# The Dynamical Structure of a Warm Core Ring as Inferred from Glider Observations and Along-Track Altimetry

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## Abstract

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## 1. Introduction

## 2. Data

#### 2.1. The Glider Survey

#### 2.2. Satellite Altimetry

## 3. Methods

#### 3.1. The Relocation Method

#### 3.2. Validation

#### 3.3. Theoretical Framework

## 4. Results

#### 4.1. Thermohaline Structure

#### 4.2. Velocity

#### 4.3. Relative Vorticity and Strain

#### 4.4. Potential Vorticity Structure

#### 4.5. Energetics

## 5. Discussion

#### 5.1. The Relocation Method

#### 5.2. The LCR’s Vertical Structure

## 6. Summary

- A new altimetry-based method to relocate gliders observations in a synoptic frame of reference was designed and applied to recent observations of a Loop Current ring in the Gulf of Mexico.
- The method was tested using an analytical anticyclonic eddy drifting on the $\beta $-plane, and shown to recover the exact vertical structure of the eddy, whatever the sampling strategy, in the ideal case of a stable and circular eddy.
- The method was successful in correcting the errors in horizontal thermohaline gradients, related to the lack of synopticity of glider surveys.
- The relocation method also allows to precisely locate the eddy’s rotation axis, yielding more reliable estimates of cyclo-geostrophic velocity, relative vorticity, and shear strain.
- The warm core ring consisted of a bowl of homogeneous negative relative vorticity, surrounded by a crown of positive shear strain, resulting in a negative Okubo–Weiss parameter in the core and positive at the periphery.
- The PV structure of the warm-core ring is largely dominated by vortex stretching.
- The along-isopycnal radial PV gradient is also dominated by gradients of the vortex stretching term.
- Sign-changes of the PV-gradient suggests that the warm core ring might be baroclinically unstable.
- The energy density partition revealed a clear dominance of available potential energy over kinetic energy.
- Available potential energy density is mostly contained within the vorticity-dominated core of the warm-core ring (negative Okubo–Weiss), where properties are expected to be well conserved. This might possibly contribute to its longevity.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Map of AVISO-gridded absolute dynamic topography (ADT) in the Gulf of Mexico on September 10. The Loop Current Ring is evident as a circular anomaly of high ADT centered near 89${}^{\circ}$W 25.5${}^{\circ}$N. The geostrophic currents are plotted as arrows. The 500 and 2000 m isobaths are plotted as thick gray lines.

**Figure 2.**(

**a**) Map of the glider survey superimposed on successive edge contours of the ring between 07/08/2016 and 01/09/2016. The edge contour is estimated using Absolute Dynamic Topography. Time is color-coded. (

**b**) Selected satellite tracks superimposed on the ring’s edge contour on the same day. Time is color-coded. (

**c**) Along-track Absolute Dynamic Topography (ADT) profiles for the 15 cross-eddy satellite tracks shown on panel (

**b**).

**Figure 3.**(

**a**) Absolute dynamic topography (ADT) against Steric height referenced at 1000 dbar. The orange dots show the ADT value at the closest grid point from the in situ vertical profile location. The green dots show the closest matching ADT value within a radius of 50 km from the in situ vertical profile. The coefficients of determinations between steric height and ADT are shown in the text box for each method. (

**b**) Estimate of the cross-eddy sea surface height (SSH) from 3 different sources. The black line is the glider-measured in situ steric height. The green squares are Absolute Dynamic Topography (ADT) interpolated from the 0.25${}^{\circ}$ grid to the glider’s location. The dashed purple line is an along-track ADT profile measured at the median time of the glider transect (August 19). (

**c**) Schematic representation of the relocation method: The along-track SSH (ADT) profile is used as a synoptic reference profile. Each glider dive is moved by a different distance $\Delta R$, so that the in situ steric height corresponds to the closest along-track altimetry value.

**Figure 4.**Properties of the idealized eddy used for validation of the relocation method. (

**a**) Vertical section of salinity. (

**b**) Same as panel (

**a**) for temperature. (

**c**): Same as panel (

**a**) for azimuthal velocity. (

**d**) Radial profile of SSH (red dotted line) and surface velocity (blue line) across the eddy.

**Figure 5.**Successive positions of the drifting eddy’s edge (contours) superimposed on the simulated glider tracks (dots). Time is color coded and ranges between 0 (dark blue) and 20 (red) days. The center of the eddy is shown by the colored crosses. Panel (

**a**) shows the updrift survey, panel (

**b**) the downdrift survey, panel (

**c**) shows a typical manually piloted survey, and panel (

**d**) a spiraling survey.

**Figure 6.**(

**a**) Measured SSH profiles for the 4 tested synthetic survey strategies (continuous colored lines) and for the synoptic case (dashed gray line). (

**b**) Same as panel (a) for the surface azimuthal velocity.

**Figure 7.**

**Left**hand side panels (

**a**,

**d**,

**g**,

**j**): Geostrophic velocity sections computed from the raw synthetic glider data using the traveled distance as the reference horizontal coordinate.

**Central**panels (

**b**,

**e**,

**h**,

**k**): Geostrophic velocity sections computed using the relocation method.

**Right**hand side panels (

**c**,

**f**,

**i**,

**l**): Difference between the synoptic and the corrected velocity sections. The first row of panels represent the updrift survey, the second row the downdrift survey, the third row the typical survey, and the bottom row the spiral survey.

**Figure 8.**Temperature (${}^{\circ}$C) and Salinity (psu) sections in corrected horizontal coordinates. The isopycnals are shown as black dotted lines. The thick contour represents the 25-isopycnal (1025 $\mathrm{kg}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{m}}^{-3}$) and the contour spacing is of 0.5 $\mathrm{kg}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{m}}^{-3}$.

**Figure 9.**Comparison of the uncorrected (

**a**) panel and corrected (

**b**) panel LCR’s geostrophic velocity fields. The uncorrected geostrophic velocity is directly computed from the glider observations using the distance traveled by the glider as an horizontal coordinate to compute density gradients. The corrected geostrophic velocity field is computed using the relocated glider dives positions. The red dotted lines represent the location of the velocity maxima in relocated coordinates.

**Figure 10.**

**top**panel: Cyclogeostrophic velocity section, using the relocated glider data. The thin dashed contours are plotted every 0.125 $\mathrm{m}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}}^{-1}$ and the thick continuous black contours every 0.25 $\mathrm{m}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}}^{-1}$.

**bottom**panel: Relative difference between the cyclogeostrophic velocity and the geostrophic velocity. The cyclogeostrophic velocity contours are shown as in the

**top**panel.

**Figure 11.**

**Top**panel: Vertical section of relative vorticity non-dimensionalized by the Coriolis frequency f computed using the corrected horizontal coordinate. The Okubo–Weiss parameter (OW) is shown as green contours. The dashed contours represent negative OW, while the continuous contours represent positive values. The thick line is the zero-OW contour.

**Bottom**panel: Same as top panel for the shear strain.

**Figure 12.**Vertical (

**upper**panel) and baroclinic (

**lower**panel) terms of Ertel’s potential vorticity (Equation (4)).

**Figure 13.**Vertical sections of Ertel’s PV anomaly (PVA) and its contributing terms. (

**a**) PVA. (

**b**) Stretching term ($f{N}_{a}^{2}$). (

**c**) Relative vorticity term ($\zeta {\overline{N}}^{2}$). (

**d**) Nonlinear term ($\zeta {N}_{a}^{2}$).

**Figure 14.**PVA profiles averaged over the core of the ring ($0<\left|r\right|<100\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}$; panel (

**a**)) and over the periphery of the ring ($100\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}<\left|r\right|<150\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}$; panel (

**b**)). The black line represents the vertical component of Ertel’s PV anomaly (PVA), the red line is the stretching term ($f{N}_{a}^{2}$), the blue line is the relative vorticity term ($\zeta {\overline{N}}^{2}$), the pink line is the non linear term ($\zeta {N}_{a}^{2}$), and the green line is the baroclinic component of PVA.

**Figure 15.**Same as Figure 13 for the radial gradient of the vertical components of Ertel’s potential vorticity anomaly.

**Figure 16.**Same as Figure 14 for the radial gradient of the vertical component of Ertel’s potential vorticity anomaly. (panel (

**a**): $-150\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}<\left|r\right|<-130\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}$; panel (

**b**): $-50\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}<\left|r\right|<-30\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}$; panel (

**c**): $135\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}<\left|r\right|<155\phantom{\rule{3.33333pt}{0ex}}\mathrm{km}$).

**Figure 17.**Vertical sections of energy density. (

**a**) Available potential energy density. (

**b**) Kinetic energy density. (

**c**) Total energy density.

**Figure 18.**Normalized cross-eddy profiles of in situ steric height (SSH; gray line), local heat content (LHC; dashed red line), available potential energy (APE; dotted blue line), kinetic energy (KE; dashed green line), and Okubo–Weiss parameter (OW; pink continuous line). The horizontal pink line shows the zero OW reference.

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## Share and Cite

**MDPI and ACS Style**

Meunier, T.; Pallás Sanz, E.; de Marez, C.; Pérez, J.; Tenreiro, M.; Ruiz Angulo, A.; Bower, A.
The Dynamical Structure of a Warm Core Ring as Inferred from Glider Observations and Along-Track Altimetry. *Remote Sens.* **2021**, *13*, 2456.
https://doi.org/10.3390/rs13132456

**AMA Style**

Meunier T, Pallás Sanz E, de Marez C, Pérez J, Tenreiro M, Ruiz Angulo A, Bower A.
The Dynamical Structure of a Warm Core Ring as Inferred from Glider Observations and Along-Track Altimetry. *Remote Sensing*. 2021; 13(13):2456.
https://doi.org/10.3390/rs13132456

**Chicago/Turabian Style**

Meunier, Thomas, Enric Pallás Sanz, Charly de Marez, Juan Pérez, Miguel Tenreiro, Angel Ruiz Angulo, and Amy Bower.
2021. "The Dynamical Structure of a Warm Core Ring as Inferred from Glider Observations and Along-Track Altimetry" *Remote Sensing* 13, no. 13: 2456.
https://doi.org/10.3390/rs13132456