In the California Current System, subthermocline, lenslike anticyclonic eddies generated within the California Undercurrent (CU) are one mechanism for lateral transport of the warm, saline waters of the CU. Garfield et al. established the name “Cuddies” for eddies of this type and hypothesized that they account for a significant fraction of the offshore transport of CU water. This study presents observations of subthermocline eddies collected from a time series of Seaglider surveys in the northern California Current System. Gliders made 46 crossings of subthermocline anticyclones and 17 crossings of subthermocline cyclones over 5.5 yr. Close inspection grouped these into 20 distinct anticyclones and 10 distinct cyclones. Water properties at the core of anticyclonic eddies were similar to those in the core of the CU over the continental slope; these anticyclones are examples of Cuddies. Anticyclonic (cyclonic) eddies had average radii of 20.4 (20.6) km, peak azimuthal current speeds of 0.25 (0.23) m s−1, and average core anomalies of potential vorticity 65% below (125% above) ambient values. Anticyclones contained an order of magnitude greater available heat and salt anomaly relative to background conditions than cyclones on average. Circumstantial evidence of eddy decay through lateral intrusions was found although this was not observed consistently. Observed eddy properties and the geometry of flow over the continental slope were consistent with eddy formation due to frictional torque acting on the CU. Loss of heat and salt from the CU due to subthermocline eddies is estimated to account for 44% of the freshening and cooling of the CU as it flows poleward.
The California Current System (CCS) is a subtropical eastern boundary current (EBC) regime characterized by strong upwelling winds, gradual variability of wind and topography in the alongshore direction, and narrow continental shelves (Hickey 1998). These traits give rise to a seasonally varying set of major wind-driven alongshore currents, which include the equatorward California Current (CC), poleward California Undercurrent (CU), poleward Davidson Current (DC), and equatorward upwelling jet. The CC occupies a broad region 0–1000 km from the shelf break, has typical speeds 0–0.1 m s−1, is strongest in summer, and transports cool, fresh water of subarctic origin southward (Hickey 1979; Lynn and Simpson 1987; Auad et al. 2011). The CU is much narrower (10–40 km wide) and carries equatorially influenced, warm, saline water poleward along the North American continental slope, reaching alongshore-average speeds of 0.1 m s−1 and peak speeds of 0.3–0.5 m s−1 at depths of 100–300 m in late summer and early fall (Hickey 1979; Huyer et al. 1989; Pierce et al. 2000; Castro et al. 2001; Collins et al. 2003; Thomson and Krassovski 2010). Poleward flow north of the CCS carries the equatorial signature of the CU into the Gulf of Alaska (Thomson and Krassovski 2010). The DC, alternately known as the Inshore Countercurrent, consists of poleward flow found at the surface over the shelf and shelf break in fall and winter (Huyer et al. 1989; Hickey 1998). In summer, the strong (peak speeds >0.5 cm s−1; e.g., Kosro et al. 1991) surface-intensified equatorward upwelling jet is present at the shelf break.
Eddies play an important role in this system by extracting kinetic and potential energy from the wind-driven circulation, and by transporting coastal water and associated heat, salt, nutrient, and biological signatures offshore (Capet et al. 2008; Checkley and Barth 2009; Chelton et al. 2011). Although EBC eddies occupy a broad spectrum of sizes and intensities, observations and models have identified a distinctive class of small anticyclonic eddies in the CCS that typically have velocity maxima at depths between 200 and 400 m (e.g., Simpson and Lynn 1990; Collins et al. 1996; Huyer et al. 1998; Garfield et al. 1999; Chereskin et al. 2000; Cornuelle et al. 2000; Kosro 2002; Kurian et al. 2011; Collins et al. 2013). These eddies carry isolated cores of water whose properties indicate origination within the CU. Observations from a multiyear RAFOS float program confirmed this (Collins et al. 2013), and Garfield et al. (1999) suggested that these features be referred to as California Undercurrent eddies or “Cuddies.”
The observational record of the CCS contains several snapshots of Cuddies, obtained from shipboard measurements or moorings, that provide descriptions of their size, kinematic strength, and core water composition (e.g., Huyer et al. 1984; Simpson and Lynn 1990; Kosro et al. 1991; Huyer et al. 1998; Chereskin et al. 2000; Jerónimo and Gómez-Valdés 2007). For example, Huyer et al. (1998) describe observations collected during two towed-body surveys off the California coast in summer 1993, which sampled two subsurface anticyclones. These eddies had peak azimuthal current speeds of 0.2–0.25 m s−1 and physical characteristics typical of Cuddies. The first eddy contained a homogeneous lens of warm, salty core water with a temperature–salinity (T–S) profile that matched those taken over the continental slope during winter. Measurements of velocity in the first eddy indicated approximate solid body rotation within the eddy core. The second eddy also contained regions of continental slope water, although its core water properties were less uniform. This eddy was occupied twice, providing an estimated offshore migration speed of 0.015 m s−1 between the two surveys. Huyer et al. (1998) concluded that the features were generated over the upper continental slope during the previous winter and spring.
A time series of quasi-isobaric RAFOS float deployments by the Naval Postgraduate School (NPS) between 1992 and 2011 has provided the most extensive information to date regarding Cuddy drift, frequency of occurrence, and average kinematic properties (Garfield et al. 1999; Collins et al. 1996, 2003, 2004, 2012; Margolina et al. 2006). Here, 38 of 65 shallow floats were entrained into looping trajectories and carried westward into the subtropical North Pacific (Margolina et al. 2006; Collins et al. 2013). Collins et al. (2013) denote long-lived (>70 days) anticyclonic trajectories as Cuddies and report that one float looped for 1650 km over 520 days. Hydrographic sections through an eddy core revealed water mass properties (T, S) similar to those found on the upper slope (Collins et al. 2013). Based on the origin of some looping trajectories over the slope, Garfield et al. (1999) suggested that Cuddy formation is likely due to frictional torque acting on the topographically trapped poleward-flowing CU, a mechanism originally suggested by D'Asaro (1988b). M. J. Molemaker et al. (2013, unpublished manuscript) have explored this in detail using an embedded high-resolution model of the Monterey Bay region. Float studies found horizontal radii on the order of the first baroclinic mode radius of deformation, though they caution that the float-inferred radii are likely lower bounds because the distance of each float from the eddy edge is unknown (Garfield et al. 1999). The ratio of anticyclonic to cyclonic polarity of the float trajectories was roughly 2:1 (Collins et al. 2013).
The predominance of Cuddies over their cyclonic counterparts has also been observed in a model study of CCS eddies (Kurian et al. 2011). This trait is found in Mediterranean outflow salt lenses (“Meddies”), which are often compared to Cuddies because of their similar structure, size, and intensity (e.g., Ruddick and Hebert 1988; Armi et al. 1989; Hebert et al. 1990; Schultz Tokos and Rossby 1991; Richardson et al. 1991; Prater and Sanford 1994; Bower et al. 1997; Richardson et al. 2000). Meddies are a type of Submesoscale Coherent Vortex (SCV; McWilliams 1985), and the characteristics of some of the looping RAFOS floats imply that Cuddies are a member of this class of eddies as well (Garfield et al. 1999). Other SCVs that appear as depth-intensified anticyclones include Labrador Sea outflow eddies (Bower et al. 2012), Beaufort Sea eddies (D'Asaro 1988a), and Red Sea eddies (Meschanov and Shapiro 1998). Equatorial 13°C water eddies, found in the subtropical South Pacific, are closely analogous to Cuddies, in that they have similar depth structure and water mass anomalies and are also likely formed within a poleward-flowing eastern boundary undercurrent like the CU (Johnson and McTaggart 2010; Colas et al. 2012).
Interest in Cuddies, and other lenslike anticyclones mentioned above, is motivated by their isolated character and homogeneous core water properties, which in some cases retain the characteristics of the eddies' generation region long after formation (e.g., Ebbesmeyer et al. 1986; Riser et al. 1986). This implies that they could be an important mechanism for lateral exchange of heat, salt, and other tracers (McWilliams 1985). Like Meddies, once Cuddies leave their generation region, waters in their core are warmer and saltier than their surroundings in the eastern Pacific (Huyer et al. 1998; Chereskin et al. 2000). This is because Cuddies originate in the CU, which carries high-T, high-S, low-oxygen, high-nutrient water along the continental slope (Lynn and Simpson 1987). As the CU flows poleward, it mixes with low-T, low-S offshore water that is carried equatorward by the CC and shelf break jet (Thomson and Krassovski 2010; Auad et al. 2011). This exchange acts to diminish the equatorial signature of the CU with distance from the equator, and temperature and salinity along its core isopycnal (and hence the core spice; Munk 1981) decreases with latitude (Thomson and Krassovski 2010). Water property anomalies associated with Cuddies suggest that they could be responsible for significant fraction of this exchange and loss of T and S from the CU (Garfield et al. 1999). Furthermore, Cuddies can persist for extended periods [e.g., 520 days reported by Collins et al. (2013)] during which they can propagate over considerable distances, demonstrating that they are a mechanism for long-range transport. Lukas and Santiago-Mandujano (2001) determined that a Cuddy generated off Baja California was likely responsible for an extremely warm, saline, low-oxygen anomaly observed in the Hawaii Ocean time series. To reach Hawaii at typical Cuddy drift speeds, the eddy observed by Lukas and Santiago-Mandujano would have had to persist for several years.
These observations provide evidence that Cuddies are important in removing coastal water from the CU and are capable of transporting this water thousands of kilometers from the CCS. Despite their potential significance, Cuddies are under sampled relative to Meddies (Collins et al. 2013). Their subsurface signature and small horizontal extent make detection, classification, and tracking difficult. As a result, estimates of their frequency of occurrence and contribution to offshore heat and salt fluxes are still poorly constrained (Kurian et al. 2011; Collins et al. 2013). Thus, further observations of Cuddies in the CCS are important for advancing our understanding of their role in large-scale property transport in the eastern Pacific Ocean.
This study presents observations of 20 anticyclonic Cuddies collected within a 5.5-yr time series of Seaglider (SG) observations over the Washington (WA) continental slope, near the northern boundary of the CCS. Analysis of these eddies focuses on their kinematic characteristics, general phenomenology, and role in lateral exchange of heat and salt off WA. Results are consistent with previous characterizations of these eddies' physical properties and support the hypothesis that Cuddies are responsible for a large fraction of the offshore transport of CU water. We also present observations of 10 cyclones of similar size and strength. The cyclones' T and S characteristics indicate that they likely play a negligible role in property transport. Section 2 describes the Seaglider-based observations, data processing, mapping, and detection of subsurface eddies. Section 3 presents average hydrographic features over the WA slope and observed eddy physical properties. Section 4 discusses Cuddies' role in offshore transport in the northern CCS and potential mechanisms of their generation and decay, with section 5 summarizing the results.
2. Data collection and processing
a. Experimental configuration
Seagliders operated off the WA coast in a series of deployments to monitor northern CCS boundary current phenomena beginning in August of 2003 and extending through January of 2009. Two brief test deployments were also carried out in late 2002 and early 2003. Gliders collected repeat hydrographic measurements over the continental slope and Cascadia Basin along two cross-shore transects that extended from the 200-m isobath to a point 225 km offshore in the region 47°–48°09′N (Fig. 1a). This offshore waypoint linked the two transects at 47°N, 128°W. The southern Grays Harbor (GH) transect extended zonally between the offshore waypoint and the shelf break at 47°N, 124°58′W. The northern Cape Flattery (CF) transect extended from the offshore waypoint to a point just northwest of the Juan de Fuca Canyon on the shelf edge at 48°09′N, 125°40′W. At the beginning of each mission, Seagliders were deployed near the shelf break at either the southern or northern inshore waypoint and navigated to the offshore waypoint of the transect pattern. Gliders then proceeded inshore along the opposite transect, before returning offshore to repeat the pattern in reverse. A single transect was usually completed in 10–14 days, during which the glider would perform 50–75 dive–climb cycles, returning 100–150 vertical profiles.
Gliders performed 20 deployments with durations between two weeks and six months. During the two longest deployments, gliders performed 12 cross-shore transects and more than 500 dive–climb cycles. In total, the time series achieved 63 transects along the CF line and 62 transects along the GH line (Fig. 1b). These were comprised of 6336 dive–climb cycles to 1000-m depth or to within a few meters of the bottom over topography. Hardware faults prematurely ended some deployments, leaving small coverage gaps in the time series, the largest of which is from mid-January to early April 2008 (Fig. 1b).
Seaglider (Eriksen et al. 2001) is a buoyancy-driven autonomous underwater vehicle (AUV) that collects high-resolution profiles of ocean properties to depths of 1000 m in a series of dive–climb cycles along a 1:3 glide slope. During a typical dive–climb cycle, the glider travels at horizontal speeds ranging from 0.15 to 0.3 m s−1 with an average speed from 0.2 to 0.25 m s−1. A single cycle from the surface to 1000 m and back typically takes 8 h, during which time the glider flies 6 km horizontally through the water. All gliders included a Paine 211–75–710–05 pressure transducer as well as a custom-fitted SeaBird Electronics (SBE)-3 thermistor and -4 conductivity cell mounted in a dorsal fin, referred to here as the “conductivity–temperature (CT) sail.” Depending on mission and battery state, gliders sampled all instruments every 5 or 10 s in the upper 80 m, an approximate thickness of the surface mixed layer during the winter months in the WA slope region. Below this depth, gliders sampled T and S every 10 s to 150-m depth, every 20 s to 300-m depth, and every minute at depths >300 m. At typical glider speeds and glide angles, a 10-s sampling interval yields observations every 0.6–1.0 m vertically. Gliders also included a SeaBird SBE-43 dissolved oxygen sensor and Western Environmental Technologies (WET) Laboratories Environmental Characterization Optics (ECO)-BB2F optical puck that measured optical backscatter and fluorescence. The oxygen and bio-optical measurements are not included in this analysis [for further discussion see Perry et al. (2008) and Pelland et al. (2013, manuscript submitted to PLOS ONE)].
For purposes of battery conservation, flow through both the oxygen sensor and CT sail is not pumped and instead is naturally aspirated by the flow relative to the glider as it descends or ascends. Because of the thermal inertia of the glass tube housing the conductivity electrodes, the water temperature within the conductivity cell Tcond may differ from temperature sampled by the thermistor Tthrm. This difference increases when the glider is moving slowly or crosses a large vertical thermal gradient. Because salinity is a much stronger function of temperature than conductivity, this means that computing salinity from samples of conductivity and uncorrected Tthrm can result in spikes or large biases, particularly when the vehicle crosses a strong thermocline.
Accurate measurements of salinity, corrected for the difference between Tthrm and Tcond, require estimates of the flushing speed of the conductivity cell, which is a function of vehicle speed and glide angle through the water. However, determination of vehicle speed and glide angle [from the steady flight equations of Eriksen et al. (2001)] requires knowledge of vehicle buoyancy, which is itself a function of salinity. Thus, measurements of salinity on each dive–climb cycle were corrected through an iterative process. From an initial guess of vehicle velocity, a first guess at Tcond was determined using the solutions of C. C. Eriksen (2013, unpublished manuscript) for Seaglider conductivity cell thermal response under flushing by sensor package motion and external flow. This yielded a corrected salinity that was used to calculate corrected density and, along with estimated vehicle volume (Frajka-Williams et al. 2011), the vehicle buoyancy. The flight equations were then solved using this buoyancy estimate and observed pitch, giving an improved estimate of vehicle speed and flushing rate of the conductivity cell. The thermal inertia corrections were reapplied with the updated speed, and the process was repeated until a convergent solution of these variables was obtained. Cycles for which the iterative procedure did not converge were discarded and any remaining salinity spikes or vehicle stalls were removed.
The horizontal component of modeled vehicle velocity was then integrated over all samples to give an estimate of vehicle displacement through still water. This allows an estimate of depth-averaged current (DAC) over each cycle through comparison of modeled displacement versus GPS-measured displacement; DAC has been judged accurate to ~0.01 m s−1 (Eriksen et al. 2001; Hátún et al. 2007; Todd et al. 2011). Seaglider measurements of salinity are accurate to 0.01 in most of the water column, or 0.03 in regions of strong vertical temperature gradient such as the seasonal thermocline below the surface mixed layer in summer. Temperature samples are accurate to 0.003°C. Conductivity cells and thermistors on WA slope gliders were calibrated by SeaBird Electronics before and after each deployment.
Observations of potential temperature θ referenced to the surface salinity S, potential density σθ, and spice πθ (Flament 2002) from each glider cast were sorted into depth bins and the mean was computed of observations within each bin. Bins had a 2-m vertical spacing from the surface to 150 m, 5-m spacing from 150- to 300-m depth, and 20-m spacing at depths greater than 300 m. The binned data for each transect were projected onto a line of constant heading between the in- and offshore waypoint and mapped along depth surfaces to a regular grid using Gauss–Markov interpolation (Bretherton et al. 1976; Le Traon 1990). Some care must be taken to consider the scales of horizontal variability that gliders are capable of resolving when choosing the horizontal length scale to use in mapping of glider data. Relative to other oceanographic sampling platforms, gliders move slowly and their samples on a depth surface are separated horizontally by 3–6 km. As a result, on a horizontal transect, high-frequency and high-wavenumber variability, primarily in the internal wave band, is aliased onto the upper end of the range of horizontal wavenumbers that is resolved by the gliders (Rudnick and Cole 2011). Thus, the maximum horizontal wavenumber gliders are capable of accurately resolving on a depth surface will be smaller than the Nyquist wavenumber and will depend on sampling strategy and the ratio of mesoscale signal to internal wave noise in the region of interest. The goal is to map the observations to a regular grid using a decorrelation scale that filters the high-wavenumber noise and retains as much of the mesoscale signal as possible.
Rudnick and Cole (2011) suggest that glider users should compute horizontal wavenumber spectra along depth surfaces to find the break in slope that represents projected variability. Wavenumber spectra computed from this time series indicate that Seagliders are capable of resolving variability to a minimum wavelength of 25 km in the WA slope region ( appendix A). We used this value for a Gaussian spatial decorrelation scale when mapping observations to a regular grid; this effectively low-pass filters the data, and spectra from the mapped observations demonstrate that the high-wavenumber noise is removed. Mapping noise-to-signal energy was 0.1 and we discarded grid points with normalized error greater than 50%.
Mapped observations of the cross-shore density field were center differenced to obtain vertical geostrophic shear of the alongshore velocity. This was then integrated to obtain vertical profiles of alongshore geostrophic velocity relative to 1000 m . Note that indicates the velocity component that is normal to the glider track line orientation (i.e., alongshore velocity); in a similar manner, , , and z indicate across-shore, alongshore, and vertical coordinates, respectively. Glider estimates of DAC provide a reference velocity that allows conversion of to profiles of absolute alongshore geostrophic velocity (e.g., Hátún et al. 2007; Martin et al. 2009; Todd et al. 2009). DAC estimates were mapped to a regular grid and profiles of were adjusted by a constant such that their vertical average matched the cross-track component of DAC. This method is similar to Todd et al. (2011), who presented the results of glider transects off the California coast.
Using maps of T and S, potential vorticity (PV) was calculated following Talley (1988) using potential density increments of 0.05 kg m−3. We extended the method of Talley by using the cross-shore shear of the alongshore velocity as an approximation of the vertical relative vorticity . Obviously this may under predict the magnitude of the relative vorticity, particularly in rotational flows (e.g., a solid-body vortex) where there are equal contributions to ζ from and . However, this remains a useful approximation for the purposes of examining the relative cross-shore structure of PV in the coastal transition zone and for detecting the PV signatures of eddies. Velocity mean and variance are polarized in the alongshore direction in the CU region over the continental slope (Garfield et al. 2001; Collins et al. 2004), and under these conditions cross-shore variability in is likely to dominate ζ. Potential vorticity calculated using this method is denoted by Π:
c. Eddy detection
Subsurface, low-stratification, high-spice anticyclones were evident from visual inspection of the mapped observations. Consistent with the definition of Cuddies (Huyer et al. 1998; Garfield et al. 1999), their velocity cores were localized beneath the seasonal thermocline. High-stratification cyclones of similar scale and kinematic strength were also noted, though these did not appear to contain high-spice cores. To count instances in which a glider track intersected an eddy, we used an algorithm designed to detect eddy crossings based on several criteria related to a priori knowledge of eddy PV and water mass characteristics.
Assuming Cuddies are generated in the CU, the algorithm searched for Π anomalies along isopycnals ranging between σθ = 26.5 and 26.9 kg m−3 in intervals of 0.05 kg m−3. These density surfaces bracket the CU core and typically are found at depths of 200–400 m. The σθ = 26.5 kg m−3 isopycnal is found only 25–50 m above the average CU water mass and velocity core level, but was chosen as the upper search boundary because the cross-shore variance of Π increased dramatically toward the surface from this level (not shown). This increased variance in Π made detection of coherent eddies difficult in the upper halocline, where the PV signal-to-noise ratio was lower. As a result, we restricted our search to σθ = 26.5 kg m−3 and deeper. Potential vorticity and its anomaly Π′ relative to the cross-shore mean profile was computed along each isopycnal. Spice anomaly from a two-year running mean of the cross-shore profile was also computed along σθ = 26.6 kg m−3. The two-year mean for spice was used because water properties over the WA slope underwent large interannual changes in θ–S between 2003 and 2009 ( appendix B). As a result, when we experimented with a spice detection criterion based on a mean cross-shore profile taken over the entire time series, some obvious eddies were not detected in 2008. The eddy PV anomalies were strong relative to any background signal and defining the PV anomaly relative to the mean profile taken across the time series was sufficient for detection purposes.
For anticyclones, locations with Π′ < −0.75 × 10−10 m−1 s−1 along any of the nine isopycnals considered, or with at least two isopycnals having Π′ < −0.4 × 10−10 m−1 s−1, were flagged as meeting the vorticity criterion for an eddy. The stronger threshold along a single isopycnal is identical to that employed by Johnson and McTaggart (2010) for detection of Peru–Chile Undercurrent eddies from Argo float profiles. The suitability of this threshold was not clear a priori because of the difference in sampling platforms and oceanic domains. However, we experimented with several thresholds and found that the level employed by Johnson and McTaggart (2010) produced the results with the most detections of visually obvious eddies and the fewest false positives. We noted visually that some eddies contained vertically broader, but weaker-magnitude vorticity anomaly signatures and we added the second multi-isopycnal threshold to detect features of this type. Stations meeting either of the low-vorticity anomaly criteria and with were flagged as anticyclonic eddy stations. Positive indicates water that is warmer and saltier than the average for that location along the CU isopycnal. For detection of cyclones, only the vorticity criteria (of positive sign) were employed, because visual inspection indicated these features did not consistently carry CU core water.
Within continuous regions that met the eddy criteria, we defined the eddy center as the largest local vorticity anomaly extremum within a 25-km radius. Extrema were required to have a local prominence of at least 0.25 × 10−10 m−1 s−1. Redundant peaks within 50 km were deleted, defaulting to the larger-magnitude anomaly. Surface-intensified eddies were discarded along with eddies smaller than 5 km and those with sufficiently weak horizontal shear , because this indicated either a feature not resolvable by the glider or an eddy that the glider had missed and detected only at its outer edge. For cyclones, the minimum shear criterion was increased to require to avoid detection of high-PV regions near the edges of anticyclones (cf. Fig. 6, described in greater detail below). Background signatures of high spice in the CU and noise in the PV field over the inner slope prevented detection of features closer than 30 km to the shelf break.
d. Eddy dynamics
We examined all eddy crossings for the possibility that some eddies may have been observed on multiple occasions and grouped together crossings that were obviously of the same vortex. It is difficult to define an objective algorithm for this purpose without continuous position information for each vortex, and we instead relied on visual identification of similar eddies. This is an inherently subjective process and likely one of the largest, albeit unknown, sources of error in this study. When considering pairs of crossings that potentially were of the same feature, we began by examining any two crossings taken within two months of one another, in which the second crossing was not made closer than 50 km to shore. Theory and observations suggest that these features will move westward away from the slope (e.g., Margolina et al. 2006; Collins et al. 2013).
We analyzed each eddy in a cylindrical polar coordinate system based on the observed eddy center. We further assumed that eddy physical structure had negligible azimuthal dependence (Elliott and Sanford 1986; Hebert et al. 1990; Martin et al. 2009) and for each eddy mapped all glider observations on depth surfaces as a function of radius r from the eddy center. This is effectively a form of azimuthal averaging, which was used to minimize errors associated with the DAC signal and to obtain a well-defined estimate of eddy physical structure. Eddy properties were mapped on a 100-m-resolution grid to a radius of 75 km, at the same depth levels as described in section 2b and with a 25-km horizontal length scale. All subsequent eddy analysis was performed on the 100-m r–z grids.
Previous observations of Cuddies (Huyer et al. 1998) and SCVs (e.g., Elliott and Sanford 1986) indicate that nonlinear terms are important in the radial force balance of small lenslike anticyclones. Elliott and Sanford (1986) showed that assuming a purely geostrophic balance underestimated the magnitude of peak azimuthal current by several centimeters per second in analysis of a subthermocline lens detected in the Local Dynamics Experiment. Around each feature center we assumed a gradient-wind radial force balance. In cylindrical polar coordinates, this is expressed as
For each eddy, we calculated geopotential relative to 980 dbar using the r–z density grid and solved (2) for υφ to obtain a first guess of azimuthal velocity. This first guess assumed no motion at 980 dbar. To determine absolute azimuthal velocities and the corresponding absolute slope of geopotential surfaces, we used mapped observations of depth-averaged azimuthal velocity as a reference. We did this by iteratively adjusting the radial slope of the 980-dbar surface at each grid station until the vertical average of azimuthal velocities obtained using (2) at that station was equal to the mapped value of . We then integrated the 980-dbar slope outwards from the eddy center to produce an arbitrary reference level height (relative to the eddy center). The reference level height was added to the first-guess geopotential grid and we refer to the resulting field as adjusted geopotential.
The region 50–75 km from each eddy core was defined as the far-field region. The average profile of adjusted geopotential over these stations was subtracted from the total grid to produce the eddy geopotential anomaly ΔΦ. The far-field boundaries were adjusted in cases where the region 50–75 km contained other eddies. We assumed a simple Gaussian structure for eddy geopotential anomaly of the form
localized about the eddy center r = 0 and z = z0. In (3), A is the maximum geopotential anomaly relative to the far field and λ (h) is the characteristic horizontal (vertical) eddy length scale. We performed a least squares fit of the model (3) to the eddy geopotential anomaly field in order to obtain estimates of A, λ, and h. Obtaining both horizontal and vertical length scales allows calculation of the eddy Burger number , where N0 is the buoyancy frequency in the far-field region at the core depth z0.
and has solutions
Vertical relative vorticity in cylindrical polar coordinates is defined as
Assuming the eddy structure (3), the positive branch of (5) is inserted into (6). The negative branch corresponds to solutions that are typically not centrifugally stable and are unlikely to persist under realistic conditions (McWilliams 2006). The first term on the right-hand side of (6) yields
and the second term is
We computed ζ at vortex middepth using (9) and the properties A, λ, and h obtained from (3). This model was then used to recompute a radial profile of q at middepth around each eddy, following Elliott and Sanford (1986). Because the coastal PV Π does not consider the effects of strong flow curvature, recomputing q provides a more accurate estimate of each eddy's core PV anomaly relative to local conditions. Rossby number Ro was computed based on the model relative vorticity at the eddy center [ζcore = ζ(0, z0)] as a fraction of planetary vorticity f (Ro = |ζcore|/f). For one anticyclone, the C1 term was large enough that the second term on the right-hand side of (9) was imaginary at (r = 0, z = z0). For this eddy, a core profile of q was not determined and it was assumed that Ro = 1.
We tested the distributions of eddy properties for normality, prior to computing confidence bounds for the means, using the method of Lilliefors (1967). For anticyclones, all distributions were significantly different from the normal distribution at the 95% confidence interval, and three of six distributions were significant for cyclones. As a result, we computed nonparametric confidence bounds by a bootstrap method using resampling with replacement and 2000 iterations for each variable, implemented by the bootci function in the MATLAB (The Mathworks, Inc.) Statistics Toolbox.
The eddy kinematic analysis assumes that gliders bisect each eddy. However, this is difficult to justify because it is probably rare that the gliders sampled directly through the center of an eddy. As a result, the length scales and dynamical properties derived in this study will likely be underestimates. Utilizing the DAC estimates (which measure both horizontal components of current, rather than only in the cross-track direction), we were able to geometrically infer an eddy center latitude and longitude for 23 (8) anticyclone (cyclone) crossings by assuming a circular eddy and purely tangential flow. For these crossings, gliders missed anticyclone (cyclone) eddy centers by 5.6 km (8.5 km) on average. For a glider traveling along a straight line through an eddy with a 25-km true radius, a miss of 8.5 km means that the observed radius is an underestimate by only 6%. However, for the remaining 23 anticyclone and 9 cyclone crossings, an eddy center latitude and longitude could not be reliably determined. It is important to note that incidental surveys place limitations on the characterization of eddy dynamics and may introduce an amount of bias that is difficult to quantify. We note that the results of this study are largely consistent with eddy properties determined from shipboard surveys and RAFOS float deployments in the CCS (Huyer et al. 1998; Margolina et al. 2006; Collins et al. 2013).
a. WA slope hydrography
This section presents a summary of relevant hydrographic features of the WA slope in order to describe the environment surrounding Cuddies and their generation in the northern CCS. Temperature–salinity structure over the WA slope is dominated by subarctic water near the surface and the equatorially influenced water of the CU (Fig. 2; Mackas et al. 1987; Masson 2006; MacFadyen et al. 2008). These two water masses are separated by a halocline that extends from σθ = 25.25 kg m−3, the base of the seasonal thermocline, to the CU core at σθ = 26.55–26.6 kg m−3. Here, θ–S-depth diagrams for the inshore region (<50 km from the shelf break) of the northern (i.e., CF) and southern (i.e., GH) transects demonstrate that there is significant variability of spice within the halocline (Figs. 2a,b). These diagrams were constructed by sorting samples from inshore profiles into bins of width 0.025 in S and 0.1°C in θ, and computing the sum of the depth intervals corresponding to all Seaglider observations collected within each bin. If the profiles are assumed to be regularly spaced horizontally, then this is equivalent to a θ–S-volume diagram; this assumption is justified by the regular horizontal spacing of glider dive–climb cycles. Values in Figs. 2a,b are normalized such that their area integral in θ–S space is equal to 1, making each an empirical probability density function.
Along the CU core isopycnal, the distribution of spice is warmest and saltiest at GH followed by CF and then the offshore region (Fig. 2c). On σθ = 26.55 kg m−3, the average salinity is 0.019 ± 0.002 lower at CF than GH (Fig. 2d). Confidence bounds are 95% from a Welch's unpaired t test for differences of means between populations (Welch 1947). The loss of heat, salt, and spice between GH and CF is not unexpected, because the equatorial signature of the CU steadily diminishes with increasing latitude (Pierce et al. 2000; Thomson and Krassovski 2010). This rate of freshening along the core isopycnal observed in this study corresponds to a decrease in salinity of 0.15 (1000 km)−1 of coastline. Thomson and Krassovski (2010) explored the large-scale decay of the signature of Pacific Equatorial Water (PEW) within the CU by calculating trends in percent PEW versus alongshore distance. In summer climatology, they found a 9.8% (1000 km)−1 decrease in average PEW within 100 km of the shelf break, while the decline in core PEW concentration was found to be 7.8% (1000 km)−1. These correspond to a freshening of 0.14 and 0.11 (1000 km)−1 along σθ = 26.55 kg m−3, respectively. The slightly higher alongshore salinity gradient within the core of the undercurrent off WA may be due in part to the incision of the Washington slope by many canyons, which may locally enhance upwelling or vertical mixing processes, leading to greater mixing with surrounding waters as the CU flows poleward (Hickey 1995).
The CU is apparent at CF and GH in averages of alongshore velocity taken over the time series (Figs. 3a,b). Along both transects there is an inshore core of poleward flow at 200–210 m depth with peak velocities of 0.045 m s−1 along CF and 0.072 m s−1 along GH. This core extends from 0 to 30 km from the shelf break off GH and from 0 to 50 km from the shelf break at CF. There is a second core of subsurface poleward flow 75 km from the shelf break along the GH transect (0.054 m s−1) and a weaker second core (0.022 m s−1) 175 km from the shelf break off CF. Several previous studies in the southern CCS, where boundary topography is more complex than over the WA slope, have observed multiple cores of subsurface poleward flow similar in appearance to Figs. 3a and 3b (Davis et al. 2008; Gay and Chereskin 2009; Todd et al. 2011). The high-spice signature of the CU is found in the density range 26 < σθ < 26.8 kg m−3 and decays with distance from shore (Figs. 3c,d).
Currents over the WA slope have a distinct seasonal cycle that reflects climatological patterns of local alongshore wind stress, wind stress curl, and remote forcing from southerly latitudes that is communicated to the WA slope by poleward-propagating coastal-trapped waves (Hickey 1979; McCreary 1981; Battisti and Hickey 1984; Werner and Hickey 1984; McCreary et al. 1987; Hickey 1989, 1998; Connolly et al. 2013, manuscript submitted to J. Phys. Oceanogr.). Averages of alongshore velocity in two-month bins (Fig. 4) show that the CU appears deep over the outer slope at both locations in May–June. During summer, the inshore core of poleward flow over the slope and surface-intensified equatorward flow (the shelf break jet) at both lines resembles the results of Pierce et al. (2000, their Fig. 3). The CU shoals and strengthens throughout the summer, reaching 0.090 m s−1 (0.098 m s−1) on the CF (GH) line at 220-m depth and 24 km from the shelf break (200-m depth and 13.5 km) in the September–October average sections.
The CU merges with the surface-intensified DC in the November–December averages (Fig. 4). It should be noted that previous studies have questioned the distinction between the DC and CU and their respective forcing mechanisms (Hickey 1998), and glider surveys in the southern CCS show that there is no clear separation between the CU and DC in the Southern California Bight (Todd et al. 2011). Off WA, locally poleward alongshore wind stress is important in forcing the DC during winter (Werner and Hickey 1984). However, models also suggest that, like the CU, this flow is enhanced by remote forcing in the CCS from latitudes that are equatorward of the WA coast (Connolly et al. 2013, manuscript submitted to J. Phys. Oceanogr.). We retain the independent naming convention, though we acknowledge that there remains some uncertainty surrounding the forcing mechanisms of the DC and its independence from the CU.
The multiple cores of poleward flow at CF and GH (Figs. 3a,b) are also apparent in the two-month-mean transects, especially during the periods of strongest poleward flow in fall and winter. The California Current appears in the westernmost 50–100 km of the survey transects in late summer and fall, consistent with the two-month-mean surface circulation calculated by Strub and James (2000). Figure 3 of Strub and James shows the California Current in the region of 47°N from July–August to November–December.
b. Eddy census
Gliders observed large cross-shore variability in spice along the core CU isopycnal relative to the offshore decay trend evident along both transects (Figs. 3e,f). Cuddies are one horizontal stirring mechanism responsible for this variance. The eddy detection algorithm determined that gliders crossed Cuddies 46 times and subthermocline cyclones 17 times (Fig. 5). From these crossings the visual inspection identified 20 distinct Cuddies and 10 cyclones. An example anticyclone is shown in Fig. 6 and an example cyclone in Fig. 7.
The anticyclone was encountered on 4 September 2004 at 140 km from the shelf break along the Cape Flattery transect and was observed again 50 km farther offshore on 20 October (Fig. 6). Observations of this eddy illustrate several of the hallmarks of anticyclonic Cuddies. It was kinematically strong with a peak eddy model azimuthal gradient-wind velocity of −0.23 m s−1 at z = −170 m and r = 10 km (Fig. 8). The vorticity Rossby number was 0.77. The geopotential radius determined from (3) was 17.4 km and vertical decay scale was 406 m (ambient N = 6.5 × 10−3 s−1; B = 2.0). This eddy had a low-stratification core lens of anomalously spicy water centered at the depth and density level of the undercurrent. The low stratification and negative relative vorticity at the eddy center correspond to very low potential vorticity at the eddy core depth (Figs. 6b,d), which is a signal in common with many other small anticyclones (e.g., Riser et al. 1986; D'Asaro 1988a; Prater and Sanford 1994; Johnson and McTaggart 2010; Carpenter and Timmermans 2012). The estimated translation speed between the two occupations was 0.0143 m s−1, close to that found for an eddy off the California coast by Huyer et al. (1998).
The example cyclone was encountered along the Grays Harbor transect 130 km from the shelf break on 28 October 2005 (Fig. 7). It was less intense than the example anticyclone, with a peak azimuthal velocity of 0.11 m s−1 at r = 12 km, z = −230 m, and Ro = 0.28. It was of similar size, with λ = 16.7 km and h = 402 m (ambient N = 4.4 × 10−3 s−1; B = 1.0). Its core was highly stratified relative to ambient conditions and it had high core potential vorticity (Fig. 7). Unlike the example Cuddy, the water within its core was not particularly spicy relative to the far field. This eddy is similar in appearance to depth-intensified cyclones that have been found paired with Meddies in the Gulf of Cadiz (Carton et al. 2002; Ambar et al. 2008).
Radial profiles of modeled azimuthal velocities for eddies of both types are shown in Figs. 9a and 9b. The anticyclones had peak azimuthal velocity magnitudes of 0.25 m s−1 and radii of maximum velocity between 10 and 25 km. Only one cyclone had a peak azimuthal velocity exceeding 0.20 m s−1, although the range of radii of maximum velocity is similar to anticyclones. Spice anomaly along the σθ = 26.55 kg m−3 isopycnal is shown in Figs. 9c and 9d. Spice anomaly in Fig. 9 is defined relative to the average taken along σθ = 26.55 kg m−3 over all profiles collected outside eddies and the CU. Spice anomalies within anticyclones were consistent with warm, saline CU water advected offshore. In contrast, some cyclones had positive anomalies of πθ, but this was not consistently observed (Fig. 9).
Normalized potential vorticity anomaly q′ at eddy middepth, computed following Elliott and Sanford (1986), is shown in Figs. 9e and 9f. Recall that q is recalculated for each eddy during the analysis phase, because the approximation to ζ that is used in Π does not consider the effects of strong flow curvature. In Figs. 9e and 9f, q′ is defined relative to the local region and normalized by the far-field value:
where 〈·〉FF is an average taken at depth z0 over all stations in the far-field region around each eddy. Normalized PV anomalies at eddy cores [q′(r = 0, z = z0)] were between −0.37 and −0.92 for anticyclones. Thirteen of 19 anticyclones for which radial profiles of q could be computed had core PV less than 50% of far-field values [q′(0, z0) < −0.5; Fig. 9]. The minimum value of q′ for anticyclones obtained from the model was −0.92, which indicates near-zero PV in the eddy core. Recall that one anticyclone also had a radial gradient of geopotential that gave imaginary values of ζ from (9) and this is not shown in Fig. 9, although for this eddy it was assumed that ζcore = −f which would give q′ = −1. D'Asaro (1988a) also reported near-zero PV in the core of Beaufort Sea anticyclones. Positive values of q′ in the cyclone cores indicate PV that is on average twice as high as the far-field values (Fig. 9). In contrast to cyclones, centrifugal instability limits the magnitude of the low-PV anomalies in the anticyclone cores, because the eddies will be unstable if the potential vorticity at the eddy core is negative (McWilliams 2006; M. J. Molemaker et al. 2013, unpublished manuscript). Aside from the contrast in core water mass characteristics, properties of WA slope subthermocline eddies show a general consistency both within and between eddy polarities.
Eddy size and dynamical properties are shown in Fig. 10, and mean values with nonparametric confidence bounds are shown in Table 1. Fifteen of the 20 anticyclones and all of the cyclones had geopotential radii below 30 km (Figs. 10a,b). The average radius of anticyclones (cyclones) was 20.4 km (20.6 km). This compares favorably with the deformation radius formed by the eddies' core density anomaly λd. Following Dewar and Meng (1995), λd is defined by
where hc is the scale height of the eddy, and the fractional density anomaly ρ′ is given by
Using the average scale height of WA slope Cuddies and a characteristic external buoyancy frequency at 200 m of N = 5.5 × 10−3 s−1 yields λd of 21 km.
Fifteen of the 30 eddies had Burger numbers (Fig. 10d, Table 1) within the stability bounds of SCVs, indicated by numerical studies, of about 0.05–1 (McWilliams 1985). The remaining eddies had Burger numbers >1. This may be indicative of vortices that have yet to adjust as they move offshore through the cross-shore gradient in stratification present in an EBC upwelling system. As this occurs, instabilities will drive an SCV aspect ratio toward f/N0 in a process known as Burger number selection (Griffiths and Linden 1981; McWilliams and Gent 1986). Eddy Rossby numbers were 0.46 (0.29) on average for anticyclones (cyclones) (Table 1); 9 of 20 anticyclones and 1 of 10 cyclones had Ro > 0.5 (Fig. 10c).
Eddy translation velocities were computed between glider crossings of anticyclones deemed to have been sampled repeatedly. We investigated propagation of cyclones as well but there were few repeat observations of eddies of this polarity and propagation vectors from these eddies are not shown. Translation speeds for Cuddies (Fig. 11) ranged between 0.002 and 0.062 m s−1 and were 0.018 m s−1 on average, which is consistent with previous observations (Huyer et al. 1998; Collins et al. 2013). The mean zonal velocity component is comparable to the westward self-advection speed expected as a result of β drift (McWilliams and Gent 1986; Dewar and Meng 1995). However, this may be a coincidence because the main mechanism for Cuddy translation in the coastal transition zone is probably passive advection in strong background currents (Dewar and Meng 1995). This is illustrated by the large spread in meridional velocities, which are inferred when an eddy was observed along one transect leg, then the other, or when an eddy moved along the Cape Flattery line.
a. Lateral tracer flux
Formulating an estimate of subthermocline eddy tracer flux out of the CU requires information about the average water property anomalies within eddies and the frequency with which they are generated off the WA coast. We assess Cuddy and cyclone water properties by computing anomalies of salt and heat within each eddy core relative to background conditions outside of the CU. Available salt anomaly (ASA) within each core is defined as
where the limits of integration in the vertical z1 and z2 correspond to the depths of the isopycnals that bound the core region. The salt anomaly is computed along isopycnals relative to a reference profile. The ASA of van Ballegooyen et al. (1994) is similar to (13). They computed the salt anomaly within isopycnal layers and then summed the contribution from all layers. We choose the lower isopycnal bound to be σθ = 26.8 kg m−3 and the upper bound to be σθ = 26 kg m−3, consistent with the density range in which the CU water mass signature is strongest (Fig. 2). The reference profile is defined as the mean along isopycnals in profiles taken outside of eddies and at least 50 km from the slope. A similar procedure is used to compute available heat anomaly (AHA).
The mean ASA (AHA) in WA slope Cuddies is 15.8 × 109 kg (3.6 × 1017 J). Confidence bounds for bulk water mass properties computed with the bootstrap method are given in Table 1. In contrast to anticyclones, the available anomalies in cyclones are an order of magnitude lower: cyclones contained on average 1.6 × 109 kg (0.4 × 1017 J) of ASA (AHA) within the core region. We computed θ–S-depth diagrams similar to those in Fig. 2 for profiles taken within eddies of each polarity (Figs. 12a,b). The weaker equatorial water mass signature of the cyclones is apparent in the halocline above σθ = 26.55 kg m−3. Additionally, the distribution of spice along the core isopycnal in cyclones is similar to the distribution in profiles collected outside eddies and the CU, while the distribution in anticyclones is noticeably offset toward higher values (Fig. 12c). Cyclone-mean salt and heat anomaly content estimates were also not significantly different from zero using the bootstrap confidence bounds (Table 1). Considering the lack of evidence for warm and salty core water signature in cyclones as outlined above, and their lower frequency of occurrence, we neglect their contribution to offshore flux of water properties from the CU region.
Simple estimates for the amount of salt and heat lost from the CU each year in the region 47°–48°09′N are 229 × 109 kg of salt and 51 × 1017 J of heat. These estimates are based on the observed poleward transport of the CU and the decay of its water mass signature between GH and CF (see appendix B). If it is assumed that gliders did not miss any eddies that passed through the transect pattern and that all eddies that gliders observed were generated locally, this implies an average generation rate of 20 Cuddies over 4.8 yr, or 4.2 yr−1, in the region 47°–48°09′N. The continuous duration of the time series when gaps are accounted for is 4.8 yr. With this frequency of generation, Cuddies would account for 29% (17% lower bound, 48% upper bound) of the calculated loss of salt and heat from the CU each year.
However, this rate is questionable given that neither of the above two assumptions regarding glider detection of eddies are justified. Gliders move slowly and almost certainly miss some eddies generated locally, which would decrease the rate of eddies observed by the glider relative to the true rate of local generation. This effect is compensated to an unknown extent by the fact that gliders are also likely to detect some eddies that were not generated within the latitude band 47°–48°09′N. The latter effect would tend to increase the ratio of glider detections to true number of local eddies generated.
We attempted to quantify the relative influence of these two factors, and the resulting bias in the above estimate of rate of eddy generation, by simulating eddy trajectories originating from different locations along the coast and measuring the probability that they were intercepted by a simulated glider track ( appendix C). For each eddy track, we randomly chose each component of velocity based on the translation velocities reported by Collins et al. (2013). We also assigned each track a random lifetime from an exponential distribution, chosen to resemble the lifetime distribution in the model results of Kurian et al. (2011). The simulations of eddy propagation and detection suggest that gliders detect only 30%–40% of eddies generated locally, but that 30% of eddies observed in the time series are nonlocal. There are numerous uncertainties associated with these methods and the simulations of appendix C should be regarded only as an order-of-magnitude estimate of the influence of eddy trajectories on their detection by the glider. Their results are reasonable, however, in that they suggest that the gliders do miss a large fraction of the local eddies but that the total number observed is partially compensated by the presence of nonlocal eddies. The simulations suggest that a ratio for observed to true local Cuddies of 1:2 is plausible, which would indicate local generation of 8.4 yr−1. The lower and upper bounds for rate of generation in this study straddle the Collins et al. (2013) estimate of 6 yr−1 generated at Cape Mendocino.
Using the elevated estimate of generation rate and average ASA/AHA would raise the Cuddies' fraction of loss from the CU to 57%. If the uncertainties in estimates of eddy frequency of generation, salt–heat content, and CU loss ( appendix B) are considered in quadrature, eddy flux accounts for 44% (20% lower bound, 88% upper bound) of the heat–salt loss from the CU each year in this region. This fraction is likely a conservative figure for Cuddies' proportional contribution to offshore flux, as presumably some of the remaining 56% is lost vertically, for example in waters upwelled to the Washington shelf or through vertical mixing.
Consider offshore flux of salt JS through the side of the CU core volume described above, parameterized as a function of , an effective regional-scale diffusivity caused by eddies:
where is the regional-scale cross-shore salinity gradient. The core volume has a western edge area of 200 m × 128 km and at 200 m is equal to 0.026 (100 km)−1. The latter value was obtained by a linear least squares fit to the mean cross-shore profile. The above parameters give an effective horizontal diffusivity caused by eddies of 460 m2 s−1. This value compares well with previous values of horizontal diffusivity obtained over the continental slope (Garfield et al. 1999; Collins et al. 2000; Todd et al. 2012).
The observations in this study do not allow for precise diagnosis of the generation mechanism of subthermocline eddies off WA. However, the observed eddy properties and WA slope hydrographic results provide some clues about their life cycle. The large anomalies of PV in eddy cores, and the lack of adjacent advective source for such low- and high-PV water, indicate that eddies have been subject to some nonconservative process. This presumably occurs during their formation along the continental slope. D'Asaro (1988b) described generation of SCVs in the Beaufort Sea by frictional torque acting on a boundary current flowing along topography and Garfield et al. (1999) hypothesized that it is responsible for the formation of Cuddies in the CU. Observations from RAFOS floats in the Atlantic Ocean have demonstrated that this is the likely generation mechanism of Meddies and Labrador Sea outflow eddies (Bower et al. 1997, 2012).
These conditions require a current trapped against sloping topography; strong negative horizontal shear (such that ζ ≤ −f) in the bottom boundary layer then creates a region of near-zero or negative potential vorticity. As the current encounters a sharp topographic headland, flow separation occurs, shedding a region of near-zero PV water, which undergoes adjustment to become a subthermocline anticyclone. This mechanism is consistent with the predominance of anticyclonic subthermocline eddies and their preferential generation near headlands (Collins et al. 2013). M. J. Molemaker et al. (2013, unpublished manuscript) have investigated the generation process in detail using a nested-grid model of the CU in the Monterey Bay region that resolves submesoscale processes. Their results indicate that as the CU separates from the slope, the regions of negative PV undergo centrifugal instability processes that promote strong diapycnal mixing. This mixing dilutes the negative PV until it is above the threshold of instability and coalesces into a coherent anticyclone (M. J. Molemaker et al. 2013, unpublished manuscript).
During fall over the WA slope, average near-bottom velocities exceed 0.05 m s−1 (Fig. 4). Assuming a large bottom frictional layer thickness of 50 m (Lentz and Trowbridge 1991) and upper-continental-slope gradient of 10% implies that the along-slope velocity decays to zero over a horizontal distance of 500 m. Under these conditions the horizontal shear is equal to −1 × 10−4, which is −0.93f at 47°N. An assumption of a 50-m-thick boundary layer (BL) is conservative in that it is at the upper range of values observed by Lentz and Trowbridge (1991). Smaller BL thickness would result in a shorter horizontal distance over which the velocity decays to zero at the side boundary and more negative values of horizontal shear. In the simulations of M. J. Molemaker et al. (2013, unpublished manuscript), the vertical relative vorticity in the bottom BL is much less than −f. Under these assumptions, the two-month averages of along-slope geostrophic velocity in this study (Fig. 4) show that near-bottom velocities large enough to produce are evident at various times each year throughout the summer, fall, and winter, indicating that the necessary conditions for anticyclone formation by the frictional torque mechanism are often present. Cyclones could be generated during periods of strong equatorward flow over the continental slope, for example during the “spring transition” (Hickey 1989; M. J. Molemaker et al. 2013, unpublished manuscript).
Float #90 of the NPS RAFOS float time series documented eddy generation in the WA slope region (Fig. 13; track data obtained from the NPS Lagrangian Acoustic Subsurface Technology Laboratory; http://www.oc.nps.edu/npsRAFOS/). This float traveled north in the CU from California and began anticyclonic looping at 47°N in autumn 2004. This eddy was not observed in the process of formation by the Seaglider deployed at that time, because the glider moved offshore from the shelf break prior to the float's arrival in the area, missing the eddy by a few days. However, the track provides evidence of the slope near GH as a generation site. If eddies are consistently generated off GH, this offers a possible explanation for the strong second core of poleward flow in the average velocity of the GH transect (Fig. 13). Averages of velocity would reflect superposition of eddies with other transects that sampled a more typical CU structure, resulting in the appearance of anomalously poleward flow near the offshore eddy limb and weakly equatorward or near-neutral flow on the inner limb. Among the 23 total anticyclone crossings along the GH line, 10 were of eddies whose centers were within 75 km of the shelf break. This compares to 6 of 23 along CF. The GH line intersects a headland in the continental slope although it is likely of insufficiently sharp curvature to induce flow separation. It is more likely that smaller submarine ridges or canyons to the south of GH with radii of curvature less than the deformation radius are responsible for generating meanders and separation in the CU. We removed the 10 crossings of the GH line with an inshore anticyclone and took the average of velocity over the remaining 52 crossings, in order to test the hypothesis that eddies were responsible for the second core of poleward flow. In the resulting averages, the second core was 0.012 m s−1 weaker but still present. Thus, we conclude that although eddies contribute to the presence of the second core of poleward flow at GH, they are not its main cause.
For subthermocline anticyclones that are stable and do not encounter mechanisms of external destruction such as seamounts or other strong PV anomalies, diffusion plays a dominant role in their decay and eventual destruction (McWilliams 1985; Ruddick and Hebert 1988; Armi et al. 1989; Hebert et al. 1990). Previous SCV observations indicate that interaction with surrounding water is mainly limited to a transition region near the velocity maximum and outside the homogeneous eddy core (Elliott and Sanford 1986). This interaction often takes place in the form of layered horizontal intrusions of exterior water into the eddy core. Intrusions were identified as the main mechanism of decay in a Meddy that was repeatedly sampled over a period of two years (Ruddick and Hebert 1988; Hebert et al. 1990).
We examined all unbinned profiles near eddy edges for evidence of lateral interleaving and intrusions. A series of vertical profiles from Seaglider 014, taken in May 2006 as the vehicle crossed a Cuddy along the GH transect, provides an example of intrusion features similar to those observed in Meddies (Fig. 14). Seaglider 014 started this transect at the offshore waypoint and moved onshore through ambient cool, fresh subarctic conditions (blue θ–S profile in Fig. 14a, 65 km from center). The glider then encountered a region of density-compensating inversions in θ–S (black, 32 km) that was followed by the homogeneous water properties at the eddy center (red, 1 km). We quantified the presence of interleaving by computing the variance of high-pass-filtered (HP) profiles of spice. For each cast, smoothed profiles of spice versus depth were computed using a triangular running mean with a 20-m half-width. These smoothed profiles were subtracted from the original measurements to produce HP spice. The variance in the HP profile was then computed in a 60-m segment centered on the depth of the σθ = 26.55 kg m−3 isopycnal. Peaks in HP spice variance were observed in two casts at the offshore eddy edge, including the highlighted cast at 30 km (Fig. 14c). Variance was minimal in the homogeneous interior region of the eddy and exhibited a modest peak in casts taken at the inshore edge.
We calculated HP spice core variance for all casts taken near anticyclonic Cuddies. These are plotted versus distance from the eddy edge (positive outward) in Fig. 15. The edge is defined as each eddy's geopotential radius λ. Average variance in 5-km bins decreases with distance inward from the edge, which reflects the lenslike character of Cuddy interior waters. Average variance in spice has a peak at 20–25 km from the edge (Fig. 15). However, this peak is modest and there is little decay in average variance with increasing distance from the eddy edge. The fact that high-spice variance near the offshore edge was observed in only two casts in Fig. 14c suggests that when interleaving does occur in Cuddies, its radial extent is small. The broad peak in the variance composite of Fig. 15 then likely reflects the fact that interleaving was not observed at every eddy and that when it was, it did not occur at a consistent distance from the edge.
where KV is the small-scale vertical salt diffusivity, is the medium-scale (cross frontal) radial gradient of salinity, and is the intrusion-scale vertical salinity gradient. In (15), it is presumed that frontal interleaving is composed of small aspect ratio intrusions that decay because of turbulence or double diffusion from thermohaline instabilities along their upper and lower edges. Radial salinity gradients at the eddy's western edge (r = 30 km) varied from −0.3 × 10−5 m−1 to −1.2 × 10−5 m−1 in the interleaving region (−300 < z < −125 m) and vertical salinity gradients at intrusive interfaces were from 0.65 × 10−2 m−1 to 0.9 × 10−2 m−1. These compare favorably with the measurements of Hebert et al. (1990), who found . We assume a small-scale vertical diffusivity at the thermohaline interfaces of KV = 10−4 m2 s−1 (Hebert et al. 1990; Ruddick and Richards 2003). Using (15), these values give = 29–673 m2 s−1, which is from one to two orders of magnitude higher than values reported by Hebert et al. (1990), owing primarily to a weaker radial salinity gradient. We repeated the calculation using observed T characteristics of the eddy edge from −3.2 × 10−5 °C m−1 to −8.2 × 10−5 °C m−1; |∂T′/∂z| = from 3.3 × 10−2 °C m−1 to 6 × 10−2 °C m−1), which gives = 16–353 m2 s−1. Note that this calculation also assumes that KV = 10−4 m2 s−1, and makes no attempt to account for unequal vertical diffusivities for heat and salt at the intrusion vertical interfaces that may result from double-diffusive mixing. The found here corresponds to an outward heat flux from 13 × 10−4 °C m s−1 to 113 × 10−4 °C m s−1. The values for u′T′ and fall in the middle of the range of lateral intrusive heat flux estimates from previous frontal intrusion studies (Ruddick and Richards 2003; Table 1).
For the Meddy, Hebert et al. (1990) compared the KH given by (15) to an inferred KH that would be required to produce the eddy's observed decay. We make a similar inference of required KH for an assumed rate of decay of the eddy in Fig. 14; however, we use the decay of T rather than of S. This rate of decay is based on T decline within a Cuddy observed by Collins et al. (2013). Assuming that radial velocity is zero and horizontal mixing is the dominant heat loss mechanism, the time rate of change of heat within a radius r0 balances with radial diffusion according to
This equation is similar to (4) of Hebert et al. (1990). The only long-term observations of Cuddy water property evolution are those of NPS RAFOS floats. Collins et al. (2013) report that their Float #105, which exhibited anticyclonic looping characteristics for >100 days, observed a steady during looping of −0.0034°C day−1. This was attributed to decay of the eddy core signature as a result of lateral entrainment of far-field waters. Using this rate of decay of T along with r0 = 30 km and the range of reported above gives = 7–18 m2 s−1. This falls at the bottom of the range of calculated effective frontal diffusivities for heat from (15), though it is unknown if the rate of decay of T observed in Float #105 of Collins et al. (2013) is typical of Cuddies. Nonetheless, the properties of the interleaving region in Fig. 14 suggest that fluxes from intrusions could be of a large enough magnitude to account for significant loss of heat and salt from Cuddy cores. The roles of horizontal and vertical diffusive flux in the decay of Cuddies and their implications for eddy persistence are important topics that warrant future study.
5. Summary and conclusions
Seaglider surveys in the northern CCS observed small subthermocline anticyclonic eddies generated from the CU, referred to previously as Cuddies. These surveys also encountered subthermocline cyclonic eddies of similar dimensions. An algorithm was created to detect instances in which Seagliders crossed an eddy, which determined that gliders encountered anticyclones 46 times and cyclones 17 times. These were estimated to represent 20 distinct anticyclonic Cuddies and 10 distinct cyclones. On average, the dynamical properties and size were consistent with SCVs. The average horizontal radius for anticyclones (cyclones) was 20.4 km (20.6 km) and the average Rossby number was 0.46 (0.29), although these estimates are biased low given that gliders did not perfectly sample each eddy. Among 30 eddies, 10 had Rossby numbers greater than 0.5. The anticyclones contained warm, saline, low-stratification cores and low potential vorticity, while the cyclones did not on average have a distinctive water mass core. The data support the hypothesis of Garfield et al. (1999) that the anticyclones are primarily formed through frictional torque acting on topographically trapped currents of the upper slope, as the necessary conditions for this mechanism are met throughout the year. We speculate that the cyclones are of similar origin. We find circumstantial evidence of decay through frontal intrusions and interleaving along the edges of the warm-core anticyclones. The 20 anticyclones observed in the time series imply a rate of generation of 4.2 yr−1 in the region 47°–48°09′N if gliders miss no eddies and sample only those generated locally. A simple estimate of sampling efficiency of the glider survey implies that this generation rate may be an underestimate by half. Estimates of eddy salt and heat content suggest that Cuddies account for 44% (20% lower bound, 88% upper bound) of the flux of these properties out of the core of the CU as it flows poleward in this region.
In addition to their role in physical processes, long-lived, coherent eddies spawned from the WA slope could conceivably be important to the biology and geochemistry of the North Pacific. Mesoscale eddies in the Gulf of Alaska are associated with enhanced primary productivity through a variety of physical mechanisms that enrich nutrient concentrations in the surface ocean (Whitney and Robert 2002; Whitney et al. 2005; Crawford et al. 2005, 2007; Ladd et al. 2009). In Cuddies, this could be accomplished by upwelling of high-nutrient CU water as a result of divergence near the edges of an eddy with a prominent surface expression (Okkonen et al. 2003), from enhanced turbulent mixing across the nutricline because of strong vertical shear around the eddy edges or by doming of isopycnals at the eddy center (Nicholson et al. 2008). Also, iron is a limiting nutrient in the Gulf of Alaska and Lam et al. (2006) forwarded the idea that eastern Pacific continental shelf sediments supply iron to the central basin. Siedlecki et al. (2012) describe a mechanism by which shelf sediment–derived iron moves out of the bottom boundary layer and offshore. This occurs as a result of the downwelling circulation on the shelf and bottom friction on the upper slope generated by along-slope jets such as the CU. If sediments were subsequently entrained within a Cuddy core, this type of eddy could plausibly act as an important long-range delivery mechanism for micronutrients to the open ocean, similar to mesoscale eddies in the Gulf of Alaska (Johnson et al. 2005; Xiu et al. 2011).
The authors are indebted to Kirk O'Donnell, James Bennett, Bill Fredericks, Troy Swanson, Neil Bogue, and Tom Lehman for their invaluable work in the Washington Coast field campaign. We are also grateful to several colleagues who assisted in the direction of the research questions addressed in this manuscript. Jody Klymak, Greg Johnson, Curt Collins, Barbara Hickey, Mike Gregg, Samantha Siedlecki, and Tom Connolly all provided helpful ideas, criticism, and discussion. Eric Kunze provided useful comments on the manuscript. We thank two anonymous reviewers whose constructive criticism greatly helped to expand and strengthen this work. Reviewer #1 encouraged an extended discussion of horizontal resolution of the Seaglider transects, while reviewer #2 pushed for greater consideration of the uncertainty associated with the estimated number of eddies generated per year. This work has been supported through National Science Foundation Grants OCE9911036, OCE0095414, and OCE0526634, with assistance in Seaglider development from the Office of Naval Research and National Oceanographic Partnership Program. Supplemental funding provided with contributions from NOAA, the National Cooperative Research Program of the NOAA Fisheries Office of Science and Technology, and the Joint Institute for the Study of the Atmosphere and Ocean.
Horizontal Resolution of Seaglider Transects
Seaglider samples on ascent and descent while traveling along a saw tooth pattern with a 1:3 glide slope. On a depth surface at the top of the water column or near 1000 m, this results in a repeating pattern of pairs of closely spaced samples that are separated by 6 km horizontally or 8 h in time. This spacing is reduced by half at the middepth point (500 m). As a result of the interval between samples, internal wave variability is aliased onto glider measurements made on a depth surface or onto measurements of the depth of an isopycnal (Rudnick and Cole 2011). This results in spurious high-wavenumber variance that is present in horizontal wavenumber spectra of these quantities taken from glider transects. We seek to map Seaglider observations with Gauss–Markov interpolation using a decorrelation spatial scale that is large enough to effectively filter out the projected variability while also retaining the mesoscale variability of interest. Rudnick and Cole (2011) suggest that in order to determine this scale, glider users should compute horizontal wavenumber spectra of θ along a depth surface or of the measured depth of isopycnals in the region of interest. Spectra should exhibit a break in slope at the maximum useful wavenumber, above which the slope will be flat or shallower than expected. Using this method, Rudnick and Cole found that Spray gliders were capable of resolving horizontal scales on depth surfaces to a minimum wavelength of 30 km in the subtropical North Pacific off Hawaii. Todd et al. (2011) also found a minimum useful wavelength of 30 km for Spray transects collected in the southern CCS.
We computed horizontal wavenumber k spectra of isopycnal depth ziso for σθ = 25.5, 26, 26.5, and 27 kg m−3 for each cross-shore transect performed by Seagliders off WA. Following Rudnick and Cole (2011), we interpolated unbinned observations of ziso to 1-km spacing and removed a linear cross-shore trend. Detrended observations were tapered to zero at the ends of each transect using a 10-km Gaussian window before taking a discrete Fourier transform. The resulting spectral estimates were then averaged over each deployment; these are shown for σθ = 26 kg m−3 in Fig. A1a. Spectra are plotted on an x axis that extends to the approximate Seaglider Nyquist wavenumber of cycles per kilometer (cpkm). The deployment-averaged spectra show a break in slope near k = 1/25 cpkm, and spectra of other isopycnals and of temperature at constant depth (not shown) similarly demonstrate enhanced noise at these wavenumbers and above. It should be noted that the break in slope in this study is less distinct than in spectra used to demonstrate this phenomenon in Rudnick and Cole (2011), whose measurements were collected off Hawaii. However, as pointed out by Rudnick and Cole, the wavenumber at which the effective noise floor occurs, and the extent to which the spectra whiten above this wavenumber, will depend on both the vehicle's sampling pattern and the true wavenumber–frequency content in the environment in which the vehicle is operating. Considering these factors, it is perhaps unreasonable to expect that horizontal wavenumber spectra collected from measurements in an eastern boundary current system will closely resemble those taken at a more southerly latitude and within the interior of the subtropical gyre. The 25-km scale is also supported by depth spectra taken from a Seaglider crossing of Line P (Freeland 2007) in January–April 2010, which show a prominent break in slope at wavelengths 25–30 km (N. A. Pelland and C. C. Eriksen 2013, unpublished manuscript). Line P extends from Ocean Station P at 50°N, 145°W to the entrance to the Strait of Juan de Fuca at 48°34.5′N, 125°30′W, 47 km to the north of the CF line (http://www.dfo-mpo.gc.ca/science/data-donnees/index-eng.html). We interpret 25 km as the minimum wavelength that Seagliders are capable of resolving in the WA coastal transition zone and following Todd et al. (2011), we use this as the Gaussian decorrelation spatial scale for mapping glider observations on each transect to a regular grid.
The interpolation algorithm acts as a low-pass filter, whose spectral response characteristics will depend on the choice of decorrelation length scale, observation error variance, and observation spacing (McIntosh 1990; Daley 1991). We investigated the spectral response of the 25-km interpolation method to verify that it suitably filters high-wavenumber noise (Fig. A1a). For each transect, we evaluated the mapping response function R(k), defined as
where I(k) is the spectrum of the unbinned data and M(k) is a spectrum computed from the mapped data. The median value of R(k) taken over all transects shows that the mapping procedure has a reasonably sharp spectral cutoff and a half-power point at a wavelength of approximately 30 km (Fig. A1b). At wavenumbers above 1/25 cpkm, R(k) has values of 0.2 or less. We conclude that the choice of 25-km decorrelation length scale achieves the desired mapping characteristics of filtering the projected variability at high wavenumbers and retaining a large portion of the mesoscale signal of interest.
Although the eddies in this study have characteristic horizontal length scales that are comparable to the minimum resolved wavelength, they are still well resolved in the mapped data. To understand why this occurs, consider a Gaussian spatial signal g(x) with decay scale a, which represents an eddy. The Fourier transform of this signal G(k) is also a Gaussian:
This result can be derived from the identity and use of the similarity theorem, which states that if [f(x)] = F(k), then [f(bx)] = |b|−1F(k/b) (Bracewell 1978, chapter 6). The energy spectral density of g(x), that is, the signal energy per unit wavenumber according to Parseval's theorem, is given by |G(k)|2. It follows that the fraction E1 of the total signal energy for g(x) contained in wavenumbers with a magnitude lower than k1 is then given by
In Fig. A1b, the lowest wavenumber at which the mapping algorithm attenuates the input signal is klow = 1/64 cpkm. Taking a = 20 km, the average size of an eddy in this study, and k1 = klow, inserting these into (A3) gives E1 = 0.950. Thus, in the case of a Gaussian eddy with an e-folding scale of 20 km, 95% of the signal energy is contained at wavenumbers lower than those affected by the low-pass filtering of the optimal interpolation algorithm. Though the true eddies are likely not fully represented by the idealized shape chosen here, this exercise illustrates why features of the scale observed in this study are adequately resolved by the mapping technique; most of their signal is contained at wavenumbers lower than those affected by the filtering of the optimal interpolation algorithm. This exercise also serves to point out, as discussed in Chelton et al. (2011), that the signal of Gaussian eddies is represented by many scales, and the e-folding length scale used in this study is only one choice by which to define the boundary of the feature. Strong eddy currents exist outside the radius defined by the e-folding scale of geopotential anomaly, and it would be possible to choose a different definition for the eddy edge that yielded longer length scales.
Alongshore Budgets of Salt and Heat in the CU
Within the alongshore region bounded by the two Seaglider transects, the core water mass volume of the CU is bounded vertically by the isopycnals 26 < σθ < 26.8 kg m−3 and extends horizontally 50 km seaward from the shelf break. To evaluate the salt and heat budgets of the CU, the core region is treated as a simplified box, with a cross-sectional area B perpendicular to the slope and alongshore length L between GH and CF. These dimensions are assumed to vary by negligible amounts over time (B varies by 3% between the two lines in the time series–average sections, and by <10% over the course of the year). Integrating the continuity equation for salt over this volume and invoking the divergence theorem yields
where is the mean salinity within the volume and ρ0 is an in situ density of 1027 kg m−3, which is assumed to vary by a negligible amount within the CU. This budget considers gain or loss of salt within the WA slope halocline (the lhs term) caused by a constant one-dimensional poleward advection along the mean salinity gradient (first term on the rhs) and losses due to eddies Fedd, vertical mixing Fυmix, and the combined effects of upwelling, cross-shore circulation, and horizontal mixing Fupw. For simplicity, (B1) also treats poleward velocity within the box as everywhere constant, thus neglecting the effects of any differential volume transport between GH and CF. This budget neglects the covariance of perturbation salinity and transport from the mean which will be addressed below.
The sum of the three loss terms on the rhs is evaluated as a residual, first by using time series–long mean values of transport and poleward salinity gradient. Mean poleward transport through this box is 0.36 ± 0.14 Sv (1 Sv ≡ 106 m3 s−1). Bounds are 95% confidence for a Student's t distribution. The mean salinity gradient SCF − SGH was evaluated as a weighted average of the differences in salinity along isopycnals that were shown in Fig. 2d:
where ΔSi is the difference in salinity along the isopycnal layer i, ΔHi is the vertical thickness of that layer in the time series average sections, and N is the number of isopycnal layers between σθ = 26 and 26.8 kg m−3 in intervals of 0.005 kg m−3. Evaluating (B2) yields SCF − SGH = −0.0182 ± 0.0002 (Fig. 2). If it is assumed that vanishes in (B1), 213 ± 83 × 109 kg yr−1 are lost through Fedd, Fυmix, and Fupw between the two sections. Similar calculations for heat yield a loss of 48 ± 19 × 1017 J yr−1.
The WA slope region has a strong seasonal cycle and we computed a second budget to consider covariability of perturbations to the time series mean that are not resolved by (B1). The advective term was computed using two-month averages of transport and salinity difference between GH and CF. Greatest advective input of salt (and heat) was in late autumn and early winter (Fig. B1a), consistent with the strength of the CU and Davidson Current during these months, and near-zero during spring. Though it is unlikely that salt and heat content of the CU core remains constant throughout the year, estimates of seasonal were not significantly different from zero, and for the purposes of this budget we assume that . The sum of the two-month advective terms is 229 ± 79 × 109 kg yr−1 of salt and 51 ± 18 × 1017 J yr−1 of heat. These estimates are 6%–8% higher than those computed from time series–average properties. All calculations of eddy flux as a fraction of CU loss of salt and heat use these higher estimates of annual loss in order to take into account variability in the seasonal cycle.
We estimate vertical diffusive flux out of the CU using Kz = from 1 × 10−5 m2 s−1 to 2 × 10−5 m2 s−1 (Yamazaki and Lueck 1987). An estimate of the flux out of the box from vertical mixing (i.e., Fυmix) using typical vertical gradients at the top and bottom of the control volume is 32–64 × 109 kg yr−1 (from −0.36 × 1017 J yr−1 to −0.72 × 1017 J yr−1) for salt (heat). If eddy loss is taken to be the product of the average Cuddy ASA and AHA and the upper-limit estimate for their generation (8.4 yr−1 of eddies), this leaves a 14%–28% (41%–42%) residual in the budget of salt (heat). The budget is likely closed by losses because of several processes that are collected into the Fupw term in (B1). These include horizontal mixing and transverse circulation; that is, zonal and vertical flow through the core volume. For example, when the CU is strong, linear theory predicts that onshore flow in geostrophic balance with the alongshore pressure gradient bifurcates at the depth of peak poleward flow (McCreary 1981). Model results indicate that in the northern CCS, this linear balance holds for time scales longer than 20 days (Connolly et al. 2013, manuscript submitted to J. Phys. Oceanogr.). Heat and salt could then be lost from the core volume as water from the CU core moves up- and downslope in the bottom boundary layer above and below the depth of peak velocity, and relatively cool and fresh water is imported laterally from offshore (Werner and Hickey 1984). With the observed , large on-shelf velocities of 0.02–0.03 m s−1 would be required if the seasonal budget were closed in fall and winter by transverse circulation only (Fig. B1). Further investigation of budget closure would require a detailed examination of the seasonal component of transverse circulation.
The assumption that salt content within the CU over the WA slope remains constant from year to year is difficult to justify. The glider time series observed interannual changes in θ–S from cool and fresh conditions over the slope in 2003 to warm and saline in 2006–07 (Fig. B1b). Water properties along σθ = 26.55 kg m−3 returned to cool and fresh conditions in late 2008/early 2009. These correspond to annual salt inventory changes on the order of the advective terms calculated above. The presence of these trends is evidence that significant interannual variability may exist in the advective input and loss terms. This is due in part to interannual signals in local and remote wind stress forcing and ENSO-driven alteration of CU strength and water properties (Whitney and Freeland 1999; Freeland 2002). Because no net interannual trend in CU salt content is observed over the course of the glider time series, we take the budget constructed from two-month averages as the best available estimate of an average of the annual loss terms over the 5.5-yr period.
Eddy Detection Efficiency of Seaglider Transects
A naive estimate of eddy frequency of generation in the region 47°–48°09′N can be obtained by dividing the number of observed eddies by the duration of the time series. However, this estimate suffers from several biases, including the unknown subjective bias associated with visual identification of similar eddy crossings. Two other major biases are associated with the following: 1) the time needed for a glider to complete an occupation of the navigational pattern, resulting in gliders missing some eddies that are generated and advected away from the study area, and 2) glider detection of eddies generated outside the study area but advected into the transect pattern. The former source of error would bias the naive estimate low while the latter would bias it high. We attempted to quantify plausible values of these two biases and their relative magnitude using a simple ad hoc 2D numerical simulation of eddy propagation and glider detection. In this simulation, 22 800 eddies were released along an idealized coastline and allowed to propagate westward. A virtual glider was moved through the domain and the number of eddies detected by the glider were counted. The eddy trajectories did not include any dynamics and were instead chosen randomly based on the statistics of observed trajectories (Collins et al. 2013).
We considered an idealized rectangular domain representing the northern CCS. The eastern boundary represented the shelf break and was oriented in a purely meridional direction. The southern boundary was taken to be 38°N (1000 km south of the GH transect line) and the northern boundary was 500 km north of GH. At the beginning of the simulation, eddies were released from the eastern boundary at points separated by 20 km meridionally; 300 eddies were released at each point giving 22 800 eddies total. Each eddy was randomly assigned a constant zonal UE and meridional VE translation velocity. These velocities were sampled from empirical distributions derived from the anticyclonic looping trajectory translation velocities reported by Collins et al. (2013). We first discarded 6 of 48 trajectories from Collins et al. that had eastward UE. We created a fit to the empirical probability distribution function of the remaining UE velocities using a Weibull distribution with a = 2.039 and b = 1.452. The PDF of the remaining VE velocities was created using an empirical kernel-smoothing distribution with a kernel bandwidth of 0.0045 m s−1. We then integrated these distributions to create cumulative distribution functions for UE and VE and randomly assigned translation velocity components to each eddy using the inverse transform method (Devroye 1986). Each eddy was also assigned a random lifetime from an exponential distribution with μ = 50, which corresponds to a median expected lifetime of 34.7 days. This value was chosen to provide a visual match to the eddy lifetime cumulative distributions shown in Kurian et al. (2011).
A glider was included in the simulation and randomly assigned an initial position and direction of travel in the navigational pattern. The simulation was then stepped forward in time in half-day increments. Eddies were allowed to propagate according to their assigned velocities and the glider moved through the transect pattern at 0.20 m s−1. At each time step, an eddy was marked as detected if it was within 20 km of the glider position. Eddies were removed from the simulation once total simulation time exceeded their assigned lifetime. The simulation was run to 400 days at which time virtually all eddies had been removed or had propagated beyond the glider transect pattern extent. A snapshot of eddy and glider positions at t = 60 days (Fig. C1a) displays the zonal spread of the eddy field and the meridional spread of eddies generated locally. After the simulation was complete, the probability of detection of an eddy released at any point along the shelf break yinit [P(detect | yinit)] was estimated by the fraction of the 300 eddies released at yinit that were detected by the glider in the simulation.
The simulation was run for 50 trials in order to account for the effect of the variable initial position of the glider. Averaged over the 50 trials, P(detect | yinit) versus yinit shows that eddies were most likely to be detected if they were released near the glider transect inshore waypoints (Fig. C1b). The percentage of all the eddies generated within the transect pattern that were detected by gliders [P(detect | local)] ranged between 0.24 and 0.37 over all trials and was 0.35 on average (Fig. C1c). These local eddies composed 70% of the eddies detected by the glider on average [P(local | detect)]. This fraction varied between 0.67 and 0.77 over 50 trials.
For each trial, we also calculated the ratio of total number of eddies observed by the glider Otot to the total number of local eddies released nlocal. The average of the ratio Otot:nlocal over all trials was 0.51. Thus the simulation results suggest that the original, naive estimate of local rate of generation would be an underestimate of the true rate by half. In the simulation, gliders only detect one-third of eddies generated locally, which biases the naive estimate low. However, this is partially compensated by detection of remotely generated eddies that propagate into the time series and account for 30% of total detections.
It should be emphasized that the orientation of the coastline is one of several gross simplifications made in the above simulation. The eddy lifetime distribution and range at which a glider is capable of detecting an eddy using the algorithm of section 2c are not well constrained. The simulation assumed a rate of eddy generation that is uniform in the along-coast direction when, in fact, observational and model results suggest preferential generation near subsurface headlands and capes (Collins et al. 2013; M. J. Molemaker et al. 2013, unpublished manuscript). The translation velocities are held constant though it is likely that ambient currents heavily influence eddy propagation, especially in the period immediately following generation. Hence, the simulation is informative in a qualitative sense only, and is intended to give an estimate of what percentage of missed eddies is plausible given the available statistical information about eddy trajectories. Better estimates of detection efficiency and Otot:nlocal would require simulations that take into account eddy and EBC dynamics and a more realistic domain.