Satellite altimetry missions such as ERS-1, TOPEX/Poseidon, ERS-2, Jason-1, Envisat, and Jason-2 have transformed our understanding of ocean circulation. . These missions have provided unprecedented sea-surface height data since 1992, showing that 80 %–90 % of the ocean kinetic energy is accounted for by mesoscale variability due to linear Rossby waves, nonlinear waves, and eddies. This variability occurs with lateral scales of tens to hundreds of kilometers and timescales longer than a few days . In other words, through satellite altimetry, we have come to realize that the ocean mesoscale is characterized by a rich field of stirring features with waves and vortices. These findings have deepened our understanding of the ocean's role in climate variability and have shed light on the intricate interactions between mesoscale features and the larger-scale oceanic processes.

Ocean mesoscale refers to the spatial scales at which the planetary vorticity (f=2Ωsin⁡(θ)), where Ω represents Earth's angular velocity and θ denotes the latitude, greatly exceeds the relative vorticity (ζ=vx-uy), where u and v represent the zonal and meridional velocity components, respectively. This condition is expressed by the Rossby number Ro=ζ/f≪1. In essence, the ocean mesoscale is characterized by a balance between the pressure gradient force and Earth's rotation, known as geostrophic balance, wherein isolines of sea-surface height align with streamlines. Consequently, variations in sea-surface height become indicative of the underlying flow patterns and provide valuable insights into the distribution and dynamics of mesoscale features.

The definition of mesoscale is closely tied to the internal Rossby deformation radius, which quantifies the scale at which geostrophy is the dominant balance. This radius varies with latitude, water column depth, and stratification (e.g. see Sect. 3.1 from ). Towards the poles, where the planetary vorticity is larger, the internal Rossby deformation radius becomes smaller. In contrast, regions closer to the equator experience larger deformation radii e.g., leading to the prevalence of larger-scale mesoscale structures. For comparison, these mesoscale eddies have a radius of approximately 8 km at high latitudes and 100 km at low latitudes e.g..

With significant advances made possible by altimetry satellites, most global studies on ocean mesoscales tend to focus on surface dynamics and structures (e.g. ). There are also different ways to define mesoscale eddies, depending on the specific research objectives. These approaches may consider factors such as the size, shape, and intensity of the vortices, and for how much time they trap waters in their interior, a.k.a. Lagrangian coherence . Different studies have focused on refining these definitions and employing advanced algorithms to detect and track vortices in the vast amount of available altimetry and profile data .

In this study, we define mesoscale eddies as long-lived swirling structures that are identified as localized extrema in snapshots of sea-surface height maps cf.,. Most eddies tracked this way are nonlinear and their particle velocities are much larger than their propagation speeds, and thus they possibly trap fluid for weeks to months . But these eddies may not be formally coherent by other metrics (e.g., ) and, for this reason, we can also call them simply as Eulerian eddies and avoid referring to them as “coherent eddies” or “Lagrangian coherent structures”. This conservative wording, however, should not downplay the relevance of these eddies for circulation, dynamics, and biogeochemistry.

Although it is relatively easier to study ocean surface data using satellites, investigating the vertical structure of mesoscale eddies globally remains a computational challenge. The vertical structure of these mesoscale eddies plays a crucial role in various ocean processes, such as heat and mass transport, nutrient dispersion, the formation of subsurface water masses, and even the behavior of the macrofauna . To gain a deeper understanding of the vertical structure of mesoscale vortices globally, we integrate vertical profiles from the World Ocean Database (WOD) with altimetry-derived mesoscale eddies data from an Eulerian mesoscale eddies atlas (META3.2 DT) . This interdisciplinary approach allows for a more comprehensive understanding of the ocean's behavior, facilitating future studies on the interactions between vortices and other oceanic features across different regions and time periods.

This paper is structured as follows: Sect.  provides an overview of the computer resources used in this project. In Sect. , we detail the datasets used and outline the methods for their processing and combination. Next, in Sect. , we discuss how these data are accessible for download or directly from a server, and in Sect. , we present examples of use for the dataset. In Sect. , we present potential avenues for future research, and finally in Sect. , we summarize the key findings and draw our final conclusions.

The analysis in this study requires substantial computational resources to process and analyze large datasets. The computations are performed on a high-performance computing cluster. The CARNiE (Collaborative Advanced Research Numerical Environment) cluster consists of queues like short-single, long-single, large-parallel, and power-single, which have varying numbers of nodes . The compute nodes in the cluster (node1 to node50) are powered by Intel Skylake processors, providing 24 cores, 48 threads, 48 Gb of memory, and 1 Tb of SSD space each. Additionally, power nodes power1 and power2 utilize IBM POWER9 processors, offering 32 cores, 128 threads, 128 Gb of memory, and 1 Tb of SSD space each. While all nodes in the cluster are equipped with GPUs, they are not used for this project. This cluster provided the computing power necessary to handle large-scale data processing tasks efficiently.

The software tools we use for the analysis include different Python packages for data pre-processing, filtering, and statistical calculations. The Python environment with all of this project's packages is available along with the code for reproducibility. The data processing and analysis procedures involve complex algorithms and require substantial human and computational time. Despite having access to the vast resources from CARNiE, substantial effort is dedicated to testing different methods of chunking the data to optimize the analyses in parallel. This involved experimenting with different ways to allocate memory resources and balance the computational load. We explore various chunk sizes, overlapping chunks, and parallelization strategies to speed up the analyses. Two essential tools for the analyses are the Dask and Dask-JobQueue Python packages , used to integrate our analysis into CARNiE's job queueing system (Slurm). Dask and Dask-JobQueue facilitate running parallel processes in Python by automatically submitting jobs and distributing tasks to multiple workers. Dask is also integrated with XArray by default, which is the most complete data analysis library for multi-dimensional arrays in Python . This integration allows us to efficiently manipulate and analyze large datasets within the CARNiE framework. Furthermore, Dask has a dashboard client that allows us to easily monitor and track the progress of parallelized processes.

The dataset is available through the Open Source Project for a Network Data Access Protocol (OPeNDAP) server at the University of Massachusetts Dartmouth (UMassD) and at Woods Hole Oceanographic Institution (WHOI). We also provide a faster option for users to access the data through an Amazon Web Services (AWS) S3 bucket in icechunk format. Users have the flexibility to subset the dataset based on their desired time range and region by directly accessing it with software such as Python XArray.

Using an OPeNDAP server and an S3 bucket to store the dataset offers several advantages. First, it provides a convenient and efficient means of data access, enabling users to retrieve subsets instead of having to download the entire dataset and subset it locally. This reduces the need for large data transfers and storage requirements on the user's end. Additionally, these options support remote data access, allowing researchers to access and analyze the dataset from different locations, promoting collaboration, and facilitating data sharing within the scientific community. Moreover, an OPeNDAP server enables future on-the-fly data processing, such as subsetting, aggregation, and interpolation, which can be advantageous for large and complex datasets, as it reduces the need for pre-processing and minimizes storage demands. Additionally, we also provide the vortex-profile dataset to download from an HTTP server.

One of the preliminary results of this dataset is the global distribution of temperature, salinity, and density anomalies. In this analysis, the combined dataset is partitioned into manageable chunks, each comprising approximately 800 casts. To handle the computational demands efficiently, we parallelize the analysis, employing 50 single-core workers, each provisioned with 3 Gb of memory. We take advantage of the capabilities of the XHistogram (https://xhistogram.readthedocs.io/en/latest/index.html, last access: 8 December 2025) package to compute the distribution of anomalies. This package seamlessly integrates with both XArray and Dask for computing multi-dimensional histograms. For enhanced granularity in our estimations, the distributions are calculated at intervals of every 25 m in depth and spatially over 5×5° grid boxes.

Generally, anticyclones appear to be more intense than cyclones in thermal and saline anomalies, and the patterns in the vertically-averaged anomalous properties highlight the strongly energetic boundary-current regions. As anticipated, cyclones, being low-pressure systems, generate upward displacement of the isopycnals and are strongly associated with negative temperature anomalies (Fig. a). Conversely, anticyclones, as high-pressure systems, are linked to positive temperature anomalies (Fig. b). The patterns in global eddy salinity anomalies are less apparent and likely depend on the distribution of water masses across the globe and the rotational sense of the eddies, sometimes compensating temperature anomalies, and, sometimes strengthening them. For most oceans, cyclones are accompanied by compensating negative salinity anomalies, with the exception of the Mediterranean Sea (Fig. c). Salinity anomalies in anticyclones exhibit regional variations, with western boundary currents displaying positive anomalies and other regions exhibiting both positive and negative anomalies (Fig. d). Cyclones show weaker negative temperature anomalies and more negative salinity anomalies compared to anticyclones, resulting in a weaker signal in the potential density anomalies (Fig. e, f), with some unexpected positive anomalies observed in a few regions.

The expected positive temperature anomalies for anticyclones and negative temperature anomalies for cyclones serve as a reliable quality control measure for the vortex profile matching method. Despite the intriguing unexpected patterns observed in the anomalous salinity of the eddy, the stratification of the ocean is mostly dominated by temperature changes, and the consistency of temperature anomalies within the eddies confirms the accuracy and robustness of the method.

Next, we expand our perspective and analyze the vertical distribution of anomalies for the first 1000 m in different regions. The regions are chosen based on the intensity of vortical activity (Gulf Stream and Kuroshio Current) or due to their exceptional patterns of temperature and salinity (Bay of Bengal and Mediterranean Sea). The anomalies in the Gulf Stream extend to the whole 1000 m range for both cyclones and anticyclones. The general median temperature anomalies reach 1.5 °C around 600 m with the 80th percentile around 4 °C for both cyclones (negative) and anticyclones (positive), although the distribution for anticyclones is bimodal, showing a branch peaking at 5 °C around 500 m (Fig. a, d). The salinity anomalies corroborate the patterns shown in Fig. , with negative values within cyclones and positive within anticyclones (Fig. b, e). The median peaks around 0.2 g kg⁻¹ at 600 m with the 80th percentile reaching 0.5 g kg⁻¹. The density anomalies follow the expected patterns of the combined effect of temperature and salinity (Fig. c, f). The vertical structure and anomalies associated with anticyclones (warm core rings) are corroborated by a recent study that employed a totally independent method (see Fig. 7 from ). The description and analysis of mesoscale eddies in the Gulf Stream encompass a wide variety of applications, including the behavior of the top predators. For example, reveals the extensive use of anticyclones (warm-core rings) by mature white sharks, suggesting that anomalies make prey more accessible and energetically profitable.

Turning our attention to Kuroshio, we find negative temperature anomalies for cyclones, with a median value of approximately -1 °C (80th percentile around -3 °C), extending to depths of around 800 m (Fig. a). In contrast, anticyclones exhibit predominantly positive temperature anomalies, with a median value of around 2 °C (80th percentile around 3.5 °C), more concentrated near the surface and shallower in depth compared to cyclones (approximately 500 m) (Fig. d). The salinity anomalies of the cyclones show negative values that intensify near the surface, with a median of approximately -0.15 g kg⁻¹ (80th percentile of around -0.4 g kg⁻¹), extending to depths of 700 m (Fig. b). Within anticyclones, the salinity anomaly patterns exhibit a bimodal distribution, with a branch that transitions from positive values on the surface to a negative peak around 500 m (Fig. e). The median anticyclonic salinity anomalies range from negative to positive values around 0.2 g kg⁻¹, with the 80th percentile approximately 0.4 g kg⁻¹. The peak values and the vertical structure corroborate the findings reported in a recent study conducted in the region , although notable salinity inversions are not observed in our analysis for cyclones. Within cyclones, the density anomalies exhibit a slightly positive median (less than 0.1 kg m⁻³), with the 20th percentile showing negative anomalies at the surface around -0.2 kg m⁻³ (extending to 300 m). The 80th percentile demonstrates positive anomalies, extending to 1000 m with a typical value of 0.3 kg m⁻³. In contrast, anticyclones display a negative median density anomaly (around -0.2 kg m⁻³), peaking at approximately 400 m depth. The 80th percentile also reveals negative anomalies, extending to 1000 m with a typical value of -0.3 kg m⁻³.

The vortices in the Bay of Bengal are shallower than in other regions (approximately 300 m) and exhibit a temperature and density peak around 100 m depth (Fig. ). The signals and vertical structure of the temperature and density anomalies support a recent study that used regional vortex-profile matching . However, the absolute salinity values presented by are more intense and less spread, likely due to their consideration of the profile position relative to the vortex center, which is not taken into account in our analyses. The greater variability of salinity anomalies near the surface is also characteristic of the region, which features multiple river plume fronts and monsoonal rainfall that can generate surface freshwater lenses . Understanding the dynamics of mesoscale vortices is crucial for predicting salinity transport pathways in the Bay of Bengal and its exchanges with the Equatorial Indian Ocean and Arabian Sea .

Mesoscale eddies play a significant role in shaping the dynamics of the Mediterranean Sea, contributing substantially to sea-surface height variability and kinetic energy at various depths (50 %–60 %, ). In this region, the temperature structure of cyclones exhibits a broad distribution, with a median around zero, indicating the presence of both warm-core and cold-core cyclones (Fig. a). While temperature does not seem to heavily influence density anomalies in the region, anticyclonic anomalies show a slightly positive curve, extending to a depth of 400 m with temperature values below 1 °C (Fig. ). On the other hand, salinity anomalies have a greater impact in the Mediterranean Sea compared to temperature anomalies. Cyclonic salinity anomalies display an exponential-like decay, with a median of 0.2 g kg⁻¹ at the surface, declining to zero at 300 m (Fig. b). The 80th percentile reaches 0.4 g kg⁻¹ at the surface. For anticyclones, salinity anomalies remain relatively constant at -0.1 g kg⁻¹ for the first 200 m (with the 80th percentile around -0.3 g kg⁻¹) before decreasing to zero at 300 m (Fig. e). Despite anticyclones exhibiting shallower salinity anomalies compared to cyclones, the combined effect of slightly positive temperature anomalies and negative salinity anomalies leads to stronger and deeper density anomalies (Fig. c, f). The vertical structure of mesoscale eddies in the Mediterranean Sea varies regionally and seasonally, yet the overall patterns described here align with recent findings, which illustrate that anticyclones extend to greater depths (up to 400 m) than cyclones (first 200 m) in the region (see Fig. 10 from ).

The analyses in Sect.  serve a dual purpose: firstly, to perform a quality check on the dataset by comparing the results with published literature, and secondly, to demonstrate the potential of the dataset for conducting global analyses of the vertical structure of mesoscale eddies. It is important to acknowledge that the current version of the analyses presented in this study focuses primarily on temperature, salinity, and density anomalies, not taking into account other biogeochemical variables, the radial distance of the profiles from the eddy center, as well as seasonal and interannual variability. However, it is worth noting that these additional properties are available within the dataset and hold great potential for future investigations. By incorporating these variables into our analyzes, we can gain a more comprehensive understanding of the complex dynamics and drivers underlying the behavior of mesoscale eddies.

The dataset used in this study is publicly available at 10.5281/zenodo.17425853 .

Updated links and the status of the servers, including access through Amazon Web Services S3 bucket, are listed in the GitHub repository. The code for processing and analyzing the dataset, including the vortex-profile matching algorithm, is available on Zenodo 10.5281/zenodo.14681279 and GitHub (https://github.com/iuryt/vortex_profile_matching, last access: 8 December 2025). Users can access the data and code for reproducibility and further research.

In this study, we construct a unique dataset by combining temperature, salinity and biogeochemical profiles from the World Ocean Database (WOD) with Eulerian mesoscale eddies identified and tracked using altimetry data (META3.2 DT). We have demonstrated the potential dataset's utility to explore global characteristics of mesoscale eddies, including their vertical extension and salinity compensation to temperature anomalies.

The primary objective of this work is to develop a comprehensive global dataset for studying the vertical structure of mesoscale eddies identified through altimetry data. We are committed to the principles of open, transparent, and accessible science, with a strong focus on reproducibility. To facilitate spatial, temporal, and source-based subset analyses, we have organized the data in a manner that supports on-the-fly remote data analysis through an OPeNDAP server, AWS S3 bucket, as well as through direct download by HTTP.

This dataset represents a powerful tool for advancing our understanding of ocean processes, enabling detailed studies on mesoscale eddy dynamics, their role in biogeochemical cycles, and their influence on regional and global ocean circulation. By integrating in situ measurements with satellite-derived eddy tracking, this resource provides a foundation for addressing fundamental questions in oceanography and offers broad potential for applications in climate science, ecosystem modeling, and operational oceanography.