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NOVEMBER 2022 I E NNA E T A L . 2643 a,b c,d,e a,b FEDERICO IENNA, IGOR BASHMACHNIKOV, AND JOAQUIM DIAS Marine and Environmental Sciences Center, Faculdade de Cienc ˆ ias, Universidade de Lisboa, Campo Grande, Lisbon, Portugal Departamento de Engenharia Geogra ´fica, Geof´ ısica e Energia, Faculdade de Cienc ˆ ias, Universidade de Lisboa, Campo Grande, Lisbon, Portugal Department of Oceanography, St. Petersburg State University, St. Petersburg, Russia Nansen International Environmental and Remote Sensing Centre, St. Petersburg, Russia Marine Hydrophysical Institute of Russian Academy of Sciences, Sebastopol, Russia (Manuscript received 7 April 2022, in final form 7 June 2022) ABSTRACT: The sea surface expressions of Mediterranean Water eddies, known as “meddies,” are observed in satellite data, and their main characteristics are measured. Satellite altimeter observations of surface expressions are detected over the meddies observed in situ using the MEDTRANS meddy dataset (1950–2013). In this study 209 observed meddy cores in the North Atlantic Ocean, selected over the period of the 22 years of sea surface height measurements with satellite altimetry (1993–2013), were analyzed. Results show relatively good agreement between the theoretical estimates of the meddy surface signals as reported by Bashmachnikov and Carton and the measured surface expressions. It was found that, on average, the theoretical results underestimate the measured sea surface elevations of the meddy surface expressions by a factor of 2. Although the variability of the measured expressions is reasonably well described by the combination of meddy core and the ocean background parameters of the theoretical expression, we cannot define a single individual parameter of the meddy core, which chiefly shapes the magnitude of the meddy surface signal. Interestingly, the overall dis- tribution of characteristics of meddy surface expressions in the Atlantic shows that the sea level anomalies formed by meddies intensify westward, growing both in magnitude and radius. This opposes the expected theoretical decrease of meddy surface signals due to a known progressive decay of the meddy cores with distance from their generation re- gion at the Iberian continental slope. This observed tendency is attributed to meddy interaction with the upper-ocean currents and other eddies (in particular in the region of the North Atlantic Current and Azores Current) that are not considered by the theory. KEYWORDS: Eddies; Mesoscale processes; Ocean dynamics; Altimetry; In situ oceanic observations; Remote sensing 1. Introduction directly affecting the environment and serving as efficient mechanisms for transporting salinity, temperature, and Deep coherent vortices (DCVs) are prevalent, observable other water properties over large distances (Richardson physical phenomena that occur throughout the ocean. Mesoscale et al. 2000). DCVs are typically identified as those with horizontal scales Mediterranean Water eddies}aspecifictype of DCV from one to several local baroclinic Rossby deformation radii also known as “meddies”}are subsurface mesoscale anticyclones (resulting in DCV radii within the order of tens of kilometers that offer excellent insight into the behavior of such dynamic enti- in the vast majority of cases). Being the result of baroclinic ties because of their observability as pronounced thermohaline instability of the major ocean currents, mesoscale DCVs typi- anomalies at middepths. Meddies in the northeastern Atlantic cally contain the highest amount of eddy kinetic energy in com- Ocean separate from the Mediterranean Undercurrent (MUC), parison with other mesoscale ocean dynamics (Cushman-Roisin which is formed by the outflow of the dense Mediterranean and Beckers 2010). In the subtropical and tropical latitudes, Water from the Gibraltar Strait, rapidly sinks to a neutral mesoscale DCVs are large enough to be subject to relatively buoyancy depth of approximately 1000 m, and then propa- intensive self-propagation and are often observed to propa- gates northward around the Iberian Peninsula. Observations gate against the mean flow (Vandermeirsch et al. 2001). Weak suggest that meddy formation occurs most often at several decay permits mesoscale DCVs to survive in the ocean from locations off the Iberian coast: Cape St. Vincent, the Portimao ˜ several months to over a year and transport water throughout Canyon, the Estremadura Promontory, and the Porto and the ocean and far from their point of origin (Chelton et al. Aveiro Canyons. Meddy formation as a result of the MUC 2011; Schouten et al. 2000). Whether through a final rapid de- interaction with capes and canyons can go through several struction or through a slow exchange across their boundaries, different mechanisms (see, e.g., D’Asaro 1988; Pichevin and DCVs release water from their cores into the surroundings, Nof 1996; Aiki and Yamagata 2004). In the cited studies the meddy generation from the MUC was suggested to go through Denotes content that is immediately available upon publica- barotropic or baroclinic instability of the MUC, while the sep- tion as open access. aration from the MUC is triggered or enhanced by the flow interaction with the sharp bathymetry. After separating Corresponding author: Federico Ienna, fienna@fc.ul.pt from the MUC, the newly generated DCVs become subject DOI: 10.1175/JPO-D-22-0081.1 Ó 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 2644 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 to their own internal dynamics and travel away from the Meddies influence the physical and chemical properties, as coast, self-propagating westward, often against the mean well as the stratification of the water column from the upper ocean to, at least, 2000 m (Mauritzen et al. 2001). As such, current (Richardson et al. 2000; Bashmachnikov et al. 2015a). meddies are known to be an important contributor to the In the Atlantic, meddies can persist for periods from months to westward and southwestward transport of Mediterranean years, typically existing for less than 1–2years (Richardson et al. Water from the Iberian margin, contributing between 50% 2000; Bashmachnikov et al. 2015a). and 100% to the formation of the Mediterranean salt tongue Typically, meddies contain a positive temperature anomaly in the Atlantic (Arhan et al. 1994; Bower et al. 1997; Maze ´ of up to 48C and a salinity anomaly of up to 1 unit, making their et al. 1997; Sparrow et al. 2002). presence readily recognizable in vertical profiles (Richardson Despite having the upper limit of their thermohaline cores at et al. 2000). Richardson et al. (1989, 1991) proposed a set of around 500 m, meddies are known to consistently transmit their criteria for identification of a meddy: salinity anomaly over dynamic signal to the ocean surface. In what was perhaps the first 0.2 (0.4 in the earlier study) in the depth range of 500–1500 m, published mention of meddies’ manifestation at the sea surface, which is generally considered to be the standard. Because of Kase and Zenk (1987) demonstrated a tendency of a surface their relatively large radii (20–60 km) and pronounced positive drifter to make a semicircle in a clockwise direction over an temperature and salinity anomalies in their cores, a large num- observed meddy. Since then, ample evidence of meddies ber of meddies have been well documented in a rich observa- forming a measurable dynamic signature at the sea surface tional history. has been collected (Stammer et al. 1991; Pingree and Le Cann The first published observation of a DCV of Mediterranean 1993a; Oliveira et al. 2000; Paillet et al. 2002; Bashmachnikov Water was made in the Gulf of Cadiz, near the MUC, on a hy- et al. 2009; Jo et al. 2015; Ciani et al. 2015, among others). drographic survey by Swallow (1969), who observed a distinct A meddy’s surface expression results from the lifting of iso- anticyclonically rotating blob of deep Mediterranean Water. pycnals throughout the water column above the meddy core. A similar observation was published by Piip (1969) in the same A propagating meddy that travels at a neutral buoyancy level year, near the Madeira–Canaries region. Since then, several throughout the ocean causes a compression of the water col- cruises have confirmed a regular emergence of such structures umn above the frontal part of its core relative to the direction in theCanaryBasin (see, e.g., Armi and Zenk 1984). In 1978, of its propagation (Fig. 1). By conservation of potential vortic- McDowell and Rossby (1978) observed a Mediterranean Water ity, this compression induces an anticyclonic rotation in the eddy as far as in the vicinity of the Bahamas and coined the upper ocean, causing isopycnal lifting that may propagate all term meddy to distinguish this specific type of eddies, generated the way to the sea surface. This mechanism may force the lift- from the Mediterranean Outflow in the Atlantic. Armi and ing the sea surface as much as 15–20 cm in the most extreme Stommel (1983) detected another meddy near the Mid-Atlantic cases. By geostrophy, this implies a sea surface anticyclonic Ridge (MAR) southwest of the Canary Islands. One of the rotation with azimuthal velocity often exceeding 10 cm s . meddies, reported by Armi and Zenk (1984), was tracked over This effect has been observed in satellite altimetry sea level two years using neutral buoyancy floats, and its gradual decay measurements (Stammer et al. 1991; Oliveira et al. 2000; was measured with repeated oceanographic sections (Armi et al. Bashmachnikov et al. 2009, 2013, 2015a; Ienna et al. 2014), 1989; Hebert et al. 1990). Further on, several meddies were direct sea surface velocity measurements (Armi et al. 1989; tracked from their generation sites in the MUC during the in Bower et al. 1997), and in high-resolution model results situ RAFOS-tracking program known as A Mediterranean (Serra et al. 2002; Ciani et al. 2015). Detailed in situ obser- Undercurrent Seeding Experiment (AMUSE) (Bower et al. vations in the subtropics have confirmed that the entire water 1997). Another set of meddies was tracked for 6–11 months column above a meddy rotates anticyclonically. The rotation south on the Azores, at distances over 1000 km from the velocity gradually decreases upward and, at the sea surface, Iberian coast, during Structure des Echanges Mer-Atmospher ` e, typically forms up to 30% of the maximum rotation velocity in ´ ´ ´ ´ ´ ´ ´ ´ 21 Proprietes des Heterogeneites Oceaniques: Recherche Ex- the meddy core still reaching 10–25 cm s (Armi et al. 1989; perimentale (SEMAPHORE) (Richardson and Tychensky Pingree and Le Cann 1993a,b; Pingree 1995; Paillet et al. 2002; 1998; Tychensky and Carton 1998), among other programs. Bashmachnikov and Carton 2012; Bashmachnikov et al. 2013). These and other studies (Paillet et al. 1999, 2002; Pingree The close coupling of meddy cores and their surface ex- 1995; Shapiro et al. 1995; Richardson et al. 2000; Carton et al. pressions has been demonstrated in several recent studies 2002; Demidov et al. 2012; Bashmachnikov et al. 2015a) have (Bashmachnikov et al. 2009, 2013, 2015a; Ienna et al. 2014). furthered knowledge on meddy formation sites, pathways, and Yan et al. (2006) used satellite altimetry to observe the trends the evolution of their cores over time. in the Mediterranean Outflow through its surface effects, Meddies propagate in the ocean because of the generation which included the surface effects of meddies. Bashmachnikov of secondary circulations as a result of a variation of the Coriolis and Carton (2012), and later Bashmachnikov et al. (2014) and parameter across the meddy core (Cushman-Roisin et al. 1990; Ciani et al. (2017), derived theoretical expressions for the in- Morel and McWilliams 1997), producing a predominantly west- tensity of meddy surface signals as a function of meddy core ward eddy self-propagation mechanism. Other secondary ef- properties and environmental conditions, for different patterns fects in the dynamics of the propagating eddies, together with of potential vorticity anomalies in and around a meddy core. the background currents and topography often add a meridio- Testing the theoretical results against surface expressions of nal (typically southward) component to the meddy motion. several observed (or modeled) meddies suggests a validity of NOVEMBER 2022 I E NNA E T A L . 2645 FIG. 1. Schematic representation of a formation process of the sea surface expression above a meddy core. The centers of the surface signal (S) and of the meddy core (M)are indicated. these theoretical approaches. These studies also found a poten- derived sea surface height (SSH) are used to detect sea level tial southern limit for detection of meddies with different radii anomalies representing surface signals of these meddies. The and depths of the cores in satellite altimetry: approximately at combination of deep in situ and satellite surface observations, 258N for larger meddies and at around 358N for smaller med- taken over the same time period, allows us to link meddy core dies. Meddies (Aiki and Yamagata 2004; Barbosa Aguiar et al. parameters to their surface signature. 2013) and their surface expressions (Ciani et al. 2015)have re- a. In situ data cently been rigorously treated in high-resolution model studies. The results of the theoretical investigations above have only The in situ positions and properties of the detected meddies been tested against a few actual observations. In this study, we (1970–2014) were previously derived in the MEDTRANS project present the first consistent analysis of the spatial variability of (Bashmachnikov et al. 2015a). Temperature and salinity from surface expressions of 209 meddies, observed throughout the vertical profiles of Nansen bottles, conductivity–temperature– northeastern Atlantic since 1993, and compare these with the density probes (CTD, XCTD), and Argo profiling drifters from theoretical estimates from Bashmachnikov and Carton (2012). the World Ocean Database (WOD) were quality controlled in The meddy cores used herein, detected in situ in Argo profilers the framework of this project (Bashmachnikov et al. 2015b). and CTD casts, are derived from the Mechanisms of Transport Middepth temperature and salinity anomalies for identification and Dispersion of the Mediterranean Water in the Subtropical of meddies were derived relative to MEDTRANS reference Northeast Atlantic (MEDTRANS) dataset as described in climatology (Bashmachnikov et al. 2015b,c), which includes Bashmachnikov et al. (2015a), and their surface expressions the gridded 3D thermohaline distributions at 30-km spatial and are detected in Archiving, Validation and Interpretation of 25-m depth intervals, available within a repository at the Satellite Oceanographic data (AVISO) satellite altimetry. This University of Lisbon (http://www.mare-centre.pt/en/research/ results in a further refinement of our understanding of the poten- data-library/medtrans-data). tial ties between surface expressions and physical and dynamic The meddy cores were identified within in situ data using a parameters of deep meddy cores, and how they are affected by slightly relaxed Richardson’scriterion (Richardson et al. 1991), the background ocean. The data used and the method for match- according to which a meddy core should form a salinity anom- ing surface-to-core are discussed in section 2. A statistical analysis aly of at least 10.2 when averaged within the depth limits of of the meddy surface expressions is presented in section 3,fol- 700 and 1300 m. Only meddies having been sampled with at lowed by an analysis of the geographical patterns observed least three profiles within the core were used for the analysis. in the distribution of properties of the surface expressions Additionally, every radial distribution of the profiles within the themselves. The results are the discussed in section 4. selected meddies was double-checked by human eye, allowing for the filtering out of erroneous profiles, as well as eliminating 2. Method the structures that do not have the distinguishable, typical lens In situ salinity and temperature profiles are used for detec- shape of a meddy, despite having technically fit the criterion tion of the meddy cores. Remote sensing data from altimeter- [see Bashmachnikov et al. (2015a, their section 2.2), for a 2646 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG. 2. (a) Distribution of all in situ meddy core observations during 1993–2014 that were used in this study. Red open circles are CTD and XCTD casts (68 meddies and 2261 profiles); blue open circles are Argo casts (294 meddies and 2551 profiles). The larger purple filled circles are a subset of MEDTRANS meddies with further statistics of core properties and correspond to the same subset plotted in (b). The mean sea surface currents are shown in black, and the locations of the North Atlantic Current (NAC) and Azores Current (AzC) are marked. The positions of three meddies 1, 2, and 3 with exceptionally high SLA (see Fig. 7) are highlighted by red symbols. (b) Temperature–salinity diagram of meddy cores used in this study; black lines are s (kg m ). The circle dimensions show radii (km) of meddy cores, and meddy core depths (dbar) are marked in color (in the case of double cores, the lower cores are selected). detailed description of how the coordinates of meddy centers beginning of the satellite altimetry era). The number of M and meddy radius R are derived from in situ data]. In this profiles in these meddy cores ranges from 3 to 40 profiles, study, we use 209 meddy cores from the aforementioned composed in total of 2261 ship CTD casts and 2559 Argo MEDTRANS dataset detectedinsitusince 1993 (the profiler casts (Fig. 2). NOVEMBER 2022 I E NNA E T A L . 2647 b. Remote sensing data anomaly. The SSH field, derived from gridded AVISO al- timetry dataset, is converted to relative vorticity v under To observe the sea surface expressions of the detected med- the traditional geostrophic approximation (Arbic et al. 2012; dies, we used satellite-derived level-4 blended SSH, obtained Vallis 2006): from the repository available at the AVISO database (avail- able since 1993). These are weekly global maps gridded at = 8 2 2 y u g h h v 2 1 , (1) spatial resolution. Because AVISO altimetry data are merged 2 2 x y f x y from a number of along-track observations from several satel- lites (CNES 2016), the accuracy of the results depends partic- where u (zonal) and y (meridional) are the sea surface velocity ularly on the distance from the nearest satellite track to the components, respectively; h is the sea level height; g is the point of interest, as well as on the time difference between the acceleration of gravity; and f is the Coriolis parameter. in situ observations and the dates of the nearest tracks, both of For each selected region of negative relative vorticity, we de- which vary over the study region and time range. This may be a fine the boundary of the SSH anomaly as the distance from the source of a certain nonphysical noise in the amplitudes and radii peak sea level height (the first-choice eddy center S)to the sur- of the observed sea surface eddy structures (Bashmachnikov rounding contour of zero relative vorticity by looking for the et al. 2020). closest zero point where v = 0 along eight equally distributed ra- In situ observations suggest the current velocities in the dial transects starting at the first-choice center. If no zero value is meddies from 10 to 30 cm s (Pingree and LeCann 1993a,b; reached within a predefined maximum radial distance, the eddy Pingree 1995; Paillet et al. 2002; Bashmachnikov et al. 2013, boundary is fixed at the nearest inflection point in the relative 2014). Taking the typical radii of the sea surface expressions 2 2 vorticity profile (i.e., where v /s = 0). When both criteria are of 30–50 km, the geostrophic sea level anomalies should range satisfied along the segment, whichever one closest to the center from 5 to 15 cm, within the along-track altimetry observations S is treated as a boundary of the surface signal (see example in (Oliveira et al. 2000). This is above formal accuracy of AVISO Fig. 3). Then the mean of the radial distances to the selected altimetry data of 4 cm, and such eddies are well discernable in boundary points of the anomalous relative vorticity patch is AVISO altimetry (Chelton et al. 2011). A number of previous called the “dynamic radius” of the surface signal R .This method studies have successfully used satellite altimetry to track has been described in detail in Bashmachnikov et al. (2017). meddy surface signals along with the meddy cores, indicat- Once the surface signal of a particular meddy n is outlined, ing that altimetry is relevant for observation of this phenom- the following characteristics of the meddy surface are derived: enon (Oliveira et al. 2000; Yan et al. 2006; Bashmachnikov et al. 2009, 2013, 2014; Bashmachnikov and Carton 2012; • the longitude and latitude of the center point of the meddy Ienna et al. 2014; Jo et al. 2015, among others). surface expression, denoted by S , The region of interest for this study, confined between • the radius of the sea surface expression R , 58 and 358W and between 258 and 458N, is known for its • the magnitude of the sea level expression SLA , moderate sea surface height variability (Sterlini et al. 2016), • the separation between the center points of the meddy core which is favorable for the detection of meddy surface sig- M and the meddy surface signal S , denoted by d, and n n nals, which often form the strongest of all anticyclonic sig- the azimuthal direction of the segment drawn between the nals in the vicinity of a meddy (see, e.g., Bashmachnikov meddy core center M and the surface expression center S , n n et al. 2009). denoted by a. c. Algorithm for detection of meddy sea surface signals Once automatically processed, a subset of the surface expres- sion measurements was further verified by human eye to verify The algorithm for detection of meddy surface signals is the work performed by the algorithm and to ensure that there intended to function as an objective method for associating were no obvious lapses in the output. known meddy occurrences (see above), to the nearest neg- ative relative vorticity anomaly (positive sea level anomaly) 3. Results occurring over a detected meddy core, as theory suggests is the case (Bashmachnikov and Carton 2012; Bashmachnikov a. Properties of sea surface expressions of meddy cores et al. 2014; Ciani et al. 2017). The analysis of the properties of the meddy sea surface sig- The algorithm starts by searching for the nearest track of a nals shows an increase of the peak sea level anomaly above satellite pass to the spatial and temporal coordinates of a given the meddy center SLA with its dynamic radius R ,whose 0 s in situ meddy core center M. The time interval between a satel- dependence can be fitted by a quadratic function (Fig. 4a), lite pass and an in situ meddy occurrence is at most 10 days. in meters, The algorithm then searches for all nearby Gaussian-like sea level anomalies in the neighboring along-track sea level profiles 29 2 24 SLA 5:7 3 10 R 2 3:4 3 10 R 1 7:8 (2) within one radial distance of the meddy core R ,and finds their 0 s center points, defined as the location of the highest individual sea level peak. Here we only consider meddy sea surface expressions with Once the center of the potential anomaly peak is detected, SLA $ SLA , where SLA is the formal maximum accu- 0 min min the next step is to evaluate the extent of the Gaussian-like racy of AVISO satellite altimetry, which ranges between 2648 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG.3.An example of an identification of a meddy surface expression (a) in the SSH (cm) and (b) in the sea surface relative vorticity (s ). The meddy center M is marked with cyan diamond, and the cyan ellipse shows the meddy boundary (the dynamic radius). The loca- tion of all in situ measurements used to identify this meddy are shown as yellow stars. The location of the center of the sea surface anom- aly S, identified as the meddy surface signal, is marked with the red triangle. The boundary of the sea surface signal is marked with the red point at the end of each of the dashed red radial segments. The final dynamic radius of the meddy surface signal R is the mean of the ra- dial distances over all of the segments. 2 and 4 cm in the northeast Atlantic. The dependence be- nearly reaching the original values of, on average, 10–20 km tween peak SLA and R suggests a linear growth of the over 2000 km from the coast (Bashmachnikov et al. 2015a). The 0 s peak surface azimuthal velocity with R , consistent with a overwhelming majority of the meddy sea surface signals dis- Rayleigh radial current profile. For meddy cores, the ratio cussed here are observed at distances of over 300 km from the of the azimuthal velocities to meddy radii (Rossby number Iberian coast and show an increase in R and of their surface in zonal bands) shows a rapid drop by about 50% within azimuthal velocity [estimated from Eq. (2) using a geostrophic 300 km from the Iberian coast most likely due to frequent approximation] toward the Mid-Atlantic Ridge. This similar meddy mergers in the Iberian Basin (Bashmachnikov et al. spatial tendency in the azimuthal velocities of both meddies 2015a). Farther away, meddy radii show a gradual decrease, and their sea surface expressions suggests a possible dynamic FIG. 4. (a) Radius R (km) plotted against the maximum sea level anomalies SLA (cm) of the meddy sea surface s 0 expressions. A quadratic fit is overlaid (red curve). (b) The azimuth angle d ( ) and the separation distance a (km) between the meddy center M and the surface expression center S, subdivided by color into azimuthal octants (d =08–458; d =458–908, etc.). The respectively colored, boxed numbers in each octant show the total number of plotted values in that octant. NOVEMBER 2022 I E NNA E T A L . 2649 coupling between the properties of meddies and their sea sur- face signals. The mean separation between M (derived in situ) and S (derived from AVISO altimetry) is d = 9 km, which, consider- ing the AVISO resolution, means that the vast majority of meddy surface signals are directly above the meddy cores. This is not immediately evident from Fig. 4b, due to repetitive overlay of the markers at small d (many of which are equal to zero). This indicates a predominant vertical alignment of a meddy and its surface signal (or another eddy), often seen in observations and numerical models (see, e.g., Carton et al. 2013; Bashmachnikov et al. 2013; Belkin et al. 2020). A few surface signals show relatively large separation over 100 km from meddy centers, still within two radial distances between S and M. Such eddies can be considered as being coupled (Carton et al. 2016). FIG. 5. Geographical distribution of quasigeostrophic potential The azimuth angles between M and S (Fig. 4b) show a rea- vorticity anomalies of meddy cores (q ˜ ;s ). Arrows mark the sonably randomized distribution around the circle, with a cer- m mean sea surface currents derived from AVISO altimetry; thin tain tendency of S being westward or southward from M. The green lines show the isobaths. latter are the main directions of meddy propagation. There- fore, the surface expressions tend to stay in front of meddies moving west and south. However, meddy surface expressions proxy term q that was obtained as described in Bashmachnikov and Carton (2012), as quasigeostrophic potential vorticity, can also be located at any azimuth relative to the meddy cen- by ters, consistent with numerical experiments with coupled vorti- ces in different layers, rotating around a common center (see, 2 2 e.g., Reinaud and Dritschel 2002; Bersanelli et al. 2016). q ˜ (0:8N 2 N ): (5) m m surr b. Meddy sea surface expressions in measurements and The factor of 0.8 is empirically derived and assumes that the rel- in theory ative vorticity of a meddy is, on average, 20.2f. The geographi- Under the quasigeostrophic approximation, the sea level cal distribution of q in meddy cores is plotted in Fig. 5,and elevation SLA caused by the underlying core can be theoreti- the corresponding values are plotted in Fig. 6b.The q values cally expressed as (Bashmachnikov and Carton 2012) obtained are almost exclusively negative, which is typical for an- ticyclonic meddies. The absolute values shown in Fig. 6 are 2 3 |q | f R m m within the reasonable range expected for meddies (Tychensky SLA , (3) 3g NH andCarton1998; Paillet et al. 2002), with an overall mean value 25 21 of q = 21.6 3 10 s . where H is the depth of the meddy core, We first evaluate the three exceptionally large meddy sea surface signals with SLA over 20 cm (Table 1). There, we g r(z) present the maximum azimuthal velocities for Rankin V Rn N 2 r z 0 radial velocity profiles (Carton et al. 2002): is the buoyancy frequency above the meddy core, r(z) is the g SLA water density at depth z, and r is the reference density. The 0 V ≈ 2 : (6) Rn f R potential vorticity anomaly of the meddy core q , which may serve as a parameter that describes the dynamic intensity of The Rayleigh V radial velocity profile was obtained from Ra the meddy, is defined as 1/2 Eq. (6) using the expression V ≈ V /e (Bashmachnikov Ra Rn 2 2 N N and Carton 2012). Despite the high SLA , the resulting veloci- m surr q (v 1 f) 2 f, (4) ties are in reasonable range, not exceeding 30 cm s (Table 1). g g This is due to the large radii of the surface expressions, as where v = ∇ 3 u is the relative vorticity, N is the buoyancy well as to the northern position of those meddies (a larger f/N frequency within the meddy core, and N is the buoyancy ratio). Further on we will see that the theoretical SLA ob- surr frequency of the water surrounding the meddy core. In this tained for these northern meddies are also above the average, study, we treat the meddies as isolated vortices with no inter- which suggests that these extreme SLA can belong to meddy action with surface currents}that is, with no potential vortic- surface signals and that they are not an artifact of the method. ity anomaly above their cores. We thus search for any direct dependence between the pa- For the majority of observations, we do not have in situ rameters of the meddy sea surface signals (R , SLA ) and the s 0 values of v for MEDTRANS meddies. Therefore, we use a parameters of the meddy cores (R , core salinity, and core m 2650 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 FIG. 6. (a) the measured maximum SLA from AVISO satellite altimetry (black) and their theoretical estimates by Eq. (3) (magenta) for the sea surface signals of meddies marked in Fig. 2a. (b) The potential vorticity anomaly of the meddy core |q ˜ | (s ) obtained from 25 21 Eq. (5); the mean value is 21.6 3 10 s (red dotted line). depth), entering Eq. (3), to see whether there are some lead- The relatively large scatter partly results from the possi- ing factors shaping the sea surface signal. In Eq. (3), R has ble errors in the theoretical estimates of SLA [in different the highest degree, indicating that the core radius might be parameters used in Eq. (3), especially in the potential vor- the parameter upon which the meddy sea surface expressions ticity estimated using Eq. (5)], as well as in observations depend most strongly. However, our results show no direct (SLA is estimated from AVISO dataset, combining sepa- relationship between either SLA or R and R (see Fig. 4, rated altimetry tracks). Besides the effect of these possible 0 s m along with Fig. A1 of the appendix). The same is true for errors, once generated, the properties of sea surface expres- other individual parameters of the meddy cores, indicating sion parameters may become decoupled from the parameters that the basic properties of meddy sea surface expressions are of the underlying meddy. Typically remaining locked with the not dominated by any single parameter of the meddy core. meddy below for at least several months (Bashmachnikov et al. We then compute the theoretical estimates of SLA using 0 2009, 2015a), a meddy surface expression may then be regarded the full Eq. (3) and compare the results with observations as separate eddy, the intensity and geometry of which are (Fig. 6a). With a correlation coefficient of 0.60, the results shaped by the immediate environment rather than by the influ- have a reasonably good agreement between the theory and ence of the meddy below. The latter effect can be seen when observation, particularly when considering the potential error considering the geographical distributions of meddy surface that exists in estimating different variables in Eq. (3), as well expressions. as in observations. While theory underestimates the magni- tude of SLA by about 50% on average, values appear to os- c. Geographical distribution of meddy surface expressions cillate consistently, which is most clearly seen in Fig. 7. This is Figure 8 shows the geographical distribution of the mea- also seen in the regression fit described by the equation sured anomaly magnitude SLA and radius R , respectively, for 0 s all output meddy surface expressions analyzed in this study. SLA 0:56 3 SLA 1 0:47 theo 0 Despite the large amount of noise, one may observe a certain with the determination coefficient R = 0.36 (Fig. 7). tendency for a westward increase in both SLA and R (see also 0 s TABLE 1. Parameters for the largest meddy surface (sfc) signals (1, 2, and 3 as in Fig. 2a) in measurements (meas) and theory. Presented are the surface expression magnitude SLA , the maximum surface azimuthal velocity of the surface expression based on Rankin V , and the Rayleigh V radial velocity profiles. For reference, the table also presents meddy core potential vorticity proxy Rn Ra q ˜ , the Coriolis parameter at the meddy core location f, and the radio of |q ˜ |/f for each of the three surface signals. m m Meddy sfc signal 1 Meddy sfc signal 2 Meddy sfc signal 3 Meas Theory Meas Theory Meas Theory SLA (cm) 23 27 21 14 17 22 21) V (cm s 27 32 29 19 23 30 Rn 21) V (cm s 16 19 18 12 14 18 Ra 21) 25 25 25 q ˜ (s 23.9 3 10 23.8 3 10 25.4 3 10 21 25 25 25 f (s ) 9.8 3 10 9.7 3 10 9.7 3 10 |q ˜ |/f 0.40 0.39 0.56 m NOVEMBER 2022 I E NNA E T A L . 2651 direction (see Bashmachnikov and Carton 2012), whereas med- dies decay and descend deeper during their westward transla- tion, particularly west of 128–158W(see Bashmachnikov et al. 2015a). The latter suggests that the ratio of R /H decreases westward, which, on the contrary, should lead to a westward de- cay of the meddy surface signals. This inconsistency may be resolved by noting a similarity between the distributions of the velocity of the mean sea sur- face currents and of the meddy surface expressions (Fig. 9). The surface expressions intensify in the vicinity of the mean geographical location of the Azores Current (along 348N), as well as near the southern branch of the North Atlantic Current (at 458N in the northwestern corner). The largest signals with SLA . 20 cm (shown as red markers in Fig. 2a), as well as the surface signals with SLA . 15 cm are observed in the North Atlantic Current (at approximately 438N), and the second larg- est values are in the Azores Current region. The most likely explanation for this intensification of the surface expressions is FIG. 7. Scatter diagram of the measured vs theoretically derived that the jet currents are intensifying the meddy surface signals. SLA of the meddy sea surface signals (see their geographical dis- This may be a result of a pulling of an anticyclonic meander over tribution in Fig. 5). Note that the values of SLA . 20 cm in theory the meddy, observed in the ocean during a meddy interaction (upward triangle), measurements (downward triangle), or both with a jet flow (see Vandermeirsch et al. 2003; Bashmachnikov (six-pointed star) have been plotted in red. et al. 2009, 2012). These interactions are out of the scope of the theory by Bashmachnikov and Carton (2012). Fig. 6a). Starting with values on the order of 3–6 cm near the There is also a less distinct tendency for northward intensi- Iberian margin, SLA increases to, on average, 7–8 cm between fication, which can also be seen in the gridded SLA (Fig. 9). 158 and 208W and continues increasing westward. Similarly, the This tendency is consistent with the theory [Eq. (3)], as the values of R start out at R ∼ 40–50 km near the Iberian margin, s s ratio f/N and the potential vorticity anomalies of the meddy and increase up to 90 km west of 20 W. cores (Fig. 5), both increase northward. The areas of intensification of meddy surface signals in Fig. 8 match well with the locations of the main regional currents 4. Discussion such as the Azores Current (AzC) and North Atlantic Current (NAC). This suggests a potential link between the intensities of The theory correctly predicts the observed northward in- the background current and that of the meddy surface signal. tensification of meddy sea surface expressions, which is due to To make the tendency for the westward increase of SLA an increase of the f/N ratio. We also observe the strongest more evident, the latter is gridded onto a regular 18 3 18 grid dispersion of meddy surface signals between 188 and 208W for (Fig. 9). The ratio f/N stays practically constant in the zonal southern meddies, and between 158 and 178W for the northern FIG. 8. Geographical distribution of the (a) maximum sea level anomaly SLA and (b) radii R of meddy 0 s surface expressions. 2652 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 dynamic instability of the main currents populates the surround- ingareawith surface-intensified eddies. A meddy surface signal may become distorted by interaction with such eddies, or a meddy core may become coupled with the anticyclonic sea sur- face structures (Vandermeirsch et al. 2003). As a result, the the- oretical link between meddies and their surface expressions becomes distorted and deviates from the theoretical estimates. Jet currents or neighboring surface eddies, may intensify or re- duce the intensity of the meddy surface signals, depending on a number of factors. For example, it has been repeatedly observed that, when interacting with the Azores Current, meddy surface signals first intensify, as the meddy becomes aligned with an anticyclonic meander, and then decreases to zero, as the meddy rapidly crosses the current. A reduction of the surface signal intensity has been also observed in cases were a meddy interacts with a surface cyclone, whereas interaction with an anticyclone may lead to an opposite effect (Bashmachnikov et al. 2009, 2013). The results of this study suggest that, once generated, meddy surface expressions could be strongly shaped by the FIG. 9. Maximum SLA distribution gridded onto a 18 3 18 grid. Contours of the mean current magnitude is overlaid. Note the immediate environment and not by the underlying core, and intensification of the surface expressions away from the Iberian that their properties become partially decoupled from the Peninsula, with a rapid increase at around 158–208W. properties of the underlying meddies themselves. This could explain some of the relatively large scatter within the ob- meddies. This feature has been reported before in observations served intensities of the surface signals versus their theoretical of properties of the meddy cores (see Bashmachnikov et al. estimates (Fig. 8). The scatter also may well be due to the er- 2015a) and is predicted accurately by the theory herein. In these ror involved in determining SLA and R from altimetry ob- 0 s areas, meddies reach their largest mean radii and show the high- servations (see, e.g., Bashmachnikov et al. 2020), as well as in est dispersion of the radii. Along with the previously observed the determination of various variables used in the theoretical fact that the surface signals remain locked to meddies for ex- calculation. In particular, these may originate from the esti- tended periods of time (Bashmachnikov et al. 2009, 2013), our mates of q ˜ , for which only a proxy could be used due to a results suggest that there exists a certain degree of coupling lack of observations of current velocity in the meddy core. between the sea surface signals and meddy core properties The errors may also arise from the calculation of R , espe- throughout their lifetimes (Bashmachnikov and Carton 2012). cially when the meddy radius is derived from a relatively small The results of this paper suggest an important drawback of number of casts, replacing the vertically varying buoyancy fre- the theory. It does not consider an effect of the background quency profiles with a mean value. Additional uncertainty current velocity on the meddy surface signals. This effect is arises from the method of meddy coupling with what is con- particularly evident in the large-scale spatial distribution of sidered to be their surface expressions. We cannot be abso- the properties of meddy surface signals. Meddy cores decay in lutely sure that all the detected sea surface expressions are their intensity as they travel away from their formation sites really meddy surface signals, and some of them may be just at the Iberian Peninsula (Richardson et al. 2000). Meddy radii, coupled (or even uncoupled) surface eddies of other origin. on average, decrease after meddies leave the Canary Basin, while meddies descends to deeper levels throughout westward 5. Conclusions propagation toward the Mid-Atlantic Ridge or along the African continent (Bashmachnikov et al. 2015b). Combined to- In this study we discuss whether meddy sea surface expres- gether, these factors should lead to a decrease in the intensity sions are fully determined by properties of the underlying SLA and radius R of the meddy surface signatures with the meddies that have initially generated these signals. This link 0 s distance from the Iberian Peninsula. However, we observe an follows from theoretical studies (Bashmachnikov and Carton opposing tendency of a westward intensification of meddy sur- 2012; Bashmachnikov et al. 2014; Ciani et al. 2015). We take face expressions and a certain increase in their radii. The areas advantage of 22 years of satellite altimetry data and the of the most pronounced intensification correspond well to the MEDTRANS database (the most complete set of historical positions of the main currents in the region: the North Atlantic meddy observations at this time) to correlate meddy cores and the Azores currents. This suggests that the westward with the signatures they produce at the sea surface for more growth of surface signals may be attributed to their interac- than 200 meddies detected between 1993 and 2014. tion with the currents. In this study, a link between the intensity SLA or radius A background current may intensify the signal in two ways. R of the sea surface signals and some individual properties First, a strong background flow may increase the rate of interac- of the meddy cores, the stratification above the cores, or tion of a meddy with the background ocean. Second, the nondimensional numbers (the meddy aspect ratio or the f/N NOVEMBER 2022 I E NNA E T A L . 2653 FIG. A1. Meddy core properties plotted against surface expression properties: (a) core properties R vs s , fitted m m linearly; (b) core and surface R vs SLA ; (c) core and surface R vs s ; (d) core and surface s vs SLA ; (e) core and m 0 s m m 0 surface R vs R ; and (f) core and surface SLA vs A R /H, plotted on a logarithmic scale and fitted linearly. m s 0 m m ratio) was initially sought. The purpose was to see whether prin- underestimates the sea level anomalies, on average, by a factor cipal properties of meddy surface signals could be defined by of 2. Second, the meddy surface signatures increase in intensity any individual parameter entering Eq. (3) (from Bashmachni- from the Iberian Peninsula to the Mid-Atlantic Ridge, while the kov and Carton 2012). The statistics obtained suggests rather a observed evolution of the meddy cores (which, on average, be- weak or no relation with any of the parameters; however, a rela- come weaker, smaller and deeper, having traveled large distan- ces along the deepening isopycnals) suggests the opposite tively high correlation of 0.6 between the theoretical estimate of tendency. This systematic bias should be attributed to a partial the full Eq. (3) and the observations was derived. decoupling of the signal and the meddy core in a complex dy- These results, in particular the latter result, show an overall namic environment, not described by the simplified theory. In encouraging agreement with the theory, helping to confirm particular, we attribute the latter discrepancy to the theory not the validity of both the theory and the applied method of accounting for an interaction of meddies with the upper-ocean meddy coupling with the upper-ocean anomalies. A some- currents, as well as with eddies of different origin, both intensi- what large divergence between observations and theory fying westward. does, however, exist. Some of the scatter can be attributed to errors in both the remote sensing measurements and the estimates of in situ derived variables. Acknowledgments. Publication of this work is supported Two consistent discrepancies between the observed and the by “Portugal Twinning for Innovation and Excellence in theoretical datasets are derived in this study. First, the theory Marine Science and Earth Observation” (PORTWIMS) under 2654 J OUR N A L O F P HY SI C A L O C E A N OGR A P HY VOLUME 52 Oceanogr., 116,80–94, https://doi.org/10.1016/j.pocean.2013. the European Union’s Horizon 2020 research and innovation 06.016. programme, Grant 810139. Author Ienna acknowledges sup- Bashmachnikov, I., and X. Carton, 2012: Surface signature of port by Instituto Dom Luiz institute (UID/GEO/50019/2019), Mediterranean water eddies in the Northeastern Atlantic: ˜ ˆ by the Fundac¸ao paraaCiencia e Tecnologia. Author Bash- Effect of the upper ocean stratification. Ocean Sci., 8,931–943, machnikov acknowledges financial support from the Russian https://doi.org/10.5194/os-8-931-2012. Science Foundation (RSF), Grant 22-27-00431. Authors Dias }}, F. Machın, A. Mendonc¸a, and A. Martins, 2009: In situ and and Ienna acknowledge financial support by FCT through remote sensing signature of meddies east of the mid-Atlantic MARE’s strategic programme (UID/MAR/04292/2021). ridge. J. Geophys. Res., 114, C05018, https://doi.org/10.1029/ 2008JC005032. Data availability statement. Data from the MEDTRANS }}, D. Boutov, and J. Dias, 2013: Manifestation of two meddies dataset are openly available from the repository at the Uni- in altimetry and sea-surface temperature. Ocean Sci., 9,249–259, https://doi.org/10.5194/os-9-249-2013. versity of Lisbon’s MARE Centre (https://www.mare-centre. }}, X. Carton, and T. V. Belonenko, 2014: Characteristics of pt/en/research/data-library/medtrans-data). Satellite data used surface signatures of Mediterranean water eddies. J. Geo- in this study are available from the repository at the Archiving, phys. Res. Oceans, 119, 7245–7266, https://doi.org/10.1002/ Validation and Interpretation of Satellite Oceanographic data 2014JC010244. (AVISO) database via the JPL PO.DAAC website portal. }}, F. Neves, T. Calheiros, and X. Carton, 2015a: Properties Results from the meddy surface expression algorithm result- and pathways of Mediterranean water eddies in the Atlantic. ing from this study are openly available through direct con- Prog. Oceanogr., 137,149–172, https://doi.org/10.1016/j.pocean. tact with the corresponding author (email: fienna@fc.ul.pt) 2015.06.001. at the University of Lisbon. }}, }},A.Nascimento, J. Medeiros,I. Ambar,J.Dias, and X. Carton, 2015b: Temperature-salinity distribution in the northeastern Atlantic from ship and Argo vertical casts. APPENDIX Ocean Sci., 11,215–236, https://doi.org/10.5194/os-11-215-2015. }}, A. Nascimento, F. Neves, T. Menezes, and N. V. Koldunov, Additional Plots of Meddy Core Properties vs Surface 2015c: Distribution of intermediate water masses in the sub- Expression Properties tropical northeast Atlantic. Ocean Sci., 11, 803–827, https:// As an addendum to the data presented in this work, the doi.org/10.5194/os-11-803-2015. meddy core properties measured in situ have been plotted Bashmachnikov, I. L., M. A. Sokolovskiy, T. V. Belonenko, D. L. Volkov, P. E. Isachsen, and X. Carton, 2017: On the vertical against several surface signal properties measured by remote structure and stability of the Lofoten vortex in the Norwegian sensing. Figure A1 presents these plots, which can be consid- Sea. Deep-Sea Res. 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Journal of Physical Oceanography – American Meteorological Society
Published: Nov 21, 2022
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