META 3 . 1 exp : A new Global Mesoscale Eddy Trajectories Atlas derived from altimetry

This paper presents the new global Mesoscale Eddy Trajectories Atlases (META3.1exp DT allsatellites, https://doi.org/10.24400/527896/a01-2021.001, Pegliasco et al., 2021a and META3.1exp DT twosatellites, https://doi.org/10.24400/527896/a01-2021.002, Pegliasco et al., 2021b), composed of the eddies’ identifications and trajectories produced with altimetric maps. The detection method used is a heritage of the py15 eddy-tracker algorithm developed by Mason et al. (2014), optimized to manage with efficiency large datasets, and thus long time series. These products are an improvement of the META2.0 product, produced by SSALTO/DUACS and distributed by AVISO+ (https://aviso.altimetry.fr) with support from CNES, in collaboration with Oregon State University with support from NASA and based on Chelton et al. (2011). META3.1exp provides supplementary information such as the mesoscale eddy shapes with the eddy edges and 20 their maximum speed contour, and the eddy speed profiles from the center to the edge. The tracking algorithm used is based on overlapping contours, includes virtual observations and acts as a filter with respect to the shortest trajectories. The absolute dynamic topography field is now used for eddy detection, instead of the sea level anomaly maps, to better represent the ocean dynamics in the more energetic areas and close to coasts and islands. 25 To evaluate the impact of the changes from META2.0 to META3.1exp, a comparison methodology has been applied. The similarity coefficient is based on the ratio between the eddies’ overlap and their cumulative area, and allows an extensive comparison of the different datasets in terms of geographic distribution, statistics over the main physical characteristics, changes in the lifetime of the trajectories, etc. After evaluating the impact of each change separately, we conclude that the major differences between META3.1exp and META2.0 are due to 30 the change in the detection algorithm. META3.1exp contains smaller eddies and trajectories lasting at least 10 days that were not available in the distributed META2.0 product. Nevertheless, 55% of the structures in META2.0 are similar in META3.1exp, ensuring the continuity between the two products, and the physical characteristics of the common eddies are close. Geographically, the eddy distribution mainly differs in the strong current regions, where the mean dynamic topography gradients are sharp. The additional information on 35 the eddy contours allows more accurate collocation of mesoscale structures with data from other sources, so META3.1exp is recommended for multi-disciplinary applications. https://doi.org/10.5194/essd-2021-300 O pe n A cc es s Earth System Science Data D icu ssio n s Preprint. Discussion started: 17 September 2021 c © Author(s) 2021. CC BY 4.0 License.


Introduction
Mesoscale eddies are ubiquitous in the global ocean. Ranging from tens to hundreds of kilometers and spanning 40 days to years (Morrow and Le Traon, 2012), mesoscale eddies strongly participate in the redistribution of energy, heat and salt in the ocean, and other bio and chemical components (Beal et al., 2011;Chaigneau et al., 2011;Gaube et al., 2014;Gruber et al., 2011;Zhang et al., 2014). The physical characteristics of eddies are also coupled with biologic data to infer the behaviour of marine animals (Braun et al., 2019;Chambault et al., 2019;Christie et al., 2010;Siegel et al., 2008;Staaterman et al., 2012), and can be used to track pollutants (Brach et 45 al., 2018;Gilchrist et al., 2020). Over the past three decades, the development of altimetry maps with an increasing accuracy has made their observation at global scale possible.
Nowadays, lots of methods have been developed to detect and track eddies. The difficulty in defining a mesoscale eddy is linked to its separation from the background oceanic field. Eddies are mainly generated by current instabilities, or from ocean instabilities due to wind or topographic obstacles, creating variability around 50 the ocean's mean state. As such, they are often considered as anomalies. Moreover, in a homogeneous background, rotating structures are associated with high and low pressure or sea level surfaces through the geostrophic equilibrium. Thus, a large number of studies detect eddies in Sea Level Anomaly (SLA) maps where anticyclones (respectively, cyclones) are associated to areas with positive (negative, respectively) anomalies, delimited in space by geometric criteria (Chaigneau et al., 2008(Chaigneau et al., , 2009Faghmous et al., 2015;Liu et 55 al., 2016). Other studies are more interested in the rotation of the coherent structures to separate them from a non-rotative background with the Okubo-Weiss parameter, or by rotational speed consideration (Isern-Fontanet et al., 2003;Le Vu et al., 2018;Mkhinini et al., 2014;Morrow et al., 2004;Nencioli et al., 2010).
Many regional studies on the detection and tracking of mesoscale eddies have been conducted, but global analyses are rare due to the lack of globally accessible databases of mesoscale eddies. It is simpler to properly 60 tune a detection algorithm in a restricted area, where such characteristics as the Earth's rotation or the ocean stratification are homogeneous, than to take into account their variability at a global scale (Zhang et al., 2013). It is also faster, less consuming of computing capacities and easier to manipulate reasonable quantities of data, concentrated in time and space. As mesoscale eddies generated by the destabilization of strong currents are different from island generated eddies for example, and because the water masses differ from an oceanic basin 65 to another, a regional approach was often chosen to better integrate the eddies' specificities.
Nevertheless, some global databases of mesoscale eddies exist (Chelton et al., , 2007Faghmous et al., 2015;Martínez-Moreno et al., 2019;Tian et al., 2020;Zhang et al., 2013). The first global database was presented in Chelton et al. (2011), covering the 1993 -2008 period (hereafter CH11). This database was regularly updated until 2016 to consider the extending period, the changes of the input altimetry maps (weekly 70 then daily production, improvement of the standards) and was available on the Oregon State University (OSU) affiliated webpage (http://wombat.coas.oregonstate.edu/eddies/index.html). The production of the database was We aim here to present a new version of the daily global Mesoscale Eddy Trajectories Atlas (META3.1exp), distributed by AVISO. The main changes with this new system are that the eddy detection is made on filtered ADT maps with geometrical detection method, the main atlas provides eddy trajectories lasting more than 10 85 days, but also identifies the trajectories shorter than 10 days, and the lone eddies which are identified only one day. The source code is written in Python and is made freely available under a GPL V3 license (https://github.com/AntSimi/py-eddy-tracker), inherited from the Py-Eddy-Tracker (PET) of Mason et al. (2014) and improved after a fruitful collaboration between E. Mason (IMEDEA) and CLS. This new atlas is available in two versions using the ADT maps detections: with two-satellites, the T/P-Jason and ERS-Envisat-Saral dual 90 sampling giving the most consistent spatial coverage over the full time series, and all-satellites using all available missions for the best possible sampling coverage, albeit that varies over time.
This paper compares this new product to the current AVISO operational version META2.0. Such a comparison is complex due to the size of the datasets and the diversity of variables describing the mesoscale eddies within similarly organized atlases. The originality of the methodology we developed is its capacity to match eddies 95 from different atlases as well as comparing the global distributions of parameters. The Similarity Coefficient (SC) employed here is based on the ratio between the common area of two eddies and their total area. The algorithm is able to rapidly process the large global atlases over the whole altimetry period. After pairing the eddies between the two datasets, we separate 1) the common and similar eddies which have the highest SCs, 2) the common but different eddies with moderate SCs, 3) the eddies only present in one dataset and thus 100 presenting a novelty with regards to the other dataset, and 4) the eddies with multiple matches. These groups of eddies provide not only statistics about the detected eddies, but also insights about how the associated trajectories are distributed.
Four major changes are made in the evolution of the processing from META2.0 to META3.1exp. First, the change in the detection algorithm from the historical OSU code  to PET algorithm (Mason 105 et al., 2014) impacts significantly on the number of detected eddies and their surface characteristics (amplitude, radius). Secondly, the tracking scheme was modified to use the eddies' overlap in successive daily maps instead of searching for new eddy candidates in a restricted area, increasing the length of many trajectories. Thirdly, we have changed the input fields from SLA to ADT maps, in order to better identify eddies in energetic regions with strong Sea Surface Height (SSH) gradients and where recurrent mesoscale structures exist, either as eddies 110 or meanders. Many geographically correlated eddies are formed near coasts, bathymetric changes, from windorographic effects, or current retroflections, and have an imprint in the Mean Dynamic Topography (MDT).
Using the ADT rather than SLA field provides a more consistent eddy detection and presence in such oceanic regions. Finally, the preprocessing step of filtering, inherent of the OSU and PET methodologies, was modified to better separate the eddies from the background large-scale ocean circulation. We produced intermediate 115 datasets to independently assess how each change impacts on the atlas of eddy trajectories. This paper is organized as follows. In Sect. 2, we present first the altimetry gridded maps used to detect eddies, the differences and similarities between the OSU and PET detection and tracking algorithms, and the methodology developed to efficiently compare the different atlases. In Sect. 3, we illustrate how each change made from META2.0 to META3.1exp impacts on the detected eddies and their statistics, and present some 120 META3.1exp characteristics with regards to META2.0. We document the availability of META3.1exp in Sect. 4 and provide a summary in Sect. 5.

Altimetric fields for eddy detection
In the continuity of the CH11 dataset, the META2.0 product is based on the SLA maps produced by the 125 Copernicus Climate Change Service (C3S) and distributed in the C3S Climate Data Store (https://cds.climate.copernicus.eu/). These maps are built using at most two altimetric missions, with the Topex-Poseidon and Jason satellites on the same long-term ground tracks, and a second satellite mission, mainly on the ERS-Envisat-Saral-Sentinel-3A ground tracks. As the sampling and the represented scales are stable throughout time, this dataset is considered to be homogeneous in time in terms of climate signals and mesoscale content. 130 The META3.1exp has been computed as well from the C3S dataset to ensure continuity for the users but a second production, based on the Copernicus Marine Environment Monitoring Service (CMEMS, marine.copernicus.eu) products built from the complete altimetric constellation has been performed. The allsatellites merged product is built with all the available satellites at a given time, improving the small scales representation in the maps due to the diversity of the tracks' location and the different repetition periods of the 135 altimetric missions (Pascual et al., 2006). The mesoscale eddies retrieved from these products are thus improved at small scales.
Beside the input constellation, the products have an additional difference regarding the temporal mean reference used to compute anomalies. For the two-satellites product, the SLA is obtained as the difference between the along track instantaneous Sea Surface Height (SSH) and the Mean Sea Surface (MSS), the gridded proxy 140 derived from all the available altimetry missions. For the all-satellite product, SLA is obtained as the difference between the SSH and the Mean Profiles (MP), the most precise MSS, available on the long-term repeat tracks (for details see Pujol et al., 2016). This different strategy to remove a MSS will also have slight impact on the eddy field.
The META3.1exp product is based on the ADT. The ADT is the sum of the SLA and the Mean Dynamic 145 Topography (MDT), the later corresponding to the mean oceanic circulation derived from multiple satellite and in-situ data. The accuracy of the MDT has greatly improved in recent years, giving robustness to the ADT fields (Rio et al., 2014).
The input fields (SLA or ADT, C3S or CMEMS) are all global daily products, with a ¼° grid resolution, using the most recent reprocessing version (DT2018, Taburet et al., 2019). The along-track data are filtered with a low 150 pass Lanczos filter depending on the latitude (250 km near the Equator, down to 55 km at high latitudes) and subsampled at 14 km (Pujol et al., 2016). Each daily map is produced with an optimal interpolation using spatial and temporal decorrelations scales varying with latitude (Pujol et al., 2016). When several satellites are used, a weight is attributed to each mission to take into account their noise and thus, their confidence level. The mapping procedure tends to filter out the smaller scales, but the effective resolution of the DT2018 global 155 maps was estimated to range from ∼100 km wavelength at high latitude to ∼800 km wavelength in the equatorial band, meaning that ∼25 km radius structures are properly resolved at high latitudes, ∼200 km radius structures are resolved in the equatorial band and ∼50 km radius structures are resolved at mid-latitudes .

Detecting mesoscale eddies
The META2.0 detection algorithm (OSU) is similar to Chelton et al. (2011), based on the fact that closed contours of SLA correspond approximately to the streamlines of a geostrophic flow. The method aims to find a geographic region of connected pixels having all SLA values below (or above) the local maximum (or minimum) SLA value for anticyclonic (or cyclonic) eddies. Several SLA extrema are authorized within one 165 eddy region. There is a 1 cm threshold for amplitude (the absolute SSH difference between the edge and the extremum of the structure), a maximum of 1000 pixels within a structure, and gaps between pixels in longitude and latitude are not allowed. These restrictions avoid the detection of ameba-like regions as eddies, because eddies are expected to show more compact form to maintain their rotation. The eddy center location provided in META2.0 is the centroid of the SSH of the connected pixels. The eddy radius is the radius of the circle that has 170 the same area as the region within the closed contour of SSH with maximum averaged speed. The effective radius, computed for tracking purposes but not delivered, is the radius of the circle with the same area as the connected pixels. Eddies can thus be represented by the location of their center and by their speed radius. No detection is made within ± 2.5° latitude of the equator, due to the non-geostrophic balance near the equator.
The OSU detection differs from the original Chelton et al. (2011) methodology as the minimum of 8 175 consecutive pixels is not required, since we found that the smallest amplitude criteria prevents the detection of structures with unrealistic small radii. Note that the SLA fields are filtered before the eddy-detection in order to remove the large scale anomaly patterns, such as the chevron like patterns near the equator or the El Niño induced displacement of warm water from west to east in the Equatorial Pacific, following the procedures of Chelton et al. (2011). The filtering step is made in OSU with a 2D Lanczos filter, with a 1000 km half-power 180 cutoff wavelength in latitude and longitude to take into account the latitudinal variation of the dimension of a grid pixel.  Kurian et al. (2011) and Penven et al. (2005). Working either on SLA or ADT fields, the SSH contours are interpolated instead of using the SSH pixels. The SSH fields are 185 also high pass filtered for META3.1exp, although we changed the half-power cutoff wavelength of the 2D Lanczos filter, setting it to 700 km. More details on this choice are provided in Sect. 3.1.1. Eddy detection is made by scanning closed contours from SSH maxima downward for Anticyclonic Eddies (AEs) and from SSH minima upward for Cyclonic Eddies (CEs). For the outermost closed contour encompassing only one extremum, a shape error test is performed. This test, similar to Kurian et al. (2011) verifies that the ratio between the areal 190 sum deviations of the contour from its best fit circle and the area of this best fit circle is below a certain value.
This specification aims to avoid the selection of eddies with shapes too different from circles, where rotation is https://doi.org/10.5194/essd-2021-300 not possible, as for banana shapes for example. In Mason et al. (2014) and Kurian et al. (2011), the shape error was limited to 55%. We increase this value to 70% to ensure that elongated eddies are detected, a case often visible in highly dynamic regions and when eddies are interacting. 195 The META3.1exp dataset includes both the effective contour (outermost closed contour) and the speed contour (contour with the maximum averaged speed around it). The effective radius is deduced from the best-fit circle applied to the effective contour; similarly, the speed radius is derived from the best-fit circle applied to the speed contour. We chose to decrease the amplitude threshold from 1 cm to 0.4 cm, since with a minimum of 5 consecutive pixels within a contour we ensure a minimum geographic imprint instead of limiting the amplitude 200 parameter. As only one extremum is accepted within an eddy, contrary to OSU, the position of this extremum is provided, but the location of the center is deduced from the best-fit circle of the speed contour. The change in the number of extrema allowed within an eddy contour impacts strongly on the eddy detection and the eddy's characteristics, and will be presented with more details in Sect. 3.1.3.
We also provide a new characteristic, the mean speed profile between the effective contour and SSH extremum, 205 as proposed by the AMEDA detection and tracking algorithm from Le Vu et al. (2018). This speed profile is useful for dynamical investigations and comparisons with theoretical eddy shapes. Specifying the speed and effective contours are very helpful for the colocation of altimetric-derived eddies with external data, such as Sea Surface Temperature (SST), ocean color, surface salinity, winds, and in situ measures as Argo floats, XBT or CTDs, Niskin bottle sampling, larvae presence, since they allow a more precise anisotropic positioning of the 210 mesoscale eddies.
To ease the manipulation of these large files, the speed profiles and the contour data are regularly interpolated over 50 evenly spaced points.

Tracking
The META2.0 dataset is composed of trajectories lasting more than 28 days, following the four weeks minimum 215 eddy duration of Chelton et al. (2011). This limitation was linked to the weekly availability of the maps, and is close to the mean temporal resolution of 34 days of the altimetry maps . The tracking procedure consists of searching for an eddy at the time step t + dt (dt = 1 day) in a restricted area around the center of the eddy considered at t. After analyzing the mean displacement of eddies in the previous META1.0exp, the restricted area was set to evolve with latitude. From high latitudes towards 25° in latitude, the 220 radius of the restricted area is set to 50 km, then a progressive increase is made to reach a radius of 100 km at 10° latitude, since the eddies are larger and travel faster in the equatorial band. Searching within the restricted area prevents the association of unrelated eddies resulting in large jumps within a trajectory. The variation of the candidate eddy size at t + dt (amplitude and effective radius) must fall between 0.4 and 2.5 times the reference eddy size at dt. If several candidates are found at t + dt, the eddy added to the trajectory is the one minimizing a 225 cost function based on the distance between the centers.
As for other tracking procedures (Chaigneau et al., 2008;Faghmous et al., 2015;Laxenaire et al., 2018;Le Vu et al., 2018;Li et al., 2016;Pegliasco et al., 2020), we have to deal with the "missing eddy" problem, i.e., the disappearance of an eddy for some days between altimetric groundtracks in the mapped SSH fields, or due to restrictions imposed by the detection procedure. This "missing eddy problem" is solved by authorizing the 230 research of a new candidate eddy over several days, we chose four days. To consider the eddy's displacement, https://doi.org/10.5194/essd-2021-300 the radius of the search area is increased by ⅓ each supplementary day ( Figure 1a). If after 1, 2, 3 or 4 days a candidate is available, it is associated to the trajectory. The days without eddies are flagged to identify a virtual eddy, whose characteristics are interpolated from the two detected eddies. Thus, there are at most three consecutive virtual observations over the 4-day gaps. Due to the extension of the search area, candidates may be 235 found that cross land. To avoid this, a land management checks if the core of the eddies, represented as the fifth of their respective speed radius, is able to move from one eddy to another without crossing land ( Figure 1b).
When crossing land, the eddy tracking association is not allowed. If after 4 days of research, no candidates are found, the trajectory is stopped. The tracking procedure used in META3.1exp is different, based on the overlap of the effective contours and not on the search over a restricted area. Tracking by overlap has shown its robustness with daily mapped data 245 (Keppler et al., 2018;Laxenaire et al., 2018;Li et al., 2016;Pegliasco et al., 2020Pegliasco et al., , 2015, since the day-to-day general displacement of mesoscale eddies does not exceed 10 km. Here eddy candidate is retained if the overlap ratio, defined as the ratio between the overlapping area and the union of the two eddies' area, is more than 5%. This allows us to track a small eddy included in a large eddy (or the reverse situation) due to eddy splitting (or merging). Note that 95% of the eddy associations have an overlap ratio greater than 20%. No restrictions are 250 imposed on the radius or amplitude variations, since we observed that in the case of merging of two small eddies into one, or splitting of one large eddy in two, the rapid variation of the radius ends prematurely one trajectory and start a new one in META2.0. In the case of several candidate eddies, the larger overlap ratio is retained.
Even if the merging and splitting events are not recorded in the tracking procedure for META3.1exp, the overlap method ensures the continuity of the trajectory when merging or splitting events occurs. The tracking 255 procedure allows us to search for a candidate eddy for up to 5 days instead of 4 (thus, a maximum of 4 consecutive virtual observations), since the overlap ensures a geographic proximity. This proximity was the only criterion in the cost function used in META2.0 in case of several candidates, whose number increases significantly when the radius of the search area and the time increase.
To test the ability of this new tracking to produce robust trajectories, we investigate the characteristics of the 260 trajectories obtained with the two different methods (restricted area and overlap) from a similar detection, made with the PET algorithm on the two-satellites ADT maps high-pass filtered with a 700 km wavelength cutoff. Table 1 shows that more observations are associated with trajectories lasting at least 10 days when the overlap https://doi.org/10.5194/essd-2021-300  percentages are obtained relatively to the sum of the observations within trajectories ≥ 10days, < 10 days and the untracked eddies for the first three columns, and relatively to the number of observations in the trajectories ≥ 10 days or < 10 days, respectively, for the last columns. When evaluating the distribution of the number of trajectories for different lifetimes (Figure 2a), we should keep 280 in mind that the majority of the trajectories built have lifetimes between 10 -30 days, whether we use the overlap method (55 %) or the restricted area method (60 %) but only involved a small number of individual eddies (21 % for the overlap; 28 % for the restricted area) (Figure 2b). This implies that the analyses made on the remaining trajectories is representative of only half of the trajectories but concerns 70 -80 % of the individual eddies. Whatever the tracking method, the trajectories lasting more than 6 months represent only a 285 few percent of the dataset, but the overlap method detects twice as many very long trajectories than the restricted area method. Note that the occurrence of four consecutive virtual eddies in the case of the overlap https://doi.org/10.5194/essd-2021-300 We can thus conclude that the overlap tracking is able to efficiently associate detected eddies into long 290 trajectories, with no overuse of virtual observations for the longest trajectories.

A similarity coefficient to compare atlases
With the development of multiple detection and tracking algorithms, the eddy community lacks a tool able to provide quantitative and qualitative comparison of the atlases. The similarity coefficient provides the association 295 of detected and tracked eddies between two (or more) atlases, with the quantification of the similarity of their respective physical characteristics.

Principle
The similarity coefficient (SC) compares the eddies detected in different databases having the same formalism : each eddy is saved with a rotating sense, position, amplitude, radius, time, trajectory, and contours. As for the 300 tracking procedure, when we want to associate similar eddies within a trajectory, here we search for one eddy at a time t in one atlas (the reference) and check if there is a corresponding eddy in another atlas (the study) at the same time, using the overlap of the effective contours of those eddies. The similarity coefficient is defined in Eq. (1) as the ratio between the intersection of the eddies' effective areas in the reference and the studied atlases and the union of their effective areas, expressed in percent : 305 Here, we will investigate the SC computed for anticyclones and cyclones separately, but the SC can also be performed by cross-referencing anticyclones and cyclones, in order to evaluate the occurrence of opposite 310 detection in the atlases.
When an eddy has no match in the other atlas, its similarity coefficient is 0 %. When the two eddies are identical (same contour and position), their similarity coefficient is 100 %. We define four specific groups of eddies depending on their SCs : i) unmatched eddies, with no association or very low overlap (SC < 5 %) ; ii) different eddies (eddies with low SCs, between 5 and 20 %) ; iii) intermediate eddies (eddies with SCs between 20 and 315 40 %) ; iv) similar eddies (eddies with high SCs, over 40 %) (Figure 3). Eddies can be well positioned but with different radii: in the idealized case of two eddies represented by circles where one is included in the other, a SC above 40 % implies a maximum ratio between the eddies' radii of √40 % ≈ 0.63, thus very similar eddies in location but also physical characteristics. Eddies with no similarity coefficient (0 %) are the novelty, as they were not present in one atlas. Eddies with low SCs are representative of the differences between the two atlases, 320 as they are present in both but quite different in their location and characteristics. Note that with the SC definition used here, an eddy included in another eddy or shifted eddies are treated similarly (

330
After the visualization of the SCs between different atlases, we noticed that some complex oceanic regions (high latitudes where sea ice can be present, semi-enclosed seas with complex dynamics and topography) have lower SCs and more unmatched eddies than in the open ocean, thus we decided to restrict the similarity coefficient applications to the major open oceanic basins. Only ~10 % of eddies are removed from the analysis with this open ocean selection. These non-selected eddies are available in both META2.0 and META3.1exp, users 335 interested in these critical zones are welcome to analyze them regionally and provide feedbacks. The following results are all obtained with this geographic mask.

340
To evaluate the ability of the similarity coefficient in depicting changes with accuracy, we present here the results obtained with the following datasets. The reference atlas is the detections made with PET on twosatellites ADT maps and the study atlas is made with PET on the all-satellites ADT maps. Both atlases use the high-pass filter with a 700 km cutoff wavelength. The only difference between the atlases is the number of satellites used in the production of the SSH maps and the way the along-track SLA is built (see Sect. 2.1). 345 The similarity coefficient captures well the influence of the temporal variation of the satellite constellation in the  where the additional satellites enhance the mesoscale representation. Thus, the increased number of eddies with the lowest similarity coefficients testifies for a repositioning of the mesoscale structures. The new eddies are captured by the higher spatial resolution of the satellite tracks in the all-satellite product.

Assessment of the PET algorithm and parameters 380
We recall that in addition of the modification of the tracking scheme, three major changes are made from the META2.0 to the META3.1exp version : 1) the change of input maps, from SLA to ADT; 2) the change in the filtering step, from 1000 km to 700 km for the cutoff wavelength of the 2D filter; 3) the detection algorithm evolution, from OSU to PET. These changes need careful evaluation, not just a simple analysis of the distribution of the main characteristics of the detected eddies in the final META2.0 and META3.1exp products, 385 even with the similarity coefficient. With a direct comparison, the impact of the various changes on the eddies' main characteristics will be mixed and could compensate each other. Thus, we produced intermediated atlases to assess separately each change.
For each comparison step, we characterized the continuity between the tested datasets, the novelty, and their differences. 390

Eddy detection and tracking from SLA to ADT
Historically, the detection of eddies was made on SLA maps, whatever the detection method (Chaigneau et al., 2009(Chaigneau et al., , 2008Chelton et al., 2011Chelton et al., , 2007Dilmahamod et al., 2018;Dong et al., 2014;Mason et al., 2014;Morrow et al., 2004;Yi et al., 2014), mainly because the SLA maps were the most reliable altimetric field, due to residual geoid errors in the mean. The collocation of in situ data with detected eddies confirmed the robustness 395 of SLA-based detections in the open ocean, with a clear distinction between AEs and CEs in agreement with the theory (Castelao, 2014;Chaigneau et al., 2011;Keppler et al., 2018;Melnichenko et al., 2017;Pegliasco et al., 2015;Zhang et al., 2016;Zu et al., 2019). Nevertheless, those studies were conducted in open-ocean regions where the MDT is mostly homogeneous, thus the SLA was able to represent correctly the mesoscale eddies following their basic description : rotating structures in a homogeneous background, which appear as anomalies. 400 But in specific areas where the mean circulation has strong spatial gradients, various studies highlighted the discrepancies between in situ observations and SLA-detected eddies, such as in the Mozambique Channel (de Ruijter et al., 2002;Halo et al., 2014;Schouten et al., 2003). The SLA, as stated by its name, is an anomaly over a temporal mean. But when the temporal mean contains the signature of a mean mesoscale structure, such as a recurrent meander or eddy, the SLA only reflects the variation of the sea surface height relative to the mesoscale 405 structure (Rio et al., 2014). Thus, a positive SLA can either represent an anticyclonic eddy, the weakening of a cyclonic meander or eddy, or the reinforcement of an anticyclonic meander or eddy. Similarly, a negative SLA https://doi.org/10.5194/essd-2021-300 can be a cyclonic eddy, reflect the weakening of an anticyclonic circulation or the reinforcement of a cyclonic circulation.
With the more recent improvements in the quality of the MDT (Rio et al., 2014), several studies started being 410 based on ADT-detected eddies, in the Agulhas Retroflection region (Doglioli et al., 2007;Laxenaire et al., 2019Laxenaire et al., , 2018Rubio et al., 2009)       We applied the PET detection algorithm to SLA maps filtered with a 1000 km half-power cutoff wavelength, 515 and tracked the detected eddies with the restricted area method. We lowered the minimum lifetime threshold to 10 days and provide statistics only for the open ocean. The first striking result is that even with minimum lifetimes of at least 10 days, the PET-detected eddies outnumbered the OSU-detected eddies by a factor of 1.7, with respectively 5936 daily eddies for PET (59.4 million over the total period) and 3445 daily eddies for OSU (34.9 million over the total period). Table 2      The new eddies, represented by the unmatched PET-detected eddies, have a quantity comparable with the similarly detected eddies (33% of the PET dataset for the unmatched eddies, 39% for the high SCs eddies, Table   2). The new eddies are over-represented in the smallest effective radius classes (Figure 8b, dark red). These 550 eddies that were not detected with OSU may arise from three OSU thresholds in the detection scheme : the absence of detection near the Equator (± 2.5°), the amplitude limitation at 1 cm, and the absence of gaps between pixels in latitude or longitude. The PET algorithm detects eddies near the equator, accepts amplitudes amplitudes higher than 1 cm, including 555 daily eddies with amplitude higher than 2 cm, are located mainly in the coastal areas, in the ACC, in the Irminger Sea and East of the Reykjanes Ridge. Note that the requirement of having no gap between adjacent pixels combined with the 1 cm amplitude threshold in the OSU algorithm might block the eddies' detection near the coastline due to the presence of land pixels, whereas the PET algorithm, 560 with the interpolation of the SSH levels, can more easily close contours in these areas.

Adaptation of the filtering step
Regardless of their size or amplitude, we are interested in the behavior of these new detected eddies from a dynamical point of view, since being part of a long trajectory is a synonym of persistency. We note that these new, unmatched PET-detected eddies are present homogeneously from 15 % to 85 % of the normalized lifetimes, with a slightly higher amount present during the early phase (0 -15 % of the normalized lifetime) and 565 at the very end (85 -100 % of the normalized lifetime) (not shown). Smaller eddies are expected to be particularly involved in the growth and the decay of the trajectories. This result reinforces the robustness of the new eddies, for the smallest as well as for the larger ones.
Eddies with multiple associations are particularly numerous when comparing the OSU and PET detections (~17 % of the datasets). The multiple matches category is divided in three subgroups : the parents of twins, 570 where one eddy matches with two eddies; the twins, associated with a unique parent eddy; and the complex multiple matches, where more than two parents or children associations coexist. This last subgroup represents only ~2 % of the datasets. It is more frequent to associate one larger eddy detected with OSU with two smaller eddies detected with PET than the reverse : 12 % of the OSU-detected eddies are parents, and 3 % are twins, whereas 1 % of PET-detected eddies are parents and 15 % are twins. This is directly linked to the possibility in 575 the OSU detection to have more than one extremum within an eddy. This specificity was initially developed to treat the SSH irregularities or to detect eddies in close proximity, and avoid too large changes in the eddy's characteristics from one weekly map to another . With the improved altimetric maps available daily nowadays, detecting eddies with more than one extremum often results in the association of two unrelated eddies, with clear separated trajectories, but in close proximity. The OSU multiple extrema eddies also 580 tend to have large effective radii and amplitudes compare to the corresponding unique PET-detected eddies.
This implies that when the multiple extrema structure separates in two (or more, but rarely) eddies, the change in radius and amplitude is quite important, and thus exceeds the limitations specified in the restricted area tracking. Thus, instead of following one of the two (or more) structures, the trajectory is stopped and a new one starts for each separated eddy. 585 One example of the complex associations of eddies in a double extrema eddy detected by OSU is highlighted in Figure 9. One single META2.0 main dark green trajectory is followed along its path west of Australia for more than 6 months. The PET detected eddies are associated in three smaller but coherent trajectories (PET1, PET2, PET3, see Figure 9). At first, PET1 (in yellow) is coherent with the beginning of the META2.

Assessment of META3.1exp product 640
The new META3.1exp product differs from the META2.0 product for the input SSH field, the half-power cutoff wavelength used to filter it, the detection and the tracking algorithms. We saw in the Sect. 3.1. that the change of the input field from SLA to ADT slightly decreased the number of detected eddies, whereas the change in the cutoff wavelength from 1000 km to 700 km increased the number of detected eddies, but neither changes https://doi.org/10.5194/essd-2021-300 impacted strongly the radii and amplitudes' distributions. On the other hand, the PET algorithm detected many 645 more eddies than the OSU algorithm on the same maps (1.7 times more), and the change from the restricted area method to the overlap tracking increased also the number of trajectories lasting more than 10 days, especially for the longest lifetimes. Thus, when comparing directly the META2.0 and META3.1exp number of eddies and trajectories (Table 3), we can attribute the higher number of eddies in META3.1exp (1.8 times more) to the change of the algorithm. This implies more built trajectories, and the change in tracking increases the percentage 650 of trajectories lasting more than 30 days in the META3.1exp product compared to the META2.0 product. The number of eddies involved in the longer trajectories is similar in percentage between the two products, but represent almost twice as many eddies in META3.1exp than in META2.0. Note that the short trajectories (10 to 30 days) of META2.0 were not delivered to the users, but were processed here to be coherent with the META3.1exp description. 655 Lifetime (days) [10, 30[ [30, 90[ [90, 180[ [180, 270[ [270, 360   As noted in the previous section, the difficulty in comparing mesoscale eddies atlases is to identify which eddies 660 are new, and in the conserved eddies, if they are similar or not. We provide in Figure 10 the global distribution for the effective radius and the amplitude of eddies detected and tracked for at least 10 days in the META2.0 and the META3.1exp product. Remember that 62 % of the META2.0 eddies are associated with high SCs with the PET-detected eddies over the same input field (SLA filtered with a 1000 km half-power cutoff wavelength) and that 33% of the PET-detected eddies are new, with a high proportion of small size eddies, both in amplitude 665 and radius. The shorter trajectories lasting from 10 to 30 days have more than 5 % of the involved eddies with effective radii below 50 km in the META2.0 product, whereas a large number of eddies with these small dimensions are part of the trajectories of META3.1exp, whatever their lifetime (Figure 10a). Indeed, a large number of eddies with amplitudes below 1 cm that are detected in META3.1exp (but not in META2.0) are associated with short trajectories, but there are still small-amplitude eddies present in the longer trajectories 670 (Figure 10b), especially at the start and the end of the trajectories. It is clear that the smaller structures have a physical consistency since they contribute to the short and the long trajectories, despite being close to the resolution of the altimetric maps.

Code and datasets availability
The detection and tracking algorithms, as well as the implemented similarity coefficient, are freely released 705 under a GPL V3 license (https://github.com/AntSimi/py-eddy-tracker) in the Python language. A large gallery of illustrated and documented routines to help with the data manipulation and visualization is available, and is updated when new methods are developed (https://py-eddy-tracker.readthedocs.io/en/v3.3.1/).  Pegliasco et al., 2021b) presented here is based on the two-710 satellites maps (C3S), ensuring a stability of the represented scales in space and time. This product is recommended for long-term analyses, including climate studies. The META3.1exp_allsat (https://doi.org/10.24400/527896/a01-2021.001, Pegliasco et al., 2021a) is based on the CMEMS all-satellites maps to take advantage of all the constellation, providing a better but inhomogeneous representation of the smaller scales in space and time depending on the available satellites (Figure 4). 715 The META3.1exp two-satellites and all-satellites products are available without restrictions on this AVISO repository : https://data.aviso.altimetry.fr/aviso-gateway/data/. The associated handbook describes the variables stored in the NETcdf files (SALP-MU-P-EA-23489-CLS, 2021). Six files are provided for each META3.1exp (Table 4). For both cyclones and anticyclones, the untracked files contain all the individual eddies with no association in trajectories, the "short" files are for the trajectories lasting strictly less than the minimum lifetime 720 parameter, set here at 10 days, and the "long" files are for the trajectories lasting at least the minimum lifetime parameter. The global attributes of each file inform the users of the algorithm version used to product them, with their specific detection and tracking parameters. Be aware that the files are compressed, but loading them to use them will decompress the files. Since the contours are the more memory consuming, we recommend loading the files without these variables and make an extraction of the time period and geographic area of interest with the 725 EddySubSetter application.

Summary
This paper aims to present the new global Mesoscale Eddy Trajectories Atlas (META3.1exp). Numerous 730 evolutions have been made from the META2.0 product, mainly to provide useful characteristics for users, in particular the eddy contours, which are mandatory for efficient colocation of eddies with other data. Moreover, some details of the detection and tracking algorithm were developed for weekly altimetric maps, with less accuracy than the daily products available nowadays, and needed to be adapted. The code is freely released under a GPL V3 license (https://github.com/AntSimi/py-eddy-tracker) in the Python language and routines for 735 data manipulation and visualization are documented.
The changes between the META2.0 and META3.1exp concern the input Sea Level field, its filtering, the detection algorithm, and the tracking scheme. We developed a methodology to compare intermediate datasets where only one change is made at a time, and to compute a similarity coefficient between matching eddies, from https://doi.org/10.5194/essd-2021-300 Performing the detection of mesoscale eddies on the ADT instead of SLA maps allows us to better represent the 745 ocean dynamics, since the SLA detected over strong MDT features represents their variability (weakening, reinforcement, displacement) but not their absolute polarity (anticyclones or cyclones). This eddy-detection change isolated from the others slightly reduced the number of detected eddies. Nevertheless, a large majority of eddies (77 %) are very similar between the ADT and the SLA detection in the open ocean, with no marked influence on the radius and amplitude distributions. The major impact induced by the use of ADT maps is the 750 geographical reorganization of the trajectories, with preferential occurrence of anticyclones (respectively, cyclones) over anticyclonic (respectively, cyclonic) MDT patterns in the META3.1exp dataset. To take into account the sharp gradients introduced in the ADT by the MDT while maintaining the mesoscale patterns in the filtered maps, the half-power cutoff wavelength was reduced from 1000 km to 700 km. This change increased slightly the number of detected eddies, and the similar eddies (87 % of the dataset) had their radius and 755 amplitude increased, but not significantly. The tracking scheme was also changed to improve the trajectories' reliability. Instead of searching for the eddy candidates to associate with the trajectory over a restricted area, the overlap method needs an overlap between the eddy and the next candidates, and the larger overlap is associated with the main trajectory in the case of multiple candidates. The number of consecutive virtual eddies introduced to respond to the "missing eddy problem" was increased from three to four. The overlap method follows eddies 760 over longer lifetimes, and this occurs without overuse of the virtual observations on the constitution of trajectories.
The major change comes with the detection algorithm change, from OSU, the historical detection algorithm, to the PET algorithm used to build the META3.1exp product. The PET algorithm detection is responsible for almost doubling the detected eddies compared with META2.0. Nevertheless, more than 60 % of the META2.