© Acta hydrotechnica 19/30 (2001), Ljubljana
ISSN 1581-0267
25
UDK / UDC: 504.4:519.61/.64:546.49:551.46(262.3) Prejeto / Received: 25.8.2001
Izvirni znanstveni prispevek / Original scientific paper Sprejeto / Accepted: 21.12.2001
DOLGOTRAJNA 3D SIMULACIJA TRANSPORTA IN DISPERZIJE
ŽIVEGA SREBRA V TRŽAŠKEM ZALIVU
LONG-TERM 3D SIMULATION OF THE TRANSPORT AND DISPERSION
OF MERCURY IN THE GULF OF TRIESTE
Dušan ŽAGAR., Rudi RAJAR, Andrej ŠIRCA, Milena HORVAT, Matjaž Č ETINA
Za dolgotrajno simulacijo transporta in disperzije živega srebra v raztopljeni in na delce vezani
obliki smo dopolnili obstoječ i tridimenzionalni matematič ni model PCFLOW3D, s katerim je
mogoč e upoštevati gibanje vode zaradi vpliva vetra, plimovanja in gibalne količ ine rek, ki vtekajo v
zaliv ter stratifikacijo. Zbrani in prikazani so podatki o temperaturnih in slanostnih razmerah ter
vetru na območ ju Tržaškega zaliva. Ta se skupaj s podatki o pretoku, temperaturi ter vsebnosti
živega srebra v vodi in na delcih lebdeč ih plavin, ki dotekajo v zaliv s Soč o, predstavljajo vhodne
podatke modela. Z izdelanim scenarijem za dolgotrajne simulacije, ki temelji na sezonsko
povpreč nih vrednostih posameznih parametrov in z dodatnimi krajšimi vložki moč nega vetra in
visokih pretokov Soč e smo nadomestili dosedanji nač in simulacij s povpreč nimi letnimi vrednostmi.
Za verifikacijo in umerjanje izpopolnjenega modela smo uporabili meritve in opazovanja iz let 1995
– 1 997. Č eprav nekateri kompleksni procesi pretvorb živega srebra še niso povsem raziskani in jih
zato ni bilo mogoč e upoštevati pri simulacijah, je doseženo kvalitativno dobro ujemanje rezultatov
in meritev. Kjer je bila mogoč a kvantitativna primerjava, je ujemanje rezultatov v okviru faktorja
dve.
Ključ ne besede: živo srebro, matematič no modeliranje, 3D model,Tržaški zaliv
An existing three-dimensional mathematical model PCFLOW3D was upgraded to simulate long-
term transport and the dispersion of mercury in its dissolved and particulate form. Hydrodynamics
due to wind, tidal forcing and river inflow momentum can be simulated, and stratified conditions
can be taken into account. Data on temperature and salinity fields and winds in the Gulf of Trieste,
Soč a River discharges, suspended sediment concentrations and temperatures were collected and
interpreted. These data, together with measurements of mercury concentrations in the water,
suspended sediment, bottom sediment and pore waters in the Soč a River and the Gulf of Trieste are
used as input for the model. A scenario for long-term simulations on the basis of seasonally
averaged parameters and a few shorter inserts of strong wind and high discharges of the Soč a
River was developed as a substitute for simulations based on annual averaged input data.
Measurements and observation data from 1995 – 1997 were applied to verify and calibrate the
PCFLOW3D model. Although some complex mercury transformation processes are not well known
and were therefore not taken into account in the simulations, an acceptable qualitative agreement
of results and measurements was achieved. Whenever a quantitative comparison was possible, an
accordance of measured and computed results within a factor of two was attained.
Key words: mercury, mathematical modelling, 3D model, Gulf of Trieste.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
26
1. UVOD
Tržaški zaliv, skrajni severovzhodni del
Severnega Jadrana, obsega območ je v obsegu
25 x 30 km (slika 1 ). Povpreč na globina znaša
okrog 1 6 m, v najglobljem delu pa doseže 25
m. Meritve v zalivu kažejo moč no povišane
koncentracije živosrebrovih (Hg) spojin v
vodi, sedimentu in vodnih organizmih.
Koncentracije v naravnem zaledju so v vodi in
organizmih Tržaškega zaliva presežene za red,
v sedimentu pa celo za dva reda velikosti.
Obč asne anoksije v globljih plasteh zaliva
lahko pospešijo proces metilacije Hg, ki v
metilirani obliki škodljivo vpliva na celotno
prehransko verigo in s tem predvsem na
okoliško prebivalstvo. Raziskave dokazujejo,
da je glavni vir onesnaženja z živim srebrom v
Tržaškem zalivu zdaj že opušč eni rudnik v
Idriji. V sedimentu in lebdeč ih plavinah Idrijce
in Soč e so koncentracije Hg še vedno zelo
visoke, obe reki pa to živo srebro odnašata v
Tržaški zaliv.
1. INTRODUCTION
The Gulf of Trieste is situated in the eastern
part of the Northern Adriatic Sea. It covers an
area of about 25 x 30 km (Figure 1). The
average depth is about 16 m and reaches 25 m
in the central part. Recent measurements in the
Gulf have shown greatly increased mercury
(Hg) concentrations in the water, sediment and
some marine organisms. Concentrations in the
water and the biota were as much as an order
of magnitude higher, and concentrations in the
bottom sediment, even as much as two orders
higher than the corresponding natural
background values. Occasional anoxia at the
bottom of the Gulf may increase the
methylation of Hg; thus, there is a potential
impact on the humans living near the Gulf.
Recent studies have shown that the former
Idrija Mercury Mine, where mining was active
for about 500 years, is the main source of the
Hg pollution in the Gulf of Trieste. The
suspended and bottom sediment of both rivers,
the Idrijca River and the Soč a River is highly
contaminated with the Hg, which is carried
away to the Gulf of Trieste.
Slika 1 . Lega Tržaškega zaliva (levo), definicijsko območ je modeliranja in merske toč ke v
Tržaškem zalivu (desno).
Figure 1. The Gulf of Trieste: location (left) and the extent of the computational domain and
measuring points (right).
 
Gulf of Trieste
ADRIATIC / JADRAN
SREDOZEMSKO MORJE
500 km
40 N
16 E
Lignano
Grado
Monfalcone
Trieste
Koper
Piran
Soca
Tržaški zaliv
MEDITERRANEAN SEA

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
27
Še 10 let po zaprtju rudnika v Idriji se
koncentracije živega srebra v reč nih plavinah
ter vodi in sedimentu Tržaškega zaliva niso
znatno znižale (Horvat et al. 1 999; Horvat et
al. 1 998, Žagar in Širca, 2001 ). Zato je v teku
obsežna raziskava o kroženju živega srebra v
Tržaškem zalivu, pri kateri za določ itev
fizikalnih, bioloških in kemič nih parametrov
poleg meritev uporabljamo tudi matematič no
modeliranje. Sprva smo za simulacijo
hidrodinamič nih parametrov ter transporta in
pretvorb živega srebra razvili in uporabili
dvodimenzionalni (2D) stacionarni model
STATRIM. Rezultati 2D simulacij so
predstavljeni v Rajar et al. (1997) in v Širca in
Rajar (1997b). Z 2D modelom pa ni bilo
mogoč e izrač unati porazdelitve posameznih
parametrov po vodnem stolpcu, zato smo za
nadaljnje simulacije nadgradili obstoječ i
tridimenzionalni (3D) nestacionarni model
PCFLOW3D in ga uporabili za simulacijo
transporta in disperzije živega srebra v
Tržaškem zalivu. Več ina živega srebra v
zalivu je vezanega na delce lebdeč ih plavin,
zato je bilo treba razviti nov modul za
transport lebdeč ih plavin. Opis prvotnega
modela, sedimentacijskega modula in nekatere
simulacije transporta lebdečih plavin so
podrobno opisane v Rajar et al. (2000), Rajar
et al. (1 998) ter Rajar in Č etina (1 997).
2. OPIS TRIDIMENZIONALNEGA
MODELA PCFLOW3D
   Prvotni model PCFLOW3D za rač un
hidrodinamič nih parametrov ter transporta in
diperzije, izdelan na FGG, je bil že več krat
verificiran in uporabljen za reševanje
praktič nih problemov (modeliranje tokov in
širjenja polutantov) v Sloveniji in tujini.
PCFLOW3D je nestacionarni nelinearni
baroklini model, sestavljen iz hidro-
dinamič nega (HD), transportno-disperzijskega
(TD) in novega sedimentacijskega (ST)
modula. Diagram poteka modela je prikazan
na sliki 2, v nadaljevanju pa je podan kratek
opis posameznih modulov.
Even 10 years after the closure of the Idrija
Mercury Mine, concentrations in river
sediments, water and the sediment at the
bottom of the Gulf do not show a significant
decrease (Horvat et al. 1999, Horvat et al.
1 998, Žagar and Širca, 2001 ). Therefore,
extensive research on Hg cycling in the Gulf is
in progress. Besides the measurements of
physical, chemical and biological parameters,
mathematical modelling was also used to
simulate Hg cycling in the Gulf of Trieste. A
two-dimensional (2D) steady-state model
STATRIM was developed first for the
simulation of hydrodynamic circulation and
Hg transport and fate. Some of the results of
the 2D simulations using annually averaged
input data are described in Rajar et al. (1997)
and in Širca and Rajar (1997b). The simulation
of vertical distribution of the parameters was
not possible with the 2D model; therefore an
existing three-dimensional (3D) unsteady state
model PCFLOW3D was upgraded and used to
simulate the transport and dispersion of Hg in
the Gulf of Trieste. As most of the Hg flowing
to the Gulf, is bound to suspended sediment
particles, a new sediment transport module
was first developed and included into the
model. The basic model, the new sediment
transport module and some simulations of the
transport of suspended sediment are described
in detail in Rajar et al. (2000), Rajar et al.
(1 998) and Rajar and Č etina (1 997).
2. DESCRIPTION OF THE THREE-
DIMENSIONAL MODEL
     The PCFLOW3D hydrodynamic and
transport-dispersion model was developed at
the Faculty of Civil and Geodetic Engineering
of the University of Ljubljana. It has already
been applied to many practical hydrodynamic
and pollutant dispersion problems in Slovenia
and abroad. It is a non-linear baroclinic model
composed of three modules: a hydrodynamic
(HD) module, a transport-dispersion (TD)
module, and a recently developed sediment-
transport (ST) module. Figure 2 shows the
flow chart of the model and a short description
of the modules is given below.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
28
2.1 HIDRODINAMIČ NI IN
TRANSPORTNO-DISPERZIJSKI
MODUL
Diskretizacija diferencialnih enač b poteka
po metodi kontrolnih volumnov, sistem enač b
pa rešujemo s pomoč jo hibridne implicitne
numerič ne sheme. Koeficienta turbulentne
viskoznosti in difuzije sta v horizontalni smeri
konstantna, v vertikalni smeri pa je uporabljen
Koutitasov model turbulence. Z modelom je
mogoč a tudi simulacija nekaterih biokemič nih
procesov.
Enač be obeh modulov rešujemo soč asno,
saj izračunana porazdelitev temperature,
slanosti in poljubnega polutanta, ki lahko
vpliva na gostoto vode, hkrati vpliva tudi na
hitrostno polje. Tako lahko z modelom
upoštevamo tudi gostotne tokove in
stratifikacijo, ki je obič ajno izrazitejša v
toplejši polovici leta. Z modelom je mogoč a
tudi simulacija toplotnega onesnaženja;
vgrajene so enač be za rač un transporta in
disperzije toplote iz atmosfere ali drugih virov.
Transportno enač bo v modelu lahko rešujemo
po metodi konč nih razlik (MKR) ali po metodi
sledenja delcev (MSD), kar je odvisno od
konkretnega problema, ki ga rešujemo. Za
rač un transporta živega srebra smo uporabili
MKR.
V 3D modelu še niso vključ ene enač be za
simulacijo procesov pretvorb živega srebra. Z
modelom je trenutno mogoče rač unati
transport in disperzijo nemetiliranega in metil-
živega srebra v raztopljeni in partikularni
(vezani na delce lebdeč ih plavin) obliki.
2.1 HYDRODYNAMIC AND
TRANSPORT-DISPERSION MODULES
The HD and TD modules are both based on
the finite volume method; the system of
differential equations is solved using a hybrid
implicit scheme. In the horizontal plane, the
eddy viscosity and diffusivity are constant,
while in the vertical direction the simplified
one-equation turbulence model of Koutitas is
included. The simulation of some biochemical
processes has also been included.
The TD module, which is solved coupled
with the HD module, simulates temperature,
salinity or any contaminant which can
influence water density and, at the same time,
the velocity field. Therefore, stratified
conditions during the warmer half of the year,
as well as density-driven flow, can be
simulated using the model. The simulation of
transport and the dispersion of heat from heat
sources and from the atmosphere has also
recently been included to enable the simulation
of thermal pollution in surface waters. There
are two methods of solving the transport
equation in the model, a Eulerian finite
difference method (FDM) and a Lagrangean
particle tracking method (PTM). Each of them
has its benefits as well as its deficiencies. The
FDM was used for the Hg transport
simulations.
Hg transformation equations have not yet
been included in the 3D model. In the present
state, the transport of dissolved and particle-
bound Hg in both non-methylated and
methylated forms was simulated.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
29
2.2 MODUL ZA TRANSPORT PLAVIN
Z modulom za transport plavin, ki temelji
na enač bah iz literature (van Rijn, 1 993), so
mogoč e simulacije za nevezane delce plavin.
Temelj sedimentacijskega modula predstavlja
advekcijsko-disperzijska enač ba, zapisana za
koncentracijo lebdečih plavin, pri č emer
upoštevamo empirično rešitev za hitrost
usedanja delcev (van Rijn, 1993). Robni pogoj
ob dnu predstavlja usedanje oz. resuspenzija
delcev, ki je odvisna od strižnih hitrosti ob dnu
zaradi vpliva tokov (rezultat HD modula) in
valovanja. Za izrač un debeline nanešenega oz.
odnešenega materiala uporabimo kontinuitetno
enač bo za plavine.
2.2 THE SEDIMENT-TRANSPORT
MODULE
The sediment transport module is based on
the equations of van Rijn (1993). Non-
cohesive sediment material can be simulated.
The module basically resolves the advection-
diffusion equation for suspended sediment
concentration, where the empirical equation
for the sedimentation velocity of the particles
is accounted for (van Rijn, 1993). As the
bottom boundary condition, resuspension or
settling of the suspended sediment which
depends on the bottom shear stress caused by
current velocities (result of the HD module)
and wave parameters is calculated. The mass
conservation equation for the sediment is used
to calculate erosion/deposition thickness at the
bottom.
Slika 2. Diagram poteka modela PCFLOW3D
Figure 2. Flow-chart of the PCFLOW3D model.
 ADVECTION AND
DISPERSION OF
TEMPERATURE
AND SALINITY
 THE PCFLOW3D MODEL STRUCTURE
TOPOGRAPHY
WIND
TIDE
IN FLO W
VELOCITIES
SURFACE ELEVATIONS
HYDRODYNAMICS
TEMPERATURE FIELD
SALINITY FIELD
DENSITY FIELD
TEMPERATURE
SALINITY
IN FLO W
 SEDIMENT
TRANSPORT
 TOPOGRAPHY
WIND
SEDIMENT PARAMETERS
SETTLING VELOCITY
WAVE PARAMETERS
BOTTOM SHEAR STRESS
SEDIMENT
TRANSPORT
PARAMETERS
DISTRIBUTION OF
SUSPENDED SEDIMENT
EROSION / DEPOSITION
THICKNESS
FDM FDM
TRANSPORT OF POLLUTANTS (MERCURY)
 INFLO W
ADVECTION AND
DISPERSION OF
DISSOLVED
POLLUTANTS
DISTRIBUTION - 
CONCENTRATIONS
 INFLO W
ADVECTION AND
DISPERSION OF
PARTICULATE BOUND
POLLUTANTS
DISTRIBUTION - 
CONCENTRATIONS
 FDM FDM PTM
INFLO W
 ADVEKCIJA IN
DISPERZIJA
TEMPERATURE
IN SLANOSTI
 STRUKTURA MODELA PCFLOW3D
TOPOGRAFIJA
VETER
PLIMOVANJE
VTOKI / IZTOKI
HITROSTI
KOTE GLADINE
HIDRODINAMIKA
POLJE TEMPERATUR
POLJE SLANOSTI
GOSTOTA
TEMPERATURA
SLANOST
VTOKI / IZTOKI
 TRANSPORT
PLAVIN
 TOPOGRAFIJA
VETER
PARAMETRI PLAVIN
HITROST USEDANJA
PARAMETRI VALOVANJA
STRIZNE NAPETOSTI OB DNU
PARAMETRI
TRANSPORTA
PLAVIN
KONCENTRACIJE 
LEBDECIH PLAVIN
DEBELINA
EROZIJE / DEPOZICIJE
MKR-MKV MKR-MKV
MODUL ZA TRANSPORT POLUTANTOV (Hg)
 VTOK
ADVEKCIJA IN
DISPERZIJA
RAZTOPLJENIH
POLUTANTOV
PORAZDELITEV -
KONCENTRACIJE
 VTOK
ADVEKCIJA IN 
DISPERZIJA
POLUTANTOV VEZANIH
NA DELCE PLAVIN
PORAZDELITEV -
KONCENTRACIJE
 MSD
VTOK PLAVIN
MKR-MKV MKR-MKV
HIDRODINAMICNI
MODUL
SEDIMENTACIJSKI
MODUL

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
30
3. DOLGOTRAJNE SIMULACIJE
3.1 OSNOVNI PRINCIP
Za pravilno delovanje nestacionarnega 3D
modela moramo zagotoviti veliko količ ino
vhodnih podatkov. Na relativno velikem
območ ju Tržaškega zaliva je soč asno merjenje
vseh parametrov v zadostnem številu merskih
toč k tako rekoč neizvedljivo.
Pri modeliranju dolgotrajnih procesov
obič ajno zadošč ajo stacionarne simulacije s
č asovno povpreč nimi vhodnimi podatki za
daljša časovna obdobja, kalibracija in
verifikacija modela pa zahtevata simulacije v
realnem č asu za krajša obdobja, za katera
imamo na voljo rezultate meritev. Transport in
disperzija živega srebra pa je izrazito
nestacionaren proces. Več kot 90 odstotkov
letnega vnosa lebdeč ih plavin, ki jih v zaliv
prinese Soč a, je posledica dveh visokovodnih
valov, ki se praviloma pojavljata ob
pomladanskem in jesenskem deževju. Prav
tako so najpomembnejši vzrok za premešč anje
plavin obdobja moč nega vetra (burje), ki
ponavadi nastopajo pozimi, med novembrom
in februarjem.
Popolna nestacionarna simulacija za
obdobje več mesecev kljub številnim
meritvam različnih vhodnih parametrov
modela ni bila izvedljiva, zato smo uporabili
nov pristop. Povpreč ne letne vhodne podatke
smo nadomestili s sezonsko povpreč nimi, pri
č emer smo upoštevali štiri glavne sezone, ki
bolj ali manj sovpadajo z letnimi č asi. Dodali
smo še vložke moč nega vetra in visokovodnih
valov Soč e, ki se z visoko stopnjo verjetnosti
pojavljajo vsako leto ob skoraj istem č asu.
Prav ti vložki so zelo pomembni, saj
predstavljajo bistveno izboljšavo v primerjavi
z dosedanjim modeliranjem s stacionarnimi
modeli.
Poleg tega smo popolnoma nestacionarne
simulacije nadomestili s t.i. kvazi-
stacionarnimi simulacijami. Pri tem nač inu ob
vsaki bistveni spremembi vhodnih parametrov
nekaj č asa rač unamo popolnoma nestacionarno
stanje. Po določ enem času pa, ko se
hidrodinamič ni parametri ter temperaturna in
slanostna polja ustalijo, jih fiksiramo in v
3. LONG-TERM SIMULATIONS
3.1 THE BASIC PRINCIPLE
The unsteady state 3D model needs a very
large amount of input data to work properly. In
a relatively large area, such as the Gulf of
Trieste, it is very difficult to measure all the
parameters simultaneously in enough sampling
points.
Usually steady state simulations with time-
averaged input data are sufficient for the
modelling of long-term processes, while real-
time simulations over the short time periods of
the measurements must be performed to
calibrate and verify the model. However, Hg
transport and dispersion was found to be a
highly unsteady state process. It is known that
over 90 % of the annual inflow of suspended
sediment and Hg are flushed into the Gulf with
two flood waves of the Soč a River, usually
during spring and autumn rains. It is also
known that strong wind is the most important
cause of the transport processes in the Gulf.
This latest phenomenon mostly occurs during
the winter months between November and
February.
Despite numerous measurements of
different parameters, it was not possible to
perform fully unsteady state simulations over
several months; therefore, a new approach was
used. Annually averaged input data were
replaced with seasonally averaged input data.
Four main seasons, more or less identical to
the calendar seasons, were accounted for. A
few inserts of strong wind and the Soč a River
flood-peaks, which statistically occur with
high probability at approximately the same
time every year, were added to the main
seasons. These inserts are of great importance,
as they represent a significant step forward in
comparison with the previously performed
steady state modelling.
Furthermore, real-time modelling was
replaced by the quasi-steady state principle.
Here, an unsteady state simulation is
performed for a certain period of time after
input parameters have been changed
significantly. Afterwards, when the
hydrodynamic parameters and temperature and

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
31
nadaljnjem računu obravnavamo kot
nespremenljiva. Od tod naprej rač unamo samo
transport in disperzijo živega srebra. Na ta
nač in moč no zmanjšamo č as rač una, saj za
račun hidrodinamičnih parametrov z
upoštevanjem gostotnih tokov in stratifikacije
porabimo okrog 80 odstotkov skupnega č asa
rač una.
Tipič no leto smo na koncu razdelili na 1 2
sekvenc (slika 3), ki jih rač unamo zaporedno;
krajše (nekajdnevne) rač unamo popolnoma
nestacionarno, pri daljših (nekaj tednov do
nekaj mesecev) pa uporabimo že omenjeni
kvazistacionarni pristop.
salinity fields are stabilised, they are treated as
fixed, and only the transport of Hg is further
calculated. In this way the computational time
is also essentially reduced, as about 80 % of
the total computational time needed is used for
the hydrodynamics computation when density
driven flow and stratified conditions are taken
into account.
Finally, a typical year was partitioned into
12 sequences (Figure 3), which were simulated
successively. With the shorter (up to a few
days long) sequences, unsteady state
calculations were used, while with the longer
(a few weeks to a few months long), the quasi-
steady state principle, as described above, was
used.
Temp./ Slan.
 Mesec / Month
0
200
800
Pretok Soce [m3/s]
400
600
1000
1200
Sequence
1400
Autumn
      Nov.      Dec.      Jan.      Feb.
Winter Spring
      Mar.      Apr.      Maj      Jun.
0.0
1.0
      Sep.
Summer
      Avg.      Jul.
Aut.
      Okt.
2.0
3.0
4.0
5.0
6.0
Hitrost vetra [m/s]
SEZONSKO POVPRECENI PARAMETRI
SEASONALLY AVERAGED PARAMETERS
      1      2      3      4      5      6      7      8      9      10
7.0
      11      12
Temp / Sal.
v
Sekvenca
Jesen Poletje Pomlad Zima Jesen
Discharge
Wind speed
Slika 3. Sezonsko povpreč ni parametri v Tržaškem zalivu
Figure 3. Seasonally averaged parameters in the Gulf of Trieste.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
32
3.2 VHODNI PODATKI
3.2.1 VETER
Smer in jakost sezonsko povpreč nih vetrov
nad Tržaškim zalivom (preglednica 1 ) je bila
določ ena z metodo VECTRA (Širca, 1 996;
Širca in Rajar, 1 997a), pri kateri za izrač un
upoštevamo vektorsko vsoto posameznih
znač ilnih vetrov (unit winds). Pri izrač unu smo
upoštevali uradne (HMZ RS) merjene urne
vrednosti jakosti in smeri vetra za obdobje od
1 975 do 1 990 za postajo Beli Križ.
Pozimi nad Tržaškim zalivom burja (smer
NE) pogosto doseže najvišje hitrosti tudi nad
30 m/s, za modeliranje pa je pomembnejši
podatek, da lahko s hitrostjo 16 m/s piha
neprekinjeno tudi več dni. Iz podatkov meritev
je razvidno, da se v hladnejši polovici
tipič nega leta glede na pogostost pojavljata
dva maksimuma burje (februarja in
novembra), ki hkrati skoraj toč no sovpadata
tudi z maksimumoma jakosti (preglednica 2).
Zaradi razmeroma velike dolžine nedvomno
največ prispevata k transportu živega srebra v
Tržaškem zalivu. Za določ itev jakosti in smeri
vetra je bila uporabljena ista metoda kot za
določ itev povpreč nih sezonskih vetrov.
3.2 INPUT DATA
3.2.1 WIND
Seasonally averaged wind force and
direction above the Gulf of Trieste (Table 1)
was evaluated using the VECTRA method,
which takes into account vectorial sum of the
unit winds (Širca, 1996; Širca and Rajar,
1 997a). The official data for the Beli Križ
Measuring Station (hourly measured wind
directions and speed for the period from 1975
to 1990) were used for calculation.
In winter time the burja wind (direction
NE) above the Gulf of Trieste often reaches
peak velocities over 30 m/s, and, even more
important for modelling, it can blow with a
velocity of 16 m/s for several days
continuously. It is evident from the official
measurements that during the colder half of a
typical year, there are two peaks of the burja
wind (in February and November). These two
peaks coincide almost exactly with the wind
force peaks (Table 2), and, due to their length,
the two peak-wind inserts undoubtedly
contribute the most to the Hg transport in the
Gulf. The same method as described above
was also used to evaluate the wind direction
and velocity of the wind peaks.
Preglednica 1 . Sezonski povpreč ni veter nad Tržaškim zalivom
Table 1. Seasonally averaged wind above the Gulf of Trieste
Sezona
Season
Smer
Direction
Hitrost
Velocity
[°][ m / s ]
Zima     (jan., feb., mar.)
Winter (Jan., Feb., Mar.)
66.6 2.2
Pomlad (apr., maj., jun.)
Spring (Apr., May, June)
101.6 1.1
Poletje  (jul., avg., sep.)
Summer (July, Aug., Sep.)
64.7 1.0
Jesen    (okt., nov., dec.)
Autumn (Oct., Nov., Dec.)
69.8 2.3

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
33
Preglednica 2. Vložki vetra (merska postaja Beli Križ)
Table 2. Wind inserts (Beli Križ measuring station)
Smer
Direction
Mesec
Month
Pogostnost
Frequency
Trajanje
Duration
Hitrost
Velocity
[%] [dni - days][ m / s ]
NE
Februar
February
37.4 11 6.4
NE
November
November
32.8 10 6.2
3.2.2 SOČ A
Sezonski pretoki in visokovodni vložki
Soč e temeljijo na meritvah, opravljenih na
vodomerni postaji Solkan, tik pred slovensko-
italijansko mejo (preglednica 3). Med
Solkanom in izlivom Soč e v Tržaški zaliv
dotekata v Soč o še dva več ja pritoka, Vipava
in Ter (Torre). Podatki za Vipavo so razvidni
iz preglednice 3, hidrologija italijanskega dela
Soče pa je slabše raziskana, saj po
razpoložljivih podatkih pretokov nihč e ne
meri. V spodnjem toku Soče obdelavo
podatkov otežuje tudi kompleksen sistem
nadzemnih in podzemnih tokov v vzhodnem
delu Furlanske nižine in Krasa ob slovensko-
italijanski meji. Največ ja neznanka v tem delu
ostaja reka Ter, ki se ji (odvisno od gladine
talne vode) vzdolž toka pretok poveč uje ali
zmanjšuje in poleti obč asno sploh ne priteč e
do sotoč ja s Soč o (Mosetti, 1 983, Širca et al,
1 999). Skupna prispevna površina poreč ja
Soč e nad Solkanom znaša 2235 km
2
, pod
Solkanom pa 1065 km
2
, zato je pretok ob ustju
določ en kot 1 .5-kratni skupni pretok Soč e in
Vipave. Povpreč ni letni pretok na izlivu v
Tržaški zaliv tako znaša 1 68 m
3
/s, ta številka
pa se dobro ujema z vrednostmi drugih
avtorjev, ki znašajo od 165 m
3
/s (Mosetti,
1983) do 172 m
3
/s (Benini, 1974).
3.2.2 THE SOČ A RIVER
Seasonally averaged discharges, as well as
the Soč a River flood-peak inserts, are based on
measurements in the cross-section at Solkan
(Table 3). There are another two important
tributaries of the Soč a River between Solkan
and the river mouth: the River Vipava, which
mainly flows through Slovenian territory, and
is well elaborated (Table 3), and the river
Torre. The hydrology of the Italian part of the
Soča River watershed is less known.
Continuous measurements are not available
downstream of Solkan. Moreover, a complex
system of surface and groundwater flows
exists in the eastern part of the Friuli plain and
the karst area of Kras at the Slovenian – Italian
border. The most important unknown of the
lower reach represents the Torre River, which,
according to the saturation conditions of the
plain, either loses or gains water along its
flow, and sometimes, during the summer
months, even disappears underground
(Mosetti, 1983, Širca et al, 1999). The total
catchment area of the Soč a River in Slovenia
is 2235 km
2
, while the catchment area in Italy
is 1065 km
2
. The mean discharge at the river
mouth is, therefore, considered to be equal to
150 % of the sum of the mean discharges at
Solkan and Miren. The annually averaged
discharge of the Soč a River at its mouth was
thus set to 168 m
3
/s. The number can be
compared with the values of other authors,
which are between 165 m
3
/s (Mosetti, 1983)
and 172 m
3
/s (Benini, 1974).

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
34
Preglednica 3. Meseč ni in sezonski povpreč ni pretoki Soč e
Table 3. Monthly and seasonally averaged discharges of the Soč a River
Pretoki
Discharge
Mesec
Month
Soč a
(Solkan)
Vipava
(Miren)
Σ Soč a +
Vipava
Soč a na ustju
The Soč a River
mouth
Sezonski
povpreč ni
Seasonally
averaged
[m
3
/s] [m
3
/s] [m
3
/s] [m
3
/s] [m
3
/s]
Jan 72 22 94 141
Feb 70 20 90 135 150
Mar 94 21 115 173
Apr 109 20 129 194
Maj / May 116 16 132 192 190
Jun 109 13 122 183
Jul 69 9 78 117
Avg / Aug 59 7 66 99 120
Sep 82 14 96 144
Okt / Oct 109 20 129 194
Nov 144 27 171 257 209
Dec 94 26 120 180
Povpreč ni letni
Annually averaged
94 18 112 168 168
Sezonski povpreč ni pretoki so določ eni iz
povpreč nih meseč nih pretokov, podanih v
literaturi (za Solkan v VGI (1982), za Miren
pa v vodnogospodarskih osnovah (ZVSS,
1978)).
Opisana metoda ekstrapolacije pretokov je
za kratkotrajna obdobja manj zanesljiva, kljub
temu pa je bil isti princip uporabljen tudi za
rač un visokovodnih vložkov. Najprej smo iz
statistič nih podatkov ugotovili trajanje in
intenziteto tipič nih vložkov. Tipič ni majski
visokovodni val traja okrog 5 dni, novembrski
pa okrog 4 dni. Intenziteta je bila določ ena s
pomočjo srednjih visokih pretokov, tj.
povpreč ja visokih pretokov v nekem daljšem
(dolgoletnem) obdobju. Gledano po mesecih,
imajo meseč ni srednji visoki pretoki (prvi
stolpec preglednice 4) v Solkanu za obdobje
od 1926 do 1975 dva maksimuma, ki se
pojavljata maja in novembra.
Seasonally averaged discharges are
evaluated from measurements (monthly
averaged discharges) from other authors (for
Solkan in the VGI (1982); for Miren in the
water management plans (ZVSS, 1978)).
Although with a lower reliability for shorter
events, the same relationship between
discharges as described above was used to
determine discharges during the flood-peak
inserts. First, the duration and intensity of
typical flood peak inserts was determined. The
typically observed duration of the May and
November flood-peak was about 5 days and
about 4 days respectively. The intensity of the
inserts was evaluated from the mean high
discharges (i.e. an average of high discharges
during a longer period). The mean high
discharges averaged for individual months (the
first column in Table 4) at Solkan, between the
years 1926 and 1975, have two peaks, which
occur in May and November respectively.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
35
Po verjetnostni analizi predstavljata zgornji
vrednosti za oba meseca visoka pretoka s
povratno dobo 2.5 leti (Q
2.5
), kar pokaže
interpolacija med Q
2
 in Q
5
 (2. in 3. stolpec
preglednice 4). To sicer pomeni, da se
dogodek zgodi le na 2.5 leta, vendar pa smo na
ta nač in z modelom upoštevali tudi vpliv manj
pogostih dogodkov, ki pa imajo velik vpliv na
dotok živega srebra v Tržaški zaliv. Petdnevno
obdobje s povpreč nim pretokom 473 m
3
/s ima
povratno dobo dve leti, zato je upoštevana
dolžina pomladnega vložka 5 dni. Trajanje
jesenskega vložka je krajše, saj bi imelo
petdnevno obdobje s povpreč nim pretokom
950 m
3
/s povratno dobo kar 50 let. Upoštevana
dolžina jesenskega vložka je tako 2 dni.
According to probability analysis these
values represent an event with a recurrence of
2.5 years (Q
2.5
), for both May and November,
as is evident from the interpolation between Q
2
and Q
5
 (the second and the third column in
Table 4.4). Such discharges (Q
2.5
) were used in
model simulations, as also, in that manner, less
frequent events with a significant influence on
mercury transport in the Gulf were taken into
account. The recurrence of a five-day long
insert with a mean discharge of 473 m
3
/s is
two years; therefore, the length of the spring-
insert was set to five days. The autumn-insert
is shorter, as the recurrence of a five-day long
insert with a mean discharge of 950 m
3
/s is
about 50 years. A two-day long autumnal
insert was adopted.
Preglednica 4. Visokovodni vložki Soč e (meritve - Solkan)
Table 4. The Soč a River flood-peak inserts (measurements – Solkan)
Mesec
Month
sr
Q
v
Q
2
Q
5
Trajanje
[dni]
[m
3
/s] [m
3
/s] [m
3
/s] [dni – days]
Maj / May 476 416 687 5
November 914 821 1299 2
Dvodnevnemu vložku z najvišjim pretokom
sta dodana še dan prej in dan kasneje s
pretokom 230 m
3
/s. Tako imata pomladni in
jesenski vložek Soč e v Solkanu približno enak
volumen odtoka, ki znaša okrog 200 milijonov
m
3
 (VGI, 1 982). Dimenzije majskega vložka
potrjuje tudi obdelava odvisnosti med
volumnom in pretokom v Solkanu (VGI,
1982), iz katere je razvidno, da znaša srednji
pretok petdnevnega visokovodnega vala s
povratno dobo 2 leti okrog 475 m
3
/s, odtekli
volumen pa nekoliko presega 200 milijonov
m
3
. Jesenski vložek lahko primerjamo z
registriranim visokovodnim valom novembra
1997, katerega povratna doba pa znaša po
različ nih podatkih od 5 do 30 let. Pod
sotoč jem z Vipavo je bil takrat v dveh glavnih
dneh odtekli volumen okrog 200 milijonov m
3
,
č e upoštevamo še narašč anje pretoka dan prej
in upadanje nazaj na normalni novembrski
pretok, ki je trajalo še štiri dni, je bil skupni
odtekli volumen pod sotoč jem Soč e z Vipavo
v enem tednu novembra 1 997 približno 380
milijonov m
3
.
A day before and a day after, with a
discharge of 230 m
3
/s were added to the two-
day long autumn-insert. Thus, both flood-peak
inserts have approximately the same volume of
about 200 millions m
3
 (VGI, 1982). The
volume of the spring-insert was also confirmed
by the relationship between discharge and the
flood-wave volume for the cross-section in
Solkan (VGI, 1982). It is evident that the mean
discharge of a five-day long flood-wave with a
recurrence of about two years is approximately
475 m
3
/s, and the volume of the flood-wave
somewhat exceeds 200 millions m
3
. The
autumn-insert can be compared with the
observed flood wave of the Soč a River in
November, 1997, which had a recurrence of
between 5 and 30 years from different sources.
Below the confluence of the Soč a and Vipava
rivers, the volume of the main flood wave (in a
duration of two days) was about 200 million
m
3
. Taking into account one day of water
rising before and four days of returning back
to the normal November discharge, the total
volume of the flood wave in a single week in
November, 1997 was about 380 million m
3
.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
36
V modelu so bili kot vhodni podatki ob
visokovodnih vložkih uporabljeni pretoki Soč e
na ustju, kot so navedeni v preglednici 5.
The data from Table 5 (discharges at the
Soč a River mouth) were used as the input data
for flood-peak insert simulations.
Preglednica 5. Visokovodni vložki Soč e na ustju (vhodni podatki za model).
Table 5. Flood-peak inserts at the Soč a River mouth (input data for simulations).
Mesec (vložek)
Month (insert)
Pretok na ustju
Discharge at the
river mouth
Trajanje
Duration
[m
3
/s] [dni - days]
maj (celoten vložek)
May (complete insert)
714 5
november (1.dan)
November (1
st
 day)
345 1
november (2. in 3. Dan)
November (2
nd
 and 3
rd
 day)
1371 2
november (4.dan)
November (4
th
 day)
345 1
Preglednica 6. Povpreč ne sezonske temperature vode v Soč i (most pred izlivom)
Table 6. Seasonally averaged water temperature in the Soč a River
Sezona Temperature
Season [°C]
Zima / Winter 7.7
Pomlad / Spring 12.9
Poletje / Summer 16.3
Jesen /Autumn 9.2
Za simulacije stratificiranega stanja je
pomemben tudi podatek o temperaturi Soč e na
ustju. Na voljo so bile meritve temperature pod
zadnjim mostom pred ustjem Soč e (manj kot
kilometer od izliva Soče) v približno
dvotedenskih intervalih od leta 1974 do 1995.
Največ ja gostota meritev je bila od leta 1 978
do 1987. Za nameravane simulacije s 3D
modelom so bile iz podatkov statistič no
izračunane povprečne sezonske vrednosti
(preglednica 6).
The water temperature of the Soč a River at
its mouth is another important factor in the
simulation of the stratified conditions.
Measurements of water temperature under the
last bridge, situated less than one kilometre
from the river mouth, were available.
Temperature was measured in about two-week
intervals between the years 1974 and 1995,
and more frequently between the years 1978
and 1987. Seasonally averaged water
temperatures were statistically evaluated from
the measurements (Table 6) and used in the 3D
modelling.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
37
Na voljo so bili podatki meritev
raztopljenega živega srebra v Soč i pri nizkih
pretokih oktobra 1997, med visokovodnim
valom novembra 1997 in ob srednje nizkih
pretokih decembra 1 998 ter v Tržaškem zalivu
ob ustju Soč e maja in septembra 1 995 (Horvat
et al. 1999). Iz meritev je razvidno, da so
koncentracije raztopljenega živega srebra v
Soč i in Tržaškem zalivu le malo odvisne od
pretoka Soč e in letnega č asa in znašajo pri
vseh meritvah v Soč i od 1 .6 do 3.5 ng/l, v
zalivu blizu ustja (merska toč ka D6 na sliki 1 )
pa od 4.5 do 5 ng/l. Višje koncentracije v
morju so posledica sprošč anja živega srebra iz
partikularne v raztopljeno obliko na območ ju
mešanja sladke in slane vode. Procesa ni bilo
mogoč e neposredno vključ iti v model, zato je
pri vseh simulacijah in v vseh letnih č asih
upoštevana koncentracija na ustju 5 ng/l.
There were several measurements of
dissolved Hg in the Soč a River available:
during the flood-wave in November, 1997, the
mean low discharge in December, 1998 and
the low discharge in October, 1997
respectively. In the Gulf of Trieste,
measurements were performed in May and
November, 1995 (Horvat et al. 1999). It is
evident from the data that the interdependence
between the discharge of the Soč a River and
the concentrations of dissolved Hg is very low.
In the Soča River, concentrations vary
between the range of 1.6 and 3.5 ng/l, while in
the Gulf, near the river mouth (point D6 in
Figure 1), concentrations between 4.5 and 5
ng/l were measured. Higher concentrations in
the seawater are due to Hg release from
particulate to its dissolved form within the
freshwater and saltwater mixing zone. It was
not possible to include the process itself in the
model; therefore, a Hg concentration of 5 ng/l
was taken into account with all simulations in
any season.
3.2.3 TRŽAŠKI ZALIV
Rezidualni tokovi zaradi plimovanja v
Tržaškem zalivu so reda velikosti 1 mm/s,
hitrosti rezidualnega toka zaradi vpliva vetra
pa dosegajo vrednosti 2 do 3 cm/s (Širca,
1996). Vpliv plimovanja na gibanje vode v
zalivu pri simulacijah s 3D modelom ni bil
upoštevan, saj so rezidualni tokovi zaradi
plimovanja v zalivu vsaj za red velikosti
manjši od rezidualnih tokov zaradi vetra, ki je
glavni vzrok gibanja vode. Poleg tega pri
dolgotrajnih simulacijah, predvsem v obdobjih
šibkega vetra in nizkih pretokov Soč e, že
napaka, ki nastane pri rač unu koncentracij
polutanta zaradi numerič ne difuzije, ki se ji z
uporabo obstoječe numerične sheme ne
moremo izogniti, bistveno presega napako
zaradi neupoštevanja plimovanja.
Predvsem v toplejšem delu leta na
disperzijo živega srebra v vertikalni smeri
vplivajo tudi stratificirane razmere v zalivu. Za
simulacije je bilo treba za vsako sezono
zagotoviti podatke o porazdelitvi temperatur in
slanosti v vseh toč kah rač unske mreže. V
celotnem zalivu so bile izmerjene temperature
in slanosti sredi posameznih letnih č asov
(februar, maj, avgust, november) soč asno v 27
toč kah zaliva (slika 1 ) v 5 m intervalih po
globini.
3.2.3 THE GULF OF TRIESTE
Typical tide-induced residual currents in the
Gulf were of the order of 1 mm/s, while
typical wind-induced residual currents reached
2 to 3 cm/s (Širca, 1996). As the tide-induced
currents were at least for an order of
magnitude smaller than the wind-induced
residual currents, the effect of the tide on the
circulation in the Gulf was not taken into
account with the 3D simulations. Moreover, by
computation of the concentrations of
pollutants with long-term simulations,
particularly during calm periods, the error due
to tidal forcing exclusion was significantly
exceeded by the error caused by false
diffusion, which could not be avoided using
the existing numerical scheme.
Stratified conditions within the Gulf and
their impact on the dispersion of Hg along the
water column were also a very important
factor, particularly during the warmer half of
the year. Temperature and salinity distribution
along the entire computational domain had to
be evaluated for the four main seasons.
Measurements were performed simultaneously
in 27 sampling points within the Gulf (Figure
1), in the middle of each main season
(February, May, August, November) in 5-m
intervals along the depth.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
38
Pri simulacijah smo uporabili numerič no
mrežo, kjer smo definicijsko območ je po
globini razdelili na 25 slojev, debeline 1 m. V
horizontalni ravnini smo območ je razdelili na
43 × 42 celic, z dimenzijami od 300 × 300 m
ob ustju Soč e do največ 900 × 900 m. Za
vsako rač unsko celico smo morali zagotoviti
podatka o temperaturi in slanosti.
Najprej smo iz podatkov meritev z linearno
interpolacijo izrač unali temperaturo in slanost
pod merskimi toč kami v vsakem sloju. Nato
smo nad vsakim slojem z uporabo trikotne
mreže napeli ploskev temperatur in slanosti z
orodjem Quicksurf, s katerim smo tudi
izvrednotili celotne matrike temperatur in
slanosti v vsaki celici definicijskega območ ja
za vse štiri sezone.
Dosedanje izkušnje z gostotnimi gibanji
(Rajar et al. 1 997) kažejo, da je potrebno
‘glajenje’ matrik temperatur in slanosti,
dobljenih z interpolacijami iz meritev, sicer se
pri simulacijah lahko pojavijo težave s
stabilnostjo numerič ne sheme. Poleg tega bi
bila pri simulaciji dolgotrajnih procesov
konč na slika temperatur in slanosti nerealna
tudi zaradi vtoka Soč e, gostotnega gibanja in
disperzije temperature in slanosti zaradi
gibanja vodnih mas. Vhodne podatke modela
(zač etno stanje) smo izboljšali tako, da smo za
vsako od glavnih sezon izvedli simulacijo
hidrodinamič nih parametrov ter advekcije in
disperzije temperature in slanosti ob hkratnem
upoštevanju vseh dejavnikov, ki vplivajo na
gibanje vode (veter, vtok Soč e in gostotno
gibanje). Simulirali smo izbrano č asovno
obdobje (od 8 h ob moč nem vetru in/ali
visokem pretoku Soč e do dveh dni ob šibkem
vetru in nizkih pretokih), dokler na celotnem
definicijskem območ ju niso bile dosežene
pričakovane hitrosti. Takšno porazdelitev
slanosti in temperatur smo v nadaljevanju
uporabili kot zač etno stanje za rač un transporta
in disperzije raztopljenega živega srebra.
Koncentracije živega srebra v sedimentu na
dnu Tržaškega zaliva so zelo visoke, ob ustju
Soč e dosegajo 25-30 µ g/g suhe teže. Iz
sedimenta se živo srebro sč asoma izloč i v
porne vode in zaradi difuzije prehaja v
okoliško vodo. Porne vode so zato pomemben
vir raztopljenega živega srebra še dolgo č asa
The computational grid with a maximum of
25 layers, each 1 m thick, was used. In the
horizontal plane, the computational area was
divided into 43 × 42 cells, with dimensions
from 300 × 300 m near the Soč a River mouth
to 900 × 900 m. Temperature and salinity
values in each cell of the computational grid
had to be provided.
First, temperature and salinity values in
each layer below the sampling points were
calculated using linear interpolation.
Afterwards, an envelope of temperature and
salinity concentrations for each layer was
constructed on the basis of a triangular grid
using Quicksurf software. Finally, with the
same tool, complete temperature and salinity
matrices in each cell of the computational
domain for all four seasons were calculated.
Temperature and salinity matrices
calculated in that manner need to be
‘smoothed’ to avoid stability problems with
the numerical scheme during computation
(Rajar et al. 1997). Additionally, with long-
term simulations, the final distribution of
temperature and salinity would be unreal due
to the Soč a River inflow, density-driven flows
and, most importantly, due to advection. To
get the best possible initial state for each of the
main seasons, simulations of hydrodynamic
quantities and the advection and dispersion of
temperature and salinity, with all forcing
factors taken into account (wind, river inflow
and density-driven flow) were performed.
Computations for set amounts of time (from 8
hours with strong wind and/or high discharge
of the Soč a River, up to two days with weak
wind and lower discharges) were performed,
until the expected velocities were reached
within the entire computational domain. Such
matrices of temperature and salinity
distribution were finally used as an initial state
to simulate the transport of Hg in its dissolved
form.
In the bottom sediment of the Gulf, Hg
concentrations are highly increased, and reach
about 25-30 µ g/g dry weight near the Soč a
River mouth. Hg bound to sediment particles
is gradually being released into the pore water
and, due to molecular diffusion, also proceeds
to the surrounding water. Therefore, pore

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
39
po zmanjšanju ali celo prenehanju dotoka
živega srebra v okolje. V letih 1 995 in 1 996 so
bile v merski toč ki AA1 (slika 1 ) izvedene
meritve koncentracij živega srebra v pornih
vodah v sedimentu na mestu samem z
bentoško komoro (benthic chamber) (Covelli
et al. 1999).
Meritev je bila zaradi zahtevnosti postopka
in visoke cene izvedena v eni sami toč ki
zaliva, zato rezultatov meritev ne moremo
posplošiti na celotno obravnavano območ je.
Vsekakor pa je jasno, da je količ ina živega
srebra, ki se sprošč a z dna (po Covelli et al.
znaša okoli 470 kg/leto) dovolj velika, da jo bo
treba v prihodnje upoštevati pri modelnih
simulacijah.
waters are a significant source of dissolved Hg
for a long time after the inflow of Hg has
begun to reduce or has even ceased. Hg
concentrations in the pore water of the bottom
sediment of the Gulf were determined by an in
situ benthic chamber experiment at location
AA1 (Figure 1) during 1995 and 1996 (Covelli
et al. 1999).
These measured values cannot be applied to
the whole area of the Gulf, as only one
location was observed, due to the difficulty
and expense of the experiment. The high
amount of Hg being released (according to
Covelli et al. about 470 kg/year) from the
bottom sediment is very significant, and needs
to be taken into account with future modelling
and simulations.
3.3 REZULTATI SIMULACIJE
Z zbranimi podatki smo izdelali konč no
razdelitev tipič nega leta na sekvence in
pripravili podatke za simulacijo (slika 3). S
temi podatki smo izvedli simulacijo za
obdobje od 1.novembra 1994 do 1.julija 1995.
Krajše sekvence smo obravnavali popolnoma
nestacionarno, rač un je potekal v realnem
č asu, pri daljših pa smo uporabili kvazi-
stacionarni pristop. Čas nestacionarne
obravnave je bil v posameznih daljših
sekvencah različ en, odvisen pa je bil od
pretoka Soče, hitrosti vetra in zač etnih
temperaturnih in slanostnih pogojev v zalivu.
Nestacionarne simulacije so tako trajale od 8
ur v primeru moč nejšega vetra in/ali visokega
pretoka Soč e, do nekaj dni pri šibkem vetru in
nizkem pretoku Soč e.
Meritve celokupnega raztopljenega živega
srebra so bile opravljene 25. junija 1995
(Horvat et al. 1 999) v 1 4 toč kah na površini in
ob dnu, primerjava rezultatov modela in
merjenih vrednosti pa je prikazana na sliki 4 in
v preglednici 7.
3.3 RESULTS OF THE SIMULATION
Input data for the simulations were prepared
and the final partitioning of a typical year was
carried out using the collected data (Figure 3).
With these data a simulation for the period
between 1 November, 1994 and 1 July, 1995
was performed. Fully unsteady state
simulations (real-time modelling) were applied
with the shorter sequences and quasi-steady
state modelling with the longer ones. The
duration of the unsteady state treatment was
different with individual longer sequences, as
it depends on the discharge of the Soč a River,
the wind force and temperature / salinity
conditions in the Gulf, respectively. Unsteady
state simulations in duration from 8 hours with
strong wind and/or high discharge of the Soč a
River, up to a few days with weak wind and
lower discharges, were applied.
Measurement of total dissolved Hg was
performed on 25 June, 1995 (Horvat et al.
1999) in 14 sampling sites at the surface and at
the bottom. In Figure 4 and Table 7 a
comparison between the measurements and the
results of the model simulation is given.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
40
     MERITEV            REZULTAT MODELA
MEASUREMENT PCFLOW3D MODEL
Slika 4: Primerjava merjenih in izrač unanih koncentracij celokupnega raztopljenega živega srebra
(junij 1995) v površinskem sloju (zgoraj) in v sloju ob dnu (spodaj).
Figure 4: Comparison of measured and simulated concentrations of total dissolved mercury (June,
1995) in the surface layer (above) and the bottom layer (below).

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
41
Preglednica 7. Primerjava merjenih in izrač unanih koncentracij celokupnega raztopljenega živega
srebra (junij 1995) v površinskem sloju in v sloju ob dnu
Table 7. Comparison of measured and simulated concentrations of total dissolved mercury (June,
1995) in the surface layer and the bottom layer
Globina
Depth
Merjena
koncentracija
Measured
concentration
Izrač unana
koncentracija
Calculated
concentration
Odstopanje
Ratio
Merska toč ka
Sampling point
[m] [ng/l]
[ng/l] [-]
D6 ↑ 0.5 4.90
3.45 -30 %
D6 ↓ 3.5 1.31
1.53 +17 %
A4 ↑ 0.5 3.47
2.25 -35 %
A4 ↓ 11.5 1.08
1.35 +25 %
A29 ↑ 0.5 1.53
1.68 +10 %
A29 ↓ 9.5 1.28
1.21 -5.5 %
A20 ↑ 0.5 2.31
1.52 -34 %
A20 ↓ 3.5 1.34
1.16 -13 %
CZ ↑ 0.5 0.97
1.72 +77 %
CZ ↓ 23.5 1.18
1.43 +21 %
F2 ↑ 0.5 0.95
1.33 +40 %
F2 ↓ 20.5 1.23
1.21 - 1.6 %
F0 ↑ 0.5 0.68
1.38 +103 %
F0 ↓ 20.5 1.09
1.18 + 8.3 %
4. ZAKLJUČ KI
Iz primerjave rezultatov simulacije in
meritev lahko sklepamo naslednje:
Kvalitativno je ujemanje rezultatov na
površini zelo dobro. Relativno dobro
kvantitativno ujemanje, povsod v mejah
faktorja dve, je bistven napredek v primerjavi
z rezultati 2D simulacij. Disperzija živega
srebra v površinskem sloju je nekoliko
prevelika, kar je predvsem posledica
numerič ne difuzije, ki pa se ji s trenutno
vgrajeno numerič no shemo ni mogoč e izogniti.
Kljub zvišanju koncentracij raztopljenega
živega srebra v Soč i je ujemanje v bližini ustja
slabše, saj z modelom še ne moremo
upoštevati sprošč anja živega srebra z delcev
plavin, ki je prisotno v območ ju mešanja
sladke in slane vode. Proces sprošč anja živega
srebra iz partikularne v raztopjleno obliko še
ni dovolj dobro raziskan, da bi ga bilo mogoč e
vključ iti v model.
4. CONCLUSIONS
The following conclusions can be made
from the results of the simulation and
measurements:
At the surface, a very good qualitative
agreement of modelling results and measure-
ments was achieved. Relatively good quanti-
tative agreement, always within a factor of
two, was a significant improvement in compa-
rison with the 2D modelling. The dispersion of
Hg at the surface was somewhat too high,
mostly due to false diffusion, which cannot be
avoided using the existing numerical scheme.
In spite of an additional increase of
dissolved Hg concentrations in the Soč a River
due to the Hg release from particulate to
dissolved form, agreement of the
measurements with the simulation is less
accurate near the river mouth. Additional
research of the Hg release from particulate
matter to its dissolved form in the freshwater /
saltwater mixing zone is needed before
including the process in the 3D model.

Žagar, D., Rajar, R., Širca, A., Horvat, M., Č etina, M.: Dolgotrajna 3D simulacija transporta in disperzije živega srebra
v Tržaškem zalivu - Long-Term 3D Simulation of the Transport and Dispersion of Mercury in the Gulf of Trieste
© Acta hydrotechnica 19/30 (2001), 25-43, Ljubljana
42
V modelu še ni upoštevano zvišanje
koncentracij ob dnu zaradi sprošč anja živega
srebra iz pornih vod v sedimentu, ki lahko
precej spremeni sliko koncentracij ob dnu.
Zato je ujemanje ob dnu kvalitativno nekoliko
slabše, kvantitativno pa še vedno v mejah
faktorja dve. Omeniti pa je treba, da tudi na
rezultate meritev pri tako nizkih
koncentracijah vpliva mnogo dejavnikov in je
zato zanesljivost meritev v mejah ± 20 %
(Horvat et al., 1 999). Č e torej upoštevamo
nezanesljivost analiznih metod in vhodnih
potatkov ter napako pri modeliranju, lahko
zaključ imo, da je ujemanje rezultatov dobro.
Poleg numerične difuzije na rezultate
modela nekoliko vpliva tudi uporaba
razmeroma preprostega modela turbulence.
Slednji kljub zmanjšanju vertikalnega
koeficienta turbulentne difuzije v
stratificiranih razmerah daje nekoliko
previsoke vrednosti koeficientov, predvsem pri
šibkejšem vetru. Prednostna naloga pred
nadaljnjim modeliranjem je torej vgradnja
izpopolnjenega modela turbulence z dvema
enač bama (k-ε model) in numerič ne shema
višjega reda toč nosti (npr. Quickest).
The increase of concentrations at the sea-
bottom due to benthic fluxes, which can
significantly change Hg concentrations within
the bottom layer, was not taken into account in
the present state of the model. Therefore,
qualitative agreement in the bottom layer is
somewhat less accurate, but quantitatively still
within a factor of two. However, the reliability
of the measurements with such low
concentrations is limited by several factors,
and the accuracy does not exceed the limits of
± 20 % (Horvat et al., 1999). By taking into
account the unreliability of the analytical
methods, uncertainty of the input data and the
inaccuracy of the modelling, the agreement of
the results and measurements can be
considered good.
Besides the false diffusion, the results are
also influenced by the use of a relatively
simple model of turbulence. Despite adapting
the eddy diffusivity to stratified conditions, the
values of the vertical coefficients are
somewhat too high, particularly in weak wind
conditions. A two-equation turbulence model
(k-ε model) and a numerical scheme of a
higher order of accuracy (e.g. Quickest) will be
included in the model as soon as possible.
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Naslov avtorjev – Authors’ Addresses
dr. Dušan Žagar, prof. dr. Rudolf Rajar, doc. dr. Andrej Širca
izr. prof. dr. Matjaž Č etina
Univerza v Ljubljani – University of Ljubljana
Fakulteta za gradbeništvo in geodezijo – Faculty of Civil and Geodetic Engineering
Jamova 2, SI-1000 Ljubljana
e-mail: dzagar@fgg.uni-lj.si
dr. Milena Horvat
Institut Jožef Stefan
Jamova 39
SI-1000 Ljubljana