Warm Atlantic-origin waters are modified in the Lofoten Basin in the Nordic
Seas on their way toward the Arctic. An energetic eddy field redistributes
these waters in the basin. Retained for extended periods, the warm waters
result in large surface heat losses to the atmosphere and have an impact on
fisheries and regional climate. Here, we describe the eddy field in the
Lofoten Basin by analyzing Lagrangian simulations forced by a high-resolution
numerical model. We obtain trajectories of particles seeded at three levels – near the surface, at 200

The Lofoten Basin (LB) in the Norwegian Sea is an important region for the
retention and modification of the warm Atlantic Water (AW) as it flows
northward towards the Arctic Ocean

Both the Slope Current and the LB (here defined as the central basin enclosed
by the 3000

The vigorous eddy field is thought to have an impact on the thickening of the
AW layer in the LB and towards the slope. For example, studies of regional
hydrographic observations

The exchange of AW with the LB (AW–LB exchange) has also been studied
extensively. Earlier literature has suggested that much of the warm AW in the
LB stems from anticyclonic eddies in the form of long-lived coherent vortices
that shed off from the Slope Current and then bring with them heat and
vorticity westward into the basin

To describe and quantify the role of the eddy field for the AW–LB exchanges, it
is important to note that energetic vortices not only carry around the
properties trapped in their cores but also stir and transport more passive
water masses surrounding them. In an idealized simulation of an unstable
eastern boundary current over steep topography with a deeper basin to the west
(mimicking the domain we study here),

In this work we study the eddy field around the LB from a Lagrangian
perspective. We perform Lagrangian simulations forced by high-resolution model
outputs and extract eddy signals from synthetic particle trajectories using
the method of multivariate wavelet ridge analysis

The Lagrangian trajectories are integrated by using output from a
high-resolution Regional Ocean Modelling System (ROMS) configuration in the
Nordic Seas. ROMS is a hydrostatic model solving the primitive equations on a
staggered C grid with terrain-following vertical coordinates

The Lagrangian simulations are the same as in

In all simulations we deploy particles at three levels (15, 200 and
500

To identify long-lived coherent vortices in the Lagrangian trajectories, we
perform a multivariate wavelet ridge analysis (MWRA), which has been
developed for the purpose of finding “loops” in drifter trajectories and
hence identifying whether the drifters are inside coherent vortices. We
describe the basic concepts of the method here, but more details can be found
in

A drifter deployed in position

The MWRA routine looks for “ridge points”. A ridge point is defined as a
point on the

After identifying the ridges, the MWRA routine outputs the longitudes and
latitudes of each ridge. At a given position and time along a ridge, the curve
traced out by its instantaneous motion can be described as an ellipse with
major axis

An example of the MWRA routine applied to the ridge (cyan) of the green
trajectory in Fig.

List of output from the MWRA routine. In descriptions,

For each drifter the MWRA routine may find zero, one or several separate ridges, each one given with indices along the drifter trajectories. This means that for a given drifter trajectory, we are able to identify where and when the drifter experiences ridges. By applying the routine to a large number of drifter trajectories, we can describe the eddy characteristics and behavior using statistics. Furthermore, since we also track the drifters before and after they experienced ridges, we can compare the eddy characteristics and behavior with that of the ambient flow outside eddies.

To objectively select ridges that are associated with eddies, some choices are
made. Before running the MWRA routine, we choose a frequency band of

This second threshold is chosen as a function of the number of oscillations
within the wavelet we use, leading to the problem of first choosing wavelet
duration

In terms of time, we choose a minimum ridge length of 2

Distribution of ridge points in the radius–orbital velocity (

After running the routine, the orbital velocity (

We compare three groups: cyclonic ridges, anticyclonic ridges and the
ambient flow. In the following, it is implied that a ridge is similar to a
vortex, and we will refer to these as cyclonic (“C”;

The drifter data set suggests that coherent vortices, detected as ridges,
cover a small fraction of the total drifter data points. The evolution of
the fraction of ridge points for each day after deployment, normalized by the
number of available drifter data points for the given days, shows that about
6

To study whether this fraction is actually representative of the prevalence of
coherent eddies in the domain, we compare it with a more classical vortex
detection criterion based on the Okubo–Weiss parameter:

We obtain a mean OW field from the ROMS model using daily fields of OW between
1 January 1996 and 1 January 2000 and then averaging these in time for each
model grid point. The same daily fields of OW are interpolated to the drifter
trajectories, and these drifter-sampled OW values are then time-averaged in a
set of geographic bins. Maps shown from the ROMS model and the 2D drifters
(after binning) at 15

Statistics for drifters in 2D and 3D simulations containing ridges, showing the number of drifters (NODs) that contained ridges with corresponding percentages in parentheses of total drifters studied for the given deployment depth (DD;

The fraction of drifter data points with

We now focus on the coherent vortices found by the MWRA routine. Although the
fraction of ridge points is relatively small, about 30

The number of ridges (NORs) after dividing into cyclonic and anticyclonic
(Table

Relative frequency distributions (RFDs) of selected parameters are summarized
in Fig.

Relative frequency distributions (RFDs) of

The shape, size and lifetime of eddies depend on the regions where they are
observed. Geographical distribution of ridges is estimated by obtaining
density maps by counting the occurrences of ridge points in geographical bins
of size

Density distribution of

The location of the first occurrence of a ridge in a trajectory is counted in
the same geographical bins (thick black contours in
Fig.

Averaged

The spatial distributions of

The size, shape, nonlinearity, lifetime and generation sites of eddies
influence the properties and fate of water masses trapped inside the
eddies. How their water properties change with time can be related to
processes within the eddies: how they drift, interactions with other eddies or
the ambient flow, or how they are affected by the atmospheric forcing. Here
and in Sect.

Averaged velocity fields at 200

The AF drifters on average follow the Eulerian mean flow from the ROMS model
(i.e., residual drift of the AF flow is small)
(Fig.

The AW modification is particularly strong in regions with large eddy activity, such as the LBE and the secondary EKE maximum in the southeast of the LB

We first estimate the characteristic temperature anomalies for the cyclonic
and anticyclonic ridges and compare these to AF drifters. To remove the
spatial and seasonal variability embedded in the drifter temperatures, we
compute a background temperature climatology from the ROMS model by taking
seasonal averages of temperature for winter (January–March), spring
(April–June), summer (July–September) and fall (October–December) between
1996–2000, the same period as the Lagrangian simulations. These are
interpolated onto the drifter trajectories and subtracted from the
temperatures to give temperature anomalies. The RFDs of anomalies from the 3D
drifters (Fig.

RFDs of temperature anomalies for 3D drifters deployed at

Warm and cold temperature anomalies for anticyclones and cyclones, respectively, can impact the cooling and warming experienced by water masses inside them. Since cooling and warming are related to an increase or decrease in density, this may also affect the vertical motion of the water masses. We therefore compute daily temperature changes and vertical displacements along drifter trajectories and assign these values to the drifter's mean position that day. With a lifetime of 1 year this is 364 data points for each drifter or less if a drifter runs aground or exits the domain earlier. The daily temperature changes and the vertical displacements for 3D drifters are then binned as before.

Averaged

For 3D drifters deployed at 15

As in Fig.

There is no obvious relation between the temperature changes and the vertical
motion in the different flow categories (Figs.

Time series of

The vertical displacements indicate a net sinking in the domain for the
ambient flow, and this is even more enhanced in anticyclones
(Fig.

Cooling of the water parcels is typically accompanied by an increase in
density (Fig.

The temperature and density changes are stronger in the LB compared to the
full domain (Fig.

To calculate the net temperature and vorticity fluxes into the LB, we tag all
drifters that passed through the basin (so both entering and exiting). The net
fluxes are then computed as the difference between fluxes in and fluxes out
for each drifter. Note that a drifter can enter and exit the LB several times, and we thereby compute fluxes for all drifter segments in the basin. We
interpret each drifter as carrying a given mass, and by doing the calculation
only on drifters that entered and then exited the basin the calculation
approximately conserves mass. For each entry/exit we obtain the values of
temperature

The drifters can enter and exit as ambient flow, anticyclones or
cyclones. However, it is possible that a drifter changes its category in the
basin, meaning that it may for instance enter while being trapped within an
anticyclone but exit as part of the ambient flow. We are interested in whether
such transitions may play a role in the dynamics and therefore separate the
calculations of

Estimates of the

Summed over all categories, the net temperature flux into the basin is
positive (Fig.

The net vorticity flux into the basin is positive and is also dominated by the
AFi and AFo categories (Fig.

The number of observations is also given in
Fig.

Recall that the AF category includes anything which is not classified as
coherent vortices, such as the mean flow, filaments and other submesoscale
features.

The relatively small fraction of ridge points (6

So at late stages after deployment, more drifters experience

The MWRA detects long-lived coherent eddies by design, requiring sustained
looping by drifters. The most sensitive parameter choice in this routine is
the choice of minimum ridge length (RL). For the above analysis we used an RL
of 3.1 cycles (Sect.

The indications shown in Fig.

The eastern Nordic Seas that we study here are primarily
temperature-stratified. We hence expect that water parcels that are cooled
will eventually sink from gravitational adjustment. An indication that this
process is taking place near the surface, where parcels are directly exposed
to air–sea heat loss, is seen in Fig.

The most pronounced signal seen in Figs.

So the observed vertical motion of water masses in and around the LB can therefore be related to several processes. On the one hand, cooling and densification can cause subduction, but only if the water masses get heavier than their surroundings. The vertical motion can also be related to motion along sloping isopycnals. For eddies, a secondary vertical motion within the eddy may also occur. In the first and third case the water masses change their properties and exhibit water mass transformation, while the second case is adiabatic. We propose that actual water mass transformation takes place mainly near the surface but also in vortices at depth since here too the 2D and 3D temperature and density changes are different.

The fact that the ambient flow dominates the net vorticity fluxes (and
temperature fluxes) into the LB is consistent with the idealized model
simulations of

As mentioned above, at 500

In this study we have investigated the eddy activity in the Norwegian Sea,
with a focus on the Lofoten Basin (LB), using a Lagrangian framework. We used
high-resolution model fields and analyzed about 200 000 2D and 3D synthetic
drifter trajectories seeded at 15, 200 and 500

The drifters sampled larger radii for the anticyclones (20–22

An individual water parcel (drifter) trapped in an eddy typically contributed
more than a parcel associated with the ambient flow to temperature and
vorticity fluxes into the LB. However, since an overwhelming fraction of
drifter data points were not ridge points (about 94

The results presented here have some caveats. One particular issue that raises
many questions is the very small fraction of ridge points found, leading to a
speculation on the real role of coherent vortices. Moreover, the fraction of
ridge points was low compared to the fraction of drifter data points that
detect an Okubo–Weiss value smaller than zero – a more traditional measure
of eddies. But we saw that the two estimates could be brought into closer
agreement by either setting a shorter allowable ridge length or by requiring
that a drifter tracks

To summarize, our study has used realistic modeling and a novel Lagrangian method to detect and characterize coherent eddies in the Norwegian Sea, to compare the movement and transformation of water parcels in eddies and the ambient flow and also to assess the relative contributions to transport of heat and vorticity into the Lofoten Basin. The indication by the synthetic Lagrangian observations that long-lived coherent eddies may be less prevalent and contribute less to heat and vorticity fluxes than previously thought motivates further comparison with Eulerian studies. We have indicated that filaments may contribute significantly to net fluxes. Possible future studies should look closer into this, including the role of vortices as a stirring agent for filaments. Furthermore, the link between the generation of eddies on the slope and their interaction with the LB at deeper layers and, finally, the possible link between vortex secondary circulation and the transformation of AW also warrant further studies.

The ROMS model fields used to perform the Lagrangian
simulations are available at the Thredds Service at the Norwegian
Meteorological Institute (

JD performed the Lagrangian simulations and the multivariate wavelet ridge analysis, analyzed the data, and wrote the paper. PE and IF provided ideas and discussions that helped interpreting results and shaping the paper throughout the process.

Ilker Fer is a member of the editorial board of

This study received funding from the Research Council of Norway, through the project Water mass transformation processes and vortex dynamics in the Lofoten Basin in the Norwegian Sea (ProVoLo, project 250784). The ROMS simulation was made by Marta Trodahl and Nils M. Kristensen of the Norwegian Meteorological Institute and run on resources provided by UNINETT Sigma2-The National Infrastructure for High Performance Computing and Data Storage (projects NN9431K and NS9431K). The drifter simulations were performed on servers provided by the Norwegian Meteorological Institute in Oslo, Norway. We thank Jonathan M. Lilly for help with running and interpreting results from the multivariate wavelet ridge analysis and Knut–Frode Dagestad for the help with performing the Lagrangian simulations. We also want to thank the reviewers Sarah Gille and Stefanie Ypma for providing constructive feedback that helped to improve the paper.

This research has been supported by the Norges Forskningsråd (grant no. 250784).

This paper was edited by Erik van Sebille and reviewed by Sarah Gille and Stefanie Ypma.