1. Introduction
The Denmark Strait Overflow (DSO) is one of the major export routes for the dense waters formed in the Arctic Ocean and the Nordic seas. The dense waters pass through the Irminger Basin (IB) toward the North Atlantic where they supply about one-third of the North Atlantic Deep Water, a major component of the global thermohaline circulation (Dickson and Brown 1994). The DSO transmits the climate signals from its source regions, modified en route by mixing and entrainment, and affects the properties throughout the water column in the North Atlantic (Dickson et al. 2008; Yashayaev and Dickson 2008).
The 620-m-deep Denmark Strait (DS) sill (DS sill) is the main gateway for dense waters exiting the Greenland Sea to the Irminger Basin and is a key location for observing the DSO at the start of its transit to the North Atlantic (Dickson et al. 2008). Measurements show that the dense overflow through the sill is fast (speeds frequently exceed 1 m s−1) and occurs as pulses of dense water (referred to as boluses) cascading to the deep water to the south of the sill at intervals of 2–5 days. On longer time scales, DSO appears as a steadier and hydraulically controlled flow with a mean transport of approximately 3 Sv (1 Sv ≡ 106 m3 s−1; Käse and Oschlies 2000; Macrander et al. 2007; Jochumsen et al. 2012). Temperature and salinity of DSO vary on a time scale of a few days, owing to mesoscale activity and intense mixing processes near the sill (Rudels et al. 1999; Tanhua et al. 2005). The seasonal signals in the DSO transport and properties are weak (Dickson and Brown 1994; Jochumsen et al. 2012). The overflow composition exhibits interannual-to-decadal variations; however, it is most likely linked to changes in the upstream source waters or pathways (Rudels et al. 2003). These changes in turn are possibly linked to atmospheric forcing and in particular to variations in the North Atlantic Oscillation (Yashayaev and Dickson 2008; Serra et al. 2010).
During the first 250 km of the DSO descent from the sill, hydrographic sections show that the mixing is intense (Voet and Quadfasel 2010). The volume transport nearly doubles through entrainment (Dickson et al. 2008), mainly of the warm and saline Irminger Current (Tanhua et al. 2008). Farther downstream, there are two major measurement sites used to monitor the dense overflow in the Irminger Basin. At the Spill Jet (SJ) section, 285 km southwest from DS sill, the DSO follows the continental slope transporting approximately 5 Sv (Brearley et al. 2012).1 The variability due to passage of the DSO boluses is pronounced at this site. The boluses are associated with cyclonic eddies that occupy intermediate and surface layers and are visible in satellite imagery (Bruce 1995; Spall and Price 1998). Ship surveys at the SJ section suggest that dense waters spill over the shelf break into the Irminger Basin (Rudels et al. 2002; Pickart et al. 2005; Falina et al. 2012). These spilling events are believed to feed the East Greenland Spill Jet, a strong flow of intermediate waters banked against the slope and overlying the DSO at the SJ section (Pickart et al. 2005). At 530 km downstream of the Denmark Strait, an array of current meters moored on the East Greenland slope off of Angmagssalik has been operated continuously since 1998.2 At this section, the transport of DSO is estimated to have increased to over 7 Sv in a long-term average (Dickson et al. 2008). This increase is due to entrainment of Iceland–Scotland Overflow Water and Labrador Seawater (Tanhua et al. 2008). The variability due to the DSO boluses is less distinct at the Angmagssalik section; the dense plume is characterized by broad maxima in the frequency spectrum at 1–10 day periods (Voet and Quadfasel 2010).
There have been several modeling studies of the DSO. A series of papers considered the dynamics at the Denmark Strait sill (e.g., Spall and Price 1998; Käse and Oschlies 2000; Käse et al. 2003; Haine et al. 2009). Others, such as Köhl (2010) and Hall et al. (2011), adopted a large-scale perspective, focusing on the variability of the DSO source upstream of the Denmark Strait sill and its major pathways. The spatial discretizations of the models were too coarse to resolve the evolution of the DSO downstream of the sill. The highest resolution to date was achieved by the study of Magaldi et al. (2011), 2-km grid spacing in the horizontal and 97 vertical levels. Still, their configuration lacked adequate vertical resolution to resolve the dense boluses because the vertical grid spacing at the relevant depths (2000 m) was 100 m, which is similar to the bolus height in the Irminger Basin [Käse et al. (2003), their Fig. 6].
Because of the sparseness of observations and the resolution limitations of numerical experiments, there are several open issues regarding the DSO in the Irminger Basin. First, the observations suggest there are alternate pathways of dense waters on the continental shelf in the Denmark Strait that are missed by the main measurement arrays. Dense water (potential density 
Second, the DSO transformation rates that change the water temperature, salinity, and density downstream of the Denmark Strait are not well quantified. For this reason, it is difficult to identify DSO water (DSOW) at different measurement sites in the Irminger Basin or to estimate its volume transport. Dickson and Brown (1994) used a convenient criterion, 
Third, the time scales of the DSO transit through the Irminger Basin are uncertain. The transit times are usually inferred by correlating hydrographic records from different stations. This method gives a time scale of 10 weeks for propagation from the Denmark Strait to the Angmagssalik section (Dickson et al. 2008). One can also estimate the advective time scale from the velocity records. The mean overflow speed in the Irminger Basin is ~0.3 m s−1 (Girton and Sanford 2003; Dickson et al. 2008). This value implies a much shorter transit time of 3 weeks. It is unclear how to reconcile these estimates and how to relate them to trajectories of individual water particles.
This paper explores the pathways and evolution of the DSO in the Irminger Basin. We employ the Lagrangian (particle following) framework because it traces the water masses directly. Water property transformation is easily assessed from time series of the properties along particle trajectories (Döös 1995; Song and Rossby 1997; Dutkiewicz et al. 2001). Lagrangian instruments provide the high space–time resolution needed to resolve mesoscale and submesoscale processes that mix and exchange properties between water masses. To observe dense and deep flows, acoustically tracked subsurface floats have been used (Rossby et al. 1986). These floats have been successfully applied at the Iceland–Faroe Ridge and in the Norwegian Sea (Søiland et al. 2008; Rossby et al. 2009) but not yet in the DSO. In lieu of real observations, we use a high-resolution regional ocean model (Magaldi et al. 2011) and integrate over 10 000 Lagrangian particles to study the transit of dense waters through the Irminger Basin. The particles are deployed on a section crossing the entire Denmark Strait in waters denser than 
The paper is organized as follows. Section 2 presents the numerical model and the particle integration technique. In section 3, we show model results on the spatial distribution and properties of the dense flows and the results on the mean pathways, transformation, and transit times. The summary and discussion are given in section 4.
2. Methods
We describe here the numerical model, as well as the integration technique that we use to simulate Lagrangian particles using the model fields.
a. Numerical model
We employ a hydrostatic version of the Massachusetts Institute of Technology General Circulation Model configured for the Irminger Basin. The model setup is identical to that of Magaldi et al. (2011) except that it has increased vertical resolution (see below). The model simulates summer 2003 (1 July–31 August). As the overflow transport and properties throughout the Irminger Basin show little variation at seasonal time scales (see the introduction), this period resolves the primary variability of the overflow. In fact, Dickson and Brown (1994) verified that the overflow diagnostics at the Angmagssalik section converge in about one month. Also, Haine et al. (2009) found that the dense water flux in the Denmark Strait is controlled by the internal ocean dynamics rather than the seasonally modulated atmospheric forcing. The interannual variations of dense overflows have been addressed elsewhere (Köhl 2010; Serra et al. 2010). Our configuration focuses on the high spatial resolution needed to resolve the processes controlling the dominant variability (Haine et al. 2009).
The model uses partial bottom cells and a rescaled height coordinate to accurately simulate flows over steep topography (Adcroft and Campin 2004). It also features a nonlinear free surface, a flow-dependent Leith biharmonic viscosity, and a third-order advection scheme with zero explicit diffusivity for tracers. The K-profile parameterization (Large et al. 1994) is used with a background vertical viscosity of 10−5 m2 s−1. The equation of state is according to Jackett and McDougall (1995). There are three open boundaries (north, east, and south); the west boundary is closed at the east coast of Greenland. The boundary conditions for tracers and velocities are obtained from the 
The model has a nominal horizontal spacing of 2 km. The only change with respect to the setup of Magaldi et al. (2011) is increased vertical resolution, from 97 to 210 levels, with gridcell height ranging from 2 m at the surface to 15 m at depths greater than 100 m. This change improves the simulation of the overflow occupying the 1000–2000-m-depth range in the Irminger Basin (the vertical grid size is reduced from 100 to 15 m at these depths). To our knowledge, this is the highest-resolution ocean model configuration of the overflow into the Irminger Basin to date.
b. Integration of synthetic Lagrangian particles
The numerical particles are simulated offline using output velocity fields from the model. The deployment strategy is discussed in the next section, following the presentation of the model results regarding the dense water masses. Here, we focus on the technical aspects of the integration. The particles are fully Lagrangian, that is, they move in three dimensions. There is no explicit diffusion in the particle code as we assume that all the information about the flow is contained in the model velocity field. For the particle code, we employ the matrix laboratory (MATLAB) software. The particles are advanced using ode23t, a trapezoidal solver with a second-order predictor and third-order corrector scheme.3 The relative tolerance is set to 10−6, the absolute horizontal and vertical tolerance values are 1 m and 
Once the particle trajectory integration is completed, time series of temperature and salinity are obtained by linear interpolation from the model property fields onto particle trajectories at each time step using the zero gradient condition at the boundary. The model equation of state (Jackett and McDougall 1995) is then used to compute the density.
3. Results
a. Dense circulation in the numerical model and comparison with data
To evaluate the model realism and give context for the particle deployment strategy, we first present Eulerian results on the dense water flows. We define the dense waters by 
Dense water in the DS/EGS/IB model. For clarity, only a subset of the model domain is shown. (a) Occurrence frequency (%) of dense waters (
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
The positions of major hydrographic and mooring sections focused on the DSO are marked with red lines in Fig. 1a. The hydrographic section at the Denmark Strait sill is centered at 66° latitude, −28° longitude (Girton and Sanford 2003; Macrander et al. 2007). Approximately 300 km downstream along the continental slope is the Spill Jet section (65° latitude, −33° longitude; Pickart et al. 2005). Another 300 km along the slope, the Angmagssalik array (ANGM) is moored (63° latitude, −36° longitude; Dickson et al. 2008; Hall et al. 2011). Note that the model dense waters extend northwest of the sill on the shelf, consistent with observations (Macrander et al. 2007; Brearley et al. 2012). Also, as reported in observations (Rudels et al. 2002), dense waters fill the 650-m-deep Kangerdlugssuaq Trough that cuts the strait and shoals gradually toward the shelf break near the SJ section. The flow in the trough is cyclonic and can potentially drain dense water toward the shelf break. On the Dohrn Bank, there is an anticyclonic recirculation that facilitates the transfer between the trough and the sill and redistributes dense waters on the shelf.
We report the model volume transports first. Magaldi et al. (2011) analyzed the same model configuration but with lower vertical resolution. They found that the dense water transports at Denmark Strait sill (−2.9 ± 1.7 Sv for 
We also verify that the model reproduces the hydrographic structure and variability of the overflow at the Denmark Strait and downstream. The dense waters cascade from the Denmark Strait sill at 2–5-day intervals in the form of 30–50-km-wide dense water boluses. The descent of model boluses leaving the sill is shown by Magaldi et al. (2011), their Fig. 5, replicating the observations from Käse et al. (2003). Figure 1b further visualizes the mesoscale variability at the Strait in a snapshot of the depth-averaged density field for model points satisfying 
The conventional Denmark Strait sill section misses much of the dense water spread over the strait. Therefore, we extend the section toward the coast to capture the entire dense water layer and refer to it as the extended Denmark Strait section (DSE; marked in Fig. 1a). A snapshot of density along this section is shown in Fig. 2a. It shows a dense water bolus passing through the sill on 4 July. The densest fraction (
Water masses at the DSE section. (a) Density on 4 Jul 2003, seen from the south. The distance along the section is calculated with the origin at the deepest location of the DS sill (66.0° latitude, −27.4° longitude). Deployment locations of the three particle groups (KANGER, SHELF, and SILL) are indicated with white dots, the white-dashed lines separate the groups. (b) Corresponding θ (°C)–S diagram, color coded by the along-section distance [the key to the distance markers is included at the bottom of (a)]. The 
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
The potential temperature θ–salinity S diagram corresponding to Fig. 2a appears in Fig. 2b and is color coded by position on the section. The densest (
Between boluses, the volume of dense water in the sill decreases and the height of the plume reduces from 300 to 20–50 m, consistent with observations (Bruce 1995; Käse et al. 2003). The cold, freshwater (θ < 1°C and S < 34.9) is then absent from the θ–S diagram and the front lies 50 km closer to the shelf. This westward front migration during low-overflow events has been observed by Rudels et al. (1999). The dense waters in the Kangerdlugssuaq Trough and on the shelf, on the other hand, exhibit much less temporal variability.
At the SJ section, our simulation replicates the results of Magaldi et al. (2011) faithfully representing the observed hydrography. At the Angmagssalik section, the overflow core [identified by 
b. Particle deployments at the Denmark Strait
To resolve the cycle of volume transport variability at DS sill due to boluses [2–5-day period, e.g., Girton and Sanford (2003) and Macrander et al. (2007)], particles are released every 12 h for 5 days starting 1 July 2003. This schedule samples the dominant volume transport variability [see Fig. 6 of Magaldi et al. (2011), which is consistent with the observations of Dickson et al. (2008)]: the first 2.5 days correspond to low flow through the sill and the second 2.5 days capture the passage of a dense water bolus. The particle initial positions are separated by 2 km in the horizontal and 25 m in the vertical directions and all particles initially have 
Particles deployed at the Denmark Strait sill (do > −70 km) correspond to the conventional overflow (SILL, 3301 particles), which has received most of the observational focus.
Particles deployed on the adjacent shelf: do between −160 and −70 km along the section, depth shallower than −320 m (SHELF, 1827 particles).
Particles deployed in the Kangerdlugssuaq Trough, d < −160 km (KANGER, 6685 particles).
Note that the SILL subset, which tracks the conventional DSO, contains only 28% of the dense waters across the DSE, while KANGER and SHELF fractions add 56% and 16%, respectively. In terms of volume transport, the mean southward transport attributable to the particles (the product of the particle speed perpendicular to the section and the cross-sectional area of the model grid cell) is 2 Sv. The contribution of the SILL particles to the volume transport over the 5-day deployment period is 94% (varying between 1 and 3.2 Sv). The SHELF and KANGER particles are moving in both directions across the section because of flow reversals associated with the recirculations. Their average contributions to the volume transport are 4% and 2%, respectively.
We refer to the part of the Denmark Strait to the northwest of the sill, encompassing the shelf adjacent to the sill and the Kangerdlugssuaq Trough, as the “continental shelf.”
c. Particle trajectories—A general description
Trajectories are shown in Fig. 3a and are color coded by the initial distance along the section. Animations of particle evolution, in a horizontal and three-dimensional view are accessible as supplemental material at the Journals Online website. Weekly snapshots of the particle positions are shown in Fig. 4. The preferred pathways are shown in Fig. 5a.
Particle trajectories from the DS. (a) Trajectories color coded by deployment subset (blue, cyan, and red mark SILL, SHELF, and KANGER particles, respectively). For clarity, only every 30th particle is shown. (b) Particles that reached 62° lat within 57 days (%), projected on the initial position along the DSE section. The distributions were calculated in 20 km × 30 m bins. The black-dashed lines separate the particle deployment groups.
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
A sequence of particle positions at days 1, 8, 15, 22, 36, and 43 of the simulation projected onto the horizontal plane (colors as in Fig. 3). See also the animations in the supplemental material at the Journals Online website (http://dx.doi.org/10.1175/JPO-D-13-023s1.txt, http://dx.doi.org/10.1175/JPO-D-13-023s2.m4v, and http://dx.doi.org/10.1175/JPO-D-13-023s3.m4v).
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
(a) Pathways of the dense water deployed at the DS. The shading shows the fraction, at each place, of the total number of particles for the given set that visits that place during the 60-day simulation. Only dense particles (
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
The particles reveal the complexity of the pathways of dense water from Denmark Strait. They clearly depict the “conventional” route along the East Greenland shelf break. But the trajectories on the shelf part of the strait trace multiple recirculations and some of them spill off the shelf and contribute to the along-slope flow. During the 2-month integration, 3737 particles (32% of the total deployment) reach 62°N. Of these, 61% were deployed at DS sill (SILL particles), 24 % at the SHELF, and 15% at KANGER (Table 1). Over one-half of the particles (6906 or 59%) stays within 200 km of their release position. The majority of these (78%) are deployed in the Kangerdlugssuaq Trough. Only five particles reach 69° latitude and all are from the KANGER group. We now look at the evolution of particles released in different locations along the DSE section.
Particle position statistics for the whole dataset (ALL) and each of three subsets (SILL, SHELF, and KANGER; see text). No. is the total number of particles; Exit is the number of particles that exit at 62° lat during the 8-week simulation; North-DSE is the number of particles that are north of the DSE section after the 8-week simulation; 200 km-DSE is the number of particles located within 200 km of the DSE section after the simulation; No. (shelf) is the number of particles present on the East Greenland shelf (west of −34° lon and water depth <500 m) for at least 1 day during the simulation.
The SILL particles (blue trajectories in Fig. 3a, blue dots in the animations accessible as supplemental material at the Journals Online website and in Fig. 4, and the bottom right panel in Fig. 5a) show two distinct behaviors. The majority (69%) cascade over the sill, follow the shelf break southward (the conventional route), and reach 62° latitude within the integration period. The particles released in the core of a dense bolus in the deepest part of the sill have the highest exit rate (nearly 100%; Fig. 3b). Some of them cascade to the sea floor and proceed as a dense water plume, others occupy shallower depths as intermediate waters, implying that water mass modification occurred along their trajectories (see section 3e). Some 178 particles ascend up onto the continental shelf for at least 1 day. Most of these particles enter the shelf near a deflection in the 500-m isobath (65° latitude, −34° longitude; see the animation in the supplemental material at the Journals Online website at http://dx.doi.org/10.1175/JPO-D-13-023s1.txt and http://dx.doi.org/10.1175/JPO-D-13-023s2.m4v) that probably destabilizes the along-isobath flow. Almost one-quarter of the SILL particles (22%) get swept by the anticyclonic recirculation on the Dohrn Bank and directed into the Kangerdlugssuaq Trough and are still found within 200 km of the release site at the end of the simulation (Table 1).
About half of the SHELF particles (cyan trajectories in Fig. 3a, cyan dots in animations and in Fig. 4, bottom left panel in Fig. 5a), after looping for about a week in the anticyclonic recirculation on the Dohrn Bank (see the animations in the supplemental material at the Journals Online website at http://dx.doi.org/10.1175/JPO-D-13-023s1.txt, http://dx.doi.org/10.1175/JPO-D-13-023s2.m4v, and http://dx.doi.org/10.1175/JPO-D-13-023s3.m4v), spill off the shelf break from −29° to −30° longitude and proceed along the shelf southward. These particles reach 62° latitude within the simulation period, constituting almost one-quarter of the particles that exit (Table 1). Many particles (44%) recirculate on the Dohrn Bank and in the Kangerdlugssuaq Trough, and the remainder are en route along the shelf break.
The majority (81%) of the KANGER particles (red trajectories in Fig. 3a, red dots in animations available in the supplemental material at the Journals Online website at http://dx.doi.org/10.1175/JPO-D-13-023s1.txt, http://dx.doi.org/10.1175/JPO-D-13-023s2.m4v, http://dx.doi.org/10.1175/JPO-D-13-023s3.m4v, http://dx.doi.org/10.1175/JPO-D-13-023s4.m4v, and http://dx.doi.org/10.1175/JPO-D-13-023s5.m4v and in Fig. 4, upper panel in Fig. 5a) recirculate in the Denmark Strait and are found there at the end of the simulation (see also Fig. 3b). The remaining particles are carried by the cyclonic flow in the Kangerdlugssuaq Trough toward the shelf break and spill into the Irminger Basin near the SJ section. The first spilling of KANGER particles, deployed on the western flank of the trough, and thus advected directly toward the shelf, occurs approximately 3 weeks after the deployment. This provides an estimate of the half-recirculation period in the trough (see section 3f). The spilled particles join the dense flow along the slope and eventually exit at 62° latitude. The particles released at the western flank of the trough have a higher (~40%) exit rate because the cyclonic circulation in the trough carries them directly toward the shelf break thus facilitating their spilling (Fig. 3b). During the 2-month record, the KANGER particles comprise 15% of the total particle exits at 62° latitude (Table 1).
The contribution of continental shelf particles to the dense water particles at the downstream sections (No. dense) are summarized in Table 2. Overall, these KANGER and SHELF particles supply almost 35% of the particles at the SJ section (17% each). At the Angmagssalik array, 300 km farther downstream, KANGER and SHELF particles make up 9% and 17% of the dense particles, respectively. Thus, the dense water particles originating on the continental shelf in the Denmark Strait make up a substantial part of the dense particles in the Irminger Basin.
Transit time statistics from the DS to the SJ and Angmagssalik sections. No. is the number of particles recorded; 
d. Mean evolution south of the Denmark Strait
We look now at the mean evolution of the particles classified by their release site. We compare the particle statistics to the results of Girton and Sanford (2003). They describe hydrographic observations conducted during two cruises in August 1997 and September 1998 in the first 250 km downstream from the Denmark Strait sill. These observations are most relevant to our results as the properties of the dense waters in the years 1997/98 and in 2003 were similar in otherwise variable conditions (Yashayaev and Dickson 2008).
To allow comparison with these data that sampled the dense waters on the slope, we also consider dense particles located over a seabed deeper than 600 m. These are called SLOPE particles and the mean pathway of these observations (from averaging in 10-km bins) is shown in Fig. 5a. Figure 5b shows the evolution of the mean potential density on particle subsets with downstream distance. We include observations from Girton and Sanford (2003), their Fig. 10 that should be compared to the SLOPE particles. Their density evolution (Fig. 5b) matches the observations well. There is a small discrepancy of ~0.02 kg m−3 at 100 km from the sill that can be attributed to the flow variability. The rapid density decrease at 125–200 km emphasized by Girton and Sanford (2003) is reproduced by the SLOPE particles.
Figure 5c shows the evolution of the mean vertical position in the same format as Fig. 5b. However, the comparison with Girton and Sanford (2003) is not straightforward. They used an averaging technique that emphasizes the densest waters and is difficult to reproduce here. Weighting the SLOPE particles by their deviation from 
Now, consider the unconventional pathways. The SHELF particles begin with a lower average density than the SILL particles (Fig. 5b) but their density decrease is (on average) weaker than the particles released in the sill. This is likely related to the presence of the front in the sill and cross-frontal mixing involving mostly the SILL particles. As a result, at the SJ section the SHELF particles approach the SILL particles in the mean density. On average, the SHELF particles undergo a greater increase in depth and are deeper than the SILL particles at the SJ section. The KANGER particles undergo strong mixing during spilling off the shelf at 150–230 km [see the next section and Magaldi et al. (2011)]. They become lighter than SILL or SHELF particles (by 0.01 kg m−3) and remain slightly higher (by 100–200 m) in the water column during their subsequent transit along the shelf break.
Beyond 250 km from the DSE section, the ensemble-mean densities for all the particle subsets remain fairly constant implying that diapycnal mixing with other water masses is weak. This is true also for the temperature and salinity. This result agrees with Voet and Quadfasel (2010) who inferred a small change in the mean temperature downstream of the SJ section based on moorings and hydrographic sections along the slope.
e. Property changes
Now, consider the property changes along the particle trajectories. Figure 6a shows the time series of the fraction of particles that remain dense (
Water-mass property transformation. (a) Particles in different density classes (%; relative to the total number of particles deployed) as a function of time: dense (
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
Figure 6b shows locations of strong transformation, that is, particle positions at times when the density tendency on trajectories (
Figure 6d shows locations where the density 
As a result of transformation, the particles span a wide range of densities at the SJ section. We average 
Density diagnostics at the SJ section. (a) Average 
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
The inset panel in Fig. 7a shows the dominant contributions from SILL, SHELF, and KANGER particles to the DSO at the SJ section. Unsurprisingly, the core of the dense water plume centered at ~1700 m is formed mainly of SILL particles. However, the SHELF particles dominate the deepest parts of the overflow; they are also the densest. The likely reason is that SHELF particles spill from the DB about 200 km upstream of the SJ section avoiding strong transformation experienced by the other particles.
f. Transit time statistics
Next, we focus on the transit-time statistics to the SJ and Angmagssalik sections. Figure 8 shows particle transit time distributions (PTTDs) at the SJ (Fig. 8a) and Angmagssalik (Fig. 8b) sections.7 The number of particles arriving at the two sections, the modal transit times, and the mean transit times are listed in Table 2. Because some particles do not reach the two sections within the integration period, 〈τ〉 is biased low. To estimate this bias and get a more robust estimate of the mean transit time, we fit PTTD tails with exponential functions and extrapolate. This estimate, 〈τ〉∞, is also listed in Table 2.
Transit times from DS. (a) PTTDs for the SJ section color coded by the deployment site. The thick lines show distributions obtained from all particles, the dashed lines show distributions derived from dense particles (
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
First, note that Fig. 8a shows that modal transit times computed for all the particles and only the dense ones are very similar (see animations available in the supplemental material at the Journals Online website at http://dx.doi.org/10.1175/JPO-D-13-023s1.txt, http://dx.doi.org/10.1175/JPO-D-13-023s4.m4v, and http://dx.doi.org/10.1175/JPO-D-13-023s5.m4v). The implication is that the velocity field carrying the transformed particles is similar to the one carrying the dense particles. Consistently, the horizontal velocity field at the East Greenland shelf break varies little in the vertical [see Magaldi et al. (2011), their Fig. 14, and Brearley et al. (2012), their Fig. 6b]. For that reason we focus on the travel time statistics computed from all the particles.
The modal transit times for the SILL particles are very distinct and centered at 5 and 13 days for the Spill Jet and Angmagssalik sections, respectively (Fig. 8a and Table 2). The SILL particles, which are the majority of the particles arriving at the two sections during the simulation, determine the modal peaks for the whole dataset. The SHELF particles also exhibit a clear mode in transit times, but it occurs 5–6 days after that of the SILL. This difference approximates the time for recirculation of the SHELF particles on the Dohrn Bank before they spill off the shelf break. The PTTD of the KANGER set is much broader, with two peaks corresponding to the two events of spilling over the shelf break (at 25 and 50 days at the SJ section and 30–40 days and >50 days at the Angmagssalik section). See the animations available in the supplemental material at the Journals Online website at http://dx.doi.org/10.1175/JPO-D-13-023s1.txt, http://dx.doi.org/10.1175/JPO-D-13-023s2.m4v, http://dx.doi.org/10.1175/JPO-D-13-023s3.m4v, http://dx.doi.org/10.1175/JPO-D-13-023s4.m4v, and http://dx.doi.org/10.1175/JPO-D-13-023s5.m4v for visualization of the spilling events.
Remarkably, the shapes of the SILL and SHELF PTTDs at the two sections are very similar (Figs. 8a,b). The PTTD at the Angmagssalik section is delayed by 6–7 days relative to that at the SJ section. This delay provides an estimate for the mean advective time scale between the sections and corresponds to a mean speed of ~0.6 m s−1. The similarity of the PTTDs is consistent with advection by the shelf break current downstream of the SJ section (see Fig. 1a), with little dispersion of the particles compared to that occurring in Denmark Strait and on the shelf (Fig. 5a).
The modal transit times for the dense particles arriving at the SJ section, projected onto their deployment location along the DSE section, are shown in Fig. 8c. In general, the transit times decrease with the distance from the Greenland coast. The SILL particles are the fastest (~1 week). The particles deployed on the western side of the Kangerdlugssuaq Trough have smaller 
Figure 8d shows the PTTDs against distance from the DSE section. The modal speed calculated from the slope of the line traced by modal peaks (black dashed line) is as low as 0.2 m s−1 in the first 50 km from the Denmark Strait, then increases to over 0.7 m s−1 where the particles descend into deep water, and then remains almost constant until the Angmagssalik section (0.58 m s−1 as calculated from the slope between 175 and 625 km). These speeds are consistent with those estimated from observations by Krauss (1996). He found maximum speeds of 0.5–0.6 m s−1 at the overflow interface, associated with the passage of boluses. The mean speeds, derived from the mean transit times (orange line), are lower than the modal speeds, but follow a similar pattern. The mean particle speed is low (~0.2 m s−1) within the first 150 km (where most recirculation takes place; see Fig. 1a and the animations available in the supplemental material at the Journals Online website at http://dx.doi.org/10.1175/JPO-D-13-023s1.txt, http://dx.doi.org/10.1175/JPO-D-13-023s2.m4v, http://dx.doi.org/10.1175/JPO-D-13-023s3.m4v, http://dx.doi.org/10.1175/JPO-D-13-023s4.m4v, and http://dx.doi.org/10.1175/JPO-D-13-023s5.m4v), and increases past the SJ section to ~0.4 m s−1 in the shelfbreak jet.
These particle transit-time statistics are derived from an 8-week-long integration, and 70% of the particles remain in the domain during this period. Nevertheless, the modal transit times for the SILL and SHELF particles are robust because the simulation period is approximately three times longer than the modal times at Angmagssalik for these particles. Their mean transit time statistics are biased low, but only by 1–2 days (Table 2). It is likely that further modal peaks exist for the KANGER particles at τ > 57 days. Thus, it is not possible to obtain robust estimates of 〈τ〉 for them from extrapolation although 〈τ〉 is likely much longer for KANGER particles than the other sets.
4. Summary and discussion
In this study, we explore the fate of dense water at the Denmark Strait. Using a high-resolution model, we deploy over 10 000 particles in the model's dense waters at the Denmark Strait and follow them through the Irminger Basin. To our knowledge, this is the first Lagrangian study of the DSO. The main findings and their implications are as follows.
We confirm that the model's deep circulation is realistic. The model accurately reproduces volume transports, hydrographic properties, and overflow structure in the Denmark Strait. Several phenomena previously seen in observations are captured by the model, such as the presence of fresh lenses capping the dense water plume, the westward migration of the front during low-overflow periods at the sill, and the presence of dense water on the continental shelf (Rudels et al. 1999, 2002). The model volume transports and hydrography compare well with the measurements at the SJ section (285 km downstream) and at the Angmagssalik section (530 km downstream).
The particles are deployed in waters satisfying 
From the particles, we derive pathways, quantify the rates of density transformation, and estimate travel time distributions for transit through the Irminger Basin. The particles show that the DSO plume has other sources in addition to the dense boluses crossing the sill. The particles released on the continental shelf northwest of the sill (SHELF particles) and in the Kangerdlugssuaq Trough (KANGER particles) comprise over 70% of the particles deployed along the DSE section. These particles cross the shelf and spill over the shelf break, consistent with the observations of dense waters on the shelf (Rudels et al. 1999, 2002; Pickart et al. 2005; Macrander et al. 2007; Brearley et al. 2012). The particles reveal the complexity of the pathways of dense water from Denmark Strait (Figs. 5a and 9). Over three-quarters of the particles released in the Denmark Strait sill (the conventional part of the overflow) cascade over the sill and follow the route along the shelf break to the Angmagssalik section. However, almost one-quarter of the SILL particles recirculate anticyclonically on the Dohrn Bank and advect into the Kangerdlugssuaq Trough. Nearly one-half of the dense SHELF particles follow the same route. The other SHELF particles recirculate for about one week on the DB before spilling off the shelf break from −29° to −30° longitude and joining the along-slope route. The KANGER particles recirculate cyclonically in the trough and begin spilling off of the shelf break near the SJ section after 3 weeks. The complex pathways in the strait and on the shelf retard the southward progression of the particles, and after two months nearly 60% are still within 200 km of their deployment site. Most of these are from the KANGER and SHELF deployments (78% and 12%, respectively) and the remaining 10% are SILL particles swept via the anticyclone on the Dohrn Bank toward the Kangerdlugssuaq Trough.
Fates of dense DS water. The schematic diagram is based on Figs. 3, 4, 5, and 7. It shows the pathways of dense (
Citation: Journal of Physical Oceanography 43, 12; 10.1175/JPO-D-13-023.1
The SHELF and KANGER particles constitute 17% and 9%, respectively, of the dense water particles recorded at the Angmagssalik section during the 2-month simulation. This contribution of continental shelf particles is likely an underestimate because most of SHELF and KANGER particles are still in the Denmark Strait when the simulation ends. These Lagrangian results cannot be converted into Eulerian volume transports split into source components at downstream sections because the particles crossing a particular section sample only a subset of all the possible upstream origins.
Property time series along the particle trajectories visualize water mass transformation processes. We verify that particles recorded along the conventional DSO route evolve consistently with the hydrographic observations by Girton and Sanford (2003) of the mean DSO plume position and density. The particles reproduce the rapid density decrease in the first 200 km from the sill, followed by little density change between the SJ and the Angmagssalik sections, consistent with observations (Voet and Quadfasel 2010). This gives confidence that our short-time particle experiment represents the observed properties of the dense waters.
There are two main regions of rapid transformation along the slope. The first is immediately downstream of the sill where dense boluses descend into the Irminger Basin. The second is upstream of the SJ section, where KANGER particles spill off the shelf. In both places the dense waters mix with the warm salty Atlantic waters, in line with observations by Tanhua et al. (2005) and Brearley et al. (2012). Notably, the densest particles in the along-slope flow at the SJ section are those released on the shelf. This is consistent with Rudels et al. (2003) and Falina et al. (2012), who observed shelf water with 
As a result of this transformation, the Denmark Strait waters decrease their density. At the Angmagssalik section, 30% of the particles have transformed to intermediate density (27.7 ≤ 
Finally, we estimate transit times from Denmark Strait. The modal transit time for the particles released at the DS sill to the SJ section is 5–6 days. The corresponding speed is 0.65 m s−1. The modal transit time from the sill to the Angmagssalik section is 2–3 weeks. The particles released on the shelf adjacent to the sill recirculate before spilling over the shelf break and joining the overflow from the sill, and their modal transit times are longer by about a week. The mean transit times are 1–6 days longer than the modal times for these two sets of particles. The KANGER particles recirculate in the Denmark Strait for several weeks (80% remain within 200 km of their release site during the 2-month simulation). The KANGER particle transit time distributions to the SJ and Angmagssalik sections are broad and the mean transit times have not converged. Their modal transit times are 3 and 5 weeks to the SJ and Angmagssalik sections respectively, significantly longer than for the particles released near and at the DS sill.
This study addresses the fate of the dense waters at the DS. It relies on particle deployments at the DS and the forward integration of their trajectories. It focuses on pathways and travel times to the sections downstream and on transformation of the dense waters. It is also possible to diagnose the origin of dense waters at sections in the Irminger Basin. Addressing this question requires particle deployments at the sections of interest and the backward integration of their trajectories. Such an experiment would reveal the origins of water entrained into the DSO. We will address this issue in a future study. Future work will also quantify the mixing rates and eddy fluxes responsible for the density transformation and entrainment in the overflow, which is essential to the proper parameterization of these processes.
Our modeling study has elucidated the complexity of the dense overflow in the Irminger Basin that is not apparent in the available observations (see Fig. 9 for a schematic summary). In particular, we have mapped the dense water pathways on the shelf and showed that this water makes an important contribution to the overflow. If these findings are confirmed by future measurements, our perception of Denmark Strait Overflow should be recast to include dense water masses on the continental shelf with different pathways, histories, and time scales. Such an effort to observe these components of the Denmark Strait circulation is an important priority.
Acknowledgments
The authors acknowledge comments and inspiring discussions with Robert Pickart, Wilken-Jon von Appen, Kial Stewart, Stephen Jeffress, and Alex Fuller. Special thanks to Kial Stewart for help with digital media production. This work was supported in part by NSF Grants OCI-108849, OCE-0726640, and OCI-0904338. Data-intensive computations have been performed on the Johns Hopkins Data-Scope funded by OCI-1040114.
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The dense current following the shelf break, comprising DSOW and entrained waters, is also referred to as the Deep Western Boundary Current (Brearley et al. 2012).
Angmagssalik is the former name of the southeast Greenland town of Tasiilaq.
We tested ode45, ode15s, ode113, ode23t, and ode23bt from the MATLAB suite. Considering particle displacement statistics, the differences between the solvers were insignificant. The fastest solver for this problem was ode23t.
The sensitivity study relied on simulating a cluster of 81 particles released at the Denmark Strait sill. We varied the time step and inspected the mean horizontal and vertical positions, velocity distributions, spectra and autocorrelations, and travel times to the Angmagssalik section. The horizontal velocity and travel time statistics converged at dt = 0.25 day, but the vertical position statistics required dt = 15 min to do so. This time step resolves the Lagrangian decorrelation scale, which is ~1 day and ~0.25 day for horizontal and vertical components, respectively.
Figure 1 of Magaldi et al. (2011) shows the full domain. All of the figures here only display the central area of interest.
Plus/minus bounds indicate the standard deviations of transport time series and are measurements of model transport variability.
We use “transit-time distribution” in a different way than Haine and Hall (2002) who refer to the Green's function of the advection–diffusion equation. In their definition, transit time means the elapsed time since a fluid parcel at an interior point last had surface contact. Their transit-time distribution is equivalent to the asymptotic distribution of particle transit times for particles released at the SJ and Angmagssalik sections and integrated backward until they reach the sea surface. This is a different diagnostic than that presented here although both may legitimately be called transit-time distributions.
