Northward transport of subtropical water and advection velocity field
Figure a shows the density of tracks of tracers launched
along 37∘ N and across all the latitudes in the central JS for the
whole period of integration. The density is shown in greyscale in the logarithmic scale, log10Nφ. The magenta areas in
Fig. a along the coastal line indicate that the AVISO grid cells there
touch the land, and we did not compute trajectories there. An uneven density of
points in Fig. a means that the northward transport of subtropical
waters is meridionally inhomogeneous with “gates” with increased density of
points. The gates are such spatial intervals along a given zonal line across
which subtropical tracers prefer to cross.
Any tracer, as a passive particle, is able to cross the fixed latitude in the
northward direction if the northward component of the velocity field is
nonzero at its location. In Fig. b we plot distribution of the
northward component of the AVISO velocity field averaged over the whole
period of integration as follows:
v+(λ,φ)=1n∑θ(v(λ,φ))v(λ,φ),
where v+(λ,φ) is a northward (positive) component of the
velocity at the point (λ,φ), θ(v) the Heaviside function
and n the number of days in the period from
2 January 1993 to 15 June 2015. Comparing the Lagrangian representation in
Fig. a with the Eulerian one in Fig. b, it is clear that
areas with increased density of points in Fig. a correlate well
with areas with increased average values of the northward component of the
AVISO velocity field in Fig. b. Thus, the northward transport of
subtropical waters in the central JS is determined mainly by the local
advection velocity field, more precisely by local values of its northward
component. The greater is that northward component at a given point and the
longer is the period of time when it is positive, the more tracers are able
to cross the corresponding latitude.
The density difference in some meridional ranges in Fig. a may be
very large because of the logarithmic-scale representation. There are even
some places in the northern frontal area where the northward transport has
not been observed during all the simulation period, from 1993 to 2015. They
are marked by magenta rectangles in Fig. a. One “forbidden” zone
is situated in the deep Japan Basin with the centre at about
41.5∘ N, 134.2∘ E, and another one is situated to the south
off Vladivostok from 43 to 41∘ N approximately along the
132∘ E meridian. We stress that they are forbidden only to northward
transport of tracers but can be and really are open to transport in other
directions.
The “forbidden” zones exist due to long-term peculiarities of the advection
velocity field there. The zone to the south off Vladivostok exists due to a
quasi-permanent southward jet approximately along the meridian
132∘ E from 43 to 40∘ N (VMJ in Fig. ). It turns
to the east at about 40∘ N and contributes to the eastward
transport. In fact, the northward velocity is practically zero in this area
(see Fig. b) and, therefore, the northward transport is absent. The
other “forbidden” zone exists due to two factors: the presence of a
quasi-permanent anticyclonic eddy with the centre at about 41.3∘ N,
134∘ E in the deep Japan Basin (AC in Fig. ) and the
eastward zonal jet blocking northward transport across it. Topographically
constrained anticyclonic eddies with the centre at about
41–41.5∘ N, 134–134.5∘ E have been regularly observed
there .
Meridional distributions of the number of tracers which
crossed indicated zonal lines (solid curves), of the averaged northward
component of the AVISO velocity in cm s-1 (arrows) and of the number of
crossings of those zonal lines by available drifters (dashed curves). The
period of observation is from 2 January 1993 to 15 June 2015.
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Density plots show in the logarithmic scale
how many and at which final longitudes λf the tracers with
initial longitudes λ0 were able to cross the zonal lines
(a) 40∘ N and (b) 42∘ N for the whole
simulation period. The tracers were launched weekly at the line
37∘ N from 2 January 1993 to 15 June 2013. (c) Meridional
distribution of the number of tracers which crossed the zonal line
42∘ N for the whole simulation period. This line is divided into eight
intervals numbered by Roman numerals.
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Transport pathways of subtropical water and its intrusions across the Subpolar Front
Now let us look more carefully at the meridional distribution of subtropical
tracers crossed the Subpolar Front for the whole period of simulation. We
choose for reference four zonal lines along the AVISO grid at 42.125, 41.875,
40.125 and 39.875∘ N. They are shown in Fig. by solid
curves with superimposed meridional distributions of the averaged northward
AVISO velocity (arrows). The number of crossings of those latitudes by the
available 333 drifters is shown by dashed curves. The correspondence between
the peaks in the meridional distributions of the tracers, drifters and the
averaged northward AVISO velocity is rather good for all the chosen zonal
lines, confirming their direct connection. However, the comparison with
drifters should be taken with care because of a comparatively small number of
available drifters. Drifters are not ideal passive tracers, and their motion
is subjected to submesoscale features which were not caught by
altimetry-derived data. Moreover, the drifters have not been launched at the
zonal line 37∘ N like artificial tracers in simulation. Their launch
sites for more than 20 years have been distributed rather randomly over the
basin.
The local maxima and minima of the distribution functions correspond to gates
and conditional barriers, respectively. The very eastern,
138–140∘ E, and western, 129–131∘ E, gates are provided
mainly by the near-shore branch of the Tsushima Warm Current and the East
Korean Warm Current, respectively. The central gate, 133–137∘ E,
probably exists due to topographically constrained features over the Yamato
Rise there (see Fig. S1 in the Supplement). The transport through that gate
will be shown to be enhanced due to a specific disposition of frontal eddies
regularly observed there. The intervals between the gates may be called
“conditioned barriers” because of a comparatively small number of tracers
crossing zonal lines there, and because they used to “open” for
comparatively short time intervals.
Figure a, b shows in accordance with task 2 at which
final longitudes λf the tracers, launched with the initial
longitudes λ0 at the line 37∘ N, reached the zonal lines 40
and 42∘ N for the whole period of integration. The meridional
distribution of the number of tracers with pronounced peaks which crossed the
zonal line 42∘ N for the same period is plotted in
Fig. c. This zonal line was divided into eight meridional
intervals numbered by the roman numerals in Fig. b and
c with horizontal straight lines running via local minima at the
distribution in Fig. c.
The Tsushima Warm Current contributes mainly to the eastern peak VIII in the
distribution in Fig. c. Black across all the
range of initial longitudes λ0 in Fig. b indicates
that fluid particles, crossing eventually the line 42∘ N through the
gate 138–140∘ E, could have any value of the initial longitude
λ0 at the zonal line 37∘ N. They could reach that gate in
different ways: either to be initially trapped by the near shore branch or to
be advected by the offshore branch and then to enter the near-shore branch.
Moreover, those particles could be involved initially in the East Korean Warm
Current and then be transported to the east along the Subpolar Front to
eventually join the Tsushima Warm Current. Thus, the subtropical tracers,
crossing the gate VIII, may have rather distinct values of some Lagrangian
indicators, e.g. travelling time and distance passed.
There is a narrow barrier, the white strip in Fig. b
between gates VIII and VII, with the centre at the local minimum at
137.8∘ E in Fig. c. A comparatively small
number of tracers have been able to cross the line 42∘ N there for
the whole simulation period. Gate VII between 136 and 137.8∘ E
(Fig. b, c) provides northward transport of subtropical
tracers by means of a quasi-permanent vortex pair located there. The number
of subtropical tracers passing through this gate is much smaller than that
passing through gate VIII (remember the logarithmic scale in
Fig. ). Only a small number of tracers, launched
initially at the very eastern part of the zonal line 37∘ N, were
able to cross the line 42∘ N through that gate, because most of the
eastern tracers passed through the gate VIII to be captured by the near-shore
branch of the Tsushima Warm Current. Most of the tracers passing through
gate VII came from the western and central parts of the material line at
37∘ N. The numbers of subtropical tracers passing through the
central and western gates are much smaller as compared with those passing by the
eastern ones. We distinguish two central gates V and III, 134–135.5 and
132.5–133.5∘ E, respectively, and the western gates I and II
(Fig. c) in the range 130–132.5∘ E. It follows
from Fig. b that the western and central gates collect
subtropical tracers mainly from the western part of the initial zonal line,
from 129 to 133∘ E. In other words, water parcels from its eastern
part (133–137∘ E) practically do not pass through those gates at
the latitude 42∘ N. Thus, the western part of the initial material
line at 37∘ N contributes to all the peaks in the tracer
distribution 42∘ N, whereas its eastern part contributes mainly to
the Tsushima peak.
To visualise the transport paths by which subtropical tracers reach the
northern frontal area we compute so-called tracking maps in Fig. S4 in the
Supplement showing where the subtropical tracers, which crossed eventually
the zonal line 42∘ N, wandered for the whole integration period.
The T–λf plots show when and at
which longitudes the tracers, launched at the zonal line 37∘ N, eventually
crossed the zonal lines (a) 40∘ N and
(b) 42∘ N in the period from 1 March 1995 to 1 March 1996.
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(a) The Lagrangian map documents intrusions of
subtropical water to the southern coast of Russia through the western gate.
Greyscale shows travelling time T in days that it took for
subtropical tracers to reach their locations on the map from latitude
37∘ N to the dates shown. “White” tracers are those which did
not come from latitude 37∘ N for the integration period,
140 days. Locations of available drifters are shown by full circles for 1 day before and after the dates indicated. (b) The drift map
documents a streamer-like northward transport of subtropical water across the
front through a central gate with the help of the cyclone with the centre at
41.5∘ N, 134.4∘ E. Red and green code the waters
that entered the studied area for 2 years through its southern and northern
boundaries, respectively. White indicates the tracers arriving at the coast.
![]()
The drift maps in (a) September and (b) October of
2003 with snapshots of the drifter's track superimposed show how the vortex
pair facilitates transport of subtropical tracers to the northwest through
the eastern gate.
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The T–λf plots in Figs. S2 and S3 in the Supplement show
when and at which longitudes the tracers, launched weekly at the zonal line
37∘ N from 2 January 1993 to 15 June 2013, reached the zonal lines
40 and 42∘ N, respectively. This was designated in Sect. 2 as task 3.
As an example, we show in Fig. a typical T–λf
plot for the tracers crossed eventually the zonal lines 40 and 42∘ N
in the period from 1 March 1995 to 1 March 1996. This demonstrates the eastern
gates VIII and VII (Fig. ) through which the subtropical
tracers cross the corresponding latitudes. The locations of the central and
western gates fluctuate in time, and some gates may be even closed for a
while to the northward transport. The patchiness in the plot means that
subtropical tracers prefer to cross the zonal lines in specific places
(note the peaks in Figs. ) and during specific time intervals. Any
patch with a large number of tracers somewhere, for example at the central
meridional gate, means that a water mass proportional to the size of this
patch passed through the central gate across a given latitude during the
period of time proportional to its zonal size. Thus, the northward transport
of subtropical water across the Subpolar Front occurs in a proportion-like
manner. Specific oceanographic conditions may arise in a given area and at a
given time which produce a large-scale intrusion of subtropical water to the
north by means of mesoscale eddies present there.
To document intrusion of subtropical water there, we compute the
backward-in-time Lagrangian maps for a recent review of
backward-in-time techniques see. This is a realisation of
task 4 in Sect. 2. The basin, shown in Fig. a, is seeded with a
large number of tracers for each of which we compute the time required for a
tracer to reach its location on the map on a fixed date from the latitude
37∘ N. This is what is known as a residence–time map
. The travelling time T in days is shown in greyscale. The map in Fig. a illustrates the
mechanism of penetration of subtropical water northward through the
western gate. A vortex street with four anticyclones is formed in the
fall of 2005 to the north of the Subpolar Front in the western part of the
sea. Their centres are marked in Fig. a by the
triangles at coordinates 39.1∘ N, 131.5∘ E;
39.3∘ N, 130.1∘ E; 40.8∘ N, 131.4∘ E and
41.7∘ N, 130.8∘ E. Subtropical “grey” tracers propagate
along the unstable manifolds of the three hyperbolic points between and
around the eddies to the north a simple description of the notion
of stable and unstable manifolds in fluid flows can be found e.g.
in. The hyperbolic points are marked by crosses in
Fig. a with the coordinates 39.2∘ N, 130.8∘ E;
40.3∘ N, 130.5∘ E and 41.6∘ N, 130.9∘ E.
Thus, the vortex street provides an intrusion of subtropical water towards the
southern coast of Russia. The evidence of at least two anticyclones in the
AVISO velocity field is confirmed by tracks of two available drifters. Their
locations are shown in Fig. a by full circles for 1 day before
and after the date indicated on the map. Drifter no. 56739 has been
trapped by the anticyclone with centre at 39.3∘ N,
130.1∘ E and drifter no. 56746 by the anticyclone with
centre at 40.8∘ N, 131.4∘ E. We have found similar episodes
with penetration of subtropical waters far to the north to the coast of
Russia through the western gate in different years. Peripheries of mesoscale
eddies in the ocean are known to be transport pathways larvae, fish and
other marine organisms (see e.g. ; ; and
references therein). In our case they might be transport for
heat-loving organisms to reach the southern coast of Russia
.
An example of the intrusion of subtropical water through the central gate
across the Subpolar Front is shown in Fig. b with another kind of
Lagrangian map, the so-called backward-in-time drift maps
computed as part of task 4. The red and green
colours in the backward-in-time drift maps code the waters that entered the
studied area for 2 years through its southern and northern boundaries,
respectively. At the beginning of September 1995 a mesoscale cyclonic eddy
to the north of the Subpolar Front with centre at about 41.5∘ N,
134.4∘ E “grabbed” some subtropical water at its southern
periphery and pulled it to the north. In the course of time the streamer-like
intrusion of subtropical tracers reached latitude 42∘ N moving
to the north (Fig. b).
The transport of subtropical waters through the eastern gate VII (see
Figs. and ) occurs mainly due to the
existence of a quasi-permanent vortex pair labelled AC-C in the mean field
in Fig. . This provides a propulsion of some subtropical tracers to
the northwest whereas most of them, propagating along the eastward frontal
jet, join with the Tsushima Warm Current and flow out to the Pacific through
the Tsugaru Strait. The maps in the Supplement (Figs. S5 and S6) document a typical situation with a propulsion of subtropical
water to the northwest in September–October 2003. The study and analysis
of Lagrangian drift maps, computed for the whole observation period, have
shown that frontal eddies facilitated the northward transport of
subtropical water across the Subpolar Front via the central and eastern
gates.
To illustrate how this quasi-permanent vortex pair works we show in
Fig. the drift map for tracers distributed over the area and
advected for 2 months backward in time starting from the dates indicated.
The values of displacements of the tracers, D, in km are shown in
greyscale. The black tracers have been displaced for the same time
considerably as compared to the white ones. To verify our simulation we show
in Fig. positions of drifter no. 35660 by full circles for 2 days before and after the date indicated with their size increasing in time.
The entire track of that drifter, launched on 2 May 2003 at the point
34.925∘ N, 129.3∘ E, is shown in Fig. S7 in the Supplement.
At the beginning of September 2003 (Fig. a) the vortex pair at the
entrance to the gate VII consists of an anticyclone with the centre at about
42∘ N, 137.7∘ E and a cyclone at 41.25∘ N,
138.35∘ E. The cyclone pulls some subtropical water from the
eastward frontal jet round its northern periphery in a streamer-like manner
(see the black tongue in Fig. a). Then this water is wound by the
anticyclone round its southern periphery and propelled northeast.
This is confirmed by snapshots of the track of drifter no. 35660 for
September–October 2003 (see Fig. S6 in the Supplement). Being at the
beginning of September in the main stream (Fig. a), it has drifted
round the cyclone for the first half of September, then round the anticyclone
for the second half of September and at the beginning of October. Eventually
drifter no. 35660 crossed the latitude 42∘ N (Fig. b)
and moved to the north lugged by modified subtropical waters.
The effect of possible altimetry errors on
statistical features of Lagrangian transport
It has been shown statistically that the average northward component of the
AVISO velocity field dictates preferred near-surface transport pathways of
subtropical waters in the central JS. The ability of satellite altimetry to
accurately measure sea level anomalies has vastly improved over the last
decade. However, there are still some measurement errors due to different
reasons that lead to errors in the velocity field provided by AVISO.
In this section we discuss the possible effect of errors in the altimetry
field on our simulation results. The AVISO velocity field has errors as
compared with a “true” velocity field. The difference could be simulated by
adding a noise Δ(u,v) in the velocity data. The question is how
reliable are our statistical simulation results based on an imperfect AVISO
velocity field? All the simulation results, based on the average AVISO
velocity as in Fig. , are supposed to be reliable because the
errors are averaged out for 22 years. As to other simulation results, they
depend on possible noise Δv in the AVISO northward component v+
which could, in principle, change the results but only if the noise were
strong enough to change the direction of the meridional velocity, i.e. if
Δv>|v|. If the average AVISO northward component 〈v+〉 is
large enough as in the areas with dominated northward currents, we do not
expect that it would be changed there significantly under the influence of
noise. So, locations of the preferred transport pathways are not expected to
be changed significantly.
If the average AVISO northward component 〈v+〉 is small,
then two options are possible.
It is small due to domination of a southward current somewhere, i.e.
v-≫Δv. It is clear that possible noise has practically no effect
on northward transport in this case. For example, the forbidden zone in
Fig. a to the south off Vladivostok, where northward transport has
not been observed during the whole observation period, should be located
there at any realistic level of noise because it exists due to the domination of
a sufficiently strong southward jet (VMJ in Fig. ).
The average AVISO northward component 〈v+〉 is small due to a smallness of
the absolute velocity, i.e. u2+v2∼Δv. In this case
northward and southward transports are equalised, and they are small if the
noise is small enough. Such a situation is unlikely along the Subpolar Front
because of the presence of numerous mesoscale eddies along the front where
the absolute velocities are not small.
The influence of possible errors in altimetry-derived velocity field on
concrete mesoscale features has been studied by , and
by analysing how an additional noise
in the advection equations might change Lagrangian coherent structures
revealed by the finite-time and finite-size Lyapunov techniques. Strongly
attracting and repelling individual Lagrangian coherent structures in the
California Current System have been shown to be robust to perturbations of
the velocity field of over 20 % of the maximal regional velocity
. Individual trajectories have been shown to be sensitive
to small and moderate noisy variations in the velocity field but statistical
characteristics and large-scale structures like mesoscale eddies and jets are
not .