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Ocean Dynamics DOI 10.1007/s10236-008-0159-0
Temporal and spatial circulation patterns in the East Frisian Wadden Sea
Stanev · Grayek · Staneva
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AUTHOR'S PROOF!
Metadata of the article that will be visualized online
1 Article Title Temporal and spatial circulation patterns in the East Frisian
Wadden Sea
2 Article Sub- Title
3 Article Copyright - Springer-Verlag 2008
Year
(This will be the copyright line in the final PDF)
4 Journal Name Ocean Dynamics
5
Family Name
6 Particle
Stanev
7 Given Name Emil V.
8 Suffix
9 Organization GKSS Research Centre
10 Corresponding Division Institute for Coastal Research
Author
11 Address Max-Planck-Strasse 1, Geesthacht 21502, Germany
12 Organization University of Oldenburg
13 Division Institute for Chemistry and Biology of the Sea
14 Address Carl-von-Ossietzky-Strasse 9-11, Oldenburg 26111,
Germany
15 e-mail emil.stanev@gkss.de
16
Family Name
17 Particle
Grayek
18 Given Name Sebastian
19 Suffix
20 Author
Organization University of Oldenburg
21 Division Institute for Chemistry and Biology of the Sea
22 Address Carl-von-Ossietzky-Strasse 9-11, Oldenburg 26111,
Germany
23 e-mail
24
Family Name
25 Particle
Staneva
26 Given Name Joanna
27 Suffix
Author
28 Organization GKSS Research Centre
29 Division Institute for Coastal Research
30 Address Max-Planck-Strasse 1, Geesthacht 21502, Germany
31 e-mail
32 Received 14 May 2008
33 Revised

AUTHOR'S PROOF!
Schedule
34 Accepted 18 October 2008
35 Abstract This work deals with the analysis of simulations carried out with a primitive
equation numerical model for the region of the East Frisian Wadden Sea. The
model, with 200-m resolution, is forced by wind, air–sea heat, and water fluxes
and river runoff and is nested in a German Bight 1-km-resolution numerical
model, the latter providing tidal forcing for the fine resolution model. The
analysis of numerical simulations is focused both on responses due to
moderate conditions, as well as to extreme events, such as the storm surge
Britta, for which the model demonstrates very good skills. The question
addressed in this paper is how well the model output can be compressed with
the help of empirical orthogonal function analysis. It is demonstrated that, for
the short-time periods of the order of a spring–neap cycle, only a few modes
are necessary to almost fully represent the circulation. This is just an illustration
that the circulation in this region is subject to the dominating tidal forcing,
creating clear and relatively simple response patterns. However, for longer
periods of about several months, wind forcing is also very important, and
correspondingly, the circulation patterns become much more complex. Possible
applications of the results in hindcasting and forecasting of hydrodynamics and
sediment dynamics in the coastal zone are considered.
36 Keywords
Tidal basins - Statistical characteristics - Predictability of circulation
separated by ' - '
37 Foot note
information
Responsible Editor: Jörg-Olaf Wolff
Submitted to Ocean Dynamics, WATT Special Issue (May 2008). Last
resumbission October 2007.

AUTHOR'S PROOF!
Ocean Dynamics
DOI 10.1007/s10236-008-0159-0
JrnlID 10236_ArtID 159_Proof# 1 - 04/11/08
Temporal and spatial circulation patterns
in the East Frisian Wadden Sea
Emil V. Stanev · Sebastian Grayek · Joanna Staneva
Received: 14 May 2008 / Accepted: 18 October 2008
© Springer-Verlag 2008
1 Abstract This work deals with the analysis of simula-
2 tions carried out with a primitive equation numerical
3 model for the region of the East Frisian Wadden Sea.
4 The model, with 200-m resolution, is forced by wind,
5 air–sea heat, and water fluxes and river runoff and is
6 nested in a German Bight 1-km-resolution numerical
7 model, the latter providing tidal forcing for the fine
8 resolution model. The analysis of numerical simula-
9 tions is focused both on responses due to moderate
10 conditions, as well as to extreme events, such as the
11 storm surge Britta, for which the model demonstrates
12 very good skills. The question addressed in this paper
13 is how well the model output can be compressed with
14 the help of empirical orthogonal function analysis. It
15 is demonstrated that, for the short-time periods of the
16 order of a spring–neap cycle, only a few modes are
17 necessary to almost fully represent the circulation. This
18 is just an illustration that the circulation in this region
19 is subject to the dominating tidal forcing, creating clear
20 and relatively simple response patterns. However, for
21 longer periods of about several months, wind forcing is
22 also very important, and correspondingly, the circula-
Responsible Editor: Jörg-Olaf Wolff
Submitted to Ocean Dynamics, WATT Special Issue
(May 2008). Last resumbission October 2007.
UNCORRECTED PROOF
E. V. Stanev (B) · J. Staneva
Institute for Coastal Research, GKSS Research Centre,
Max-Planck-Strasse 1, 21502 Geesthacht, Germany
e-mail: emil.stanev@gkss.de
E. V. Stanev · S. Grayek
Institute for Chemistry and Biology of the Sea,
University of Oldenburg, Carl-von-Ossietzky-Strasse 9-11,
26111 Oldenburg, Germany
tion patterns become much more complex. Possible ap- 23
plications of the results in hindcasting and forecasting 24
of hydrodynamics and sediment dynamics in the coastal 25
zone are considered. 26
Keywords Tidal basins · Statistical characteristics · 27
Predictability of circulation 28
1 Introduction 29
A considerable body of work concerning the response 30
of the coastal ocean to tides based on local observa- 31
tions, tidal gauges data, etc., already exists. However, 32
spatial patterns are much less clear because direct ob- 33
servations over large areas with high spatial resolution 34
are limited. Remote sensing data also do not help 35
much: altimeter data are not precise enough in the 36
near coastal zone and ocean color or AVHRR data 37
are affected by cloud conditions and do not provide 38
complete information with sufficient temporal resolu- 39
tion. In the East Frisian Wadden Sea, which is the area 40
of our research interest, the temporal and spatial vari- 41
ability derived from statistical analyses of outputs from 42
numerical models has not been sufficiently explored, 43
although some initial steps have already been made 44
(Stanev et al. 2007b). 45
The work presented here has been carried out within 46
the framework of the research programme “BioGeo- 47
Chemistry of Tidal Flats,” which combined various 48
research activities aimed to improve the basic under- 49
standing of functioning of these areas, including circu- 50
lation and sediment transport (Staneva et al. 2008a, b). 51
Our major aim here is to make an initial effort towards 52
developing techniques that would enable the best use 53

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of data for state estimates and forecasting purposes.
One necessary step, before going deeper into this issue
and before addressing data assimilation, is to understand
the dominating statistical properties of coastal
dynamics.
The German Bight (Fig. 1a), which is bordered by
the coasts of the Netherlands, Germany, and Denmark,
is situated in the south-eastern corner of the North Sea.
It is well established that the wind in this area results
in a cyclonic residual circulation, i.e., a circulation in
the direction of propagation of the tidal wave (from
west to east along the southern boundary and from
south to north along the western coasts of Germany and
Denmark).
The East-Frisian Wadden Sea is one of the shallowest
areas of the German Bight, being characterized by
a series of barrier islands, each 5–10 km long in the
east–west direction and 2–3 km wide (Fig. 1b). The tidal
range varies from ∼ 2.5 m (Isles of Borkum and Sylt) to
a)
b)
UNCORRECTED PROOF
∼ 3.5 m (the Elbe Estuary), i.e., the region is exposed 73
to upper meso-tidal conditions. 74
Wadden Sea water periodically mixes with North Sea 75
waters (during flooding) and is partially transported 76
into the North Sea (during ebb). In this way, the 77
Wadden Sea acts as a buffer mixing-zone between 78
ocean and land. The exchange of water and properties 79
between the Wadden Sea and the German Bight are 80
known from numerical simulations (Stanev et al. 2003, 81
b, 2007b) and numerous observations (see this special 82
issue). 83
It is well-known that one fundamental characteristic 84
of the East-Frisian Wadden Sea is the vigorous 85
suspended matter dynamics (Santamarina Cuneo and 86
Flemming 2000; Burchardetal.2008) triggered by the 87
turbulence due to velocity shear (Stanev et al. 2007a) 88
and wind waves (Gayer et al. 2006; Stanevetal.2006). 89
Understanding sediment dynamics is, thus, crucially de- 90
pendent upon the knowledge of the turbulence regime. 91
Therefore, specific attention in this paper is also paid 92
to the question of how complex the turbulence patterns 93
are in the region of the East Frisian Wadden Sea. 94
Detailed validation of numerical models against ob- 95
servations at fixed locations (Stanev et al. 2003, 2007b), 96
and over larger areas (Staneva et al. 2008a, b) demon- 97
strates a good quality of numerical simulations and 98
motivates us to address the question: what are the 99
dominating temporal and spatial patterns? Provided 100
that the latter show some robustness, we could hope 101
that it would not be too difficult to extend this research 102
towards the issue of predictability, which has never 103
been addressed for this region. 104
The paper is structured as follows: Section 2 de- 105
scribes the numerical model and setup, Section 3 106
provides a description of the simulated spatial and 107
temporal patterns, and Section 4 presents the statisti- 108
cal reconstruction of simulations. The paper ends with 109
brief conclusions. 110
2 Numerical model 111
Fig. 1 Topography of the German Bight (a) and East Frisian
Wadden Sea (b). Dashed line in b contours regions, which are
subject to drying. The position of continuously operating data
stations are given with red squares
The model system used here consists of two models 112
with different horizontal resolution: a German Bight 113
model (GBM) and a Wadden Sea model. Both models 114
are based on the 3-D General Estuarine Transport 115
Model (Burchard and Bolding 2002), in which the equa- 116
tions for the three velocity components u,v,andw; sea- 117
level elevation (SLE) ζ ; temperature T; and salinity S, 118
as well as the equations for turbulent kinetic energy 119
(TKE) and the eddy dissipation rate due to viscosity, 120
are solved. The models use terrain-following equidis- 121
tant vertical coordinates (σ coordinates) and are capa- 122
ble of simulating drying and flooding of tidal flats. The 123

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vertical column is discretized into ten nonintersecting
layers. The application of the models to the area of our
study is described by Staneva et al. (2007b, 2008a,b),
and we refer to these papers for more details.
The Wadden Sea model with a resolution of 200 m
is nested in a GBM with a resolution of about 1 km
(Staneva et al. 2008a, b). Both models use spherical
horizontal grids. The atmospheric forcing for both models
is computed through bulk aerodynamic formulas
using 6-hourly European Centre for Medium-Range
Weather Forecasts (ECMWF) reanalyses data. Below,
we briefly formulate the differences in the forcing of the
two models.
For the outer mode (GBM), the river run-off for the
rivers Elbe, Ems, and Weser is taken from the 1-hourly
data provided by the Bundesamt für Seeschifffahrt und
Hydrographie (BSH). The lateral boundary conditions
of sea surface elevations, salinity, and temperature are
taken from the operational BSH model (Dick and Sötje
1990; Dick et al. 2001).
For the inner (Wadden Sea) model, the forcing at the
open boundaries is taken from the simulations with the
GBM (Staneva et al. 2008a, b) and interpolated in time
and space onto the grid points along the boundaries of
the Wadden Sea regional model. The nesting is oneway,
i.e., the nested model receives boundary values
from the coarser model but does not influence the
coarser resolution model. The fresh-water fluxes from
the main tributaries in the region are taken from the
observations compiled by Reinke et al. (2000). Initial
conditions are set to zero for sea level and velocity.
Temperature and salinity are taken from climatology.
The experience with the coupled GBM and Wadden
Sea model showed that the circulation reaches a quasiperiodic
state in only a few tidal cycles.
The present study analyzes numerical simulations
carried out for the period September to December
2006. This 4-month period is enough to resolve the
dominant temporal scales associated with tidal (floodebb,
spring–neap) and atmospheric (synoptic) forcing.
Compared to earlier modelling studies for the same region
based on this model, the present one also demonstrates
the response to extreme events. One such event
was the storm surge Britta on 1 November 2006. This
event extended over the entire North Sea (Fig. 2a, b),
atmospheric pressure was below 984 hPa, and extreme
values of sea level (Fig. 2c) were reached in many continental
locations (e. g. Emden 3.59 m above the mean
high water), as well as at barrier islands (Langeoog
und Wangerooge). This storm surge belongs to the
strongest ones observed in the last 100 years along
the Lower Saxony coast. The maximum observed wind
speeds on most barrier islands were above 125 km/h
UNCORRECTED PROOF
a)
b)
c)
Fig. 2 Surface pressure (a), satellite image (b), and visual observation
(c) during storm surge Britta. Courtesy: European Centre
for Medium-Range Weather Forecasts (ECMWF), National
Oceanic and Atmospheric Administration (NOAA), and
Niedersächsischer Landesbetrieb für Wasserwirtschaft, Küstenund
Naturschutz (NLWKN), Aurich, Germany

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(the estimates based on ECMWF reanalysis data, Fig. 3,
give slightly lower values).
The results from our simulations are described in
more detail by Staneva et al. (2008a, b). In the present
paper, we focus on the circulation (Fig. 4), in particular,
as it concerns the transport through the straits. The
general pattern is characterized by extreme velocities in
the tidal inlets, westward currents in front of the barrier
islands during ebb, and eastward currents during flood.
Extremely stormy weather during some periods enabled
us to analyze the response of the model in very
special conditions. Although Fig. 4b and d correspond
to the same tidal phases (shortly after the flood starts,
i.e., shortly after low water) during two consequent
neap–spring tidal periods, the East-Frisian Wadden Sea
does not get dry during the first period (storm Britta).
Also noteworthy is the much higher ebb velocity during
storm Britta (compare Fig. 4a and c), particularly on the
tidal flats.
The comparison with observations (Fig. 5) demonstrates
that the model replicates well the major sealevel
variability in the area of our simulations. The
reason for this good agreement between the Wadden
Sea model and the observations needs to be explained.
Sea level displays rather homogeneous patterns
with very small gradients in the north–south
direction (Fig. 4). A more detailed analysis of our
simulations demonstrates that the sea level in the
Wadden Sea model (a very small coastal area) responds
synchronously to external forcing, which is provided by
the GBM. This forcing shows almost equal oscillations
along the northern model boundary with some phase
lag (Fig. 6a). It becomes clear from Fig. 6b that the
30
UNCORRECTED PROOF
a)
b)
c)
d)
25
WSPD [m/s]
20
15
10
5
Fig. 4 Simulated surface velocities during ebb (a and c) and flood
(b and d). a and b correspond to 1 November, c and d to 11
November. Colors illustrate gradients in sea level
0
0 500 1000 1500 2000 2500 3000
Time [hours since 2007-09-01 00:00]
Fig. 3 Mean wind magnitude in the model region during the
period of simulations based on ECMWF reanalysis data. The
vertical dashed lines display the two analysis periods, “calm” and
“windy”
reason for the success of the model system in simulating 210
storm surges is not only the Wadden Sea model but also 211
the GBM, which realistically simulates the transition of 212
sea level from the open ocean to the coast. In the GBM, 213

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4
3
Simulated and observed sea level during storm conditoions
SLE model
SLE observations
a)
2
[m]
1
0
- 1
- 2
1 2 3 4 5 6 7 8
Days from 30.10.2006
Fig. 5 Simulated (blue line) and observed (red line) sea level
elevation at data station in Otzumer Balje (see Fig. 1 for the
location) during storm conditions
214 amplitudes and phases differ substantially in the north–
215 south direction, the slope ranging from ∼1 m/200 km
216 during normal conditions to ∼2.5 m/200 km during
217 storm Britta. The reason for extremely high water was
218 the long duration of strong northwest wind (up to
219 156 km/h) working in parallel with the tides.
220 3 Empirical orthogonal function—analysis
221 of simulations
222
3.1 Temporal variability
UNCORRECTED PROOF
223 Statistical decomposition of time-space signals with the
224 help of empirical orthogonal function (EOF) analysis
225 facilitates the understanding of the most important spa-
226 tial patterns and their temporal evolution (see, e. g., von
227 Storch and Zwiers 1999). The latter are usually called
228 principle components (PC). Sometimes, a direct link
229 can be seen between the spatial (EOF) and PC patterns
230 from one side and physical processes from the other
231 side, which is not theoretically justified by the method.
232 However, we will demonstrate that, in our particular
233 case, as in many other cases, most of the statistical
234 information has a high level of physical consistency (see
235 also Stanev et al. 2007b).
236 The overall behavior of dynamics can be better un-
237 derstood if we analyze the complete dataset; therefore,
238 we do not process each individual field one by one,
239 but take sea level and two velocity components as one
240 state vector. The advantage of this approach is that it
b)
Fig. 6 a SLE along the northern boundary of the Wadden Sea
model (locations are taken at equal distances of 12 km). The
black line corresponds to the location just north of the WATTdata
station in Otzumer Balje (Fig. 1). b SLE along the meridian
passing through the WATT-data station in Otzumer Balje (locations
are taken at equal distances of 25 km). The thick black line
gives the course of sea level closest to the northern boundary of
the Wadden Sea model. The blue line displays SLE closest to the
northern boundary of the GBM
is coherent with procedures used in some data assimila- 241
tion techniques. The disadvantage is that it might not 242
clearly display some major physical characteristics of 243
individual fields. To simplify the analysis and to avoid 244
transformations from sigma into z-coordinate system, 245
we analyze surface and bottom properties only. From 246
the analyzed fields, we present here the statistical char- 247
acteristics of sea level and surface currents. 248
From the period September–December, we chose 249
two periods, which are characterized by calm weather 250

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(18 September 2006–2 October 2006, hereafter “calm”)
and weather dominated by strong winds (1–14
December 2006, hereafter “windy”, see Fig. 3). For
these periods, we process the model data sampled with
60-min resolution. Furthermore, to ensure homogeneous
datasets in “calm” and “windy,” we exclude from
the analysis locations that fall dry.
Another analysis has been performed for the whole
period of integration using filtered model output. Filtering
is performed with a diurnal time-window. This
analysis is briefly called “no-tidal,” although filtering
retains in the analyzed data, along with the synoptic
variability, longer-term variability associated with the
spring–neap tidal cycle.
The percentage of variance explained by the first
three oscillation modes in “calm” and “windy” cases
(Table 1) demonstrates that the tidal signal (see also
Fig. 7) is the strongest one. As the response of the
shallow Wadden Sea to tidal forcing is relatively simple
(Stanev et al. 2003, b), a very limited number of modes
describes the total variance quite well.
A comparison between PC-1 (Fig. 7a) and the analyzed
fields demonstrates that this component almost
repeats the tidal oscillations of the sea level. PC-2 shows
a phase shift of about a quarter tidal period relative
to PC-1 and corresponds to velocity oscillations. This
curve represents semidiurnal tidal oscillations modulated
by spring–neap periodicity. The well-known
asymmetry associated with the nonlinear response of
tidal flats (Stanev et al. 2003) is seen in this signal:
different times are needed to establish maximum flood
or maximum ebb velocity (Fig. 8). In particular, longer
time is needed for the currents to evolve from maximum
ebb to maximum flood than for the inverse
transformation (note that negative PC-2 corresponds
to flood). This does not only support the theoretical
results mentioned above, which have been mostly
applied to tidal channels, but also demonstrates that
the so called “ebb-dominance,” or, according to the
terminology of Friedrichs and Madsen (1992), “shorterfalling
asymmetry,” dominates the tidal response in this
region as a whole.
PC-3 (Fig. 7c) represents ∼6-hourly periodicity,
which is associated with the maximum in current magnitude
(twice per tidal period). This type of variability
UNCORRECTED PROOF
a)
b)
c)
Fig. 7 The first three PCs in “calm” corresponding to dynamical
variables (sea level and velocity) (a–c)
t1.1 Table 1 Percentage of
Mode Calm Windy
variance explained by
t1.2 No Dynamics TKE Dynamics TKE
the first three EOFs
t1.3 1 82.7 86.3 83.1 85.4
t1.4 2 16.7 6.7 16.3 6.8
t1.5 3 0.2 2.7 0.2 2.8
t1.6 Sum 99.6 95.7 99.6 95.0

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is similar to the type of variability detected in observations
(Stanev et al. 2007b), namely, the two maxima are
different (the one during flood is higher; see Fig. 8).
TKE has been analyzed separately from dynamic
variables (sea level and velocity) as a single state
vector. The major characteristics of the PCs of TKE
is the quaterdiurnal periodicity (about 6 h), which
is pronouncedly modulated by the spring–neap signal
(Fig. 9). This is just an illustration that the level of TKE
in the Wadden Sea is very sensitive to this important
astronomical forcing. The second important characteristic
of turbulence is the strong difference in the PC
maxima during flood and ebb. This gives a clear support
of earlier theories about asymmetric responses (Stanev
et al. 2007b), which are enhanced during spring-tide.
Comparison between the PC-1 of TKE and the sea level
curve (not shown here) demonstrates that maximum
amplitudes in TKE are reached at high water during
spring tide. This result could provide an indication
that, during this part of the tidal period, resuspended
sediment and sediment eroded from the bottom (here,
we assume that concentrations are expected to reach
higher values if turbulence is stronger) is transported
landwards. This could provide an explanation as to why
tidal flats tend to accumulate sediment.
Comparison of the PCs during calm and windy
weather shows that no remarkable differences can be
identified (see also Table 1). This supports the idea
that, in the Wadden Sea, tidal response is dominating,
therefore, the corresponding curves from the “windy”
period are not shown here. However, the model output
from which frequencies higher than diurnal ones
have been filtered out gives quite a different view on
the temporal variability (Fig. 10). In this data set, the
UNCORRECTED PROOF
a)
b)
c)
Fig. 9 The first three PCs in “calm” corresponding to TKE (a–c)
Fig. 8 Time-zoom in the first three PCs, PC-1 (black), PC-2
(green), and PC-3 (yellow) of sea level and velocity in “calm”
first three EOFs describe 76.3%, 11.0%, and 5.6% of 330
the total variance (97.9% in total). PC-1 shows some 331
correlation both with the course of SLE forcing (dashed 332
red line in Fig. 10a) for some of the extreme events 333
and wind magnitude (dashed blue line in Fig. 10a) for 334

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a)
b)
c)
UNCORRECTED PROOF
Fig. 10 The first three PCs in “no-tide” corresponding to dynamical
variables (sea level and velocity). Dashed lines in a and b give
the course of wind magnitude (blue) and sea level at the open
boundary (red) scaled and shifted in order to enable comparison
with the PCs
335 longer-term variability. PC-2 is dominated by extreme
336 events (storm surge Britta), while PC-3 is modulated by
337 spring–neap oscillations, particularly for the calmer first
338 part of the analyzed period (see Fig. 3).
One comparison between Figs. 10 and 3 is wor- 339
thy of discussion for its geophysical relevance. Wind 340
speed maxima during storm surge Britta and during 341
the “windy period” are comparable. However, the re- 342
sponse of sea level in the coastal area is very different. 343
Furthermore, the projections of these events on the 344
PCs differ. While the extreme signal during the “windy 345
period” is seen in PC-1 (Fig. 10a), there is just noise 346
during this period in PC-2 (Fig. 10b). Obviously, the 347
extreme wind did not last long enough and was rather 348
variable during the “windy period.” This signal is re- 349
duced significantly due to filtering with the diurnal time 350
window (Fig. 10). Consequently, the ocean response in 351
the model was weak even though the integration has 352
been carried out with nonfiltered data. 353
3.2 Horizontal patterns 354
The first EOF in the “calm” period (Fig. 11a) is posi- 355
tive throughout the model area. This oscillation mode 356
displays the vertical motion of the sea level caused 357
by tides, which is unidirectional over the entire area. 358
The east–west gradient illustrates the fact that the tidal 359
range in this region increases from west to east. Tidal 360
channels show a tidal range as high as the adjacent 361
open-ocean areas north of them. 362
A parallel analysis of the entire data set includ- 363
ing data in the regions reaching a dry state was also 364
conducted. Results are not shown here because data 365
series are not homogeneous (sea level is “frozen” in 366
the model when the water column thickness reaches the 367
minimum allowable value of 2 cm). Nevertheless, the 368
two analyses demonstrate no big differences in the deep 369
regions. In the regions undergoing drying and flooding, 370
EOF-1 of the sea level follows the bottom topography 371
(smallest variability in areas remaining dry for longer 372
times) and, as it was the case for deep data only, has the 373
same sign throughout the model area. 374
EOF-2 (Fig. 11b) shows an east–west propagation 375
pattern and gives a measure of the phase difference 376
between channels and the areas north of the barrier 377
islands. The delay is approximately equal to the time 378
needed for the tidal wave to cover the distance of about 379
one barrier-island length (notice that we observe same 380
colors, green in this case, in front of Spiekeroog and 381
behind Langeoog islands). 382
From the horizontal pattern of EOF-3, it seems 383
plausible that this mode corresponds to another known 384
physical process, that is the east–west asymmetry of 385
6-h variability, which is enhanced during flood. Notice 386
that, in this case, the response of the tidal channels is 387
coherent with the processes north of the tidal inlets. 388

AUTHOR'S PROOF!
Ocean Dynamics
JrnlID 10236_ArtID 159_Proof# 1 - 04/11/08
Fig. 11 The first three SLE
EOFs in “calm” (a–c)
a)
b)
c)
UNCORRECTED PROOF
389
390
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393
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397
398
399
400
401
Furthermore, bearing in mind that (1) this variability
pattern is dominated by 6-h oscillations and (2) that
the analysis of the entire data set (deep area and area
undergoing drying) shows inverse trends in the deep
part and over the tidal flats, one could also conclude
that this signal is indicative of the transformation of the
tidal response in the Wadden Sea in a way that the ∼6-
hourly variability is coherent over the entire region of
the tidal flats (see also Stanev et al. 2003).
EOF-1 of zonal surface velocity (Fig. 12a) displays
an inverse correlation between the variability in tidal
channels and the shallow area adjacent to the northern
coasts of the barrier islands (the north-west tips
of the barrier islands give the “origin” of the inverse 402
to the tidal channels signal). Furthermore, a negative 403
correlation is also observed between the area along the 404
northern model boundary and the shallows north of the 405
barrier islands. The latter structure is indicative of 406
the rotational character of the tidal excursions north of 407
the barrier islands. This type of oscillation is coherent 408
with the vertical motion of sea level (see Fig. 7). 409
EOF-1 of meridional surface velocity (Fig. 12b) 410
shows a pronounced anticorrelation between processes 411
in the tidal channel Otzumer Balje (and, to a lesser 412
extent, in the Accumer Ee) and the ones north of the 413
islands of Spiekeroog and Langeoog (blue colors in 414

AUTHOR'S PROOF!
JrnlID 10236_ArtID 159_Proof# 1 - 04/11/08
Ocean Dynamics
a) b)
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433
c) d)
e) f)
Fig. 12 The first three surface velocity EOFs in “calm”, a, c, ande, U;b, d,andf, V
UNCORRECTED PROOF
inlets and red colors north of the islands). A similar
anticorrelation is observed between processes in tidal
channels and tidal flats in the EOF analysis in which
data in the areas undergoing drying are also processed
(not shown here).
EOF-2 of the zonal and meridional surface velocities
(Fig. 12c, d) displays some important characteristics of
the dynamics of tidal channels. The inverse correlation
(in particular, in u-EOF-2) enables us to identify the
split of channels areas as flood- and ebb-dominated
ones, which is also known from observations (Stanev
et al. 2007b). The transformation of the v-signal along
tidal channels (maxima and minima in Fig. 12d) gives
a clear support of the theory (Stanev et al. 2007b) that
tidal channels in the East Frisian Wadden Sea evolve
from ebb-dominated (between barrier islands) to flooddominated
(in their shallowest extensions).
North of the barrier islands, an eastward “protrusion”
of v-EOF-2 pattern is clearly seen, which is in-
dicative of the export patterns from the tidal flats (from 434
the western inlet to the eastern one). 435
The horizontal patterns of the 6-h variability (see 436
Figs. 7c and12e, f), which is mostly associated with 437
currents magnitude, show quite different patterns for 438
the two velocity components. While for the meridional 439
transport the maximum variability is limited to the 440
narrow area between neighboring islands (Fig. 12f), 441
maximum variability of zonal transport is observed 442
north of the barrier islands and in the zonal part of 443
the channels. The latter is to be expected. However, 444
what is not so trivial is the inverse correlation between 445
u-patterns in different zonal sections of the channels, 446
indicating a more complicated evolution of the tidal 447
responses. 448
The horizontal patterns of TKE provide indirect 449
information about the location of areas favorable to 450
deposition and erosion. EOF-1 pattern, which is a uni- 451
directional variability over the entire area (Fig. 13a), 452

AUTHOR'S PROOF!
Ocean Dynamics
JrnlID 10236_ArtID 159_Proof# 1 - 04/11/08
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a)
b)
c)
Fig. 13 The first three TKE EOFs in “calm” (a–c)
UNCORRECTED PROOF
clearly demonstrates large differences in the magnitudes
of oscillations in tidal channels and flat areas in
front and behind the barrier islands. In addition to the
well known asymmetries explaining tendencies of erosion
and deposition in the Wadden Sea (Groen 1967;
Postma 1982; Stanevetal.2003b, 2007b), we see in the
TKE-EOF-1 pattern different magnitudes in deep parts
of the channels and their northern extensions from one
side and in the remaining areas from the other side.
EOF-2 of TKE seems easier to interpret. This variability
is strongly dominated by the neap–spring cycle,
enhancing velocity magnitude along the channels
(Fig. 13b). Eastern and westernmost areas of the open
sea are inversely correlated, which demonstrates the
sensitivity of TKE patterns to different tidal ranges
in these zones. As for the TKE-EOF-3 (a very lowmagnitude
signal), the major horizontal characteristics
are the opposing trends occurring in the channels north
and south of the straits.
The analysis of temporal and spatial variability in 472
the no-tide case is focused on transport characteristics 473
because they give the clearest illustration of the re- 474
sponse to extreme events. With respect to the sea-level 475
characteristics, we will only mention that the response 476
is relatively simple, as can be seen from Fig. 4, display- 477
ing a uniform in the north–south direction field. The 478
EOF-1 (not shown here) shows a unidirectional change 479
throughout the area. 480
EOF-1 of the zonal surface velocity component 481
(Fig. 14a) has the same sign throughout most of the 482
area. This could be explained by the adjustment of 483
zonal circulation to winds with dominating zonal com- 484
ponents. The strongest response (largest values of 485
EOF-1) is observed in the open sea, which decreases 486
with decreasing distance from the barrier islands. The 487
EOF-1 and EOF-2 patterns of bottom velocity (not 488
shown here) are similar to the ones in Fig. 14a, b, re- 489
vealing that, in this area, there is no substantial change 490
of dynamics with respect to the vertical coordinate. 491
Another interesting difference from tidal cases is 492
observed in the no-tidal case: the zonal motion north of 493
the islands displays some undulated patterns (Fig. 14a), 494
which coincide well with irregularities in the bottom 495
relief. This EOF structure is not observed in the case 496
of tidal response. 497
In EOF-1 of meridional surface velocity (Fig. 14b), 498
some pronounced differences from the “calm” period 499
are obvious: the meridional transport in the channels 500
Otzum Ee and Accum Balje is split into two: south-east 501
of the tidal inlet, the correlation is positive with the 502
oscillations along the coast of the western island. The 503
blue-colored area (negative values) originating from 504
the north-western tips of the barrier islands extends 505
from north-west to south-east, thus cutting the area 506
with positive values in two. In this way, a quadropul-like 507
pattern is formed, which is characteristic for the regime 508
of a two-way transport in the inlets driven by wind. 509
EOF-2 corresponding to longer-term variability of 510
zonal surface velocity (Fig. 14c) is completely different 511
from the one in the case of tidal forcing. The pattern 512
north of the barrier islands (alternating positive and 513
negative correlations) could indicate divergence and 514
convergence in this component. As a whole, tidal flats 515
and the areas north of the barrier islands are negatively 516
correlated. 517
The propagation pattern associated with EOF-2 of 518
meridional transport (Fig. 14d) is relatively simple and 519
clear: the area north of the inlets is well defined and 520
usually negatively correlated with the variability in 521
most parts of the remaining open sea. This shows how 522
the response to extreme events (storm Britta in this 523
case) is horizontally structured. 524

AUTHOR'S PROOF!
JrnlID 10236_ArtID 159_Proof# 1 - 04/11/08
Ocean Dynamics
a) b)
525
526
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528
529
530
531
532
533
534
535
536
537
538
539
540
c) d)
e) f)
Fig. 14 The first three surface velocity EOFs in “notide”, a, c,ande,U;b, d,andf,V
UNCORRECTED PROOF
The two EOF-3 (Fig. 14e, f) reveal the responsepatterns
to the neap–spring cycle (see Fig. 10). Although
this is a relatively weak signal compared to the
one originating from extreme events, it is very well
structured. The zonal component reflects an inverse
correlation between western and central regions north
of the barrier islands, while the meridional component
pattern north of inlet is “divided” in two. This illustrates
that evolution triggered by a neap–spring cycle might
affect transport in the area of tidal deltas (Fig. 15).
4 Statistical reconstructions
Provided that major processes could be well described
by only a few EOFs, one might want to ask the question
about the quality of statistical reconstruction and
forecast. In order to address this issue, we use simulations
during the “calm” period and the “windy” pe-
riod. Then, using ten modes only, we reconstructed the 541
simulations. Comparison between real (model output) 542
and synthetic (reconstructed using limited amount of 543
EOFs) data demonstrates that the mean error is about 544
0.03 sigma (“sigma” is the root mean square deviation) 545
for the sea level and 0.12 and 0.19 sigma for u and v, 546
correspondingly. These are very small errors. 547
Motivated by the above results, we go one step 548
further and ask the question: could a reconstruction 549
(forecast) be done based on a limited amount of input 550
information? In the Otzumer Balje (see Fig. 1b for the 551
location), a continuously operating data station has 552
been deployed (Staneva et al. 2008a, b). The measured 553
data (sea level temperature, salinity, and velocity at 554
several levels) are available online and the use of 555
these data for forecast purposes seems challenging. 556
In the past few years, a similar data station operated 557
by the Gesellschaft zur Förderung der Kernenergie 558
in Schiffbau und Schiffstechnik Research Centre was 559

AUTHOR'S PROOF!
Ocean Dynamics
JrnlID 10236_ArtID 159_Proof# 1 - 04/11/08
a) b)
c) d)
e) f)
Fig. 15 Forecast error for sea level (a, b), u-surface-velocity
(c, d), and v-surface-velocity (e, f). Left column: based on one
data station, right column: based on two data stations. The
560 deployed in the Accumer Ee (square in Fig. 1b). The
561 second question is: would it be possible using data from
562 both stations to increase the quality of reconstructions,
563 compared to the case of only a one-station statistical
564 forecast?
565 Led by the two questions above, we take the model
566 data only in the positions of data stations and construct
567 by multivariate EOF analyses of extracted variables
568 the PCs of “observations” (synthetic observations) for
569 both periods (PC oc and PC ow ). Indices “o,” “c,” and
570 “w” stand for “observations,” “calm,” and “windy,”
571 respectively. For the forecast based on one data station
572 (sea level and two velocity components at sea surface
573 and bottom), we are able to calculate five PCs at most.
574 For the forecast based on two data stations, ten PCs can
575 be derived. We use the same amount of global domain
576 PCs from the “calm” period (PC gc , here, index “g”
577 stands for “global”) to “train” the forecast. Therefore,
578 we apply a linear regression on PC oc and PC gc and
579 obtain a set of linear parameters (L c ) to convert PCs
heading of each plot contain the area mean values of errors of
reconstruction, forecast using one data station, and forecast using
two data stations
UNCORRECTED PROOF
of observations into PCs of the global domain. Finally, 580
the forecast of the “windy period” (F w )iscalculatedby: 581
F w = EOF c · L c · PC ow (1)
For comparison, we also calculate a reconstruction 582
of the “windy period” (R w ) from the first ten EOFs and 583
PCs of the “windy period” by: 584
R w = EOF w · PC w (2)
The root mean square forecast and reconstruction 585
errors are calculated at each grid point and are shown as 586
maps of percentage of standard deviation. The heading 587
of each plot shows the area mean values of errors 588
of reconstruction, the forecast using one data station, 589
and the forecast using two data stations. Obviously, 590
the statistical forecast is worse than the reconstruction. 591
However, taking into consideration the usual errors in 592
observations, the results are encouraging. 593
Something unexpected from our reconstructions de- 594
serves to be mentioned here. The initial expectation 595

AUTHOR'S PROOF!
JrnlID 10236_ArtID 159_Proof# 1 - 04/11/08
Ocean Dynamics
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602
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607
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was that adding one more data stations would substantially
increase the accuracy of the forecast. This,
however, appeared not to be the case because the
two data stations are very well correlated (see results
in Section 3). Actually, not much new information is
added by adding data from the second station. Additional
reconstructions and forecasts based on different
positions of data stations (not shown here) indicate that
some improvement is still possible by optimizing the
deployment of stations.
5 Conclusions
This paper presents a statistical analysis of numerical
model simulations, which could be considered as a
first step towards data assimilation of continuous observations
in the Wadden Sea. This could have direct
application when deciding about space reduction using
EOFs. Some of the results support, in a more objective
way, earlier results based on more limited analyses. In
particular, temporal asymmetries due to specific hypsometric
properties of tidal basins (ebb-dominance, or
according to the terminology of Friedrichs and Madsen
(1992) “shorter-falling asymmetry”), evolution of tidal
signals along channels from ebb dominated between
the barrier islands to flood dominated in their shallow
extensions (Stanev et al. 2007b) are captured well by
the statistical analyses and present fundamental temporal
and spatial variability patterns for this area. We
demonstrated that the coupled model system and its
regional setup are quite successful in simulating not
only tidally driven circulation, but also extreme events
such as the storm surge Britta on 1. November 2006.
Parallel statistical analysis of circulation and turbulence
supports our earlier studies. It was demonstrated
that the level of TKE in the Wadden Sea is
very sensitive to the spring–neap tidal forcing. More
specifically, the large differences in the maxima in PC
during flood and ebb are enhanced during spring-tide.
Thus, the higher level of turbulence could result in
an increase of sediment concentrations during flood.
Consequently, increased sediment concentration leads
to an enhancement of landward sediment transport,
which could provide an explanation as to why tidal flats
tend to accumulate sediment.
It has been shown that, without losing much detail,
the information about circulation is easily “compressible”
using several EOF modes only. Furthermore, it
appeared possible to relatively correctly reconstruct
and statistically forecast spatial dynamics using local
measurements only. This allows us to conclude that
the proposed method could be used as a reliable tool
UNCORRECTED PROOF
for simple and rapid estimates of the sea state in the 646
vicinity of the continuously operating data station in 647
the Spiekeroog Inlet. These conclusions hold only for 648
the tidal part in the small domain. The nontidal part is 649
much more complicated and further research is needed, 650
involving data assimilation practices in order to clarify 651
details about predictability of currents in the Wadden 652
Sea, given their smaller spatial and temporal correla- 653
tion scales and their strong interaction with the sea 654
bed behind the islands. For the entire German Bight, 655
however, our preliminary analyses on simulations with 656
the GBM show that the reconstruction of nontidal 657
dynamics is also reasonably good, though errors are 658
higher than in the small area addressed in the present 659
study. 660
Our belief is that the results presented are relevant 661
to other similar cases of coastal dynamics and could 662
motivate wider application of the techniques used here 663
beyond the currently studied area. 664
Acknowledgements We acknowledge the financial support of 665
Deutsche Forschungsgemeinschaft through the research project 666
“BioGeoChemistry of Tidal Flats,” and the EC-funded IP 667
ECOOP. 668
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UNCORRECTED PROOF
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