini, A., and R. S. Pickart, 2022: Meanders of the West Greenland current near Cape Farewell. *Deep-Sea Res. I*, **179**, 103664, https://doi.org/10.1016/j.dsr.2021.103664.

—, —, I. A. Le Bras, F. Straneo, N. P. Holliday, and M. A. Spall, 2021: Cyclonic eddies in the West Greenland boundary current system. *J. Phys. Oceanogr.*, **51**, 2087–2102, https://doi.org/10.1175/JPO-D-20-0255.1.

Pegliasco, C., A. Delepoulle, E. Mason, R. Morrow, Y. Faugère, and G. Dibarboure, 2022: META3.1exp: A new global mesoscale eddy trajectory atlas derived from altimetry. *Earth Syst. Sci. Data*, **14**, 1087–1107, https://doi.org/10.5194/essd-14-1087-2022.

Pennelly, C., and P. G. Myers, 2020: Introducing LAB60: A 1/60° NEMO 3.6 numerical simulation of the Labrador Sea. *Geo-sci. Model Dev.*, **13**, 4959–4975, https://doi.org/10.5194/gmd-13-4959-2020.

Pickart, R. S., D. J. Torres, and R. A. Clarke, 2002: Hydrography of the Labrador Sea during active convection. *J. Phys. Oceanogr.*, **32**, 428–457, https://doi.org/10.1175/1520-0485(2002)032<0428:HOTLSD>2.0.CO;2.

Pujol, M.-I., Y. Faugère, G. Taburet, S. Dupuy, C. Pelloquin, M. Ablain, and N. Picot, 2016: DUACS DT2014: The new multi-mission altimeter data set reprocessed over 20 years. *Ocean Sci.*, **12**, 1067–1090, https://doi.org/10.5194/os-12-1067-2016.

Rieck, J. K., C. W. Böning, and K. Getzlaff, 2019: The nature of eddy kinetic energy in the Labrador Sea: Different types of mesoscale eddies, their temporal variability, and impact on deep convection. *J. Phys. Oceanogr.*, **49**, 2075–2094, https://doi.org/10.1175/JPO-D-18-0243.1.

Saenko, O. A., F. Dupont, D. Yang, P. G. Myers, I. Yashayaev, and G. C. Smith, 2014: Role of resolved and parameterized eddies in the Labrador Sea balance of heat and buoyancy. *J. Phys. Oceanogr.*, **44**, 3008–3032, https://doi.org/10.1175/JPO-D-14-0041.1.

Stegner, A., and D. G. Dritschel, 2000: A numerical investigation of the stability of isolated shallow water vortices. *J. Phys. Oceanogr.*, **30**, 2562–2573, https://doi.org/10.1175/1520-0485(2000)030<2562:ANIOTS>2.0.CO;2.

—, B. Le Vu, F. Dumas, M. A. Ghannami, A. Nicolle, C. Durand, and Y. Faugère, 2021: Cyclone-anticyclone asymmetry of eddy detection on gridded altimetry product in the Mediterranean Sea. *J. Geophys. Res. Oceans*, **126**, e2021JC017475, https://doi.org/10.1029/2021JC017475.

Straneo, F., 2006: Heat and freshwater transport through the central Labrador Sea. *J. Phys. Oceanogr.*, **36**, 606–628, https://doi.org/10.1175/JPO2875.1.

Tagklis, F., A. Bracco, T. Ito, and R. M. Castelao, 2020: Submesoscale modulation of deep water formation in the Labrador Sea. *Sci. Rep.*, **10**, 17489, https://doi.org/10.1038/s41598-020-74345-w.

Thomsen, S., C. Eden, and L. Czeschel, 2014: Stability analysis of the Labrador Current. *J. Phys. Oceanogr.*, **44**, 445–463, https://doi.org/10.1175/JPO-D-13-0121.1.

Valcke, S., and J. Verron, 1997: Interactions of baroclinic isolated vortices: The dominant effect of shielding. *J. Phys. Oceanogr.*, **27**, 524–541, https://doi.org/10.1175/1520-0485(1997)027<0524:IOBIVT>2.0.CO;2.

Verron, J., and S. Valcke, 1994: Scale-dependent merging of baroclinic vortices. *J. Fluid Mech.*, **264**, 81–106, https://doi.org/10.1017/S0022112094000595.

Wang, Z., Q. Li, L. Sun, S. Li, Y. Yang, and S. Liu, 2015: The most typical shape of oceanic mesoscale eddies from global satellite sea level observations. *Front. Earth Sci.*, **9**, 202–208, https://doi.org/10.1007/s11707-014-0478-z.

Wunsch, C., 2008: Mass and volume transport variability in an eddy-filled ocean. *Nat. Geosci.*, **1**, 165–168, https://doi.org/10.1038/ngeo126.

Yang, Z., G. Wang, and C. Chen, 2019: Horizontal velocity structure of mesoscale eddies in the South China Sea. *Deep-Sea Res. I*, **149**, 103055, https://doi.org/10.1016/j.dsr.2019.06.001.

Yule, A. J., 1978: Large-scale structure in the mixing layer of a round jet. *J. Fluid Mech.*, **89**, 413–432, https://doi.org/10.1017/S0022112078002670.

Zhang, Z., and B. Qiu, 2018: Evolution of submesoscale ageostrophic motions through the life cycle of oceanic mesoscale eddies. *Geophys. Res. Lett.*, **45**, 11847–11855, https://doi.org/10.1029/2018GL080399.

—, M. Miao, B. Qiu, J. Tian, Z. Jing, G. Chen, Z. Chen, and W. Zhao, 2024: Submesoscale eddies detected by SWOT and moored observations in the northwestern Pacific. *Geophys. Res. Lett.*, **51**, e2024GL110000, https://doi.org/10.1029/2024GL110000.

Zou, S., A. S. Bower, H. Furey, R. S. Pickart, L. Houpert, and N. P. Holliday, 2021: Observed deep cyclonic eddies around southern Greenland. *J. Phys. Oceanogr.*, **51**, 3235–3252, https://doi.org/10.1175/JPO-D-20-0288.1.