A Lagrangian-trajectory study of a gradually mixed ... - Kristofer Döös

B.F. Jönsson et al. / Continental Shelf Research 31 (2011) 1811–1817 1813
eddies of importance for the dynamics of the Baltic. For the present
investigation with focus on the north-eastern Baltic, the remotely
applied boundary conditions at the border to the North Sea do not
give rise to any spurious effects. Given 0.21 0.21 gridded standard
meteorological forcing (sea-level pressure, geostrophic 10 m wind
components, 2 m air temperature and relative humidity, precipitation,
and cloud cover) provided by the Swedish Meteorological and
Hydrological Institute (SMHI) at 3-hour intervals, the circulation
model yields the evolution in time of the velocity, temperature and
salinity fields. As an example of what can be achieved within the
RCO framework, Fig. 2 also includes a long-term average of the
modeled salinity along the central axis of the Gulf of Finland. The
two data sets show a high degree of resemblance to one another,
with the exception of a more pronounced Neva-river plume in the
observations. This discrepancy indicates that the RCO model may
have too large a diffusion (which in turn affects the distribution
of tracers).
In the present study, a trajectory scheme based on results due
to Döös (1995) as well as Blanke and Raynaud (1997) was used to
compute Lagrangian paths from the three-dimensional velocity
fields in the Gulf of Finland provided by the RCO model. The
trajectory algorithm is based on analytical calculations using a
prescribed velocity field which is five-fold more highly resolved in
time than the circulation-model data, from which it is generated
by linear interpolation. This permits analyses of the water-parcel
motion over smaller scales than the model grid by interpolation
of the zonal, meridional, and vertical velocities defined in the
corners of the grid cell.
It should be noted that true Lagrangian trajectories are
only affected indirectly by the sub-grid parameterisation of
viscosity and diffusion implemented within the circulation model.
(An alternative method of water-mass analysis is based on the
tracer equation, which includes diffusion in contrast to what is
the case for true Lagrangian trajectories. However, this diffusion is
not only physical, but also numerical due to, e.g. finite-difference
truncation error.) Following Döös and Engqvist (2007), sub-grid
turbulence affecting the trajectories has thus been parameterized
by adding a random turbulent velocity at each ‘‘high-resolution’’
time step, this in order to include a measure of turbulent diffusion
in the analysis of the present study.
It should furthermore be underlined that the trajectory calculations
can be run in an autonomous fashion with regard to the
circulation model, i.e. off-line. This makes it possible to carry
through the analysis without having to take recourse to excessive
computer resources.
Convection has not been taken into account in the present
study, but the effects of this process have been examined in the
course of a previous investigation (Döös, 1995) by assigning a
water parcel a random depth whenever it enters a convectively
unstable water column. (Like the velocities used to calculate the
trajectories, these convective events also originate from the
circulation model.) This study showed, however, that the effects
of convection did not affect the results to any significant degree.
To examine the behavior of the system, all water parcels
entering the Gulf of Finland from the Baltic and the river Neva
were ‘‘tagged’’ with the aim of determining the origin of the water
masses characterizing the system in ‘‘steady state’’. This refers to
when the number of water parcels released into the system equals
that exiting and when a ‘‘saturated’’ ratio between the number of
trajectories originating from the two sources is established over a
meridional transect half-way into the Gulf. These criteria were
found to be amply satisfied for numerical experiments of an
approximately 5000-day duration, well above the estimated turnover
time of the system (Andrejev et al., 2004b) being 1–2 years.
Every 6 h trajectories were seeded over the exit from the
river Neva as well as over the entire breadth and depth of the
Hanko–Hiumaa transect delimiting the Gulf of Finland from the
Baltic proper. Each trajectory was specified as representing a
volume flux of 100 m 3 s 1 , which, based on a transport of
7–8000 m 3 s 1 entering the Gulf, yielded a sufficient number of
trajectories, in this case around 80 each 6th hour. The sensitivity
was tested by stepwise increasing the volume flux associated
with each trajectory, corresponding to a decrease of the trajectory
‘‘density’’. The threshold when a further decrease of this density
had a degrading effect on the outcome was found to be around 50,
i.e. considerably below the value of 80 trajectories ‘‘seeded’’ every
6 h during our numerical simulations.
All trajectories leaving the system were removed from the
model run at a meridional transect located 5 grid-points west of
the Baltic Proper boundary where source water originally was
tagged (cf. Fig. 1). The rationale behind this procedure was to
reduce the computational costs and to, as far as possible, prevent
trajectories from recirculating, which would have entailed the
risk of multiple tagging of water parcels. When the trajectory
integrations had attained a steady state in the sense described
above, the results were analyzed using techniques to be outlined
in what follows.
3. Mixing and water mass composition
Before proceeding with a discussion of the overall results from
the numerical experiments, we examine some specific features in
order to judge whether the model can be regarded as performing
in an adequate fashion. The underlying rationale is that even if a
circulation model yields more-or-less correct overall results,
considerable local irregularities may arise, in particular adjacent
to the boundaries of the system. In the larger Baltic perspective,
the Gulf of Finland can be looked upon as a marginal area, and
thus the modelers in the course of developing the RCO formalism
did not focus specifically on this region, even though the discharge
from the river Neva potentially could create anomalies
here. The model results were thus verified by collating the timeaveraged
RCO-generated velocity fields with the results from
earlier studies. One interesting area for comparisons of this type
is located close to Moshnyi Island in the inner part of the Gulf,
where Andrejev et al. (2004b) reported exceptionally long residence
times of the water. This state of affairs also manifests itself
in the present circulation-model results, assuming the form of a
prevalence of stable, highly persistent eddies in the area. In
general, the time-averaged RCO velocity fields employed for
calculating the trajectories proved to be in agreement with
well-known transport patterns (Palmén, 1930) characterizing
the Gulf of Finland. Thus high-saline water from the Baltic Proper
enters the Gulf as a deep boundary current adjacent to the
Estonian coast, whereas transports associated with the river Neva
discharge tends to take place on the Finnish side of the Gulf.
Once each experiment had been concluded, analysis of the
trajectory behavior was undertaken by calculating a mixing ratio
R defined as the number of trajectories from Neva divided by the
total number of trajectories within each grid-box. This was done
for each cell in the Gulf of Finland modeling domain, the value
R¼1 representing a situation where all water originated from the
river Neva, the value R¼0 indicating the presence of only Baltic
water. To investigate the relative water-mass composition along
the main axis of the Gulf of Finland, this distribution was
averaged across the Gulf. By also carrying through a vertical
integration, it proved feasible to construct a Hovmøller diagram
representing the evolution of this water-mass distribution along a
section in the Gulf of Finland as a function of time, cf. Fig. 3. From
this diagram it can be concluded that a saturated ratio between
the number of trajectories originating from the two sources was