M ulti-disciplinary/scale m odeling o f the Scheldt Estuary and tidal
river netw ork (a collection o f articles from 2009 to today)
de Brauwere A nouk
Université catholique de Louvain, Institute o f Mechanics, Materials and Civil Engineering (IMMC), 4
Avenue G. Lemaître, Bte L4.05.02, B-1B48 Louvain-la-Neuve, Belgium
E-mail: anouk.de brau we re@uclouvain.be
From 2007 to today, A n ou k de Brauwere has been the d riving force behind several innovating
m odelling developm ents w ith applications to the Scheldt Watershed. Functioning as a bridge
between hydrodynam ica! m odellers at UCL and tw o teams o f environm ental expe rim en talists at VUB
(metals) and ULB (fecal bacteria), she coordinated the im plem entation o f a m ulti-disciplina ry, and
multi-scale reactive tra n sp o rt m odel to study environm ental questions in the Scheldt Basin. The key
concept o f th is study was ‘ in te g ra tio n ’: integ ra tion o f the necessary m u lti-d isp lin a ry knowledge
(hydrodynam ics, com p uta tio na l flu id mechanics, m icrobiology, (geo)chem istry), but also the spatial
integration o f m orph olo gica lly and dynam ically d is tin c t regions, resulting in a single model
representing the whole tid a l continuum from Ghent to the North Sea. Thanks to th is integrative
nature, the m odel has a unique potential to study processes and concentrations at the basin-scale,
i.e. e x p lic itly including all forcings. This offers possibilities not o nly to better understand the
processes and th e ir effects, but also to assess the im pact o f hypothetical fu tu re (managem ent or
accidental) scenarios fo r the whole Scheldt Watershed and the North Sea.
Three main study subjects were studied so far:
1. Hydrodynamica! modelling and timescales for water transport
This new model was b u ilt using the general architecture o f the Second-generation Louvain-la-Neuve
Ice-ocean Model (SLIM, w w w .clim a te .b e /slim ). The specificity o f th is m odel is th a t it uses the fin ite
elem ent m ethod to solve the governing equations, which allows fo r the use o f unstructured meshes
fo r the spatial discretisation o f the dom ain. An unstructured mesh has a resolution th a t can greatly
vary over the dom ain, i.e. in sub-regions o f interest or subject to more com plex dynamics the
resolution (and thus the com putational e ffo rt) can be increased compared to o the r areas. This
im plies a great fle x ib ility th a t has unique advantages fo r m ulti-scale/physics problem s. In the case
o f the Scheldt, th is fle x ib ility has enabled the integration o f the upstream tid a l river netw ork, the
Scheldt Estuary as well as the N orth-w estern European C ontinental Shelf in one single model. The
large marine part facilitates a more accurate sim ulation o f the tides or storm surges as th ey enter
the Scheldt Estuary. Yet, as the mesh is less resolved in th is large part o f the dom ain (grid size ~
50 km com pared to a resolution down to 60 m in the estuary), the com putational cost is only
doubled compared to a situation where o nly the Scheldt Estuary and the tid al rivers would be
included.
A fte r having validated the hydrodynam ica! m odel (de Brye et al., 2010), the m odel was not yet
practical fo r environm ental applications. In th is form , the inform a tion is s till very com plex (fields
varying spatially and te m p o ra lly at a high resolution) and hence d iffic u lt to use fo r diagnostic
purposes. Therefore, it is useful to derive diagnostic variables which sum m arize some o f the main
tra n sp o rt features present in the com plex raw hydrodynam ica! outputs. This is the general
m otivation behind the use o f tim escales like w ater residence tim e and w ater age, which are often
used in b io log ica l/ch em ical/g eo lo g ica l studies to express the tim e spent by w ater in a given dom ain
which
can
then
be
conveniently
com pared
to
o the r
tim escales
of
more
b io log ica l/ch em ical/g eo lo g ica l relevance. We com puted these tim escales fo r the Scheldt Estuary,
com bining rigorous theoretical form ulas w ith the com plex hydrodynam ica! m odel, such th a t we can
be co nfid en t th a t th ey integrate all relevant physical processes (tim e-varying residual current, tides,
tu rb u le n t diffusion).
The d e fin itio n o f the residence tim e is the tim e th a t w ill be spent by a given w ater parcel in the
estuary u ntil it leaves it fo r the firs t tim e. According to th is d e fin itio n , it is clear th a t the residence
tim e is both variable in space (as it depends on where the w ater parcel is at the m om ent the tim e
m easurem ent is started) and tim e (since it w ill depend on the actual hydrodynam ica! co nditions at
the in itia l or release tim e). Therefore, in a firs t study we com puted the residence tim e fo r IB boxes
in the estuary (spatial variability) and fo r d iffe re n t in itia l tim es (tem poral variability) (de Brauwere et
al., 201 la).
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Great.
Britain
continental
Europe
Bath
Canai,
Port of
Antwerp
docks
mouth
U l I C I IL
Durme
Terneuzen
Canal
upstream
estuarine
limit
Scheldt
D ender
V
' Dyle
JOeine
Nete
Grote
Nete
Senne
50.93
The spatial variation was a pp ro xim a tely as expected, i.e. m onotonically decreasing tow ards the
m outh - except th a t fo r the m ost upstream box the residence tim e was close to zero. A t firs t, this
may seem co un ter-in tu itive but in fact it is in line w ith the d e fin itio n : close to the upstream
boundary o f the estuary the w ater w ill also q uickly ‘ leave the estuary fo r the firs t tim e ’, due to the
tides periodically pushing the w ater upstream . Obviously, th is is not consistent w ith the em pirical
meaning generally a ttrib u te d to the residence tim e: it is supposed to express the to ta l exposure o f
a w ater body in a dom ain. In order to account fo r th is generalisation an alternative tim escale has
been defined: the exposure tim e. When com puted fo r the IB boxes in the Scheldt Estuary, the
exposure tim e in the m ost upstream box is indeed the highest, and in any box it is higher than the
respective residence tim e.
To investigate the tem poral va ria b ility o f the residence and exposure tim e, we com pared the
tim escales com puted fo r initia l tim es in w in te r and summ er, and fo r each season at high and low
tide. As expected, the tim escales are longer in summ er, due to the lower upstream river discharge.
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Equally expected was the fact th a t at low tide the tim escales were longer than when starting at high
tide - because at low tide the w ater w ill firs t be pushed up the estuary. However, it was to ta lly
unexpected to fin d th a t the difference between the high and low tide tim escales were so large: up
to alm ost 20 days. In o th e r words, at the m ost dow nstream box, the exposure tim e o f w ater parcels
‘ released’ at a 6 hour interval varies between 9 (start at high tide) and 28 days (start at low tide)!
These results illustrate th a t the seem ingly simple concept o f residence tim e hides several subtleties
th a t are often not considered in applications, but may be o f sign ifican t im portance. These
observations m otivated us to fu rth e r refine th is study. A firs t refinem ent consisted o f com puting the
‘ partial exposure tim e s ’ o f the IB estuarine boxes, i.e. the to ta l tim e spent in each box, instead o f
in the whole estuary. Doing th is fo r w ater in itia lly in each box at a tim e, we obtained a ‘connectivity
m a trix ’, relating the initia l position o f w ater w ith the tim e it spends in each box. T his inform a tion is
nothing but a sophisticated sum m ary o f the com plex underlying hydrodynam ics, b ut now it is much
more useful fo r applications, e.g. to q uickly assess the im pact o f an accidental p o llu tio n event
somewhere in the estuary on the d iffe re n t sub-regions o f the estuary, or to evaluate how long w ater
stays in subregions known to be favourable fo r the grow th o f a certain species.
In a subsequent refinem ent e ffo rt, we increased the resolution o f the com puted residence and
exposure tim e, such th a t th e ir value is now known fo r every m odel grid cell and m odel tim e step (de
Brye et al., 2012). This is appealing because it provides actual ‘ m ovies’ o f the tim escales varying in
tim e and space. However, the results are again too com plex to be easily usable fo r diagnostic
applications. The tidally-averaged pictures reveal th a t the residence and exposure tim es e x h ib it
su rp rising ly little lateral variation, i.e. the lo n g itu d in a l trend observed w ith the 13 boxes is relatively
accurate. In contrast, there is great spatial heterogeneity in the tem poral va ria b ility associated w ith
the tim escales, resulting fro m a com plex interplay o f bathym etry and w ater discharge.
Besides th is detailed study o f the residence and exposure tim es, the w ater age was also
investigated. As opposed to the firs t tim escales, the age is defined as the tim e since a given w ater
parcel has entered the estuary. Again, the age varies in space and tim e, but it is also dependent on
the ‘entrance’ th ro u g h which the w ater entered. In o th e r words, fo r each d iffe re n t w ater source, a
d iffe re n t age can be defined. In the case o f the Scheldt Estuary, a d is tin ctio n was made between
w ater com ing fro m upstream (freshwater), fro m dow nstream (sea water) and from lateral inputs like
canals and harbour locks.
With the above tim escale studies in the Scheldt Estuary, it has become a benchm ark application. For
instance, one recent study illustrated the m eaning o f another tim escale fo r w ater renewal, the socalled ‘ influence tim e ’, again on the Scheldt Estuary (Delhez et al., in review). New ongoing w ork
consists o f com puting yet another new tim escale, the ‘ partial age’ (a generalisation o f the age
concept), in the Scheldt Estuary.
2. Modelling Escherichia coli concentrations as an indicator of fecal pollution
Due to its intensive agriculture, high concentration o f in d u stry and large population density, the
Scheldt Watershed is subject to sign ifican t p ollutio n pressure. Discharge o f wastewaters or ru n -o ff
loaded w ith animal or human fecal m aterial degrades the m icrobiological w ater quality, i.e.
increases the risk o f having m icrobial pathogens present in the natural surface water. Because these
pathogens are too diverse, and often present o nly at very low concentrations, it is not feasible to
system atically m o n ito r all th e ir concentrations. Instead, it has been decided to measure the
concentration o f a small num ber o f so-called ‘fecal ind icato r bacteria’, o f which Escherichia coli
(E. coli) is one o f the m ost im portant. Its concentration in the Scheldt Watershed has been
m onitored in 2007-8 by colleagues at the ULB, but the results were so variable in tim e th a t they
were d iffic u lt to interpret. It is well known th a t E. coli concentrations can vary over orders o f
m agnitude in natural systems, but the possible causes in the case o f the Scheldt were too num erous
(water discharge, upstream inputs, wastew ater trea tm en t plant inputs, interaction w ith sediment,
tides, tem perature effect) to disentangle them em pirically. If we could o nly sim ulate all these effects
in a single model, we m ig ht be able to q u a n tify th e ir relative im portance... So, an E. coli m odule was
added to SLIM.
A firs t model considered only the tid al part o f the Scheldt Basin, and represented the bacteria as a
single pool (de Brauwere et al., 2011b). Yet, the results were already quite interesting. Indeed, it
appeared th a t the inputs due to the w astewater trea tm en t plants, as well as the tem perature effect
were negligible to explain the observed variability. In contrast, the w ater entering the tid a l dom ain
from upstream was already highly polluted, such th a t it to a great e xten t determ ined the levels
observed in the tid al river. This was especially the case fo r the w ater com ing fro m Brussels and
entering the tid al Scheldt via the Zenne, Dijle and Rupel. In com bination w ith the tid al m ixing
action, these h ighly concentrated upstream (and side) inputs caused greatly varying concentrations
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in the Scheldt. Downstream o f the main tribu taries, the gradual decay o f the bacteria and
continuous d ilu tio n results in a steep decrease o f the E. coli concentrations dow nstream o f Antw erp.
Close to the estuary m outh, the bacteria have alm ost disappeared, and the estuary has thus
e ffectively operated as a cleaning filte r.
In a second m odel, we fu rth e r extended both the geographical dom ain and the representation o f
the bacteria pools. By coupling SLIM (tidal rivers + estuary + sea) w ith an ecohydrological m odel o f
the upstream river catchm ent (Ouattara et a i, in press), we e ffectively integrated the com plete
Scheldt Watershed in a single sim ulation (de Brauwere et a i, 2014). Instead o f using these tw o tools
as com peting models, each o f them was used in the dom ain fo r which it was o rig in a lly designed and
clearly o u tp erfo rm s the o the r m odel. This resulted in a unique coverage o f the whole Scheldt lan dsea continuum fro m the source all the way to the North Sea. As the firs t m odel showed the
im portance o f the upstream rivers (and especially the Brussels area), th is integration allowed to
include all E. coli sources e xplicitly. In addition to the geographical m odel integration, we fu rth e r
refined the m odel by d ividing the bacteria pool in free -floa ting bacteria and those attached to
particles. While the firs t are transported along w ith the water, the latter are also subject to settling
and resuspension processes. To e x p lic itly represent these processes, a new suspended sedim ent
m odel has been developed w ith in the SLIM architecture (Gourgue e t a i, in press). The results o f this
second model study confirm the previous observation on the im portance o f the tides, and the weak
effect o f the wastewater trea tm en t plants in the tid a l part. Besides, th ey suggest th a t the sedim entrelated processes are actually not essential to reproduce the median E. co li concentrations along the
Scheldt, nor the observed va ria b ility at a given location. Nevertheless, the e x p lic it d istin ction
between free and attached bacteria increases the insig ht in the system and offe rs more
interpretatio n possibilities. As an illu stratio n o f the potential o f th is new m odelling tool, we also
perform ed tw o sim ulations considering extrem e (w orst case and best case) situations o f Brussels
wastewater management. The effect o f both scenarios is clearly observable all the way to Antw erp.
Several side-studies were also perform ed related to the E. coli m odel in the Scheldt. These studies
range from sem i-theoretical considerations on the param eterisation o f the settling flu x (de Brauwere
and Deleersnijder, 2010), establishing where and when new w ater q u a lity samples should be taken
in ord er to reduce the model uncertainty m ost (de Brauwere e t a i, 2009), derivation and
com putation o f the age associated to the bacteria (M atton, 2012), to the p ublication o f an
exhaustive literature review o f the e xistin g m odels fo r fecal ind icato r organism s in natural surface
waters (de Brauwere e t a i, in press).
3. First steps towards modelling metal spéciation
Besides m icrobiological w ater quality, SLIM could also be extrem ely useful fo r the study o f other
pollutants. Especially its large dom ain, and its a b ility to provide h ighly resolved (both spatially and
tem porally) o u tp u ts makes it an interesting to o l fo r risk assessments. Therefore, we started to build
a new SLIM m odule to allow the sim ulation o f dissolved and particulate metals (Elskens et a i, in
review).
By m erging the long-term data records collected by VUB, ULB and VMM, em pirical fu nctio ns were
derived, relating the to ta l metal concentration to environm ental variables (salinity and suspended
sedim ent concentration). This means th a t if SLIM sim ulates these environm ental variables, we can
reconstruct or predict the metal concentration at each location and each tim este p o f the sim ulation.
A second em pirical fu n ctio n was estiblished linking the metal p a rtitio n in g co efficie nt (i.e. the ratio
between particulate and dissolved metal concentration) to environm ental variables. A pplying this
fu nctio n to the SLIM o utp uts and the reconstructed metal concentrations then allowed producing
high-resolution fie ld s o f dissolved and particulate metal concentration. This means th a t SLIM can be
used to produce ‘ m ovies’ o f dissolved and particulate metal concentrations, allow ing in fin ite ly more
detailed analyses than based on d irect p oint m easurem ents alone. This being said, the lim ita tio n o f
th is approach lies in the em pirical fu nctio ns, which are only valid w ith in th e ir calibration dom ain. In
o the r words, although th is com bined model is already a sign ifican t step forw ard, it cannot be
tru s tfu lly used fo r scenario evaluations or even predictions fo r periods outside the one covered by
the calibration dataset (1980-2010). Therefore, we now focus on the developm ent o f a fu lly
m echanistic metal module.
Conclusion
The cited w ork has obviously been produced by a team o f researchers. Nevertheless, it is the m erit
o f A nouk de Brauwere to have facilita te d th e ir collaboration, crossing not only scientific boundaries,
but also language and in stitu tio n a l ones. A fte r 6 years, we are proud o f the results, but are also well
aware th a t the w ork is fa r from finished. There are clear scientific challenges w aiting fo r us: closer
collaboration w ith geochem ists and environm ental chem ists to develop a m echanistic metal model,
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investigate the potential o f m odelling newly em erging p ollutants like nanom aterials and endocrine
disruptors, ecological m odelling. N otw ithstanding the sig n ifica n t e ffo rt put so fa r in the scientific
integration, we w ant to fu rth e r increase it in order to dem onstrate the usefulness o f our developed
tools. Yet, if we really w ant to go to the next level, we should include players and interests beyond
the science platform . The Scheldt Basin being densely populated, better understanding and
predicting the com plex dynamics o f the river system and its response to the diverse p ollution
pressures has a clear im portance fo r society. We see o u r application to the VLIZ North Sea Award as
a firs t a tte m p t to take th is step.
References
de Brauwere A., F. De Ridder, O. Gourgue, J. Lambrechts, R. Combien, R. P in te lo n J . Passerai, P.
Servais, M. Elskens, W. Baeyens, T. Kärnä,.B. de Brye and E. Deleersnijder. 2009. Design o f a
sam pling strategy to o p tim a lly calibrate a reactive tra n s p o rt m odel: Exploring the potential fo r
Escherichia coli in the Scheldt Estuary. Environm ental M odelling & Software 24: 969-981,
d o i:l 0 .1 0 1 6 /j.e n vso ft.2 0 0 9 .0 2 .0 0 4 .
de Brauwere A. and E. D eleersnijder. 2010. Assessing the param eterisation o f the settling flu x in a
depth-integrated m odel o f the fate o f decaying and sinking particles, w ith application to fecal
bacteria in the Scheldt Estuary. Environ. Fluid Mech. 10:157-175.
de Brauwere A., B. de Brye, S. Blaise and E. Deleersnijder. 201 la . Residence tim e, exposure tim e and
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tra n sp o rt m odel w ith em pirical fu nctio ns. Science o f the Total Environment.
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Legat, (in press). A depth-averaged tw o-dim ensional sedim ent tra n sp o rt m odel fo r
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Matton V. 2012, M odélisation de l'âge des bactéries Escherichia coli dans l'estuaire de l'Escaut,
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