' Acta hydrotechnica 22/37 (2004), Ljubljana ISSN 1581-0267 77 UDK / UDC: 519.61/.64:546.49:556.55 Prejeto/Received: 7. 6. 2004 Izvirni znanstveni prispevek Original scientific paper Sprejeto/Accepted: 9. 9. 2005 MODELIRANJE HIDRODINAMIKE IN TRANSPORTA IVEGA SREBRA V VELENJSKEM JEZERU 2. DEL: MODELIRANJE IN PREVERJANJE MODELA MODELLING OF HYDRODYNAMICS AND MERCURY TRANSPORT IN LAKE VELENJE PART 2: MODELLING AND MODEL VERIFICATION Joe KOTNIK, Duan AGAR, Rudi RAJAR, Milena HORVAT Tridimenzionalni matematič ni model PCFLOW3D, razvit na katedri za mehaniko tekoč in Fakultete za gradbenitvo in geodezijo, smo uporabili za simulacije hidrodinamike in transporta ivega srebra v Velenjskem jezeru. Popolnoma nelinearen hidrodinamič ni modul daje kot rezultat tri komponente hitrosti, potek gladine vode in tlake. S transportno-disperzijskima enač bama izrač unamo prostorsko porazdelitev slanosti in temperature (in/ali poljubnega polutanta). Iz rezultatov simulacij je razvidno, da so glavni vir ivega srebra v Velenjskem jezeru vtoki. Hidrodinamič ne simulacije so pokazale, da vtoki in iztoki povrinskih in podzemnih voda nimajo velikega vpliva na cirkulacijo vode v jezeru. Glavni vzrok za gibanje vode sta veter in temperatura vode in okolice. Simulacije transporta ivega srebra z modelom PCFLOW3D se dobro ujemajo z merjenimi koncentracijami različ nih oblik Hg in metil-Hg v Velenjskem jezeru. Izrač unane tokove vode smo preverili s primerjavo z meritvami izotopov δ 1 8 O in δ 2 H ter meritvami različ nih oblik ivega srebra in metil ivega srebra. Porazdelitev posameznih zvrsti in oblik ivega srebra ter izotopska sestava v vodnem okolju Velenjskega jezera je opisana v prvem delu č lanka. Ključ ne besede: modeliranje, sladkovodno jezero, transport, disperzija, hidrodinamika, ivo srebro, metil ivo srebro PCFLOW3D a three-dimensional mathematical model that was developed at the Chair of Fluid Mechanics of the Faculty of Civil and Geodetic Engineering, University of Ljubljana, was used for hydrodynamic and Hg transport simulations in Lake Velenje. The model is fully non-linear and computes three velocity components, water elevation and pressure. Transport-dispersion equations for salinity and heat (and/or any pollutant) are further used to compute the distributions of these parameters. The results show that the major sources of mercury in Lake Velenje are lake inflows. The hydrodynamic simulations revealed that ground and/or surface water inflow and outflow do not have much influence on water cycling in the lake basin. Wind and ambient temperature seem to have the greatest influence on water movement in the lake. Mercury transport simulations performed by PCFLOW3D show good agreement with the measured distribution of different Hg and MeHg forms in Lake Velenje. Verification of water flow was done by isotope tracers δ 1 8 O and δ 2 H and measurements of different Hg and MeHg forms. Distribution of different Hg species and forms and isotopic composition in water of Lake Velenje is described in Part 1 . Key words: modeling, freshwater lake, transport, dispersion, hydrodynamics, mercury, methylmercury 1. UVOD V prvem delu č lanka (Kotnik et al., 2003) smo opisali Velenjsko jezero in njegove lastnosti ter uporabljene analitič ne metode in rezultate meritev izotopske sestave in različ nih 1. INTRODUCTION In Part 1 of the article (Kotnik et al., 2003) Lake Velenje and its properties as well as analytical methods and measurement results of isotopic composition and different Hg species Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 78 zvrsti Hg v jezerski vodi, sedimentu in zraku. Za opis tokov (cirkulacije vode) ter transporta in porazdelitve ivega srebra v Velenjskem jezeru smo uporabili dve metodi: (i) s hidrodinamič nim modelom PCFLOW3D smo simulirali tokove in (ii) transport in disperzijo Hg smo izrač unali s transportno- disperzijskim modulom modela PCFLOW3D. Vse hidrodinamične simulacije v predstavljeni raziskavi so bile izvedene z modelom PCFLOW3D, izdelanim na Fakulteti za gradbenitvo in geodezijo Univerze v Ljubljani. Razvoj modela in njegova uporaba sta e opisana v tevilnih č lankih (Rajar in Č etina, 1986; Rajar, 1989; Rajar in Č etina 1997; irca et al., 1999a; irca et al., 1999b; Rajar et al., 2000), zato tukaj podajamo samo kratek povzetek. PCFLOW3D je tridimenzionalen, popolnoma nelinearen model, ki izrač una tri komponente hitrosti, gladino vode in tlake. Za rač un porazdelitve slanosti in temperature (in/ali poljubnega polutanta) sta v model vgrajeni transportno-disperzijski enač bi. Model je sestavljen iz hidrodinamič nega, sedimentacijskega in transportno- disperzijskega modula in je bil doslej uspeno uporabljen za reevanje prakti č nih problemov v severnojadranskem priobalnem morju in slovenskih jezerih (PCFLOW3D User’s Manual 1997; Rajar, 1989; 1992; Rajar in Č etina, 1986; 1991; 1992b; 1997; Rajar et al., 2000; irca, 1996; irca et al., 1999a; 1999b). Tudi dodatna monost simulacije razgradnje nekaterih vrst onesnaenja je bila uporabljena na praktič nih primerih kot npr. simulacija razlitja nafte in irjenja radioaktivnih polutantov. Dvodimenzionalna različ ica modela je bila razvita za simulacije hidrodinamike in ivosrebrovega cikla v Trakem zalivu (irca, 1996; irca et al., 1999a; 1999b). 2. OSNOVNI PODATKI ZA SIMULACIJE Velenjsko jezero smo razdelili v 35 29 = 1015 celic v horizontalni ravnini, s 50- metrskimi intervali v smereh Dx in Dy. V smeri z (globina) smo območ je razdelili na 19 in the water, sediment and air were discussed. With the aim of determining water circulation, mercury transport and distribution in Lake Velenje two modeling approaches were used: (i) Water circulation calculations were performed by the hydrodynamic model PCFLOW3D and (ii) Hg transport and dispersion calculations were performed by the transport dispersion module of PCFLOW3D. All hydrodynamic simulations for this research have been performed by PCFLOW3D, a hydrodynamic model developed at the University of Ljubljana, Faculty of Civil and Geodetic Engineering. Since the model development and its applications are already described in several articles (Rajar and Č etina, 1986; Rajar, 1989; Rajar and Č etina, 1992; irca 1996; Rajar and Č etina, 1997; irca et al., 1999a; irca et al., 1999b; Rajar et al., 2000), only a short summary will be presented here. The model is 3D, fully non-linear, and computes three velocity components, water elevation and pressure. Transport-dispersion equations for salinity and heat (and/or any pollutant) are used to compute the distributions of these parameters. Up to now, the model has hydrodynamic, sediment-transport and transport-dispersion modules, which have already been used efficiently for solving some practical problems in the Northern Adriatic coastal sea and Slovenian lakes (PCFLOW3D Users Manual 1997; Rajar, 1989; 1992; Rajar & Č etina, 1986; 1991; 1992b; 1997; Rajar et al., 2000; irca, 1996; irca et al., 1999a; 1999b). The simulation of fate processes for some contaminants is included, and has been used for practical applications such as oil-spill simulation and dispersion of radioactive pollutants. A two-dimensional version of the model has been developed to simulate hydrodynamics and mercury cycling in the Gulf of Trieste (irca, 1996; irca et al., 1999a; 1999b). 2. BASIC DATA FOR THE SIMULATIONS Lake Velenje was divided into 35 29 = 1015 cells in the horizontal plane, with 50 m intervals in the Dx and Dy direction. In the z- direction (depth) the field was divided into 19 Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 79 slojev debeline od 1 do 5 m (debelina slojev od dna proti povrini je bila: 5, 5, 5, 5, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 in 1 m). Od povrine do globine 20 m smo izbrali tanje sloje, saj smo eleli dobiti bolj natan č en prikaz toplotne stratifikacije v jezeru. Podatke o vetru nad Velenjskim jezerom smo pridobili na Agenciji Republike Slovenije za okolje. Meritve hitrosti in smeri vetra so potekale od oktobra 1992 do septembra 1993 na vsake pol ure. V aleki dolini prevladujejo vetrovi iz dveh smeri: gre predvsem za vzhodne in zahodne vetrove. V simulacijah smo uporabili najpogosteje vetrove hitrosti 1 m/s z zahoda, hitrosti 2 m/s z jugovzhoda in hitrosti 4 m/s z jugovzhoda. Poletne temperature jezera so bile merjene dvakrat (junija 1998 im avgusta 1998) v dvometrskih intervalih do globine 30 m. Povpreč na poletna temperatura epilimnija je bila okoli 25 C, medtem ko je bila v hipolimniju povpreč na temperatura vode med 5 in 8 C. Zimske temperature so bile merjene ob koncu zime 1998/1999. V simulacijah smo kot zimsko temperaturo vode po vsej globini uporabili 4,5 C . layers with thickness between 1 and 5 m (layer thickness from the bottom to the surface were: 5, 5, 5, 5, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 and 1 m) down to about 55 m of depth. The smaller thickness from the surface to 20 m has been chosen to account more accurately for the thermal stratification in the lake. The data about the wind conditions over Lake Velenje was obtained from the Environmental Agency of the Republic of Slovenia. Wind speed and direction were measured from October 1992 to September 1993 every half an hour. Easterly and westerly winds prevalently blow in the alek Valley. In the simulations, the most frequent winds of 1 m/s from the west, 2 m/s and 4 m/s from the southeast were used. Summer lake temperatures were measured twice (June 1998 and August 1998) at every two meters, up to 30 m of deph. Average summer water temperature in epolimnium was approximately 25 C, while hipolimnium water temperature was between 5 and 8 C. Winter temperature was measured at the end of winter 1998/1999. The winter water temperature used in the simulations was 4.5 C at all depths. Preglednica 1. Povpreč ne dotoč ne / iztoč ne hitrosti za potoka Sopota in Lepena in za iztok iz Velenjskega jezera v obdobju med januarjem 1990 in decembrom 1995. Table 1 . Average flow rates for Sopota and Lepena streams and for the outflow from Lake Velenje for the period between January 1 990 and December 1 995. Celica I (smer X) I Cell (X direc- tion)) Celica J (smer Y J Cell (Y direc- tion) Celica K (sloj) K Cell (layer) U (hitrost toka v smeri X flow speed in X direction) V (hitrost toka v smeri Y flow speed in Y direction) Sopota 25 26 20 0 0.00254 Lepena 34 18 20 0.0126 0 Iztok/Outflow 5 4 20 0 0.0151 Podatke o vtokih in iztoku vode iz jezera je priskrbela Agencija Republike Slovenije za okolje. Meritve vtokov in iztoka so potekale enkrat dnevno od januarja 1990 do decembra 1995. Povpreč ni pretok potoka Lepena je bil 0,127 m 3 /s in potoka Sopota 0,628 m 3 /s. Inflow and outflow discharge data were provided by the Environmental Agency of the Republic of Slovenia. Inflows and outflow were daily measured from January 1990 until December 1995. The average discharge was 0.127 m 3 /s for Lepena Stream, and 0.628 m 3 /s Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 80 Povpreč ni iztok v reko Pako je bil 0,755 m 3 /s. Dotoka in iztok vode so bili podani v ustreznih celicah (preglednica 1). Pri hidrodinamič nem delu simulacij je bil č asovni korak zaradi numerič ne stabilnosti omejen na DT = 180 s, pri č emer je bil uporabljen t.i. kriterij difuzije v vertikalni smeri za stabilnost modela: for Sopota Stream. The average outflow to Paka River was 0.755 m 3 /s. The two inflows and the outflow were given in isolated cells (Table 1). In the hydrodynamic part of the simulations, the time step was limited to DT = 180 s due to numerical stability. The so-called vertical diffusion stability criterion was used: v N H DT 2 2 min ≤ pri č emer je H min debelina najtanjega sloja, N v pa vertikalni kinematični koeficient turbulentne viskoznosti, izračunan po Koutitasovem modelu turbulence. Horizontalni kinematič ni koeficient turbulentne viskoznosti je bil ocenjen na podlagi izkuenj iz simulacij na drugih, podobnih jezerih; pri vseh simulacijah je imel vrednost 1 m 2 /s. 3. HIDRODINAMIČ NE SIMULACIJE Za ugotavljanje osnovnega vzorca cirkulacije vode v jezeru v različ nih razmerah smo izvedli 4 simulacije z upotevanjem različ nih smeri in hitrosti vetra ter poletno in zimsko razporeditvijo temperature po globini (preglednica 2). where H min represents the thickness of the thinnest layer and N v stands for vertical kinematic coefficient of turbulent viscosity according to Koutitas turbulence model. The horizontal kinematic coefficient of turbulent viscosity was estimated from experience with other similar simulated lakes; for all simulations it was set to 1 m 2 /s. 3. HYDRODYNAMIC SIMULATIONS In order to determine the basic pattern of water circulation in the lake under different conditions, we performed four simulations with different wind directions and velocities and with summer and winter temperature distributions throughout the depth (Table 2). Preglednica 2. Osnovni podatki, ki so bili uporabljeni pri hidrodinamič nih simulacijah. Table 2. Some basic data used for the hydrodynamic simulations. Pretok Lepene Lepena flow rate (m 3 /s) Pretok Sopote Sopota flow rate (m 3 /s) Pretok na iztoku Outflow flow rate (m 3 /s) Smer vetra Wind direction Hitrost vetra Wind speed (m/s) Razmere Conditions PRIMER1 CASE 1 0.628 0.127 0.755 SE 2 Poletne Summer PRIMER2 CASE 2 0.628 0.127 0.755 W 1 Poletne Summer PRIMER3 CASE 3 0.628 0.127 0.755 SSE 2 Zimske Winter PRIMER4 CASE 4 0.628 0.127 0.755 W 1 Zimske Winter Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 81 V prvem primeru (primer 1) smo uporabili jugovzhodni veter s hitrostjo 2 m/s v poletnih temperaturnih razmerah. V drugem primeru (primer 2) smo uporabili zahodnik s hitrostjo 1 m/s v poletnih razmerah, tretji primer (primer 3) pa je bil simulacija v zimskih razmerah z jugo-jugovzhodnikom hitrosti 2 m/s. Primer 4 je bil simulacija primera 2 v zimskih razmerah. V vseh 4 primerih je simulacija trajala 24 ur. Poglavitni rezultati hidrodinamič nih simulacij so prikazani na slikah 1 in 2. Z modeliranjem smo ugotovili, da je veter poglavitni vzrok tokov v jezeru. Ti so v veliki meri odvisni tako od hitrosti kot od smeri vetra. Simulacije z različ nim trajanjem vetra kaejo, da se je hitrostno polje v prvih 12 urah pihanja vetra spreminjalo. Po 12 urah pa so se hitrost in smer gibanja vode in vetra uskladile in se niso več spreminjale. Hitrosti gibanja vode v Velenjskem jezeru so moč no odvisne tudi od morfologije jezerskega dna. Hitrosti v povrinskem sloju so mnogo vije v najplitvejem delu jezera. Vtoki in iztok iz jezera pa celo pri simulacijah brez upotevanja vpliva vetra niso pokazali skoraj nobenega vpliva na gibanje vode. In the first case (Case 1) we used a southeasterly wind with speed of 2 m/s under summer conditions. In the second case (Case 2) a westerly wind with a speed of 1 m/s under summer conditions was used. The third case (Case 3) was a simulation under winter conditions with south-southeasterly wind of 2 m/s. Case 4 was a simulation of Case 2 under winter conditions. The simulation time was 24 hours for all four cases. The main hydrodynamic simulations results are shown on Figures 1 and 2. Modeling revealed that the wind is the main forcing factor that causes the circulation of the lake water. Water flow in the lake is strongly dependent upon wind speed and direction. Simulations with different wind duration show that, within the first 12 hours, the wind blowing over the lake changes water velocity and direction. After a 12-hour period, wind and water velocities and directions are balanced and do not change anymore. Water velocities in Lake Velenje are also strongly dependent upon the morphology of the lake basin. Surface velocities are much higher over the shallowest parts of the basin. Even in simulations with zero wind speed, the inflows and outflow show nearly no influence on water movement. Lake Velenje - Surface velocities Wind speed: 2 m/s Wind direction: SE Wind duration: 5 h Summer conditions - temperature stratification 19 Layers Sopota Lepena Outflow 0 200 400 600 m Lenght 0 0.2 m/s Velocity Lake Velenje - Surface velocities Wind speed: 2 m/s Wind direction: SE Wind duration: 24 h Summer conditions - temperature stratification 19 Layers Sopota Lepena Outflow 0 200 400 600 m Lenght 0 0.2 m/s Velocity A. B. Wind 2 m/s B B A A Wind 2 m/s A A B B Lake Velenje - W-E cross section Wind speed: 2 m/s Wind direction: SE Wind duration: 24 h Summer conditions - temperature stratification 19 Layers 0 200 400 600 m Lenght 0 0.2 m/sV e l o c i t y Lake Velenje - N-S cross section Wi nd speed: 2 m/s Wind direction: SE Wind duration: 24 h Summer conditions - temperature stratification 19 Layers 0 200 400 600 m Lenght 0 0.2 m/s Velocity C.. D.. A-A B-B W E S N Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 82 Slika 1. Hidrodinamič ni rezultati v poletnih razmerah z jugovzhodnim vetrom, 2 m/s, po A.) 5 urah in B.) 24 urah simulacije v povrinskem sloju in dveh prerezih Velenjskega jezera (primer 1). Figure 1 . Results of hydrodynamic under summer conditions with southeasterly wind, 2 m/s, after A.) 5 hours and B.) 24 hours of simulation in Lake Velenje surface layer and in vertical cross- sections (Case 1 ). A. B. Wind 2 m/s B B A A Wind 2 m/s Lake Velenje - Surface velocities Wind speed: 2 m/s Wind direction: SSE Wind duration: 5 h Winter conditions 19 Layers Sopota Lepena 0 200 400 600 m Lenght 0 0.2 m/s Velocity Lake Velenje - Surface velocities Wind speed: 2 m/s Wind direction: SSE Wind duration: 24 h Winter conditions 19 Layers Sopota Lepena Outflow 0 200 400 600 m Lenght 0 0.2 m/s Velocity A A B B Outflow Lake Velenje - W-E cross section Wind speed: 2 m/s Wind direction: SE Wind duration: 24 h Summer conditions - temperature stratification 19 Layers 0 200 400 600 m Lenght 0 0.2 m/s Velocity Lake Velenje - N-S cross section Wind speed: 2 m/s Wind direction: SE Wind duration: 24 h Summer conditions - temperature stratification 19 Layers 0 200 400 600 m Lenght 0 0.2 m/s Velocity C.. D.. A-A B-B W E S N Slika 2. Hidrodinamič ni rezultati v zimskih razmerah z jugo-jugovzhodnim vetrom, 2 m/s, po A.) 5 urah in B.) 24 urah simulacije v povrinskem sloju in dveh prerezih Velenjskega jezera (primer 3). Figure 2. Results of hydrodynamic under winter conditions with south-southeasterly wind, 2 m/s, after A.) 5 hours and B.) 24 hours of simulation in Lake Velenje surface layer and in vertical cross- sections (Case 3). V preč nih prerezih se pojavi gibanje vode v obliki močnejega zgornjega in manj izraenega spodnjega vrtinca zaradi mo č ne temperaturne stratifikacije med pomladnimi in poletnimi meseci. Ta pojav je v alpskih jezerih dobro poznan. Voda iz globljih slojev ne dosee povrine jezera, zato ni neposrednega vnosa kisika v spodnje sloje, to pa v mnogih alpskih jezerih povzroča probleme s kakovostjo vode. Tudi več je hitrosti vetra ne vplivajo na kroenje vode v globljih delih jezera (nad 30 m globine). Med zimskimi in pomladnimi meseci je voda v jezeru popolnoma premeana. Temperaturne stratifikacije ni bilo opaziti. V takih primerih lahko celo ibki vetrovi povzroč ijo krono gibanje vode, ki sega od povrja do dna jezera. Meanje vode po celotni The circulation in the vertical cross section is divided into a stronger upper vortex and less intense lower vortex due to sharp temperature stratification during the spring and summer months. This phenomenon is well known in alpine lakes. As the bottom water cannot reach the surface, there is no direct oxygenation of the bottom layers, which causes water quality problems in several lakes. Water circulation in the deepest parts of the lake (over 30 m of depth) is unaffected by higher wind speeds. During the winter and spring months the water in the lake is well mixed. No temperature stratification was observed. In these cases even weak winds can cause a circulation vortex, which extends from the surface to the bottom. Water circulation from the surface to bottom thus causes well- Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 83 globini tako povzroč a dovoljen vnos kisika tudi v globlje sloje jezera. V zelo hladnih zimah gladina jezera zamrzne. Debelina ledu je lahko do 30 cm. V taknih pogojih veter nima vpliva na gibanje vode. V skladu z najpogostejimi smermi vetra lahko zaključ imo, da je v povrinskem sloju jezera najbolj pogosta smer toka z vzhoda proti zahodu. 4. PREVERJANJE A MODELA IN SIMULACIJE 4.1 PREVERJANJE Z δ δ δ δ 1 8 O IN δ δ δ δ 2 H Hidrodinamični del modela je bil predhodno umerjen in preverjen v podobnih slovenskih jezerih (Rajar in Č etina, 1992a; Rajar in Č etina 1993 Rajar et al., 1995) in v Severnem Jadranu (Rajar, 1992; Rajar in Č etina, 1992b; Rajar et al., 1995, irca 1996; irca et al., 1999a; irca et al., 1999b; Rajar et al., 2000). Meritve hitrosti vode v Velenjskem jezeru se niso izvajale. Priblino gibanje vode v povrinskem sloju smo ugotavljali s pomo č jo stabilnih izotopov δ 18 O in δ 2 H. Razmerja med vsebnostjo tejih in lajih izotopov O in H so se uporabila kot sledila za določ anje gibanja vode v Velenjskem jezeru in njegovih vtokih. Izotopska sestava kisika v vodi je bila določ ena z uporabo standardnih metod, ki temeljijo na ravnoteju z referen č nim CO 2 pri 25 o C v 24 h (Epstein and Mayeda, 1953), ki je potem merjeno na masnem spektrometru Varian MAT 250. Meritev izotopske sestave devterija v vodi temelji na redukciji vode na Cr pri 800 C. Spro č en plin vodik se potem uporabi za določitev izotopske sestave devterija v vodi (Gehre et al., 1996), ki je bila izmerjena na masnem spektrometru Varian MAT 250. Kalibracija δ 18 O in δ 2 H vrednosti je potekala s pomoč jo mednarodnih standardov VSMOW, GISP in SLAP ( vrednosti) analiziranih po enakem postopku kot vzorec. Natanč nost meritev δ 18 O in δ 2 H temelječ a na ponavljajoč ih se meritvah je bila ±0.05 in ±1.0. Rezultati simulacij in primerjava z merjenimi vrednostmi v povrinskem sloju oxygenated bottom water. In very cold winters the lake surface can be completely frozen. The ice layer can be up to 30 cm thick. Under such conditions, the wind has no influence on water movement. Regarding the most common wind directions, it can be concluded that the most common flow direction in the surface layer is from east to west. 4. MODEL VERIFICATION AND SIMULATIONS 4.1 VERIFICATION BY δ δ δ δ 1 8 O AND δ δ δ δ 2 H The hydrodynamic part of the model has been previously calibrated and verified in similar Slovenian lakes (Rajar and Č etina, 1992a; Rajar and Č etina 1993 Rajar et al., 1995) and in the Northern Adriatic Sea (Rajar, 1992; Rajar and Č etina, 1992b; Rajar et al., 1995, irca 1996; irca et al., 1999a; irca et al., 1999b; Rajar et al., 2000). Measurements of water velocities in Lake Velenje were not conducted. Approximate water movement in the surface layer was established by use of the stable isotopes δ 18 O and δ 2 H. The proportions of heavier and lighter isotopes of O and H were used as tracers of water cycling in Lake Velenje and its inflows. The isotopic composition of oxygen in water was determined using the standard method based upon equilibration with referenced CO 2 at 25 o C for 24 h (Epstein and Mayeda, 1953), which was then measured on a Varian MAT 250 mass spectrometer. Reduction of water on Cr at 800 o C to produce hydrogen gas is used to determine the isotopic composition of deuterium in water (Gehre et al., 1996). The hydrogen gas was then measured on a Varian MAT 250 mass spectrometer. The calibration of the δ 18 O and δ 2 H values analysed with respect to the international standards was carried out by analysing VSMOW, GISP and SLAP ( values) with the same procedures. The precision of the analyses of δ 18 O and δ 2 H based upon replicate measurements was ±0.05, and ±1.0, respectively. Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 84 Velenjskega jezera so prikazani na slikah 3 in 4. Simulation results and comparison to measured values in surface layer of Lake Velenje are shown in Figure 3 and Figure 4. Lake Velenje Spring 0 400 m Sopota Lepena Outflow -8.57 -8.98 Lake Velenje Spring 0 400 m Sopota Lepena Outflow -59.5 -62.1 0 300 600 m Lepena Sopota Outflow -8.57 -8.98 Wind 2 m/s -7.0 -7.4 -7.8 -8.2 -8.2 -8.2 Lake Velenje - Surface O values ( / ) Wind speed: 2 m/s Wind direction: E Simulation time: 24 h Spring conditions 19 layers δ 18 o oo Lake Velenje - Surface values ( / ) Wind speed: 2 m/s Wind direction: E Simulation time: 24 h Spring conditions 19 layers δΗ 2 o oo 0 300 600 m Lepena Sopota Outflow -59.5 -62.1 Wind 2 m/s -55 -56 -57 -58 -58 -58 Wind 0-2 m/s Wind 0-2 m/s δ O 18 δ H 2 Slika 3. Izmerjene vrednosti δ 18 O in δ 2 H (v ) in primerjava s simuliranimi vrednostmi v povrinskem sloju Velenjskega jezera (pomlad 1998). Figure 3. Measured δ 1 8 O and δ 2 H values (in ) and comparison to simulated values in the surface layer of Lake Velenje (spring 1 998). Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 85 Lake Velenje Winter 0 200 400 m Sopota Lepena Outflow -65.2 -65.2 Lake Velenje Winter 02 0 0 400 m Sopota Lepena Outflow -9.47 -9.53 δ O 18 δ H 2 0 300 600 m Lepena Sopota Outflow -9.47 -9.53 Wind 3 m/s -7.6 -7.8 -8.0 -8.0 -8.0 -8.2 Lake Velenje - Surface O values ( / ) Wind speed: 3 m/s Wind direction: E Simulation time: 24 h Winter conditions 19 layers δ 18 o oo 0 300 600 m Lepena Sopota Outflow -65.2 -65.2 Wind 3 m/s -59 -60 -60 -61 Lake Velenje - Surface values ( / ) Wind speed: 3 m/s Wind direction: E Simulation time: 24 h Winter conditions 19 layers δΗ 2 o oo Slika 4. Izmerjene vrednosti δ 18 O in δ 2 H (v ) in primerjava s simuliranimi vrednostmi v povrinskem sloju Velenjskega jezera (zima 1999). Figure 4. Measured δ 1 8 O and δ 2 H values (in ) and comparison to simulated values in the surface layer of Lake Velenje (winter 1 999). Kroenje in meanje vode, ki vteka v jezero je odvisno od hitrosti vetra in vtoč nih hitrosti. Voda, ki vteka v jezero, ima na dotoku nije vrednosti δ 18 O (pomlad: 8,57 do 8,98 o / oo ; zima: 9,4 do 9,35 o / oo ) in δ 2 H (pomlad: 59,5 do 62 o / oo ; zima: 65,2 o / oo ) kot jezerska voda. V jezeru se te vrednosti viajo v odvisnosti od količine dotekajoče vode, stopnje meanja z jezersko vodo in izhlapevanja. Razvidno je, da je porazdelitev vtekajoč e vode po jezeru odvisna predvsem od hitrosti vetra in vtoč nih hitrosti. Pozimi, ko je bil veter moč neji kot spomladi, je dotekajo č a voda po povrini jezera segla veliko dlje kot spomladi. Dejanska smer gibanja vode je podobna rezultatom simulacij. Tako vrednosti δ 18 O kot δ 2 H so pokazale enak gradient Water cycling and the distribution of inflow water depend upon wind speed and inflow velocity. The inflows have lower δ 18 O (spring: 8.57 to 8.98 o / oo ; winter: 9.4 to 9.35 o / oo ) and δ 2 H (spring: 59.5 to 62 o / oo ; winter: 65.2 o / oo ) values than the lake water. In the lake, these values are changing toward higher values depending upon the inflow water discharge, its degree of mixing with the lake water, and evaporation. As can be seen, inflow water is distributed from the inflows to the lake depending primarily on wind speed and inflow velocity. In winter, when the wind was stronger than in the spring, the inflow water flows out over the lake surface much further into the lake than in the spring. The true direction of the water movement is similar to the simulated movement. Both the δ 18 O and Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 86 koncentracij. Na obeh slikah (sliki 1 in 2) sta prikazani hitrostni polji v povrinskem sloju jezera. Simulacijo smo izvedli z uporabo podobnega vetra, ki je pihal nad jezerom na dan, ko smo opravljali meritve. Omeniti je treba, da je to preverjanje zgolj kvalitativno, posredno in zelo priblino. To je bil le poskus korelacije hitrostnih polj v povrinskem sloju vode s porazdelitvijo različ nih izotopov istega elementa. Meritve izotopov so lahko zelo uporabne pri sledenju gibanja vode. Za bolje rezultate pa bi bilo treba izvesti mnogo več meritev in simulacij (Wachniew in Rozanski, 1998). δ 2 H values gave the same gradient of concentration. On both figures (Fig. 1 and Fig. 2) the velocity fields in the water surface layer are shown. The simulation was performed using wind conditions similar to those found over the lake on the day when the samples were collected. It should be noted that this verification is only qualitative, indirect and very approximate. This was a trial to correlate water velocity fields to the distribution of different isotopes of the same element. Isotope measurements can be very useful for water movement tracing. For more detailed results many more measurements and simulations should be done (Wachniew and Rozanski, 1998). 4.2 MODELIRANJE TRANSPORTA IVEGA SREBRA IN PRIMERJAVA Z MERITVAMI Model PCFLOW3D vključ uje tudi tako imenovani modul za ra čun transporta (transportno-disperzijski modul), imenovan tudi modul za ra č un transporta in pretvorb snovi, s katerim lahko simuliramo transport in disperzijo določ enih masnih količ in (npr. kontaminanta). Modeliranje masnega transporta v celoti temelji na poznavanju gibanja vode, ki je rezultat hidrodinamič nega modula in dodatnega koeficienta disperzije (Nihuol et al., 1992). Ker koncentracija določ enega kontaminanta v več ini primerov bistveno ne vpliva na gostoto vode in kroenje vode, je hidrodinamič ni modul (HD) ponavadi neodvisen od transportno-disperzijskega modula (MT). Simulacije transporta različ nih zvrsti ivega srebra so odvisne od istih vhodnih podatkov kot hidrodinamič ne simulacije, obravnavane v prejnjem delu. Podatki o vetru in temperatura jezerske vode, uporabljeni v simulacijah, so bili priblino enaki kot veter in temperatura, izmerjena v dneh, ko smo izvajali meritve. V teh simulacijah so bile različ ne zvrsti ivega srebra obravnavane kot konzervativni polutanti in niso vplivale druga na drugo. Sedimentacija in resuspendiranje ter vnos iz ozrač ja in v ozrač je niso bili upotevani. S temi simulacijami smo eleli potrditi 4.2 MODELING OF MERCURY TRANSPORT AND COMPARISON TO MEASUREMENTS The model PCFLOW3D has included within it a so-called mass-transport module, also known as the transport and fate module, which simulates transport and dispersion of the relevant quantity (i.e. of a contaminant). Mass transport modeling depends entirely upon the hydrodynamic circulation obtained by the hydrodynamic module and additionally upon dispersion coefficients (Nihuol et al., 1992). As the concentration of a particular contaminant in most cases does not significantly influence water density and its circulation, the hydrodynamic module is usually independent of the mass-transport module. Mercury species transport simulations are based upon the same input data as the hydrodynamic simulations in the previous section. Wind conditions and lake water temperature used for the simulations were approximately the same as measured wind and temperature on the day when the samples were collected. In these simulations, different mercury species are conservative pollutants and do not interact with each other. There is no sedimentation or resuspension, and neither input from the atmosphere nor evasion to the atmosphere. Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 87 pravilno delovanje modela. Dokazovati bi morale, da bi bile nadaljnje simulacije cirkulacije vode zanesljive vsaj do določ ene mere natanč nosti. Ugotoviti smo eleli tudi, kaken vpliv imajo na transport ivega srebra v jezeru vtoki in različ ne hitrosti in smeri vetra. Simulirali smo dva primera transporta ivega srebra (primer A in primer B). V obeh simulacijah smo se z modelom skuali č im bolj pribliati dejanskemu stanju. Preto č ne hitrosti na vtoku so bile v obeh primerih iste in so bile enake kot pri hidrodinamič nih simulacijah. Pretoki Sopote in Lepene so bili merjeni med januarjem 1990 in decembrom 1995. V primeru A smo izvedli simulacijo vnosa ivega srebra z vtoki v jezero ter njegovo razporeditev v spomladanskih razmerah. Upotevali smo vzhodni veter s hitrostjo 2 m/s, kar je bil najbolji pribliek izmerjenim podatkom. Zač etne koncentracije različ nih oblik Hg in MeHg v jezeru prikazujemo v preglednici 3. V drugem primeru (primer B) smo simulirali zimske razmere. V tem primeru je bil veter moč neji kot pri prvi simulaciji (vzhodni veter s hitrostjo 3 m/s). Zač etne koncentracije Hg v jezeru in vtokih so prikazane v preglednici 4. With these simulations we wished to validate the model. This verification should be a proof, that further simulations of water circulation are reliable, at least to a certain degree of accuracy. We also wished to establish the influence of the inflows and of different wind speeds and directions on mercury transport in the lake. Two cases (Case A and Case B) of mercury transport were simulated. In both simulations we tried to accommodate the model to the real situation as much as possible. Inflow flow rates were the same in both cases, and were also similar in the hydrodynamic simulations. Flow rates of Sopota and Lepena Streams were measured in January 1990 and December 1995. In Case A, a simulation of mercury input from inflows and its distribution under spring conditions were performed. An easterly wind with a speed of 2 m/s was used, which was nearest to the measured data. Initial concentration of different Hg and MeHg forms in the lake and inflow water were shown in Table 3. The second case (Case B) was a simulation under winter conditions. In this case, wind was stronger than in the previous simulation (easterly wind with a speed of 3 m/s). Initial Hg concentrations in the lake and inflows were as follows in Table 4. Preglednica 3. Hitrost in smer vetra, pretok in različ ne oblike ivega srebra pri simulaciji primera A. Table 3. Wind speed and direction, flow rates, and different mercury forms used for the simulation of Case A. Hitrost vetra Wind speed (m/s) Pretok/ Flow rate (m 3 /s) THg (ng/l) DHg (ng/l) PHg (ng/l) TMeHg (ng/l) DMeHg (ng/l) PMeHg (ng/l) Sopota 0.127 2.29 0.64 1.66 0.101 0.052 0.049 Lepena 0.628 4.34 1.07 3.27 0.147 0.027 0.120 Zač etna koncentracija v jezeru Initial concentration in the lake 2 m/s, E 1.24 0.56 0.68 0.619 0.024 0.026 Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 88 Preglednica 4. Hitrost in smer vetra, pretok in različ ne oblike ivega srebra pri simulaciji primera B. Table 4. Wind speed and direction, flow rates and different mercury forms used for the simulation of Case B. Hitrost vetra/ Wind Speed (m/s) Pretok/ Flow rate (m 3 /s) THg (ng/l) DHg (ng/l) PHg (ng/l) TMeHg (ng/l) DMeHg (ng/l) PMeHg (ng/l) Sopota 0.127 1.00 0.42 0.59 0.005 0.004 0.0001 Lepena 0.628 3.39 1.11 2.27 0.066 0.009 0.056 Zač etna koncentracija v jezeru Initial concentratio n in the lake 3 m/s, E 0.97 0.73 0.25 0.0253 0.0145 0.0133 Spring Total Hg (ng/L) 0 400 m Sopota Lepena Outflow 2.29 4.34 Lake Velenje - SurfaceTHg concentrations (in ng/L) Wind speed: 2 m/s Wind direction: E Simulation time: 24 h Spring conditions 19 Layers 0 300 600 m Lepena Sopota Outflow 2.29 4.34 1.2 1.4 1.6 1.8 2 2.2 2.4 Wi nd 2 m/s Wind 0-2 m/s Winter Total Hg (ng/L) Sopota Lepena Outflow 1.0 3.39 0 400 m Lake Velenje - Surface THg concentrations (in ng/L) Wind speed: 3 m/s Wind direction: E Simulation time: 24 h Winter conditions 19 Layers 0 300 600 m Lepena Sopota Outflow 1.0 3.39 Wi nd 3 m/s 1.0 1.2 1.0 1.4 1.6 Case A Case B A. B. D. C. Slika 5. Rezultati simulacije transporta celokupnega ivega srebra in njegova porazdelitev (A., C.) v Velenjskem jezeru v pomladanskih (primer A) in zimskih (primer B) razmerah in primerjava z izmerjenimi vrednostmi (C., D.) (koncentracije so v ng/l). Figure 5. Simulation results for total mercury transport and distribution (A., C.) in Lake Velenje under spring (Case A) and winter (Case B) conditions and comparison to measured values (C., D.)(concentrations are in ng/l). Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 89 Spring Total MeHg (ng/L) Sopota Lepena Outflow 0.10 0.15 0 400 m Lake Velenje - Surface TMeHg concentrations (in ng/L) Wind speed: 2 m/s Wind direction: E Simulation time: 24 h Spring conditions 19 Layers 0 300 600 m Lepena Sopota Outflow 0.101 0.147 Wi nd 2 m/s 0.06 0.08 0.1 Wind 0-2 m/s Winter Total MeHg (ng/L) Sopota Lepena Outflow 0.005 0.066 0 400 m Lake Velenje - Surface TMeHg concentrations (in ng/L) Wind speed: 3 m/s Wind direction: E Simulation time: 24 h Winter conditions 19 Layers 0 300 600 m Lepena Sopota Outflow 0.005 0.066 Wi nd 3 m/s 0.04 0.02 0.06 Case A Case B A. B. D. C. Slika 6. Rezultati simulacije transporta celokupnega metil-ivega srebra in porazdelitev (A., C.) v Velenjskem jezeru v pomladanskih (primer A) in zimskih (primer B) razmerah in primerjava z izmerjenimi vrednostmi (B., D.) (koncentracije so v ng/l). Figure 6. Simulation results for total methylmercury transport and distribution (A., C.) in Lake Velenje under spring (Case A) and winter (Case B) conditions and comparison to measured values (B., D.) (concentrations are in ng/l). Rezultati primera A kaejo, da gibanje vode v povrinskem sloju jezera poteka preteno z vzhoda proti zahodu. Simulirane razporeditve THg (slika 5), DHg in PHg so priblino primerljive z meritvami. ivo srebro v teh treh oblikah vstopa v jezero z Lepeno in se razporedi po povrini jezera z gibanjem vode. Rezultati simulacije za različ ne oblike MeHg (slika 6) se bistveno razlikujejo od izmerjenih vrednosti drugih oblik Hg. To lahko obrazloimo z dejstvom, da je verjetno znaten dele Hg v jezeru metiliran in da razporeditev MeHg v različ nih oblikah ni odvisna samo od gibanja vode, temveč tudi od kemijskih in biolokih lastnosti jezera. Bioloki in kemi č ni vplivi v modelu niso upotevani, kar je verjetno vzrok razlikam, ki so se pojavile med rezultati simulacij in The simulation for Case A shows that water movement in the lake surface is mainly from east to west. The simulated distributions of THg (Figure 5), DHg and PHg are approximately comparable to the measurements. All three forms entered the lake mostly via Lepena Stream and are distributed across the surface of the lake by water movement. The simulation results for the various MeHg (Figure 6) forms are much more different from the measured values than are the other Hg forms. This difference can be explained by the fact that probably a significant part of Hg is methylated in the lake, and that distribution of MeHg forms depends not only on water movement, but also on chemistry and biology of the lake. Biological and chemical interactions are not included in the model and this is probably the reason for Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 90 meritvami. Pri simulaciji zimskih razmer (primer B) so koncentracije in razporeditev Hg na povrju zgolj grobo primerljive z izmerjenimi vrednostmi. V obeh primerih (za THg, DHg in PHg) simulacije in meritve kaejo, da je glavni vir Hg v jezeru potok Lepena. ivo srebro je večinoma vezano na delce. Izrač unane koncentracije in porazdelitev Hg na povrini jezera so odvisne od smeri vetra in hitrosti nad povrjem in posledi č nega gibanja vode v jezeru. ivo srebro je imelo v Lepeni za č etno koncentracijo 3,39 ng/l za THg, 1,11 ng/l za DHg in 2,27 ng/l za PHg. Koncentracije so se znievale v smeri od vzhoda proti zahodu, tako pri simulacijah kot pri meritvah vseh treh oblik Hg. Simulirane in izmerjene vrednosti različ nih zvrsti MeHg so v grobem primerljive. Glavna razlika je, da meritve kaejo vije koncentracije vseh izmerjenih oblik MeHg na zahodni strani jezera poleg deponije, simulacije pa kaejo ravno obratno sliko; vije koncentracije so bile na vzhodni strani jezera poleg vtokov, predvsem poleg Lepene. V simulacijah so se koncentracije MeHg na povrini jezera znievale od vzhoda proti zahodu. Koncentracije v sredini jezera pa so v istem velikostnem razredu za vse tri zvrsti MeHg, tako v izrač unanih kot v izmerjenih rezultatih. the differences between the simulated and measured results. In the simulation of winter conditions (Case B) concentrations and surface Hg distributions are very roughly comparable to the measured values. In both cases (for THg, DHg and PHg), the simulations and measurements show that the main source of Hg in the lake is Lepena Stream. Mercury was mostly bound to particulate matter. The simulated concentrations and Hg distribution in the lake surface depend upon wind direction and speed over the lake surface, and accordingly on water movement in the lake. Mercury is distributed from Lepena Stream with an initial concentration of 3.39 ng/l for THg, 1.11 ng/l for DHg and 2.27 ng/l for PHg. The concentrations are decreasing in the direction from east to west in both the simulations and measurements for all three Hg forms. The simulated and measured values for MeHg species are roughly comparable. The main difference is that the measurements show higher concentrations of all measured MeHg forms on the western side of the lake near to the landfill, while the simulations show the opposite situation; higher concentrations were on the eastern side of the lake near the inflows, particularly near Lepena Stream. In the simulations, MeHg concentrations in the lake surface decrease from east to west. Concentrations in the middle of the lake are in the same range for all three MeHg species, both in the simulations and measured results. 5. ZAKLJUČ KI Kot je bilo prič akovati, rezultati simulacij kaejo, da lahko rezultati modela brez nadaljnjih izboljav pokaejo zgolj osnovne znač ilnosti transporta in disperzije ivega srebra v Velenjskem jezeru. Poglavitne vzroke razlik med simuliranimi in izmerjenimi rezultati lahko povzamemo: - Vhodni podatki o vetru, ki smo jih uporabili pri simulaciji hidrodinamič ne cirkulacije, niso bili dovolj natanč ni, saj sta se hitrost in smer vetra v č asu meritev spreminjala, hitrost vetra pa tudi ni enakomerna nad celim jezerom. - V simulacijah nismo upotevali procesov pretvorb ivega srebra, č eprav nekateri od njih niso zanemarljivi (npr. izhlapevanje, 5. CONCLUSIONS As expected, the simulation results show that the model without further upgrade can give only the very basic features of the transport dispersion phenomena of mercury in Lake Velenje. The main causes of the differences between the simulated and measured results can be summarized as follows: - The wind input data used to simulate HD circulation were not quite accurate, as the wind speed and direction were changing during the time of measurement and partly also spatially over the lake surface. - The processes of mercury transformation were not taken into account in the simulations, but some of them are not negligible in reality (e.g. evaporation, Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 91 usedanje, metilacija, redukcija). - Pri simulacijah niso bili upotevani nekateri drugi pomembneji pojavi, (to so sedimentacija/resuspenzija, adsorbcija/desorpcija). Zaključ imo lahko, da so bile poglavitne znač ilnosti hidrodinamič ne cirkulacije uspeno simulirane, medtem ko moramo rezultate simulacije transporta in disperzije različ nih oblik ivega srebra obravnavati z zadrkom. Z modeliranjem smo pokazali, da je veter glavni vzrok gibanja jezerske vode. Tokovi v jezeru so moč no odvisni od hitrosti in smeri vetra. Simulacije z različ nim trajanjem vetra kaejo, da se v prvih 12 urah hitrostno polje zaradi vpliva vetra spreminja. Po 12 urah pa so se hitrost in smer gibanja vode in vetra uskladile in se niso več spreminjale. Hitrostno polje v Velenjskem jezeru je moč no odvisno tudi od morfologije jezerskega dna. Hitrosti v povrinskem sloju so bistveno vije v plitvejih delih jezera. V pre č nih prerezih se pojavi gibanje vode v obliki moč nejega zgornjega in manj izraenega spodnjega vrtinca zaradi močne temperaturne stratifikacije med pomladnimi in poletnimi meseci. Ta pojav je v alpskih jezerih dobro poznan. Voda iz globljih slojev ne dosee povrine jezera, zato ni neposrednega vnosa kisika v spodnje sloje, to pa v mnogih alpskih jezerih povzroč a probleme s kakovostjo vode. Tudi več je hitrosti vetra ne vplivajo na kroenje vode v globljih delih jezera (nad 30 m globine). Tudi vtoki vode nimajo več jega vpliva na kroenje vode, saj je pretok na vtoku premajhen. Tudi pri simulacijah brez upotevanja vetra vtoki in iztoki nimajo skoraj nikakrnega vpliva na gibanje vode. V skladu z najpogostejimi smermi vetra lahko zaključ imo, da je v povrinskem sloju jezera najbolj pogosta smer toka z vzhoda proti zahodu. sedimentation, methylation, reduction, etc.). - Some phenomena significant to the simulated events (i.e. sedimentation/resuspension, adsorption/desorption), were not taken into account in the simulations. We can conclude that the main features of the HD circulation are simulated, while the results of the simulation of transport dispersion of the different mercury forms must be regarded with caution. Modeling revealed that the wind is the main forcing factor that causes the circulation of the lake water. Water flow in the lake is strongly dependent upon wind speed and direction. Simulations with different wind duration show that, within the first 12 hours, the wind blowing over the lake changes the water velocities and direction. After a 12-hour period, wind and water velocities and directions are balanced and do not change anymore. Water velocities in Lake Velenje are also strongly dependent upon the morphology of the lake basin. Surface velocities are much higher over the shallowest parts of the basin. The circulation in the vertical cross section is divided into a stronger upper vortex and less intense lower vortex due to strong temperature stratification during the spring and summer months. This phenomenon is well known in alpine lakes. As the bottom water cannot reach the surface, there is no direct oxygenation of the bottom layers, which cause water quality problems in several lakes. Water circulation in the deepest parts of the lake (over 30 m of depth) is unaffected by higher wind speeds. The inflows also do not have much influence on water cycling because the inflow discharge is too small. Even in simulations with zero wind speed, the inflows and outflow show nearly no influence on water movement. Regarding the most common wind directions, it can be concluded that the most common flow direction in the surface layer is from east to west. ZAHVALA Za finančno pomoč pri raziskavi se zahvaljujemo Ministrstvu za olstvo, znanost in port. ACKNOWLEDGEMENTS We acknowledge the financial support of the Ministry of Education, Science and Sports of Slovenia for funding this work. Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 92 VIRI REFERENCES Epstein, S., and Mayeda, T. (1953). Variations of 18 O contents of water from natural sources. Geochimica et Cosmochimica Acta 4, 213224. Gehre, M., Hoefling, R., Kowski, P. and Strauch, G. (1996). Sample preparation device for quantitative hydrogen isotope analysis using chromium metal, Analytical Chemistry 68, 4414 4417. Nihuol, J.C., Adam, C., Brasseur, P., Djenidi, S., Haus, J. (1992). Three-Dimensional General Circulation Model of the N. Bering Seas Summer Ecohydrodynamics, Continental Shelf Research, Special ISHTAR Issue 14. Kotnik, J., Horvat, M., Fajon, V., Logar, M. and Ogrinc N. (2003). Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 1.del: ivo srebro v jezerski vodi = Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part I: Mercury in Lake Water, Acta hydrotechnica 21 (35), 87103. PCFLOW3D Users Manual (1997). University of Ljubljana, FGG Hydraulics Division, Ljubljana. Rajar, R. (1989). Three-dimensional modelling of currents in the Northern Adriatic Sea. Proceedings of the 23 th Congress IAHR, Ottawa. Rajar, R. (1992). Applications of three-dimensional model to Slovenian coastal sea. Conference on Computer Modelling of Seas and Coastal Regions, Sauthampton. Rajar, R. and Č etina, M. (1986). Mathematical simulation of two-dimensional lake circulation. Proceedings of the HYDROSOFT Conference, Southampton, Elsevier Sc. Publ. Rajar, R. and Č etina, M. (1991). Modelling wind induced circulation and dispersion in the Northern Adriatic. Proceedings of the 24 th Congress IAHR, Madrid. Rajar, R. and Č etina, M. (1992a). Mathematical modelling of circulation and of nutrient dispersion in Lake Bohinj. Gradbeni vestnik 32, 785812. Rajar, R. and Č etina, M. (1992b). Modelling of tidal and wind induced circulation and dispersion of pollutants in the Northern Adriatic. Acta Adriatica 32, 2, 785812. Rajar, R. and Č etina, M. (1993). Three-dimensional modelling of circulation and of dispersion of nutrients in Lake Bohinj. Presented at the International Conference Water Pollution, Milano, June 1993 Rajar, R. and Č etina, M. (1997). Hydrodynamic and Water Quality Modelling: an Expirience. Ecological Modelling 1 01 , 195207. Rajar, R., Č etina, M. and agar, D. (1995). Three-dimensional modelling of oil spill in the Adriatic. In Computer Modelling of Seas and Coastal Regions II, C. Brebbia, L. Traversoni and L. Wrobel (Eds.), Computational Mechanics Publications, 95102 (proceedings of the 2 nd International Conference on Computer Modelling of Seas and Coastal regions (COASTAL 95), Cancun, Mexico, September 1995). Rajar, R., agar, D., irca, A., Horvat, M. (2000). Three-dimensional modelling of mercury cycling in the Gulf of Trieste. The Science of the Total Environment 260, 109123. irca, A. (1996). Modeliranje hidrodinamike in transporta ivosrebrovih spojin v Trakem zalivu. University of Ljubljana, Faculty for Civil and Geodetic Engeenering, Dissertation, pp. 164, Ljubljana. (Transl.: Modelling of the hydrodynamics and of the transport of mercury compounds in Trieste bay) irca, A., Rajar, R., Harris, R.C. and Horvat, M. (1999a). Mercury transport and fate in the Gulf of Trieste (Northern Adriatic) a two dimensional approach. Environmental Modelling and Software 1 4, 645655. irca, A., Horvat, M., Rajar, R. Covelli, S., agar, D., Faganeli, J. (1999b). Estimation of mercury mass balance in the Gulf of Trieste. Acta Adriatica 40 (2), 7585. Kotnik, J. et al.: Modeliranje hidrodinamike in transporta ivega srebra v Velenjskem jezeru 2. del: modeliranje in preverjanje modela Modelling of Hydrodynamics and Mercury Transport in Lake Velenje Part 2: Modelling and Model Verification ' Acta hydrotechnica 22/37 (2004), 7793, Ljubljana 93 Wachniew, P. and Rozanski, K. (1998). Quantitative paleoenvironmental reconstructions on continents based on C and O isotope composition of lacustrine calcite. In: Chalenges to Chemical Geology, Reference papers from MAEGS-10, Novak M. and Roseubeum J. (eds.), Czech Geological Survey, 161174. Naslov avtorjev Authors Addresses dr. Joe Kotnik Odsek za znanosti o okolju Department of Environmental Sciences Institut Joef Stefan Joef Stefan Institute Jamova 39, SI-1000 Ljubljana, Slovenia E-mail: joze.kotnik@ijs.si doc. dr. Duan agar Univerza v Ljubljani University of Ljubljana Fakulteta za gradbenitvo in geodezijo Faculty of Civil and Geodetic Engineering Jamova 2, SI 1000 Ljubljana E-mail: dzagar@fgg.uni-lj.si prof. dr. Rudi Rajar Univerza v Ljubljani University of Ljubljana Fakulteta za gradbenitvo in geodezijo Faculty of Civil and Geodetic Engineering Jamova 2, SI 1000 Ljubljana E-mail: rrajar@fgg.uni-lj.si dr. Milena Horvat Odsek za znanosti o okolju Department of Environmental Sciences Institut Joef Stefan Joef Stefan Institute Jamova 39, SI-1000 Ljubljana, Slovenia E-mail: milena.horvat@ijs.si