The growing capacities of new products developed in operational oceanography (Schiller and Brassington, 2011; Bell et al., 2015; Chakraborty et al., 2015; Le Traon et al., 2015; Hernandez et al., 2015; Kaurkin et al., 2016; Sotillo et al., 2016) imply a need for ongoing assessment using independent high-resolution in situ data sets. Such efforts help ensure the provision of high quality services by, for example, the Copernicus Marine Service. Thus, advancement in our knowledge of the ocean depends on high quality three-dimensional (3D) observations of the global ocean. However, cruise-based in situ oceanographic sampling typically only covers small targeted regions of the ocean during short periods of time, providing knowledge of specific oceanographic features. Sustained observations in the framework of the Global Ocean Observing System (GOOS) address only a limited number of observational targets, and open ocean high-resolution measurements targeted at the mesoscale are not yet considered (Legler et al., 2015). Moreover, synopticity is a key factor in the in situ sampling of the ocean, partly solved by satellites which are able to sample the globe in a short period of time. Despite the global coverage of the remote sensing observations, they only provide a surface view of the ocean. In order to complement satellite observations, sustained observing efforts through profiling and surface drifters, expendable bathythermographs (XBTs), and moorings provide real-time in situ vertical profiles of temperature and salinity on a global, but unstructured, grid. Emerging technology, such as the recently established global underwater glider observing network could, in principle, provide the required high-resolution in situ profile data, but routine mapping of the mesoscale is not yet implemented (Liblik et al., 2016).

In order to take advantage of the global coverage provided by remote sensing observations and the available in situ vertical profiles of temperature and salinity, Guinehut et al. (2012) made the first 3D operational multi-observation estimate of the ocean state by merging remote sensing observations (sea level anomaly and sea surface temperature) with in situ temperature and salinity vertical profiles (XBTs, CTDs, moorings and Argo profiles). This multivariate observation-based product, named ARMOR3D, provides global 3D data sets of temperature, salinity, geopotential height and geostrophic currents on a 1/4° horizontal regular grid with weekly temporal resolution. Mulet et al. (2012) perform a validation of the ARMOR3D product by comparison with model reanalysis and in situ observations (ANDRO current velocities from Argo float displacements and velocity measurements from the RAPID-MOCHA current meter array). They demonstrate that the geostrophic circulation estimated using ARMOR3D temperature and salinity fields has errors of less than 10% in the ocean interior, which indicates the robustness of the application of the thermal wind equation to infer ARMOR3D geostrophic velocities on a basin scale.

Several studies have taken advantage of the ability of this product to analyze mesoscale dynamics. Buongiorno Nardelli et al. (2012) carried out the first attempt to apply the quasi-geostrophic (QG) approximation to the observation-based product in order to map 3D mesoscale dynamics. Pascual et al. (2015) and Barceló-Llull et al. (2016) derive the QG mesoscale vertical velocity from the ARMOR3D fields in order to analyze its distribution in different regions of the global ocean as well as its contribution to nutrient advection and phytoplankton growth. Mason et al. (2017) construct eddy-centric composites of tracers, geostrophic currents and QG vertical velocity diagnosed from ARMOR3D in the energetic Brazil-Malvinas Confluence region. Through subregional composites they are able to reveal and analyze mesoscale eddy heterogeneity. These studies have all pointed out that probably there is an underestimation of the inferred QG vertical velocities due to the smoothing of the ARMOR3D fields. However, the lack of independent in situ data has prevented previous studies to provide a correct quantification of this underestimation.

The objective of the present study is to characterize this underestimation using 3D high-resolution in situ CTD and horizontal current observations obtained from the intensively sampling of an anticyclonic intrathermocline eddy (ITE) inside the Canary Eddy Corridor in the northeast Atlantic (Sangrà et al., 2009; Barceló-Llull et al., 2017b). Barceló-Llull et al. (2017a) used these 3D in situ fields to infer the QG vertical velocity distribution within the anticyclonic intrathermocline eddy, as well as the vertical velocity obtained from the integration of a generalized omega equation valid for high Rossby numbers which includes the forcing contribution of the ageostrophic horizontal velocities. First, we perform a revision of the hydrographic eddy signature comparing ARMOR3D fields with high-resolution in situ data from the surface to 1,000 m depth. Then, we proceed with the analysis of ARMOR3D-derived dynamical variables such as the QG vertical velocity that has previously been computed and analyzed from ARMOR3D fields but has not yet been validated with in situ data. The final objective is to evaluate the ability of the ARMOR3D product to resolve mesoscale eddies for a specific regional case (the Canary Eddy Corridor) and reproduce their hydrographic and dynamic 3D structure. In section 2 we describe the data set used for the comparison, in section 3 we expose the results, and in section 4 we summarize the main conclusions.

Five months before the cruise, Barceló-Llull et al. (2017b) periodically monitored the signature of the eddies generated by the Canary Islands in SLA maps provided by AVISO in order to select an anticyclonic eddy with a robust signature as the target for their study. In the first stage of the eddy survey, they crossed the eddy with two perpendicular SeaSoar transects to precisely detect the eddy center from vertical sections of density. They observed that the real eddy size was smaller than was expected from the SLA maps. Then, with a high-resolution meridional section of density anomaly they estimated an eddy radius of 46 km. As the ARMOR3D geopotential height is derived from altimetry, this overestimation of the eddy size is also reflected in its signature (Figure 1). The eddy center is located as the minimum in the ARMOR3D geostrophic flow (20.1°W, 26.1°N), and the eddy radius is derived from ARMOR3D Absolute Dynamic Topography and density fields giving a value of 92 km. Note that the derived quantities from ARMOR3D fields have a precision of ±1/4°, in accordance with the resolution of the product.

The averaged outer vertical profiles (average of the two outer profiles in each extreme of the meridional transects) of temperature and salinity (solid lines in Figures 2a,d) reveal a certain level of correspondence between ARMOR3D and in situ vertical stratification, with correlation coefficients greater than 0.99 for both temperature and salinity fields and root mean square differences of 0.23°C and 0.04 g kg⁻¹, respectively, which represent 0.25 and 0.38% of the in situ vertical profile variances (Table 1). The higher differences at the eddy center profiles (dashed lines in Figures 2a,d) are observed in the upper 100 m and between 200 and 500 m depth, corresponding with regions with intense anomalies (Figures 2b–e). The anomalies of the center profiles with respect the averaged outer profiles of temperature and salinity have low correlation coefficients between both data sets of 0.42 and 0.71, respectively (not shown). Vertical sections of in situ temperature and salinity anomalies (Figures 2b,e) reveal that the PUMP eddy is characterized by a narrow cold and fresher upper layer located at 30 m depth, and a warm and salty core centered between 200 and 500 m depth. The ARMOR3D temperature anomaly (Figure 2c) also shows a warm region between 200 and 500 m depth with maximum values of +0.95^oC (Table 2) in agreement with the location of the PUMP eddy core. However, the upper layer in the ARMOR3D field is warmer than the surrounding waters. The ARMOR3D salinity anomaly (Figure 2f) also reflects the presence of the PUMP eddy between 200 and 500 m depth, although the saltier region is vertically tilted to the south. As shown in Figures 2a,d, the temperature and salinity anomalies associated with the eddy in the ARMOR3D fields are smaller than in the high-resolution in situ fields (Table 2).

The ARMOR3D density field, mainly dominated by temperature, is well correlated with in situ observations (gray contours in Figures 3b–d). The averaged outer profiles of density (Figure 3a) show good correspondence between both data sets with a correlation coefficient of 0.999 and a root mean square difference of 0.04 kg m⁻³ that represent 0.43% of the variance of the averaged outer vertical profile of the in situ density (Table 1). The ARMOR3D field (Figure 3d) shows a depression of the isopycnals below 100 m and between 25 and 27.5°N in accordance with the presence of an anticyclonic eddy, while the seasonal pycnocline remains flat. The ARMOR3D isopycnals are smooth, however the main pycnocline resembles well the depression depicted in the in situ data (Figures 3b,c). Moreover, the eddy signal can be observed from 100 m to the maximum sampled depth (1,000 m) in both fields. The upper doming of the seasonal pycnocline observed in the in situ data is the result of thermal wind balance in accordance with the vertical shear induced by the subsurface intensified anticyclonic flow (Barceló-Llull et al., 2017b). The ARMOR3D geostrophic velocities have maximum values at the surface and, in accordance with thermal wind balance, the upper pycnocline remains flat.

The zonal component of the horizontal velocity measured with the ADCP during the meridional transect (Figure 3b), which includes geostrophic and ageostrophic motions, has maxima of 0.49 (−0.53) m s⁻¹ at 97 m, while the ARMOR3D geostrophic velocity (Figure 3d) has maxima of 0.11 (−0.19) m s⁻¹ at the sea surface, which represent an underestimation of the flow by a factor of 4 (Table 3). In addition, the ARMOR3D flow is surface intensified, contrary to the observed flow that shows subsurface maxima at ~100 m depth. Inferring the zonal component of the geostrophic velocity from the in situ density of the meridional transect (Figure 3c) and assuming a level of no motion at 1,000 m depth, the maxima are 0.27 (−0.30) m s⁻¹, which represent twice the ARMOR3D geostrophic velocity. The anticyclonic circulation in the ARMOR3D field extends from 24.5°N to 27.5°N in the upper layers with the maximum intensification concentrated in the upper 500 m depth, defined as the eddy base from in situ observations (Barceló-Llull et al., 2017b) although its influence is apparent at least until the maximum sampled depth (1,000 m).

Figures 2, 3 highlight the difference in eddy sizes with each data set. In order to better compare horizontal distributions of density using the in situ 3D fields, in Figure 4 we perform a normalization of the horizontal axes using the respective estimated eddy radii: r_is = 46 km for the PUMP eddy, and r_ar = 2r_is = 92 km from ARMOR3D (Chelton et al., 2011; Gaube et al., 2013, 2014, 2015; Gaube and McGillicuddy, 2017; Mason et al., 2017). The in situ and ARMOR3D eddies have similar elliptical shapes of the isopycnals with the major axis oriented NW-SE in both data sets (Figure 4). The aspect ratio of the 26.58 kg m⁻³ isopycnal at 200 m depth is 1.44 for the in situ data and 1.38 for the ARMOR3D product. In situ geostrophic velocity magnitude is double the ARMOR3D geostrophic velocities with a similar deceleration of the flow at the northern part of the eddy (Figure 4).

The scaled geostrophic vertical relative vorticity, ζ^g/f, provides an estimate of the local geostrophic Rossby number. Figure 5 shows different vertical distributions of ζ^g/f for each data set related to the subsurface intensification of the in situ flow in contrast to the surface intensified ARMOR3D flow. The ARMOR3D field has an extreme value at the eddy center of ζ^g/f = −0.16 while with the in situ data we obtain a ζ^g/f = −0.46, almost three times larger (Table 3).

QG vertical velocity is estimated for both data sets. For the ARMOR3D case, we derive w_QGar for two consecutive weeks: 03-09-2014 and 10-09-2014, as the in situ 3D sampling was carried out in the middle of these two dates. The w_QGis is characterized by two different horizontal distributions in the seasonal and main pycnoclines (Barceló-Llull et al., 2017a), while w_QGar has the same horizontal distribution in all the water column. Figure 6 shows the horizontal distributions of w_QG at ~150 m depth. At the main pycnocline the w_QGis distribution has a quadripolar pattern, while the w_QGar distribution is composed of small cells with alternating signs located along the eddy periphery. In consecutive weeks the location of the cells seems to be slightly rotated. The maxima of vertical velocity are located at the periphery of both eddies. Besides the difference in the horizontal distribution, the magnitude of w_QG is similar for both eddies (Table 3).

We have presented a comparison of the CMEMS ocean state estimate ARMOR3D hydrodynamic fields with 3D high-resolution in situ observations in order to analyze the ability of the ARMOR3D product to describe the 3D structure of mesoscale eddies. ARMOR3D reproduces the large scale stratification of the ocean with an underestimation of the hydrographic anomalies within the eddy core, and an overestimation of the eddy radius inherited from altimetry of 92 km, in comparison with the in situ-derived eddy radius of 46 km. The overestimation of the eddy size in the SLA maps may be due to along track data coverage, their lower resolution (0.25°) and the correlation scales used to construct the product.

The PUMP eddy is characterized by a hydrographic core centered between 200 and 500 m depth. The core has warmer and saltier water properties than the surrounding waters at the same depth level (Bindoff and McDougall, 1994), as well as an elliptical horizontal isopycnal shape that is reflected in both data sets. The difference in density magnitude is due to the shallower depression of the ARMOR3D isopycnals in comparison with the deeper depressed in situ isopycnals (Figures 3, 5). The eddy signal is apparent in density and horizontal velocity to at least 1,000 m depth. The horizontal currents are most intense in the upper 500 m, which has been defined as the eddy base. The averaged outer vertical profiles of temperature, salinity and density show correlation coefficients between both data sets higher than 0.99 with root mean square differences that represent 0.3–0.4% of the in situ vertical profile variances (Table 1). The high correlation between the outer vertical profiles of the hydrographic fields is a good indicator of the ability of ARMOR3D to reproduce the subsurface vertical stratification of the ocean, as this mean outer profile may be different in other regions of the ocean. The eddy center profiles of temperature, salinity and density reveal that ARMOR3D underestimates the hydrographic anomalies. Moreover, in the upper 100 m depth ARMOR3D does not reproduce the eddy cap, i.e., the cold, saltier and denser upper region of the PUMP eddy. A global comparison with independent temperature and salinity profiles (Guinehut et al., 2012) shows that the root mean square error is higher around 50–100 m depth corresponding with the seasonal pycnocline.

Regarding the dynamical variables, ARMOR3D geostrophic velocities show a deceleration of the flow at the northern edge of the eddy, in accordance with the in situ observations, that may be due to the westward propagation of the eddy which would intensify the southern flank westward velocities and decelerate the northern flank eastward flow. However, we note that the significance of this observation is limited given that ARMOR3D underestimates the PUMP eddy geostrophic flow by a factor of 2 and describes a surface intensified flow. This surface intensification of the flow is reflected in the vertical distribution of the local geostrophic Rossby number, which has a magnitude that is underestimated by a factor of 3. Quasi-geostrophic (QG) vertical velocity inferred from the two data sets has similar magnitudes, and the upwelling/downwelling cells are located along the eddy periphery. In conclusion, ARMOR3D is capable of reproducing the large scale stratification of the ocean with an underestimation of the hydrographic anomalies and geostrophic velocities, and with similar QG vertical velocity magnitudes. On the other hand, at this date the product fails to reproduce the intrathermocline signature of the eddy, with flat isopycnals in the upper layers and a surface intensified circulation. Improvements are expected with a new reprocessed ARMOR3D product that uses sea surface salinity (SSS) fields (Droghei et al., 2016) and updated statistical profiles for the projection of surface data (SLA, SST, SSS) to depth.

The eddy analyzed in this study is an anticyclonic intrathermocline eddy (ITE). These eddies are characterized by complex baroclinic structure and intense submesoscale signatures (e.g., Lee and Niiler, 1998; Karstensen et al., 2017), making comparison particularly challenging. Better agreements between in situ and ARMOR3D fields may be expected with surface intensified anticyclonic/cyclonic eddies. However, our comparison here is justified because subsurface eddies are present all over the world ocean and may play important roles in lateral transports of momentum and hydrographic properties and also in triggering ecosystem responses (McWilliams, 1985; Pegliasco et al., 2015; McWilliams, 2016; Schütte et al., 2016a,b). Hence, it is important to evaluate the presence of this type of eddies in observation-based products and numerical models.

Anticyclonic ITEs have an upper density structure with upward displacement of the isopycnals toward the eddy center. Their surface velocity and SLA signature can also be weak (Schütte et al., 2016a) depending on the depth of their core, on the stratification and on the intensity of their anomalies within their cores. The present ITE does have a significant surface signature (maximum velocity ~0.2–0.3 m s⁻¹) so the weaker dynamical signal reconstructed by ARMOR3D may be associated with the coarse resolution of SLA and the smoothing associated with the construction of the gridded SLA maps (here illustrated by the size of the eddy, which is twice the observed one), which are known to underestimate the geostrophic flows.

Figure 7a shows the SST signal on 10-09-2017 for the PUMP eddy region together with SLA contours and the Argo float positions of the vertical profiles used to construct the ARMOR3D output. The PUMP eddy cold signature is centered at around 30 m depth with no representation on the surface layer (Figure 2b), because of this there is no cold eddy signal on the SST map. The Argo profiles are found at the periphery of the eddy, with a gradual drift toward the eddy core with time. Figures 7b,c corroborate this approximation as the vertical profiles of temperature and salinity progressively approach the PUMP eddy center profiles. To be able to resolve the subsurface intensification of the flow with ARMOR3D fields, the presence of Argo vertical profiles of temperature and salinity within the eddy core are necessary so as to obtain the correct correlation functions to reconstruct the subsurface nature of the eddy (Assassi et al., 2016).

As the upper cold signature of the PUMP eddy cannot be represented on SST maps, we analyze the PUMP eddy lifecycle using ARMOR3D fields, and the presence of Argo buoy profiles within the eddy. Using the automated eddy tracker of Mason et al. (2014) we could detect the PUMP eddy trajectory since its formation (gray dots in Figure 1). With ARMOR3D fields we can analyze the 3D hydrodynamic structure of the PUMP eddy every week since its formation until the end of October 2014. Zonal sections crossing the eddy center (Figure 8) reveal that the ARMOR3D eddy has a subsurface intensification of the flow 1 month after the eddy sampling, coinciding with the presence of an Argo buoy within the eddy core (Figure 9). In correspondence with the subsurface flow, the upper thermocline is bowl-shaped and introduces cold water upwards (Figure 9).

Our results demonstrate that, even with the presence of Argo floats, ARMOR3D may not resolve the ITE structure. To be able to reproduce the subsurface nature of ITEs it is needed the presence of Argo profiles within the eddy core. To check if we could find other examples of ITEs in the ARMOR3D data we again applied the automated eddy tracker of Mason et al. (2014) to weekly gridded CMEMS sea level anomalies at the Canary Eddy Corridor region for the period 2000-2015. We then evaluated the mean profile of the eddy geostrophic swirl speed from ARMOR3D for every identified eddy. We found that about 20% of the anticyclonic eddy swirl speed profiles had maxima between 50 and 150 m depth; this is the signature of an ITE. ARMOR3D is therefore able to detect and reproduce the vertical structure of intrathermocline eddies (subsurface intensification of the flow and cold seasonal thermocline) in the region under analysis not only for the PUMP eddy case. The ability of the ARMOR3D product to detect ITEs in other regions of the world ocean are expected to be a source of future work.

The underestimation of the local Rossby number may have important implications for the inference of the vertical velocity, as the QG approximation is valid for low Rossby numbers. If we compare the local geostrophic Rossby number inferred from ARMOR3D fields and the local Rossby number obtained with ADCP horizontal velocities (Barceló-Llull et al., 2017b) we obtain an underestimation by a factor of 4 of the total local Rossby number. If we only consider the local geostrophic Rossby number from both data sets we obtain an underestimation by a factor of 3. Besides this, we have to take into account that the in situ geostrophic Rossby field is estimated with the in situ geostrophic velocity, which is inferred with 3D density fields and considering the ADCP data at the reference level (325 m depth) (Appendix).

We note that the resolution of the 3D in situ fields obtained from the PUMP cruise is the result of a compromise between spatial resolution and synopticity of the eddy sampling (Barceló-Llull et al., 2017a), where the aim was to resolve the mesoscale circulation. Allen et al. (2001) study the implications of errors associated with sampling strategies on vertical velocity estimates. They used a sampling strategy similar to the PUMP survey to sample mesoscale structures, and they found that vertical velocity distributions remained unaltered, while their magnitudes were reduced because of the smoothing introduced by the sampling resolution, but without alterations due to quasi-synopticity. The geostrophic Rossby number and QG vertical velocity inferred here have not accounted for the ageostrophic component of the flow. To have a more realistic view of these parameters we refer to Barceló-Llull et al. (2017a). Regarding the resolution of the in situ fields, the derived parameters may be underestimated in comparison with the inclusion of small-scale features with high Ro (Klein and Lapeyre, 2009). Vertical motion is a challenging variable to diagnose and there are large errors associated with its inference due to theoretical approximations, the presence of inertial gravity waves and tides, the lack of synopticity of the experimental data, instrumental errors, the interpolation method and the scales resolved (e.g., Allen et al., 2001; Gomis et al., 2001; Naveira Garabato et al., 2001; Rixen and Beckers, 2002; Viúdez and Dritschel, 2003, 2004; Pallàs-Sanz and Viúdez, 2005). The importance of the vertical velocity has been known for decades and today is still considered a hot topic (Liang et al., 2017). This is one of the primary motivations of the Office of Naval Research (ONR) Coherent Lagrangian Pathways from the Surface Ocean to Interior (CALYPSO) program.

Data from multiplatform experiments such as PUMP can play an important role in the assessment of operational products such as those provided by CMEMS, and we expect to see more examples in the future as the need for and benefit of these types of experiments becomes apparent (Shcherbina et al., 2015; Pascual et al., 2017).

BB-L and AP: planning of the research. BB-L, AP, EM, and SM: validation and analysis of the results. All authors contributed to the drafting of the manuscript.