Introduction
Lagrangian particle tracking is a natural choice when origins or
destinations of drifting objects (or water bodies) need to be
known. Such methods have been developed for a wide range of
applications see. Examples from oceanography
are simulations of physical dispersion , possibly augmented by specific source and sink
terms e.g.. In ecosystem modelling, Lagrangian
transport models have been employed to better understand the
process of non-indigenous species invading an ecosystem
, the risk of toxic algae blooms
or larval transport and connectivity being crucial to spatial
fishery management e.g.. Lagrangian transport simulations also provide a basis
for more comprehensive individual-based models of fish recruitment
e.g..
Obviously, the quality of Lagrangian drift simulations has
a particularly high practical relevance in the context of emergency
operations like search and rescue or organization of
efficient combating of oil spills (;
Maßmann et al., ). Modelling of surface drifter trajectories is
particularly challenging as many of the input factors needed are
poorly known. Often drift properties of search objects can only be
estimated . The present study refers to a drifter
experiment conducted in the inner German Bight (North Sea) during
May–July 2015. Corresponding offline drift simulations based on
archived currents from two different models were undertaken to
assess the degree of uncertainty that must reasonably be expected
in this region.
The surface drifters deployed are ideal in the sense that their
exposure to a direct aerodynamic force from wind leeway or
windage; seems negligible. However, also Eulerian
surface currents used can be a major source of uncertainty
. The circulation model BSHcmod, which this study
mainly focuses on, is run operationally. In cases of necessity,
drifter simulations will be based on a regridded archived version
of model predictions with near-surface currents representative of
a 5 m deep top layer. Therefore, even for an ideal surface
drifter, introducing a direct wind drag can be helpful as a means
of compensating insufficient vertical resolution of hydrodynamic
currents. The second hydrodynamic model employed in this study,
TRIM, was set up with a 1 m deep top layer. Comparing drift
simulations based on outputs from the two different models helps
assess uncertainties possibly related to the vertical resolution of
near-surface currents.
More complex impacts of winds on surface currents may be mediated
via waves . found
evidence that predictability of drift trajectories can be improved
by the inclusion of numerical wave modelling. On the other hand,
Stokes drift and other wave effects are often neglected in
operational systems. According to , the main
reason for this is that wave processes are already taken into
account by empirically tuned windage coefficients that summarize
changes of an object's trajectory induced by combined impacts of
both winds and waves. The situation can differ in near-shore
regions, where wave refraction directs wave-induced transports
towards the coast .
A key objective of this study is checking whether explicit
inclusion of Stokes drift calculated with a state-of-the-art wave
model (WAM) improves drift simulations. Assessing the necessity to
distinguish between effects of direct wind drag and Stokes drift is
essential to avoid overparametrization. Waves and resulting Stokes
drift were calculated using the wind forcing also employed for
hydrodynamic simulations with TRIM. However, we did not explore
effects of including wave–current interactions into hydrodynamic
simulations .
Horizontal grid resolutions of the two hydrodynamic data sets
(900 m in BSHcmod and 1.6 km in TRIM) allow for
a proper representation of mesoscale eddies in the region of
interest. However, simulations may miss relevant sub-mesoscale
processes. According to the underestimation of
eddy kinetic energy by Eulerian flows is a common finding of many
model validation studies. This deficiency could be fixed by
a transition to an advection–diffusion equation, introducing an
additional stochastic random walk term. In this context,
specification of the proper eddy diffusivity as function of grid
resolution poses a major problem. There are, however, also concerns
regarding the simple theoretical concept. For the
advection–diffusion approach to be valid, a spectral gap should
separate processes on the scale resolved from sub-grid-scale
processes. Such a gap may often not exist see,for
instance.
compared the statistics of drifter observations
in the North Atlantic with those of drift simulations based on
Eulerian velocities from a model with about 6 km horizontal
resolution. Without a stochastic model of sub-grid-scale actions,
they found simulations to underestimate eddy energy. Simulated
absolute dispersion being too low was also reported by
evaluating drifters deployed in the Baltic
Sea. Referring to global ocean data, tuned random
turbulent velocity in their drift model to achieve better agreement
between relative dispersion of simulated trajectories and
corresponding observations. However, they found this approach was
too simple for a reasonable reproduction of Lagrangian properties.
More sophisticated analyses of the relative dispersion of pairs of
particles try to distinguish the regimes of “local
dispersion” driven by eddies comparable in size to the distance
between two drifters and of “non-local dispersion” driven by
eddies with scales much larger than this distance
e.g.. conducted such an
analysis for data from the Grand Lagrangian Deployment experiment
(GLAD), in which more than 300 drifters were deployed in the Gulf
of Mexico. Drifter launch positions spaced from 100 m to
15 km apart allowed to study sub-mesoscale dispersion
characteristics in great detail. However, referring to experimental
data in the south-western Gulf of Mexico, show
that for large initial distances the probability density functions
of pair separations get dependent on prevailing mesoscale
circulation patterns. This aspect seems particularly relevant for
the present study. Variations of the residual current regime in the
inner German Bight can very well be approximated in terms of only
2–3 degrees of freedom, depending on prevailing winds
. Tidal currents dominate short-term transports.
The data available for this study (six drifters, tracked between 9
and 54 days) are insufficient for studying features of
oceanic turbulence. Therefore, in the present model validation
study, stochastic simulation of sub-grid-scale processes will not
be considered. provide an example that even an
accurate reproduction of mean drifter pair separation does not
necessarily imply good agreement between observations and
corresponding simulations. According to , models
used in the aforementioned GLAD experiment in the Gulf of Mexico
had limited success capturing the observed drift
patterns. provide a list of typical separation
rates in different regions worldwide. For an experiment in the Ria
de Vigo estuary in north-west Spain, reported simulation
errors that were relatively small compared to those typically found
in the open ocean. This study tries to provide a realistic estimate
of how reliable operational forecasts in the German Bight, another
shelf sea region, can be expected to be. This includes gaining
preliminary indications for regions where the deterministic part of
a model needs improvement.
Drifters deployed in May 2015.
No.
Type
Start
End
Length
Dist
ΔT
Time (UTC)
∘ E
∘ N
Time (UTC)
∘ E
∘ N
(km)
(km)
(days)
1
MD03i
19 May (12:31)
7.5216
54.2160
2 Jun (21:12)
8.8338
54.5180
1032.1
91.7
14.4
2
MD03i
21 May (17:13)
7.1484
55.0752
25 May (09:47)
7.3080
55.1360
87.4
12.2
3.7
3
MD03i
21 May (17:13)
7.1480
55.0750
25 May (09:59)
7.2526
55.1160
85.7
8.1
3.7
4
MD03i
21 May (17:36)
7.1426
55.0786
24 May (15:00)
7.2960
55.0626
66.6
10.0
2.9
5
MD03i
27 May (09:49)
5.9126
54.3752
15 Jul (01:28)
8.4680
55.1232
1264.0
184.4
48.7
6
MD03i
27 May (16:01)
6.0446
54.2024
20 Jul (23:15)
8.0944
55.1930
1467.7
172.1
54.3
7
ODi
30 May (08:36)
6.7516
54.6712
8 Jun (09:59)
8.2360
55.7702
273.2
154.6
9.1
8
ODi
30 May (12:09)
6.7476
54.2554
9 Jul (19:15)
8.5282
55.2812
1203.0
161.8
40.3
9
ODi
31 May (07:46)
7.8816
54.0842
24 Jun (03:28)
8.8360
54.1316
844.3
62.6
23.8
Type: two drifter types used
(see Fig. ).
Length: sum of the lengths of
linear segments connecting observed drifter locations. Dist: linear
distance between the first and last drifter locations
observed. ΔT: days between the first and the last observation. Drifter nos. 2, 3 and 4 travelling for only few days were ignored for this study.
The paper is organized as follows: Sect. documents
how observations were taken (Sect. ) and
how corresponding model simulations were performed
(Sect. ). Section
describes two data sets used for characterizing residual current
variability in the German Bight on a daily basis. Results
(Sect. ) are presented in two parts:
Sect. provides a synoptic description of
all drifters deployed and places observations into the context of
ambient atmospheric and marine conditions;
Sect. provides the analysis of how
corresponding model simulations match observations. First, full
simulated trajectories are presented using currents from TRIM or
BSHcmod, the latter also combined with wind drag and Stokes drift,
respectively. A more detailed evaluation of model performance is
then based on subdividing drift trajectories into segments of
25 h length. Results are discussed in
Sect. ; main conclusions are provided in
Sect. .
Drifter types MD03i (panels a and b) and ODi
(panel c) used during the experiment. Both
drifter types were photographed shortly after launch so that the drogues had
not yet settled.
Results
Observations
Figure places drifter schedules into the context
of variable atmospheric winds and marine residual currents. Time
bars show travel times of all nine surface drifters. To facilitate
a synopsis of synchronous drifter movements, the time coordinate
was segmented, subjectively assigning different colours to periods
with different drift behaviour. In this context, a continuous
daily index was introduced, counting days since when the first
25 h simulation for drifter no. 5 was started on 27 May at
13:00 UTC (see Table S1). To represent
atmospheric forcing used in BSHcmod and TRIM, respectively,
simulated 10 m winds at 55∘ N and
7∘ E near the centre of the study area are shown
together with observations on the island of Heligoland
(54.10∘ N,7.53∘ E). All wind vectors
represent 25 h means and are plotted at the centre of the
respective 25 h interval starting at
13:00 UTC. The winds from three different data sources are
in reasonable agreement with each other.
Figure also includes the representation of (a)
the subjective classification of daily mean BSHcmod surface
currents and (b) the first principal component (PC1) of
25 h mean currents simulated with a 2-D version of TRIM
(see Sect. ). Positive values of
PC1 (i.e. amplitudes of the anomaly pattern shown in
Fig. b) indicate a strengthening of the mean
cyclonic circulation; negative values refer to its weakening or
even reversal. Although the two representations of residual
current variability have different roots (different models,
surface layer vs. vertical means, subjective vs. objective,
different atmospheric forcing), a clear correspondence between the
two representations is discernible. Cyclonic hydrodynamic regimes
and positive values of PC1 tend to coincide with winds from the
south-west, while anticyclonic circulations and negative
PC1 values are mainly driven by winds from the north-west
.
Figure shows six observed drifter
trajectories, disregarding the tracks of drifter nos. 2, 3
and 4 that were recorded for just a few days. A feature shared
by at least four drifters (nos. 5, 6, 7 and 8) is
a general displacement towards the north-east. Concerning
drifter nos. 6 and 8, an interesting special situation occurs
during 7–16 June (days 11–20). Figure
shows the distance between the two drifters as a function of
time. At the deployment of drifter no. 8 (30 May, day 3),
drifter no. 6 had already travelled for nearly 3 days and was
located at a distance of about 20 km from drifter
no. 8. During the next 4 days, the two drifters further
separated. On 4 June (day 8), however, they suddenly started
converging quickly. From 8 June (day 12) onward, drifter nos. 6
and 8 stayed at a distance of less than 2 km for
nearly 10 days. Just after the distance had reached its minimum
(about 800 m), the drifters started to separate
again. Other short periods of fast convergence occurred later but
never again did the two drifters come that close. During the last
8 days of their joint journey (starting at around day 35), the
distance between the two drifters showed particularly large
oscillations (Fig. ).
Figure provides magnitudes of velocities
for drifter nos. 5, 6, 8 and 9, calculated from
velocity vectors smoothed using a 25 h moving average of
hourly data. Drifter movements are particularly fast in the
beginning (days 5–6), brought about by persistent south-westerly
winds and a corresponding cyclonic circulation at that time
(Fig. ). Other periods with particularly fast
movements occur around day 35 and days 42–43. In the former case,
strong winds from the south-east trigger a very fast separation of
drifter nos. 6 and 8 (see Fig. ). In
the latter case, north-westerly winds give rise to extreme drift
speeds in the south-east direction. Drifter nos. 5 and 8 are
already in near-shore areas at that time
(Fig. ).
In their central parts, drifter trajectory nos. 5, 6
and 8 exhibit variable drift directions but mostly moderate
drift velocities (Fig. ). Although
trajectories are complex (Fig. ), they
show resemblance, explicable by moderate distances between the
three drifters. In the beginning of its journey, drifter no. 9, having
started further away in the south-east of the domain, behaves
differently (days 4–9;
see Fig. ). A much better coherence with
other drift paths is found during days 11–20 (7–16 June)
characterized by the close proximity of drifter nos. 6
and 8. The journey of drifter no. 1 has just a small overlap
with those of other drifters; the drifter is soon trapped within
the entrance to tidal basins (Fig. a).
Further details of observed trajectories will be addressed in
Sect. together with a presentation of
corresponding simulations.
Simulations
Figures in the Appendix compare drift simulations based on TRIM
(Fig. ) with three different
approaches based on BSHcmod. The three setups are (a) just Eulerian
currents (BSHcmod; Fig. ), (b)
Eulerian currents plus windage (BSHcmod + W;
Fig. ) or (c) Eulerian currents plus
Stokes drift (BSHcmod + S;
Fig. ). Numerical data displayed in
the graphs are provided in the Supplement. It appears that combining
BSHcmod currents for a 5 m depth surface layer with either
windage or Stokes drift brings corresponding simulations closer to
both observations (Fig. ) and simulations
based on Eulerian surface currents from TRIM with 1 m
vertical resolution
(Fig. ). A key effect of the
inclusion of extra wind or wave effects is the intensification of
westward transports in agreement with wind directions that occur
most frequently. One should remember that achieving reasonable
agreement between overall strengths of these transports in
simulations and observations was the criterion which led to the
specific values we assigned to α or β in
Eq. () (see Sect. ).
Analysing short-term drifter displacements on a daily basis enables
a more detailed assessment of model performance. Simulations of
25 h drift paths were initialized
every day on days 0–53 at 13:00 UTC. Full sets
of corresponding plots are provided in the Supplement. The first
collection (SM1 in the Supplement) shows 25 h drifter displacements that were
observed. The second (SM2 in the Supplement) compares corresponding simulations based
on either BSHcmod or TRIM Eulerian currents with these
observations. The third (SM3 in the Supplement) is similar except that BSHcmod
currents are complemented by parametrized windage
(BSHcmod + W). Finally, the fourth collection (SM4 in the Supplement) compares BSHcmod
simulations including either windage (BSHcmod + W) or Stokes drift
(BSHcmod + S).
Drawing on the material from SM3,
Figs. –
present results for 12
selected days, comparing simulations based on TRIM surface currents
with those based on BSHcmod + W. Each panel combines all drifters
that are available at the respective time. Observed drifter
displacements are coloured in agreement with Table S1.
Concentrating on the four drifters that travelled longest, bars in
Fig. a show daily values
of separation between observed and simulated end points of
25 h drift paths, referring again to simulations with
either TRIM or BSHcmod + W. To show the relative importance of drift
errors, total distances covered according to observations or
simulations are also
included. Figure d shows
the angles between observed and simulated drifter
displacements. Time series (25 h means) of wind speeds used
in TRIM and BSHcmod (and also BSHcmod + W) are shown in
Fig. b together with
surface Stokes drifts from wave model
WAM. Figure c copies
observed Heligoland wind vectors from Fig. .
The following description highlights some key aspects of drifter
observations and concurrent simulations during different
sub-periods of the experiment.
Observed 25 h drift paths (coloured in agreement with
Table S1) are contrasted against concurrent simulations (black) based on
BSHcmod + W (a–d) or TRIM (e–h). For 4 selected days,
panels combine all drifters observed at the time of the plot. All drift
distances were converted into 25 h mean drift velocities. Note that
the length scales shown do not correspond with the spatial scale of the
geographic map. Vectors in each panel's top right corner indicate the mean
wind velocity vector at 55∘ N and 7∘ E derived from the
respective atmospheric model used.
Continued from Fig. .
Continued from Figs. and .
Days 0–6 (27 May–2 June):
This is a period characterized by cyclonic residual currents increasing in
strength (Fig. ). Driven by winds mainly from south-west,
drifters move fast towards a north-eastern sector. Simulated drift distances
agree well with observations. Appreciable errors for TRIM arise from moderate
directional deviations in combination with large displacements
(Fig. f).
On day 2, neither model simulates the neighbouring drifter nos. 5 and 6 to move into different directions (SM3). On day 3 (Fig. a and e), only BSHcmod + W captures the deviant direction of drifter no. 7. Comparing simulations based on BSHcmod + W (Fig. a) with those based on BSHcmod (SM2) reveals that the deviant simulation of drifter no. 7 arises from spatial variation of BSHcmod currents. By contrast, inclusion of more large-scale windage affects all drifters tracked in a very similar way. On day 6 (Fig. b and f), the again deviant movement of drifter no. 7 (now rotated to the opposite direction) is no longer reproduced by BSHcmod + W.
For drifter no. 1, simulations are generally poor. On days 3–5, the drifter already enters the complex coastal bathymetry which is insufficiently resolved in both models (e.g. Fig. a and e).
Days 7–10 (3–6 June):
The strong cyclonic regime declines, strong south-west winds first cease and then blow from different directions (Fig. ). Observed displacements of drifter nos. 5, 6 and 8 take a minimum on days 7 or 8 (Figs. and a). On day 7, major directional errors occur under variable wind conditions (Figs. c, g and d). Only drifter no. 9 rotates its movement from north-east to north-west already on day 7; all other drifters follow on day 8 (Fig. d and h). Speed of drifter no. 9 shows a strong peak on day 8 (Fig. ). Observed drifter displacements seem to decrease with distance from the coast, a variation not resolved in simulations (Fig. d and h). Also considering Stokes drift does not help reproduce this spatial gradient (SM4). Sub-mesoscale differences in drift speed (e.g. day 8; Fig. d) and direction (e.g. day 10; Fig. a) giving rise to the fast convergence of drifter nos. 6 and 8 (Fig. ) remain unresolved in both models. Neither model captures the special behaviour of drifter no. 7 which continues its fast movement towards northern directions (compare Figs. d and d with Fig. d).
Days 11–14 (7–10 June):
Winds from the north-west or north trigger an anticyclonic circulation (Fig. ). On day 11, the inclusion of windage greatly reduces errors of BSHcmod simulations for drifter nos. 6, 8 and 9 (compare Fig. b with SM2), mainly due to improved drift directions. Only for drifter no. 5, moving much slower despite its proximity to other drifters, adding windage leads to drift velocity on day 11 being greatly overestimated (Fig. ).
Note that after about day 12 both observations and simulations for the two drifters (nos. 6 and 8) are more or less plotted on top of each other (applies to Fig. c and g, for instance, and various plots in the Supplement).
Days 15–16 (11–12 June):
For a short time, the circulation returns to cyclonic orientation (Fig. ). BSHcmod+W simulations greatly underestimate drift velocities to the north-west and tend to even cease on day 16 (Figs. and c). Due to low winds (from north-east or east), additional windage could not eradicate this deficiency. TRIM simulations perform slightly better (Fig. g).
Days 17–20 (13–16 June):
During days 17–19, the circulation is anticyclonic, driven by north-westerly
winds (Fig. ). Simulations based on either model
consistently produce drift velocities that are markedly rotated to the left
of observations (Figs. d, h and
d).
On day 20, the wind direction turns to the south-west in BSHcmod or west in
TRIM (Fig. ); the
residual circulation becomes cyclonic for 1 day. Under transitional
conditions, directional errors are particularly high in TRIM
(Fig. d).
Days 21–26 (17–22 June):
Residual circulation gradually changes from anticyclonic to cyclonic (Fig. ). During days 21–23, considerable errors in both BSHcmod + W and TRIM simulations resemble each other to a surprising degree (e.g. Fig. a and e). Except for drifter no. 9, drift directions are typically rotated to the left of observations (Fig. d). From about day 22 onward, drifter nos. 6 and 8 start separating again (Fig. ). Expectedly, neither model reproduces sub-grid-scale differences in speed (day 22; SM3) or direction (day 23; Fig. a and e).
Starting on about day 22, fast movements mostly in line with prevailing wind directions (e.g. Fig. a and e) and greatly exceeding simulated counterparts (Fig. ) suggest that drifter no. 9 experienced some problem with its drogue.
Days 27–28 (23–24 June):
On day 27 (Fig. b and f), strong winds from the north-west give rise to southern transports. Substantial differences between speeds of neighbouring drifter nos. 6 and 8 (unresolved in simulations) imply a short period of their fast convergence (Fig. ). BSHcmod + W simulations greatly benefit from the inclusion of windage (Fig. b and SM2), while TRIM simulations are more consistent even without windage (Fig. f). On day 28, winds abate.
Days 29–33 (25–29 June):
This is a period with variable wind directions. Drifter displacements are
generally underestimated (Figs.
and a), observed northward
transports (e.g. for drifter no. 8; Fig. e) are not
reasonably reproduced based on BSHcmod + W
(Fig. e) and even less based on TRIM
(Fig. e).
Day 34 (30 June):
Drifter nos. 6 and 8 converge quickly (Fig. ), caused by a fast west–northwest movement of drifter no. 8, not shared by drifter nos. 5 and 6 (SM3). No model resolves these substantial differences.
Days 35–38 (1–4 July):
Drifter nos. 5, 6 and 8 all move quickly into northern or north-western directions (Fig. ). Largest drifter displacements occur on day 35 (see Figs. c, g and ) with strong winds from the south-east. Drifter no. 8 moving faster and more aligned with wind direction than its companion drifters could possibly indicate problems with the drogue.
On day 36, TRIM (but not BSHcmod) assumes the wind to persist (Fig. or SM3), which results in a substantial overestimation of drifter displacements (Fig. a). According to observations at Heligoland (Fig. ), winds used by BSHcmod + W seem more realistic.
Under low wind conditions on day 37, BSHcmod + W (to a lesser degree also TRIM) very much underestimates drift speeds (Fig. ). On day 38, the process of drifter nos. 6 and 8 coming to rest is well reproduced in both models (SM3).
Days 39–41 (5–7 July):
Freshening south-westerly winds strengthen a cyclonic circulation (Fig. ). The extremely fast movement of drifter no. 8 is remarkable in reaction to this forcing (Figs. e and c). Simulations for drifter nos. 5 and 6 perform well, while the behaviour of drifter no. 8 cannot be reproduced.
Days 42–43 (8–9 July):
The wind turning from south-west to north-west implies a fast transition from a cyclonic to an anticyclonic residual current regime (Fig. ). Models perform well for drifter no. 6, while simulations for drifter no. 8 are again very poor (Figs. c and d, h).
Days 44–53 (10–19 July):
Only drifter nos. 5 and 6 are left; both of them are already located in coastal waters. Extra large differences between wind velocities used in BSHcmod and TRIM occur (Fig. b). Effects of a sudden reversal of the mean wind direction between days 50 and 51 are reasonably reflected in both models.
(a) Bars indicate distances between observed end points of
25 h drift paths and corresponding simulations based on either
BSHcmod + W or TRIM. All drift errors, coloured and labelled in terms of
days since 27 May (13:00 UTC), are assigned to the centre of the
respective 25 h period. In addition, lines show total distances
travelled. (b) Wind speeds used in the two models and surface Stokes
drifts obtained from wave model WAM. Data were extracted for the central
example location (55∘ N and 7∘ E).
(c) Heligoland winds, copied from
Fig. . (d) Angles between observed and simulated
tracer displacements. Throughout the figure, all values represent
25 h averages.
Distribution of model errors in 25 h drifter simulations. Histograms
are based on 164 simulations in total for drifter nos. 5, 6, 8 and no. 9.
Referring to drift simulations based on BSHcmod + W and TRIM,
respectively, panels (a, b) evaluate spatial separations shown in
Fig. a. For the same set of 164
simulations, panels (c, d) evaluate directional errors from
Fig. d. Red lines indicate median
values (4.6 and 5.4 km in a, b; -15 and 7∘ in
c, d).
Discussion
The model validation study suggests the assumption that inclusion
of either wind drag or Stokes drift compensates insufficient
vertical resolution (5 m) of surface currents in archived
BSHcmod output. Magnitudes of TRIM surface currents, representative
of a layer of 1 m depth, were generally similar to those
observed (Fig. a). In
many cases, however, 25 h simulations based on BSHcmod + W
outperformed those based on TRIM, in other cases (e.g. days 13–16)
TRIM simulations were in better agreement with observations
(Figs. c, g or
).
In several other studies e.g., simulated marine surface currents
were found to be too small, possibly also due to insufficient
resolution of the marine surface layer. As a side effect,
predictions may be particularly good when marine currents and winds
are nearly parallel . The drift component
most underestimated based on just BSHcmod Eulerian currents was
a displacement towards the east, along the most frequent wind
directions (compare Figs.
and ). This deficiency could
very effectively be remedied by adding direct effects of winds or
waves. However, during periods when anticyclonic residual currents
prevail (along with winds from the north-west, for instance),
currents will generally not be in the direction of winds
(e.g. day 18; Fig. d and h),
unlike the situation with south-westerly winds driving a cyclonic
circulation (e.g. day 3;
Fig. a and e). Erroneous residual
surface currents in the inner German Bight can therefore not always
be fixed by simply adding windage or Stokes drift.
In both BSHcmod + W and TRIM simulations, drifter displacements were
often rotated to the left of their observed counterparts, e.g. during days
13–23 (see Figs. d or
d and h). A parametrization of wind-induced
Ekman drift (Röhrs and Christensen, 2015) might be explored as
a means to remedy such model deficiencies including lacking representation
of the Coriolis–Stokes drift (Hasselmann, 1970; Polton et al., 2005) driven
by ocean surface waves. Fig. shows error distributions
that combine all data from
Fig. a and d,
respectively. Median errors of drifter displacements are of the order of
5 km for both BSHcmod (4.6 km) and TRIM
(5.4 km). BSHcmod + W tends to have negative directional errors
(median value of about 15∘ to the left of observations), while
the median directional error for TRIM is about 7∘ to the
right. Negative deflections of BSHcmod + W simulations happen to
coincide with what one would expect from a simple parametrization of
windage (or Stokes drift) that neglects effects of Coriolis force. However,
distributions in Fig. combine simulations under very
different wind conditions, and directional biases are not permanent. In many
cases (e.g. day 18 in Fig. d and h),
directional errors of the two simulations resemble each other. One must
therefore be very careful to interpret shifted median values in terms of
specific model deficiencies. Differences between Fig. c
and d are probably not statistically significant, so we refrained from
trying to incorporate and tune additional effects of Coriolis force.
Drifter nos. 5, 6 and 8 played a central role in this study
because their trajectories overlapped for 40 days, enabling
tentative conclusions regarding spatial scales that affected long-
and short-term drifter displacements. Wind fields resolved in
numerical models (and also corresponding fields of Stokes drift)
tend to vary smoothly on a regional scale. A substantial impact of
winds on surface currents may be one of the reasons why simulated
trajectories resemble each other more than corresponding
observations. However, also observed drifter paths show similarities
that point to the impact of large-scale forcing.
Due to bathymetric constraints and different scales of relevant
processes, spatial variability of marine currents tends to be
higher than that of wind fields . However, our
study did not show clear effects of the higher resolution in
BSHcmod regarding either space (900 m compared to
1.6 km in TRIM) or time (15 min compared to
1 h in TRIM). Both TRIM and BSHcmod are unable to reproduce
the specific behaviour of drifter no. 7 during days 7–11, for
instance (Figs. d,
and ). This could suggest that
some relevant aspects of near-shore transports are not properly
represented in both models. Surprisingly small effects of
resolutions in both space and time on the metrics for Lagrangian
predictability were also reported by .
Drifters will separate even if they are released from about the
same location. start with O
(5–10 m) initial separations to resolve initial
non-local dispersion with exponential growth of the mean
square pair separation, driven by eddies larger than the distance
between the two drifters. In the present field experiment,
simultaneous deployments of drifter nos. 2 and 3 were
originally intended to study an example of drifter dispersion. The
two drifters, both tracked over 3.7 days, stayed very close
together for some time until they abruptly started to
separate. However, this separation might have been triggered by an
unobserved interaction with the research vessel. Due to such
concerns, drifter nos. 2 and 3 were excluded from the present
analysis.
Fortunately, drifter nos. 6 and 8 offered another opportunity
to estimate predictability of drift trajectories. The minimum
distance of only 800 m qualified the two drifters as a
“chance pair” e.g.. Note, however, that
drifter nos. 6 and 8 were of different types
(see Table ) so that relative dispersion measured may not
necessarily reflect diffusivity of the flow. On the other hand, the
two drifters travelling jointly for about 10 days in a sense
justifies the assumption that consequences of different designs
were not essential. Also Fig. b and c provide
no evidence for systematic differences in observed drift speeds
during the period of interest.
From the perspective of a model with either 900 m (BSHcmod)
or 1.6 km (TRIM) grid resolution, the locations of
drifter nos. 6 and 8 almost coincided for about 10 days. The
subsequent separation rate of about 3 kmday-1
(according to visual inspection of Fig. )
indicates a lower bound of prediction uncertainty under these
specific conditions. An independent second estimate can be obtained
considering the period when the two drifters converged
(days 8–11). Assume that modelling was undertaken to determine
where an item collected on day 11 came from. Looking 4 days back
in time, the two drifters (nos. 6 and 8) have separated by about
20 km, so that the uncertainty estimate (about
5 kmday-1) even exceeds the above value. However, the
separation rate is still much lower than that reported by
their Fig. 3 under open ocean conditions near
the Kuroshio current, considering a similar constellation with two
drifters that separate after staying close for a couple of
days. A wide spectrum of typical separation rates in different
regions worldwide provided by also shows
systematically larger values.
Error bounds estimated from drifter convergence/divergence will
combine with model deficiencies that at least theoretically could
be eliminated by model improvement or calibration. However, the
above error estimates roughly fit into the general range of
simulation errors found in this study
(Fig. a and b). tried to
reproduce observed drifter trajectories with a Lagrangian
stochastic model based on Eulerian background velocities derived
from high-frequency (HF) radar observations interpolated to a regular 2×2 km2 grid. Substantial discrepancies exceeding
the expected level of HF radar measurement errors were found in
occasional periods. On average, the separation between
corresponding centres of gravity was found to be about 5 km
after 24 h, a value that compares well with estimations
from the present experiment. It remains as an open question whether
the quality of predictions would be better with HF radar
observations replacing output from numerical
models. found skills in predictions based on
currents from either a circulation model or HF radar
comparable. Both and used
hourly average velocities from HF radar observations, i.e. the same
temporal resolution as in the present study. Higher-resolution
e.g. 20 min; measurements of
currents could possibly better capture short-term fluctuations and
enhance variability in drift simulations.
According to and , “chance
pairs” should possibly be distinguished from pairs of drifters
intentionally launched together, because their behaviour may depend
on specific hydrodynamic conditions. An interesting question is
what characterizes the 10-day period when drifter nos. 6
and 8 stayed close together. The drifter convergence (days
7–10) coincided with the transition from a cyclonic to an
anticyclonic residual current circulation
(Fig. ). The anticyclonic regime forced by winds
from mainly the north-west dominated days (11–20), except for a short
episode (days 14–16) with very low winds and a circulation
returning to the cyclonic orientation for about 1 day. Drifter nos. 6 and 8 started separating again when
residual currents gradually returned to an either indifferent or
cyclonic circulation, a process probably best represented in the
time series of PC1 in Fig. . Thus, it seems that
both convergence and divergence of the two drifters coincided with
reorientations of the hydrodynamic regime.
The present data are insufficient for a discussion of to which
extent the drifters' observed responses to changing winds and
residual currents depend on drifter location. Based on model
simulations, however, there are promising techniques to better
describe regions within which separation for drifters can be
expected. Identification of Lagrangian coherent structures (LCSs) is
a field that developed recently
e.g.. applied the method to identify
transport barriers for drifters in an estuary;
discuss how such techniques could be used for optimizing drifter
deployment in the sense of maximizing their
dispersion. employed LCSs to illustrate how
mesoscale circulation shapes near-surface transports in the Gulf of
Mexico.
A couple of different processes can be relevant for an exchange of
energy and momentum between surface waves and underlying mean
currents . Under open sea conditions,
probably the most important process affecting near-surface drifters is
the Stokes drift which arises when backward motions beneath the
troughs of surface gravity waves do not fully compensate forward
motions beneath the crests. However, a key observation from our
simulation experiments is that for surface drifters the inclusion
of an explicitly simulated Stokes drift did not produce an added
value beyond a simple parametrization of wind drag in terms of
10 m winds. According to
Fig. b, wind speeds used
as forcing for either TRIM or BSHcmod are both highly correlated
with Stokes drifts calculated with wave model WAM (based on the
same wind hindcast also used as forcing for TRIM). This similarity
agrees with results reported by their Fig. 7,
for instance.
From experimental data, estimated Stokes drift to
be about twice as large as effects of direct wind drag. However, as
the roles of direct wind drag and Stokes drift are difficult to
disentangle, we did not conduct experiments with mixtures of the
two processes. For the factors α or β, we chose in
Eq. (), drift components from either windage or Stokes
drift were similar most of the time
(Fig. ). Validating modelled wave effects
based on four surface drifters deployed near the Grand Banks
(Newfoundland), considered both processes in
combination. They also found simulated Stokes drift to be linearly
related to wind velocities, so that it seems difficult to decide
whether the approximately 21 % decrease of separation between
modelled and observed trajectories after 1 day are really
attributable to Stokes drift effects. According to
, the impracticality to separate Stokes drift
effects from an empirically parametrized direct wind drag is
a major reason why Stokes drift is neglected even in most
operational search and rescue modelling systems, where a realistic
assessment of existing uncertainties and their origin is of utmost
importance.
found Stokes drift to be about 1.5 % of
wind speed; report a value of 1.6 %. These
values agree with the ratio (0.3/20) of the scales annotated on
the two y coordinates in
Fig. b. For low wind
conditions, the relative importance of Stokes drift decreased (again
in agreement with the results of ), but in these
cases the overall contributions from winds and waves are small
anyway.
In particular, growing young wind seas forced by local winds
typically produce strong surface Stokes drifts that decline fast
with depth e.g.. developed
an approximate method to efficiently calculate this near-surface
shear, underestimated by the common assumption of a monochromatic
profile. Based on these formulas, calculated in
the context of a drifter experiment in the Barents Sea and Norwegian
Sea that an average Stokes drift of 8.9 cms-1 at the
surface contrasted with an average of 3.7 cms-1 at
1 m depth. For the present study, we neither applied
theoretical profiles nor conducted an in-depth model
calibration. However, in the light of the above numbers, the
50 % factor α in Eq. () we chose for
BSHcmod + S seems to be a reasonable value for drifters representing
a surface layer of about 1 m depth. Vagueness of the factor
corresponds with that of the 0.6 % windage factor β
used in BSHcmod + W. Given the limited data, in both cases, even most
careful calibration would not lead to robust estimates. The
criterion we applied for selecting α or β is that the
overall eastward displacement of a drifter's location should
roughly agree with that observed. A convincing confirmation of our
selection was that the strength factors we chose worked
consistently well for all drifters.
Similarity between simulations with either wind drag or Stokes
drift (see SM4) is an implicit consequence of how parameters were
chosen. According to Fig. , a period with
major differences between contributions from either windage or
Stokes drift occurs during days 30–34, when indeed simulations
based on BSHcmod + W and BSHcmod + S, respectively, diverge
(see Figs.
and ). According to
Fig. b, however, results from model
version BSHcmod + W seem to be more realistic. It is interesting to
see that also TRIM simulations are particularly wrong in this
period, producing, e.g. for drifter no. 5 transports to the
south-east (Fig. b), when in
reality the drifter moved in a north-east direction
(Fig. b).
Figure compares magnitudes of
observed and simulated drift speeds on an hourly basis, referring
to trajectories of drifter nos. 5 and 6 during days 0–17 (see SM5 in the
Supplement for corresponding full time series). As in
Fig. , all simulated velocity components
were specified at observed rather than simulated drifter locations
(i.e. no drift simulation was performed), so as to avoid the
problem of spatial separation between simulations and observed
counterparts. Observed and simulated drift speeds agree
surprisingly well at least during approximately days 0–12. Nearly perfect
agreement for one drifter sometimes coincides with discrepancies
for the other, a possible manifestation of sub-grid-scale processes
(see observations at the beginning of day 5, for instance).
Together with total drift speeds,
Fig. also shows magnitudes of
simulated windage and Stokes drift. During most of the time, these
two drift components are of similar size. More short-term pulses of
Stokes drift can be discerned on days 5–6. Generally, however,
contributions from both wind and waves are smooth. A removal of
compensating tidal effects by averaging enhances visibility of the
contributions of winds or waves
(see Fig. ). Note that, due to vectors
having different directions, differences between total drift speeds
and contributions of windage do not directly translate into
magnitudes of mean Eulerian currents. For instance, a non-zero
windage effect may be offset by an opposed Eulerian current. For
BSHcmod + W simulations of drifter no. 5, we found average magnitudes
of hourly Eulerian currents to be about 0.27 ms-1 and
corresponding values for windage about 0.043 ms-1. The
resulting relative magnitude of 16 % roughly agrees with
what found for Stokes drift. According to data
from an experiment in northern Norway, Stokes drift amounted to
about 20 % of the mean Eulerian currents.
Magnitudes of drift velocities on an hourly basis, considering drifter nos. 5
(a) and 6 (b). As in Fig. ,
magnitudes of observed velocity vectors (coloured) are compared with
simulations based on BSHcmod + W. In addition, magnitudes of windage (in
BSHcmod + W) and Stokes drift (in BSHcmod + S) are shown. All model
values are specified from either atmospheric or marine fields interpolated to
observed (not simulated) drifter locations. For full time series, see the
Supplement (SM5).
In Fig. , both observations and
simulations show regular intermittent patterns in connection with
tidal cycles. Variations of maximum drift speeds indicate that
movements along different branches of tidal ellipses have
components that are alternately oriented in the same or opposite
direction of a superimposed non-tidal drift component. This
non-tidal drift is possibly but not necessarily related to wind
effects. On days 13 and 14, such non-tidal drift manifests itself
more in simulations than in observations, while during days 15 and
16 alternating drift speed maxima are more pronounced in
observations (in particular for drifter no. 6). According to
Fig. , BSHcmod + W underestimates residual
drift speeds for all four drifters tracked at that time. A fast
displacement of drifter no. 6 to the north-west can be discerned
from Fig. c. All models fail to reproduce
this movement (see Fig. c, for
instance). Considering the small values of windage and the even
smaller of Stokes drift (wind directions allow for only small
fetches over the open sea), tuning these effects cannot
substantially improve simulations.
Remember that Stokes drift and windage were calculated offline and
added to the Eulerian currents after the model had been integrated
and the fields stored. Lacking success of this approach is not to
say that deficiencies of drifter simulations are not related to
wind conditions. The problem around days 15–16, for instance,
occurs under non-stationary wind directions that affect also the
orientation of the residual current regime
(Fig. ). Changes of wave-induced forcing of the
ocean, including sea-state-dependent momentum flux and Stokes drift
, affect water level, high and low water times and
therefore also ocean currents.
warn that implementing Stokes drift as a simple
additive component of drift velocity, parameterized in terms of
wind forcing, can be inconsistent (i.e. violate conservation of
both momentum and energy) if Eulerian currents were simulated
without taking into account the reservoir of wave momentum and
energy. In the present study, the exchangeability of Stokes drift
and wind drag indicates that the role of waves as a reservoir of
momentum was not relevant at least during the period considered. One
reason for this could be that due to limited fetches the North Sea
is less swell dominated than other Nordic Seas .
Two crucial and outstanding questions are (a) whether the drifters'
behaviours are representative of surface currents and (b) if it
justifiably can be assumed that all drifters maintained their ideal
drift properties over the whole period they were tracked. Drifter
trajectories may reflect a specific exposure to winds and waves,
well illustrated by the experiment reported by
. suggested corrections to
improve trajectory simulations when wind errors and characteristics
of the specific drifters deployed are known. However, for the
present study, a tentative positive answer to the first question
could be given based on the reasonable correspondence between the
magnitudes of observed tracer displacements and their counterparts
simulated based on just TRIM Eulerian surface currents
(see Fig. a). On the
other hand, estimated a higher downwind slippage
of about 1 % of the wind speed for undrogued SVP (Surface
Velocity Program) drifters. In the context of an oil-drift study,
deployed CODE (Coastal Ocean Dynamics Experiment)-type
drifters drogued in such a way that they were supposed to
capture the upper 1 m layer velocities. Referring to
a report by estimated for these drifters
slip velocities of the order of 0.03 ms-1. In
BSHcmod + W, such velocity would match the parametrized wind drag at
a wind speed of 5 ms-1. Like contributions from wind
drag, the estimated downwind slippage of drifters is supposedly
much smaller than short-term drift velocities in a tidally
dominated regime but may nevertheless have considerable impacts on
drifter displacements in the long run. Fully disentangling effects
of wind drag on water masses and drifters, respectively, seems
hardly possible.
Answering the second question is again difficult. The joint
analysis of drifter positions and displacements in this study gave
at least some indications for possible non-ideal drifter
behaviour. A period of extreme velocities far beyond what models
predict occurs for drifter no. 9 at the end of its journey
(days 22–26; Figs. d and
a and e). These high velocities
result in a clear separation of drifter no. 9 from the formerly
concentrated group of drifters. Probably more central for the
present study is the behaviour of drifter no. 8. From day 34
onward, drifter no. 8 showed a tendency to move faster than the
neighbouring drifter nos. 5 and 6 (e.g. days 34–35, day 37 or
days 39–42; Fig. ). Strikingly, in
these cases, drifter no. 8 tended to move into directions that are
more parallel to prevailing winds (see SM1). This latter
observation also applies to the aforementioned behaviour of drifter
no. 9.
Possible reasons for the deviant behaviours of drifter nos. 8 and
9 can only be speculated. The simplest explanation would be
that the different types of the two drifters (and of drifter no. 7,
which also showed a very fast movement at the end of the time
period it was tracked) distinguishes them from other drifters
deployed (Table ). However, this explanation is not
in accord with the fact that problems did not persist throughout
the whole observational period. The special behaviour of drifter
no. 9 after about day 22 coincided with its entering a more
southern region of the German Bight
(Fig. a and e). For this region,
identified a higher variability of surface
currents, less correlated with wind conditions, which would imply
that introducing either Stokes drift or an additional wind drag
could probably be a less promising approach for model
improvement. However, still the most probable explanation for the
mismatch of observations and corresponding simulations is that the
drifter experienced problems with its drogue. Unfortunately,
drifters had no drogue presence sensor and could also not be
collected at the end of their journey to check the conditions of
the devices.
Conclusions
Trajectories of six surface drifters deployed in the German Bight
were compared with corresponding offline simulations based on
hydrodynamic data from two independent models. Successful
simulations based on BSHcmod currents archived for a 5 m
depth surface layer needed inclusion of extra wind (or wave)
effects, which was not the case for simulations based on TRIM
currents for a 1 m depth surface layer. This suggests the
assumption that the extensions in BSHcmod + W or BSHcmod + S primarily
acted to compensate insufficient vertical resolution in archived
data. There was no convincing evidence that the drifters deployed
experienced an appreciable direct wind drag. In a similar way,
attributed a bias of trajectories predicted based
on HF radar currents not to a drifter leeway but rather to the fact
that effective depth of HF radar measurements exceeded that of
surface layer drifters.
On the other hand, it is striking that often errors in simulations
based on TRIM and BSHcmod + W (or BSHcmod + S) closely resembled each
other (e.g. day 8 – see
Fig. d and h; or day 18 – see
Fig. d and h). This points to
problems shared by both models, explanation of which probably
requires analyses considering also other aspects of hydrodynamic
model output.
The present study focused on a synoptic assessment of (mainly
four) drifter trajectories overlapping in time. Expectedly,
differences between synchronous drift trajectories were much larger
in observations than in simulations, due to unresolved sub-grid-scale processes. Simulated fields of wind (not including sub-grid-scale weather phenomena and gustiness as important drivers for
drifter dispersion) and Stokes drift are even more smooth than
simulated current fields. Small-scale model data misfits can
therefore obviously not be remedied by employing windage or Stokes
drift.
Although the small number of drifters does not enable an in depth
analysis, it seems that major deficiencies of simulations often
manifest themselves under low or moderate wind speeds. For
instance, data from days 7 to 9 (see panels in
Fig. ) suggest that simulations
underestimate currents in coastal areas at that time. Insufficient
resolution of intertidal areas could be one aspect contributing to
this model deficiency. Also, on days 15 and 16, observed drifters
moving much faster than simulated (Fig. )
coincides with low wind conditions
(e.g. Fig. c and g). However, all
instances also correspond with changes in wind conditions and
transitions between different residual current regimes
(Fig. ).
On an hourly basis, contributions from windage in BSHcmod + W are
often much smaller than discrepancies between simulated and
observed drifter velocities
(Fig. or SM5), in particular
under low wind conditions. When averaging over tidal cycles,
relative contributions from wind forcing increase
(Fig. ). However, even small systematic
errors in the simulation of oscillating tides might possibly give
rise to erroneous residual current components similar in size to
the contributions from windage. A finding that needs further
analysis is whether near-shore residual currents underestimated in
simulations indicate such inaccuracies in regions where tides
increase with decreasing water depth.
This study did not substantiate benefits from including Stokes
drift simulated offline. Directions of winds and waves coincided
most of the time and effects of Stokes drift on surface currents
could successfully be mimicked in terms of additional windage. In
TRIM, such effects seemed already sufficiently parametrized as part
of momentum transfer from the atmosphere to marine currents. When
winds quickly abate, increase or turn, waves adjust with a time
lag, needing a certain fetch to fully develop. Although in these
cases the different roles of winds and waves could be more marked,
in the present study errors in atmospheric or marine circulation
modelling seemed predominant. Nevertheless, fully coupled modelling
of currents and waves could probably improve
simulated surface currents, given that the vertical resolution is
fine enough. It must also be kept in mind that the present study
did not include any extreme events.
The incident of two drifters converging quickly and separating
about 10 days later provided evidence that at least in some
situations an unavoidable increase in prediction uncertainty would
be of the order of 3–5 kmday-1, regardless of however
sophisticated a model used might be. Further studies would be
needed to substantiate this finding in terms of its
representativity and possible dependence on specific locations or
atmospheric conditions. The observed separation rate happened to
roughly agree with the average magnitude of simulation errors we
identified. More experiments would help identify the way to go for
further model improvements.