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This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution
and sharing with colleagues.
Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third party
websites are prohibited.
In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further information
regarding Elsevier’s archiving and manuscript policies areencouraged to visit:
Horizontal Lagrangian transport in a tidal-driven estuary—Transport barriersattached to prominent coastal boundaries
Florian Huhn a,n, Alexandra von Kameke a, Silvia Allen-Perkins b, Pedro Montero c,Anabela Venancio d, Vicente Perez-Munuzuri d
a Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15781 Santiago de Compostela, Spainb TRAGSATEC, Santiago de Compostela, Spainc INTECMAR, Xunta de Galicia, Spaind MeteoGalicia, Consellerıa de Medio Ambiente, Rua Roma 6, E-15707 Santiago de Compostela, Spain
a r t i c l e i n f o
Article history:
Received 13 May 2011
Received in revised form
2 March 2012
Accepted 9 March 2012Available online 28 March 2012
Keywords:
Lagrangian Coherent Structures
Transport barrier
Surface drifter
Coastal dynamics
Finite-Time Lyapunov Exponent (FTLE)
Ria de Vigo
a b s t r a c t
Horizontal Lagrangian surface transport is studied in the Ria de Vigo, an estuary in NW Spain with tidal
and wind-driven dynamics. Surface drifters and the surface flow from a high-resolution 3-D hydro-
dynamic model are compared to each other. In particular, our analysis is based on a classical
comparison of real and artificial trajectories and on Lagrangian Coherent Structures (LCS) defined as
ridges in spatial fields of the Finite-Time Lyapunov Exponent (FTLE). The trajectories of the drifters are
in good agreement with the prediction of the model in two out of four cases. Further, FTLE ridges
computed from the model velocity fields are found to mark transport barriers for the drifters. The
results indicate that the model is able to represent the general circulation in the estuary. Main patterns
in the Lagrangian surface transport in the model are shown for two typical meteorological situations,
north wind and south wind. They can be interpreted as an imprint of a 3-dimensional circulation
pattern in the Ria de Vigo and reveal in detail the separation of the time-dependent in- and outflow at
the surface of the estuary.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Chaotic horizontal transport occurs in many oceanic flows, e.g., ina tidal-driven system at the coast (Ridderinkhof and Zimmerman,1992), or at much larger scales in the open ocean (Abraham andBowen, 2002). In order to analyze transport in these flows, conceptsfrom dynamical systems theory have been successfully applied(Wiggins, 2005). The concept of Lagrangian Coherent Structures(LCS) provides a method to extract spatial geometrical structuresthat order transport in the flow (Haller, 2000; Ide et al., 2002;Lapeyre, 2002). LCS are the locally strongest repelling or attractingmaterial lines and represent the cores of Lagrangian patterns. Beingmaterial lines, i.e., a line of fluid particles, they cannot be crossed byideal tracers. Therefore, they are transport barriers separating theflow into different water masses, a fundamental and very usefulproperty of this concept. LCS are surprisingly stable against errors inthe velocity field (Haller, 2002; Hernandez-Carrasco et al., 2011) andcan still provide a sketch of the main circulation in a coastal region,when Lagrangian chaos impedes the direct comparison of trajec-tories. They reveal integrated Lagrangian information not obtainable
from single steady Eulerian velocity fields (Garcıa-Olivares et al.,2007; d’Ovidio et al., 2009; Boffetta et al., 2001). The applications ofLCS to oceanic flows range from the observations of the generalocean circulation (d’Ovidio et al., 2004; Beron-Vera et al., 2008) tovery specific exchange processes across jets (Mendoza et al., 2010)or fronts (Mancho et al., 2008). The LCS method has been used tounderstand the spreading of plankton blooms (Olascoaga et al.,2006; Olascoaga, 2010; Perez-Munuzuri and Huhn, 2010; Lehahnet al., 2007) and to manage and predict the transport of contami-nants and pollution in coastal waters (Lekien et al., 2005; Coullietteet al., 2007; Stirling, 2000), as well as to diagnose the mixing of oilspills (Mezic et al., 2010).
Only recently, coastal flows have been in the focus of studiesusing LCS, carried out in the Gulf of Eilat, Israel (Gildor et al.,2009), the Gulf of La Spezia, Italy (Haza et al., 2010) and inMonterey Bay, California, USA (Shadden et al., 2009). Coastalflows are especially challenging due to their complex 3-dimen-sional boundaries, a lack of isotropy, and a large variety ofintermittent forcings and physical processes, such as unsteadywind influenced by the coastal topography. Yet, coastal regionsare of great ecological and economical interest, and thus, intensi-fied exploration of transport as a key process is necessary.
Our study region, the Ria de Vigo, is the southernmost of thefour estuaries Rias Baixas in Galicia at the NW coast of Spain
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Continental Shelf Research
0278-4343/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.
which is shown in Fig. 1. It has a typical V-shape and graduallydeepens and widens towards its mouth. The Cies islands divide themouth into a smaller northern mouth and a larger southern mouth(Gomez-Gesteira et al., 1999; deCastro et al., 2006). Being situated inthe Iberian coastal upwelling system, the longterm circulationpattern with a time scale of some days to a week is determinedby periods of northerly winds causing upwelling (typically insummer) and periods of southerly/westerly winds causing down-welling (typically in winter) (Wooster et al., 1976; Fraga, 1981;Nogueira et al., 1997). The circulation and the resulting transporthave been studied experimentally (Piedracoba et al., 2005; deCastroet al., 2006; references therein) and by means of models (Taboadaet al., 1998; Gomez-Gesteira et al., 1999; Montero et al., 1999;Torres et al., 2001; Mıguez et al., 2001; Souto et al., 2003; Gilcotoet al., 2007). In case of upwelling, the cold, nutrient-rich upwelledwater generates a high biological production and gives rise to anintense human use of the estuary in terms of aquiculture of fish andshellfish (Figueiras et al., 2002). However, contaminations andharmful algae blooms can threaten the productivity and the balanceof the ecological system (Fraga et al., 1988; Tilstone et al., 1994).
In this study, we concentrate on the outer region of theestuary, where the interaction of the tidal flow with the wind-driven longterm flow along the coast leads to interesting chaoticdynamics. We investigate the horizontal surface transport in theRia de Vigo at the submesoscale (1–10 km) based on the highresolution hydrodynamic model MOHID and experiments withsurface drifters. We compare experimental Lagrangian drifterdata to the transport predicted by this hydrodynamic model.For our artificial tracers we concentrate here on the mostimportant forcing: the water current. This might lead to discre-pancies to the real drifters. Indeed, the accuracy of modeleddrifter trajectories can be improved taking into account a varietyof proposed forcings, e.g., wind, waves or parameterized diffu-sion-like small scale transport (Niiler et al., 1995; Ohlmann et al.,2005, 2007; Edwards et al., 2006; Abascal et al., 2009; Furnanset al., 2008; Price et al., 2006). We show that LCS in velocity fieldsfrom a coastal model are an extremely useful way to interpret thepredicted transport. Coastal hydrodynamic models might not be
as accurate as direct measurements of the surface currents viaHigh Frequency (HF) Radar (Molcard et al., 2009; Shadden et al.,2009; Ullman et al., 2006; Haza et al., 2010), but they can beavailable in coastal regions where HF Radar systems have not(yet) been installed and provide the possibility of a prediction ofseveral days. While classical numerical tracer particle studies ofcontaminants, sediments or biological tracers are common (e.g.,Montero et al., 1999; Carracedo et al., 2006; Cerejo and Dias,2007; Doos and Engqvist, 2007; Cowen et al., 2006), only recently,flows of coastal models have been analyzed using the LCS concept(Haza et al., 2007; Branicki and Malek-Madani, 2010). We stressthat we concentrate on the surface flow here, while decisivedynamics at the coast also happens in the vertical dimension.
The paper is organized as follows. In the following part wepresent the model and the drifter experiments. In the third partwe describe the data processing and the computation of the LCS.The fourth part comprises the results including a discussion andfinally we give a summary and an outlook in the fifth part.
2. Data
2.1. The hydrodynamic model
For our analysis we use the hourly output of the high resolu-tion, 3-dimensional baroclinic hydrodynamic model MOHID(www.mohid.com) that is run operationally by MeteoGalicia(www.meteogalicia.es), the official Galician meteorologicalservice. The MOHID model was developed at MARETEC at theTechnical University of Lisbon and has shown its ability tosimulate complex coastal and estuarine flows (Coelho et al.,2002; Martins et al., 2001). It solves the 3-dimensional incom-pressible primitive equations assuming hydrostatic equilibriumand the Boussinesq approximation. The turbulent vertical mixingcoefficient is determined using the General Ocean TurbulenceModel (GOTM) (Burchard and Bolding, 1999).
The model is implemented with three nested grids of increas-ing resolution. The largest grid has an extend of about 330�390 km2 covering the entire Galician coast and parts ofthe Portuguese and Cantabrian coast with a resolution of 0:061�6:7 km. It receives boundary conditions from the POLCOMS modelof the Spanish Operational Oceanographic System (www.eseoo.org) that itself is forced by data of UK Met Office’s data assimilat-ing FOAM oceanographic model and Spanish AEMET’s HIRLAMatmospheric model. Tidal data enters from Aviso’s data assimilat-ing FES2004 product via a barotropic grid of Western Iberia.Atmospherical forcing is provided by a WRF (Weather Researchand Forecasting) Model at 12 km resolution with boundaryconditions from NOAA’s GFS (Global Forecast System) model.The second grid has a resolution of 0:021� 2:2 km and comprisesthe four estuaries Rias Baixas the southernmost of which is theRia de Vigo. The finest model grid for the Ria de Vigo that we usein this study (Fig. 1) has a resolution of 300 m (156�153 gridpoints) and is integrated with a time step of 30 s. It receivesboundary conditions from the second grid and is forced by WRFwind data at a resolution of 4 km. The operative scheme iscomposed by a preliminary spin-up of five days hindcast followedby a three day forecast. For the next prediction the new initialcondition is generated by running the previous day, starting withthe hindcast output and using assimilated local meteorologicaldata during the integration. Freshwater river outflow into the Riade Vigo is predicted by the SWAT (Soil and Water AssessmentTool, http://swatmodel.tamu.edu). An accurate bathymetry iscrucial for the model, here it was constructed based on data fromthe Spanish Hydrographic Institute. The bathymetry is widelyaccurate, however, it must be mentioned that even at the high
Fig. 1. Study region: Ria de Vigo, NW Spain. An exemplary surface velocity field
from the model is shown for incoming tide where each third vector is plotted.
Contour lines and colors correspond to the model bathymetry in meters (m).
Important topographic sites: San Martino Island (A), Monteagudo Island (B), and
Cape ‘Cabo Home’ (C). (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this article.)
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–132
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resolution of 300 m the accuracy might be limited at someextreme locations, e.g., details of the flow in the channel betweenthe Cies Islands cannot be resolved.
The vertical dimension of the model grid is structured in 16cartesian z-level layers with an increased resolution in the surfaceboundary layer. We use the uppermost surface layer of the 3-Dvelocity output of the model to advect artificial tracers in 2-dimensional space. The depth of this layer varies between 1 mand 3 m as the tidal elevation adds to this layer, but generallycorresponds to the typical length of the drogues of the drifters.For the artificial tracers we assume that the vertical velocitiesclose to the surface are negligible compared to the horizontalvelocities, since the water surface imposes a boundary conditionof zero vertical flow (Branicki and Malek-Madani, 2010). This isespecially justified for floating tracers. We tested the positions ofthe resulting LCS computed from the upper three layers andobtained only small differences. For these reasons, in the follow-ing we choose the uppermost water layer. For the furtherLagrangian analysis the hourly velocity fields from the modelare used.
The model was designed as an operational model that capturesthe general circulation in the Ria de Vigo, i.e., the propagation ofthe tidal wave in the complex bathymetry and the response of theflow to changing wind forcing, which drives the important long-term flow on the shelf with typical time scales of days to weeks(Piedracoba et al., 2005). Due to its hydrostatic approximationthat neglects the vertical acceleration of fluid parcels (Marshallet al., 1997) it might not accurately represent some physicalprocesses as, e.g., non-linear internal waves, Kelvin–Helmholtzinstabilities under a fast spreading freshwater plume (Shaw andChao, 2006) or upwelling filaments (Chao and Shaw, 2002).However, these processes do not dominate the dynamics in theRia de Vigo and hardly influence the drift of surface drifters.Internal waves have been reported to form on the shelf (Fraga,1996), but there is no clear evidence that they enter the Ria deVigo and alter the horizontal circulation.
2.2. Drifter experiments
Drifter experiments in the Ria de Vigo were carried out by theTechnological Institute for the Monitoring of the Maritime Envir-onment (INTECMAR) in Vilagarcıa de Arousa, Galicia, Spain, in theframework of the AMPERA funded DRIFTER project ‘HNS, oil andinert pollution: Trajectory modeling and monitoring’. Data werecollected for the project during 17 experiments over a periodof 22 months from December 2008 to September 2010 in twoGalician estuaries, the Ria de Arousa and the Ria de Vigo. Thesubset of data in the Ria de Vigo comprises 55 drifter trajectories.Drifters were deployed in clusters inside the Ria de Vigo, left inthe water over night, and recovered the following day. Therefore,the mean duration of the trajectories is 19 h with a duration of 4 hfor the shortest and 32 h for the longest drifter run. The totaldrifter time is 1077 drifter hours.
The original experiments were designed to compare differenttypes of drifters and drogues for the management of contamina-tions and oil spills. For this study, we selected four drifter runs outof the entire data set fulfilling two criteria (Table 1): the driftersmust have sufficient current following properties (equipped withan effective drogue) and trajectories must be in the vicinity of LCScomputed from the model flow. In Table 1 we show the fourselected drifter runs with two types of drifters fulfilling theserequirements: the MD02 drifter of Albatros Marine Technologiesin three drifter launches, and the TRBUOY drifter of MarexiMarine Technology in one drifter launch. The MD02 drifter is asmall coastal drifter that is robust due to its foam protection and,therefore, suitable for applications close to rocky coasts. Both
drifters transmit their GPS position by sending SMS via the GSMsystem to a modem connected to a PC. GSM net coverage islimited to coastal areas impeeding offshore use of these drifters.Wind slip could be estimated from a single experiment withmoderate wind where a dye patch was present as a reference(Price et al., 2006). It turned out to be less than 4 cm/s for theMD02 drifter analyzed here. For the MD02 drifter the standarddeviation of the GPS position was estimated to be approximately13 m by means of an experiment where three drifters were fixedat a constant position for 3 h. This error is in the upper range oftypical values reported by other studies (Ohlmann et al., 2005;Stevens, 2009). For the TRBUOY drifters the characteristics areexpected to be likewise due to a similar construction as the MD02drifter, although no systematic analysis of the uncertaintieswas made.
3. Data processing and methods
3.1. Drifter data
Drifter position data were recorded at a period of 10–15 minfor most experiments and the period was decreased to 5 min forthe last two experiments. All data were interpolated linearly to atime series with a 2 min time step and then lowpass filtered witha cutoff frequency of 1=15 min�1. Johnson and Pattiaratchi (2004)compare the power spectra of drifter trajectories to the spectrumof a stationary test and filter high frequencies with a signal tonoise ratio smaller than 10. For our data this frequency thresholdis around 1=16 min�1 corresponding to the cutoff frequency of thefilter used. In order to compare the velocity of the drifters to thevelocity from the model a further low pass filtering up to theNyquist frequency of the model of 1=2 h�1 would be appropriate.However, this does not change the drifter trajectories signifi-cantly. Drifter positions at full hours and derived Lagrangianvelocities are then compared to the FTLE fields and Eulerianvelocities obtained from the hydrodynamic model.
3.2. Lagrangian Coherent Structures from model velocity field
In order to extract Lagrangian Coherent Structures we com-pute fields of the Finite-Time Lyapunov Exponent (FTLE) from thediscrete hourly velocity data set of the hydrodynamic model.We use a standard method to obtain the fields of the FTLE byadvecting a grid of artificial tracers for a finite time t. Artificialtracers have an initial separation of 60 m corresponding to 5�5tracer particles per model grid cell (300 m) and are advected witha fourth order Runge–Kutta scheme and a linear interpolation ofthe model velocity data to tracer positions in time and space. TheFTLE fields Lð x!,t,tÞ are computed as
Lð x!,t,tÞ ¼ 1
t ln
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffilmaxðDð x
!,t,tÞÞ
qð1Þ
Table 1Drifter experiments.
# Date
(dd/mm/yyyy)
Drifter
type
Drogue
shape
Drogue
length (m)
Number
of drifters
Duration
(h)
1 15/06/2009 Marexi
TRBUOY
Nylon
tube
1 2 27
2 14/07/2009 Albatros
MD02
Nylon
cone
1 2 25
3 04/08/2010 Albatros
MD02
Nylon
cone
2 3 24
4 14/09/2010 Albatros
MD02
Nylon
cone
2 4 24
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–13 3
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where t is the advection time and lmax the largest eigenvalue ofthe Cauchy–Green deformation tensor Dð x!,t,tÞ, computed fromthe flow map of the artificial tracers (Shadden et al., 2005;Mancho et al., 2006). Tracers are advected forward and backwardin time in order to obtain estimates of repelling (stable, divergent)and attracting (unstable, convergent) hyperbolic manifolds.We present the combined FTLE fields L7
ð x!
,t,tÞ computed asd’Ovidio et al. (2004)
L7ð x!
,t,tÞ ¼Lþ ð x!,t,tÞ�L�ð x!,t,tÞ ð2Þ
Lþ ð x!,t,tÞ is the forward FTLE field where tracers are released attime t and advected until time tþt, whereas L�ð x!,t,tÞ is thebackward FTLE field where tracers are released at time t andadvected with the negative velocity field until time t�t.
Generally, the resolution of the FTLE fields is significantlyhigher than the velocity fields from the model due to the 5�5tracer particles per model grid cell. The subgrid information in theFTLE field is contained in the time-dependent velocity field andcan be considered real (Hernandez-Carrasco et al., 2011). It stemsfrom the integration of the velocity field along the trajectories ofartificial tracers that have a length much longer than a grid cell.Moreover, subgrid flow structures can be contained in thetemporal dependence of the velocity field.
In order to obtain meaningful FTLE fields, the finite advectiontime t has to be chosen carefully according to two criteria. First, tdefines the time scale of the Lagrangian processes that will bemapped in the FTLE fields. If a certain Lagrangian structure with atypical time scale tL should be sampled, a much shorter advectiontime t5tL impedes the tracers to explore the whole structure,whereas for a much longer advection time tbtL tracers exploremany different parts of the flow, so their integrated historybecomes similar and the spatial FTLE field becomes more uniform(see Branicki and Wiggins, 2010; references therein for a detaileddiscussion).
This dependence on the advection time t can be analyzed interms of the probability distribution functions (pdfs) pðLþ ðtÞÞ ofthe values occurring in the FTLE field. For small times t the pdf isdominated by the distribution of the local instantaneous strainrate (Abraham and Bowen, 2002) and spatial FTLE fields do notshow linear structures. For large times t the pdf converges veryslowly to its asymptotic form (Abraham and Bowen, 2002), whichin the case of a delta function denotes a uniform FTLE fieldwithout any spatial information. Fig. 2 shows this evolution forthe pdfs of FTLE fields in the Ria de Vigo. With increasing t thestandard deviation of FTLE values decreases and the mean of thepdf shifts to smaller values. For closed ergodic flows all Lyapunovexponents converge to the same value l1 for t-1 and thevariance vanishes (Abraham and Bowen, 2002; Waugh andAbraham, 2008; Lapeyre, 2002), however, the flow in the Ria deVigo is an open flow and the infinite time limit is thus onlyhypothetical.
We use the pdfs of FTLE values here to investigate whether thechoice of t as a multiple of the tidal period significantly influencesthe resulting FTLE field. Obviously, in Fig. 2b the convergence ofthe pdf’s mean and standard deviation with increasing t carriesthe imprint of the tidal semi-diurnal (and quarter-diurnal) fre-quency. This reflects that the separation of tracers in the flowdoes not evolve gradually, but intermittently with the tidaloscillations in the flow. Similarly, Orre et al. (2006) reports thatrelative and absolute dispersion in a tidal model in a Norwegianfjord depend strongly on the tidal cycles and mixing predomi-nantly happens during times of high velocities between high andlow tide. However, the evolution of the pdfs in Fig. 2 is smoothenough and does not imply a special preference for the choice ofthe advection time t. Meaningful LCS can thus be obtained with tclose to a typical time scale of the flow.
Second, the limited spatial extend of the velocity data is astrong limitation to the advection time, as tracers simply leavethe region where velocity data is available. One way to deal withthis problem is to calculate FTLE values at the moment just beforethe tracers reach the boundaries (Shadden et al., 2009), but thisleads to a non-constant time t for different tracers. Lekien andLeonard (2004) adapt t to the persistence time of a dynamicalregime obtained from Open-boundary Modal Analysis (OMA) ofHF radar velocity data. Here, we simply keep t short enough toprevent the tracers in the region of interest to reach the bound-aries. FTLE values of tracers that left the region are not computed(Abraham and Bowen, 2002).
We choose t¼ 24 h for the FTLE fields shown. This time can beextended for calm meteorological situations, when the mean flowin the Ria de Vigo is small and sharp FTLE ridges do not appearuntil t reaches several days. Finally, it must be mentioned that thestudied coastal flow can be subject to several transitions, espe-cially coupled with the wind forcing, so the choice of theadvection time remains a subtle task (Branicki and Wiggins,2010).
−0.05 0 0.05 0.1 0.15 0.20
0.05
0.1
0.15
0.2
PD
F p(
Λ+ )
τ = 2hτ = 6hτ = 12hτ = 24hτ = 48hτ = 60h
0 10 20 30 40 50 60 700
0.01
0.02
0.03
0.04
0.05
0.06
τ [h]
PD
F pa
ram
eter
s [h
−1]
Mean ⟨Λ+⟩STD (⟨Λ+2⟩ − ⟨Λ+⟩2 )1/2
FTLE Λ+ [h−1]
Fig. 2. Tidal influence on particle separation. (a) Typical probability distribution
functions of a coastal FTLE field Lþ ðt, x!Þ. Distributions become narrower and
more peaked for increasing advection time t. (b) The evolution of the pdfs with
increasing advection time t shows an imprint of the tidal time scales, i.e., the pdf
parameters mean and standard deviation show semi-diurnal and quarter-diurnal
periods.
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–134
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Once reliable FTLE fields are obtained, estimates of the mani-folds, representing the LCS, are extracted as ridges in the forwardand backward FTLE field separately (Shadden et al., 2005; Sadloand Peikert, 2007). Then, the ridges are filtered using thresholdsfor the FTLE value and for the sharpness of the ridge, quantified bythe second (negative) derivative of the FTLE field across the ridge(Sadlo and Peikert, 2007).
4. Results
In Section 4.1 drifter trajectories are compared directly totrajectories of artificial tracers. In Section 4.2 we present theproperties of the obtained LCS in the Ria de Vigo and relate themto the drifter trajectories. Finally, basic circulation patterns in theRia de Vigo are discussed in terms of LCS of the surface flow(Section 4.3).
4.1. Comparison of trajectories: drifters—model
At first, we perform a classical approach and compare trajec-tories of the real drifters to trajectories of artificial tracers that areadvected with the model velocity data. Apart from the windforcing entering the hydrodynamic model, we do not use anyadditional direct wind forcing on the artificial tracers. We are
aware that the drifters could be modeled in a more sophisticatedway, taking into account its vertical extension at the boundary ofthe wind and water flow. Possible effects are drifter displacementdue to wind, wave-induced Stokes drift and sub-scale dynamicsnot resolved by the hydrodynamic model. Including these addi-tional forcings can lead to a better agreement between thetrajectories of modeled tracers and real drifters when appropriatedata of the forcings are available (Furnans et al., 2008; Price et al.,2006). Such a detailed model of drifting objects is especiallydesirable for search and rescue missions or for operationalpollution management. Here, however, the objective is to studythe surface transport as predicted by the operational model and,therefore, we use the same ideal point-like tracers for the directcomparison of trajectories as for computing the FTLE fields. Theuppermost layer of model velocity data is the most appropriate tocompare to our Lagrangian data of real drifters. In the followingthe term ‘tracer’ is used shortly for ‘artificial tracer’ in contrast to‘drifter’ for the real drifters.
Figs. 3–6 show the four drifter experiments considered due tothe presence of LCS that interact with the drifter trajectories. Thefirst panel (a) respectively shows the trajectories of real driftersand artificial tracers starting at the release point. The other twopanels (b) and (c) compare the Lagrangian velocity of the drifterswith the Eulerian velocities of the model in order to interpret theseparation of trajectories. Drifter velocities are estimated from
55’ 54’ 53’8°W52.00’
51’ 50’ 49’ 48’
11’
12’
42°N 13.00
14’
15’
16’Release pointArtficial tracersDrifter
5 10 15 20 25 30−0.3−0.2−0.1
00.1
vx [m
/s] Model
Drifters
5 10 15 20 25 30−0.3−0.2−0.1
00.1
vy [m
/s]
time [h]
ModelDrifters
−0.3 −0.2 −0.1 0 0.1−0.3
−0.25
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
Drifter velocity [m/s]
Mod
el v
eloc
ity [m
/s]
R = 0.78 ΔRMS = 5.2 cm/s
Fig. 3. Experiment 1. (a) Trajectories of drifters and artificial tracers. (b) Comparison of the Lagrangian velocity of the drifters with the Eulerian velocity of the model
interpolated to hourly drifter positions. (c) Scatter plot of Eulerian model velocity and Lagrangian drifter velocity components shown in (b) revealing the degree of
correlation between both.
50’ 49’ 8°W48.00’
47’ 46’
14.00’
14.50’
42°N15.00’
15.50’
16.00’
16.50’ Release pointArtficial tracersDrifter
0 5 10 15 20 25
−0.1
0
0.1
vx [m
/s] Model
Drifters
0 5 10 15 20 25−0.1
0
0.1
vy [m
/s]
time [h]
ModelDrifters
−0.1 −0.05 0 0.05 0.1 0.15
−0.1
−0.05
0
0.05
0.1
0.15
Drifter velocity [m/s]
Mod
el v
eloc
ity [m
/s]
R = 0.68ΔRMS = 4.5 cm/s
Fig. 4. Experiment 2. Corresponding diagrams as in Fig. 3.
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–13 5
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finite differencing of the hourly position data and the Eulerianvelocity of the model is a linear interpolation of the 2-dimen-sional model velocity field at the surface to the drifter position.Note, that the latter is not the Lagrangian velocity of the artificialtracers, but velocities are compared along the trajectories of thereal drifters. Panel (b) shows that the modeled velocities are in areasonable agreement with the measured drifter velocities. Astrong tidal signal with a semi-diurnal period can always be seenin both data sets that identifies the tide as the main forcing forboth. In panel (c) correlation coefficients Rcorr are around 0.8 forexperiments 1 and 3, while in experiments 2 and 4 the agreementis lower with correlation coefficients of 0.68 and 0.64 respec-tively. An overview can be found in Table 2. We also quantifythe deviation between drifter and model velocity componentsas Dvi ¼ vdrifter
i �vmodeli , i¼ x,y. The root-mean-square deviation
RMSðDvÞ ¼/Dv2S1=2 is a measure of the typical deviation
between model and drifter velocities. It is in the order of 5 cm/sfor our experiments (Table 2), similar to other studies wherecoastal drifters are compared to current data from High Fre-quency (HF) Radar (Ohlmann et al., 2007; Molcard et al., 2009).
Despite the reasonable agreement of the velocity data, the realand artificial trajectories in experiments 2 and 4 separate drasti-cally. The drifter trajectories of these two experiments show howvelocity differences between the artificial and real tracers at thebeginning of the experiment (here mainly in the x-direction,Figs. 4b and 5b) lead to strongly diverging trajectories in thefollowing 24 h. This divergence is partly due to the inherentbehavior of Lagrangian chaos where small initial separations growexponentially in time.
In order to quantify the accuracy of trajectory prediction (withvelocity data from High Frequency (HF) Radar), Molcard et al.(2009) and Ullman et al. (2006) set the separation of drifters andartificial tracers
dðtÞ ¼/9 r!ðtÞdrifter� r
!ðtÞtracer9S ð3Þ
in relation to the total traveled distance of the drifters
DðtÞ ¼/9 r!ðtÞdrifter� r
!ð0Þdrifter9S ð4Þ
The ratio dðtÞ=DðtÞ denotes a relative error of the trajectoryprediction and for identical trajectories it is zero. Similar Lagran-gian error metrics have also been introduced by Toner et al.(2001).
58’ 56’ 8°W 54.00’
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42°N10.00’
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14’
Release pointsArtficial tracersDrifter
5 10 15 20−0.4
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0
vx [m
/s] Model
Drifters
5 10 15 20−0.4
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0vy
[m/s
]
time [h]
ModelDrifters
−0.4 −0.3 −0.2 −0.1 0 0.1
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−0.2
−0.1
0
0.1
v drifter [m/s]
v m
odel
[m/s
]
R = 0.83 ΔRMS = 7.2 cm/s
Fig. 5. Experiment 3. Corresponding diagrams as in Fig. 3.
55’ 54’ 53’ 8°W52.00’
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/s] Model
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vy [m
/s]
time [h]
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0
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Drifter velocity [m/s]
Mod
el v
eloc
ity [m
/s]
R = 0.64 ΔRMS = 6.9 cm/s
Fig. 6. Experiment 4. Corresponding diagrams as in Fig. 3.
Table 2Comparison of real drifters with artificial tracers.
# d/D Separation
rate (km/h)
Form of
trajectoriesRMS(Dv)
(cm/s)
Rcorr
1 0.3 4/12 Directional 5.2 0.78
2 1.0 3/24 Oscillating 4.5 0.68
3 0.5 5/12 Directional 7.2 0.83
4 1.0 3/24 Oscillating 6.9 0.64
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–136
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We use this measure to further distinguish qualitatively theflows in experiments 1 and 3 from those in experiments 2 and 4(Table 2). For experiments 2 and 4 the ratio dðtÞ=DðtÞ has relativelyhigh values of the order of one, as the drifters are located in anoscillating chaotic tidal flow with several return points in thetrajectories resulting in a small traveled distance D(t). In contrast,in the unidirectional (wind-driven) less chaotic flow in experi-ments 1 and 3 the traveled distance of the drifters D(t) is large,leading to small ratios dðtÞ=DðtÞ of 0.3 and 0.5. The total separationrate between modeled and real trajectories is almost a factor2 higher for the directional flows with 4 km/12 h compared to theoscillating flows with 3 km/24 h, but is overcompensated in theratio dðtÞ=DðtÞ by the large traveled distance D(t). Our separationrates are at the lower part of the typical range of 4–25 km/dayfound in open ocean studies as reported in Huntley et al. (2011).Velocities and especially velocity gradients in our strong tidalflow can be expected to be as high as or higher than in the openocean, so it is meaningful to compare our results to separationrates in the open ocean. An important difference, however, is thepresence of the strong constraint the coastline imposes on ourmodel flow and the well-defined forcing of the tides that in largeparts determine the coastal model flow. This probably leads to therelatively low separation rates between drifters and modeledtracers that we find.
Based on the above comparison of drifter and model velocitydata, we can consider a basic validation of the model and assumethat the hydrodynamic model serves to approximately representthe flow in the Ria de Vigo. However, especially in two experi-ments we see that the flow is highly irregular and not unidirec-tional, so a small initial deviation between the drifter velocity andthe model velocity can lead to a strong separation of the artificialtracers from the drifters. This strong dependence on initialconditions is an inherent property of chaotical systems. Therefore,instead of directly comparing trajectories, we concentrate on LCSas a more suitable approach to compare the drifter data set to thehydrodynamic model.
4.2. LCS in the Ria de Vigo
As described in Section 3.2 LCS are obtained from tracersadvected with the Eulerian velocity field given by the hydrody-namic model. Fig. 1 shows an example of the model surfacevelocity field with a relatively unidirectional tidal in and outflow,that interacts in the outer parts of the estuary with the north-south flow on the shelf and with the Cies Islands off the coast.Fully developed eddies are absent, but some rotational structuresappear as recirculations behind sharp capes. These have veryshort lifetimes of few hours, mostly less than a turnover time.Thus, in the investigated flow hyperbolic separation points arepredominantly situated at the coast and are rarely found in thecalmer center of the bay. Artificial tracers mostly separate due toa drift towards a coastal boundary or an island. Therefore, mostLCS are connected to the coast with one end and extend a distanceinto the flow that depends on the advection time t (Shaddenet al., 2009; Lekien and Leonard, 2004; Lekien et al., 2005).
Fig. 7 shows a case of pronounced repelling LCS in the Ria deVigo with the above mentioned characteristics for a long advec-tion time of t¼ 60 h. Such long advection times are feasible for aslow mean flow when artificial tracers stay inside the area ofinterest. We plot a square of artificial tracers at their initialpositions consisting of three regimes separated by repelling LCSthat mark three different water bodies. The distinct final positionsof the three tracer regimes demonstrate the predicting characterof the LCS: the green tracer regime (1) leaves the estuary north-wards and enters the Ria de Aldan Bay, while the cyan regime(2) is caught at the north coast of the Ria de Vigo close to Cape
‘Cabo Home’, and the blue regime (3) is drifted eastwards into theestuary. Note the lobe defined by a strong ridge that encloses thewater body that will be exchanged through the north mouth.These semi-circular structures in context with the exchange ofwater through a narrow channel can also be observed in FTLEfields of a tidal flow in a Norwegian fjord (Orre et al., 2006) and isprobably due to strong shear. The enclosed area might even serveto estimate the exchange flux. Maximal FTLE values are around0:08 h�1 corresponding to an exponential separation at a timescale of 12 h, i.e., one tidal period.
In the following we perform a detailed comparison ofthe drifter trajectories to ridges in the FTLE field on the basis ofFigs. 9–12. The LCS are estimates of transport barriers for themodel flow and we expect those LCS to be relevant for thetrajectories of the real drifters as well, in the sense that driftersdo not cross the LCS and follow the water bodies that are definedby the LCS. In Fig. 8 an idealized sketch of LCS observed in themodel flow is completed with the principal transport directions inorder to help to interpret the following maps of extracted LCS.
Ria de Aldán
A
B
C
1 2
3
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Λ+ [h−1] τ = 60h − 05/02/2010 06:00:00
0
0.01
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8°W51.00’
Fig. 7. Prominent transport barriers in the Ria de Vigo during a period with south
wind, 05/02/2010. The FTLE field from forward advected tracers Lþ ð x!Þ shows
sharp ridges connected to capes and islands that are identified with LCS. The Cies
Islands (A and B) and the Cape ‘Cabo Home’ (C) are decisive coastal boundaries for
directing the flow and are attaching points for repelling LCS. Three regimes of
colored artificial tracers released in a square (1–3) demonstrate the distinct final
positions of the tracers after the advection time t¼ 60 h. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
this article.)
Λ+ Λ-
Fig. 8. Idealized sketch of typical obtained LCS patterns. The flow separates and
converges due to coastal boundaries (black area), hence LCS are tied to the coast.
Repelling (stable/red) LCS are extracted from the forward FTLE field Lþ and
attracting (unstable/blue) LCS are extracted from the backward FTLE field L�. The
principal directions of transport are indicated with arrows. (For interpretation of
the references to color in this figure legend, the reader is referred to the web
version of this article.)
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–13 7
Author's personal copy
The dynamics in the flow is represented by the time depen-dent FTLE field and the extracted LCS, shown here in snapshots.Animations of the FTLE fields reveal the full dynamics includingthe tidal oscillations of the LCS (see on-line supplementary data,Appendix A). Moreover, in regions where LCS are absent thetemporal dynamics of the background FTLE field is a goodestimate of the underlying flow, or simply said, the backgroundFTLE field moves almost exactly with the flow.
The main feature in Fig. 9 is an attracting (unstable/blue) LCS(L1) connected to Cape ‘Cabo Home’ (C) that marks the line ofconvergence between water entering the north mouth and waterfrom inside the Ria de Vigo. Both drifters deployed inside the Riade Vigo stay essentially east of this LCS along the entire experi-ment while being advected to the south. The drifter trajectoriesare also consistent with another attracting (unstable/blue) LCS(L2) emerging from the eastern most cape at the north coast. ThisLCS marks the abrupt movement in the drifter trajectories 4 hafter the release stemming from the change of direction of thetidal flow at low tide, see Fig. 9a and animation in supplementarydata. The repelling (stable/red) LCS (L3) connected to San MartinoIsland (A) separating the outflow through the south mouth fromthe flow towards the island is crossed by one drifter. This suggestsa slight shift between the location of the LCS in the model and thereal flow. The other drifter follows the prediction by the model.
Fig. 10 shows experiment 2 at the north coast of the Ria deVigo. LCS appear due to recirculations behind capes but are lesspronounced as the tidal flow is basically oscillating parallel to thecoastal boundary. Drifters stay between an attracting (blue/unstable) LCS (L1) and a repelling (red/stable) LCS (L2). Theobserved LCS turn out to be typical for tidal dynamics in theinner parts of the Ria de Vigo.
Fig. 11 shows experiment 3, a closeup of the separation ofdrifters in the tidal channel between San Martino Island (A) andMonteagudo Island (B). Wind and flow direction are similar toexperiment 1 (Fig. 9). Drifters were deployed in the channelduring falling tide in order to check the LCS of the outflow. Wewant to highlight that even at the small scale of the order of 1 kmthe initial LCS are principally consistent with drifter trajectories.This agreement might be explained by the well defined flow inthe small zone of interest due to a strong constraint imposed bythe surrounding coastal boundaries. The repelling LCS (L1 and L2)between the initial positions of the drifters correctly predict thatone drifter passes the channel, the second runs aground on SanMartino Island (A) and the third drifts south, passing the island onthe eastern side. Only later, the westernmost drifter crosses anattracting (unstable/blue) LCS (L3) twice indicating a deviation ofthe model from the real flow.
Fig. 12 shows experiment 4 in calm conditions, i.e., without adirected longterm flow on the shelf outside the estuary. Mixing ofneighboring water bodies and the resulting LCS are mainly due toan oscillating tidal flow around the Cies Islands. Drifter trajec-tories are consistent with a repelling (red/stable) LCS (L1) separ-ating water inside the Ria de Vigo from water that moveswestwards around the eastern cape of San Martino Island. Inthe second half of the experiment drifters move to the center ofthe basin without the influence of any further pronounced FTLEridges.
We compared drifter trajectories of four experiments to esti-mated transport barriers (LCS) from the model flow, and we findthat overall LCS serve to predict and visualize the transport at thesurface in the real flow in a global way. The used methods toestimate transport barriers (LCS) from FTLE fields turn out to beappropriate for the analyzed flow. Uncertainties of the positions ofthe transport barriers can be observed in at least two cases when adrifter crosses a pronounced transport barrier. Shadden et al. (2009)
56’ 54’ 8°W52.00’
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1km
A
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L1L2
L3
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0
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1km
A
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L1L2
L3
Λ± [h−1] t = 15h
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0
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1km
A
C
L1L2
L3
Λ± [h−1] t = 22h
−0.1
−0.05
0
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0.1
0.15
Λ± [h−1] t = 4h
Fig. 9. Drifters and LCS in experiment 1. Current positions of the two drifters are
shown as green circles, starting at the release point (black square) and moving
along the trajectories with hourly resolution (green line with black dots). The
background field is the combined FTLE field L7ð x!
,t,tÞ in units 1/h. Advection
time is t¼ 24 h. Extracted repelling (attracting) FTLE ridges are drawn in red
(blue). The failure of one of the drifters for some hours is indicated by a black line.
(For interpretation of the references to color in this figure legend, the reader is
referred to the web version of this article.)
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–138
Author's personal copy
estimates an error for the position of the transport barrier based oncrossing events. Here, the error would be in the order of 1 km,corresponding to approximately three grid cells of the model flow.In general, the model cannot be expected to represent the real flow
57’ 56’ 55’ 8°W54.00’
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L2L3
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B
L3
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0
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0.15
Λ± [h−1] t = 1h
Λ± [h−1] t = 3h
Λ± [h−1] t = 5h
Fig. 11. Drifters and LCS in experiment 3. Legend as in Fig. 9. Initial LCS correctly
indicate that one drifter goes offshore through the channel, the second runs
aground at San Martino Island (A) and the third is drifted south around the eastern
cape of San Martino Island. Later, the westernmost drifter crosses an attracting
(unstable/blue) LCS twice. The noisy structure at the bottom of the FTLE field
appears because forward advected tracers leave the region of available velocity
data. (For interpretation of the references to color in this figure legend, the reader
is referred to the web version of this article.)
49’ 8°W48.00’
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1km
L1
L2
Λ± [h−1] t = 5h
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0
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1km
L1
L2
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0
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1km
L1
L2
Λ± [h−1] t = 13h
−0.1
−0.05
0
0.05
0.1
Λ± [h−1] t = 9h
Fig. 10. Drifters and LCS in experiment 2. Legend as in Fig. 9. Drifters move in a
zone with small dispersion between two FTLE ridges that are connected to a cape
at the north coast.
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–13 9
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exactly, as the bathymetry is complex and the wind forcingincluded in the hydrodynamic model does not respect local effectslike shadowing of the mountains with a height up to 500 msurrounding the estuary. However, temporal sequences of drifter
positions plotted over the LCS positions allow for a visual compar-ison of drifter trajectories to integral geometrical structures of themodel flow. As a principal result, the subdivision of the flow intodynamically different water bodies can be roughly predicted by themodel. In contrast, the direct comparison of trajectories of driftersto simple artificial tracers reveals high discrepancies, as velocitydifferences between model and real flow accumulate in theintegration.
4.3. LCS during north and south wind conditions
The results demonstrate the relevance of the extracted LCS forthe real flow. However, LCS are highly dynamic and intermittent,especially in transient meteorological conditions (Branicki andWiggins, 2010). It is thus desirable to obtain more generalinformation about the Lagrangian transport at the surface beyondthe special cases of the four experiments. Wind forcing and theinduced flow on the shelf play an important role for the circula-tion in the outer parts of the Galician Rias (deCastro et al., 2000).At the western Galician coast two wind directions are dominantthat can also be related to upwelling and downwelling processes:northerly winds (often during summer) and southerly/westerlywinds (often during winter). Here we extract LCS in these twometeorological conditions and show a Lagrangian sketch of theshort-time surface circulation in the Ria de Vigo. Fig. 13 showsLCS of the two typical flow patterns selected as examples for itspronounced north–south mean flow on the shelf indicated bywhite arrows. The LCS are time dependent and oscillate with thetide but they are computed for a time t¼ 24 h, twice the tidalperiod, and can be considered to represent the Lagrangian patternof the short-time residual flow. Their persistence time is in theorder of days, comparable to the persistence time of the flowpattern due to the wind forcing. In contrast to Eulerian measures,the LCS reveal the spatial information where surface watermasses from the shelf and from the estuary converge or separate.The Cies Islands (A and B, Fig. 1) and Cape ‘Cabo Home’ (C, Fig. 1)play a key role for this circulation, since pronounced LCS areattached to these coastal boundaries. The inner and outer partsof the Ria de Vigo are not strictly separated, but surface waterenters (leaves) the inner parts of the estuary during south wind(north wind).
During south wind conditions (Fig. 13a), the most importantrepelling (stable/red) LCS mark the flow separation at the CiesIslands (L1) and at Cape ‘Cabo Home’ (L2). Only the water body in-between the LCS (L1) and the coast enters the Ria de Vigo at thesouth and most of the water leaves the estuary through the northmouth again. Attracting (unstable/blue) LCS connected to the CiesIslands in the north (L3) show that the outflow stays attached tothe coast, drifting north into the Ria de Pontevedra. During northwind conditions (Fig. 13b), the flow is almost inverse to the flowduring south wind conditions. A prominent attracting (unstable/blue) LCS (L4) impedes surface water to enter into the innerestuary from the north. The water body between Cies Islands andCape ‘Cabo Home’ passes on both sides of San Martino Island andis drifted offshore. Under both conditions, a transport barrierextending in north-south direction and connected to the CiesIslands clearly separates the flow that interacts with the innerpart of the Ria de Vigo from the flow that passes by on the shelf.Note the two bays Ria de Aldan and Ria de Baiona which arealmost cut off from the rest of the surface water exchange by LCSin both cases. These zones of retention can be of special impor-tance for ecological studies as high concentrations of contami-nants or biological tracers can persist in these areas. Even thoughthe discussed LCS under north wind and south wind conditionsare subject to a certain variability, they correspond to typical flowpatterns in the model appearing under similar meteorological
1km
L1
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Λ± [h−1] t = 4h
Λ± [h−1] t = 9h
Λ± [h−1] t = 15h
15’
14’
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42°N12.00
10’
9’
15°
14°
13°
11°
42°N12.00
10°
9°
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42°N12.00
10°
9°
56’ 54’ 8°W52.00
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56’ 54’ 8°W52.00
50’ 48
56’ 54’ 8°W52.00
50’ 48
Fig. 12. Drifters and LCS in experiment 4. Legend as in Fig. 9. Even though the
trajectories of drifters and artificial tracers deviate strongly in this experiment
(Fig. 6), the repelling (stable/red) LCS close to San Martino Island computed from
the model is consistent with the drifter trajectories. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
this article.)
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–1310
Author's personal copy
conditions. Their relevance for the trajectories of real surface driftershas been demonstrated for the four experiments (Section 4.2).
5. Discussion and conclusions
In this work we studied Lagrangian surface transport atsubmesoscale (1–10 km) in a tidal estuary by comparing trajec-tories of surface drifters to Lagrangian Coherent Structures (LCS)computed from the output of a coastal hydrodynamic model.Similar to recently reported results (Shadden et al., 2009), we findthat drifter paths are better characterized by LCS than by singleartificial tracers. The drifter experiments show that the positionsof the LCS have uncertainties of about 1 km as the model tends tounderestimate the dynamics. Nevertheless, the LCS give an idea ofthe fundamental structure of Lagrangian transport imposed bythe prominent coastal boundaries that can be expected in differ-ent meteorological cases. This demonstrates the importance of
the Lagrangian view on the output of coastal models and thepower of the LCS method in the analysis for these flows.
We are aware that care must be taken when analyzing acoastal flow only horizontally. Vertical flow most often cannot beneglected as upwelling and downwelling processes or typicalvertical estuary circulation imply. Vertical flow can lead todivergence in the 2-dimensional surface flow that changes theFTLE fields (Haza et al., 2010). We also observe the occurrence ofnegative FTLE values (see Fig. 2a) corresponding to zones ofhorizontal convergence. Furthermore, Branicki and Malek-Madani (2010) have suspected that a part of LCS extracted fromestuary model flows can be artifacts due to coarse boundaryconditions and imprecise forcings. In our case, the relativelyaccurate tidal forcing determines a large part of the dynamics,but coarse wind data and unresolved coastal topography, as wellas the assumed approximations for the hydrodynamic equationscan certainly limit the reliability of the model output. Never-theless and in spite of these limitations, the LCS can reveal asurface footprint of the total 3-dimensional transport given by themodel. The LCS analysis applied to model data can be especiallyinteresting in regions where direct measurements of the velocityfield (e.g., HF Radar) are not available.
Due to its importance in fishery and seafood production theRia de Vigo is a region of intensive biological and ecologicalstudies where the transport of nutrients, plankton, fish eggs,larvae, etc., plays an important role. Visualized surface transportpatterns can be a useful hint for such studies. They can help totake horizontal transport processes into account as an explana-tion for biological observations (Perez-Munuzuri and Huhn, 2010;Lehahn et al., 2007).
Future work could deal with a closer look at the position errorof the LCS which can be determined by lines of drifters deployedacross a predicted LCS. Moreover, the challenging task of3-dimensional LCS in coastal models has been addressed byBranicki and Malek-Madani (2010) and reliable results would bevaluable for many ecological transport problems.
Acknowledgments
This work was financially supported by Xunta de Galicia throughthe project DRIFTER (ERACCT2005-016165) within the framework ofthe EU ERA-Net initiative (6th Framework Program), the ResearchGrant no. PGIDIT09MDS009CT and the Interreg IV-A (Galicia-Northof Portugal) project RAIAco (0520_RAIA_CO_1_E). A.v.K. and F.H.receive funding from FPU nos. AP-2009-0713 and AP-2009-3550.We especially want to thank Garbine Ayensa Aguirre for helping tocollect the drifter data and the Galician Coast Guard for supportingthe field work, as well as Eva Perez for making accessible themodel data.
Appendix A. Supplementary materials
Supplementary data associated with this article can be found inthe online version of http://dx.doi.org/10.1016/j.csr.2012.03.005.
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20’
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42°N12.00
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Λ± [h−1] 05/02/2010 14:00:00
Λ± [h−1] 16/06/2010 05:00:00
Fig. 13. Examples of LCS in the Ria de Vigo for two typical meteorological situations:
(a) south wind in winter and (b) north wind in summer. White arrows denote the
approximate direction of the mean flow on the shelf. LCS (denoted L1–L4) allow to
distinguish the water entering, leaving and passing by the Ria de Vigo.
F. Huhn et al. / Continental Shelf Research 39–40 (2012) 1–13 11
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