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Jožef Stefan
International
Postgraduate School

Jamova 39
SI-1000 Ljubljana
Slovenia

Phone: +386 1 477 31 00
Fax: +386 1 477 31 10
Email: info@mps.si

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Course Description

Modeling in the Environment

Program

Ecotechnologies, third-level study programme

Lecturers:

prof. dr. Rudolf Rajar

Goals:

The students will become acquainted with different types of mathematical models, with which we simulate environmental phenomena. We shall describe the basic modules of the models (hydrodynamic, transport/dispersion and bio-chemical module). The emphasis will be on the description of modeling of pollution processes in surface waters. The students will be able to access for which environmental problems the modeling can be used efficiently. They will be able to simulate some simple cases by themselves, and for more complex cases they will be able to chose the right methodology and to find collaborators for solving the problem.

Content:

1. Introduction: General description of models. Modeling of environmental processes. Applicability and usefulness of environmental models.

2. Types of models. Stochastic, deterministic models. Dimensions of models: 0 dim, 1,2,3 dim. models. Modules: hydrodynamic, transport/dispersion and biochemical modules.

3. Basic equations- (short overview). Equation of continuity, dynamic equation, advection-diffusion equation. Monod equation for degradation of matter. Calculation of mass balance of a pollutant.

4. Case studies: (1) Transport processes and transformation of mercury (Hg) in Idrijca and Soča rivers and in the Gulf of Trieste. (2) Modeling of Hg in the Yatsushiro Sea and Minamata bay. (3) Simulations of transport of sediment and plutonium in the Mururoa lagoon. (4) Modeling of agricultural pollution in the lagoons of the NW Mexico (5) Modeling of dynamic of a landslide in Log pod Mangartom.

5. Seminar: Modeling of pollution of a lake with oil spill.

Course literature:

Rajar R., Četina M., Matematično modeliranje v hidrotehniki (1). Koristno orodje, s katerim lahko ponazarjamo dogajanje v naravi, Delo, Ljubljana, Znanje za razvoj, 16. 2. 1994.

Rajar R., Četina M., Matematično modeliranje v hidrotehniki (2). Največ prinaša hitrost projektiranja, kar pomembno vpliva tudi na ceno, Delo, Ljubljana, Znanje za razvoj, 23. 2. 1994.

Rajar R., Četina M., Matematično modeliranje v hidrotehniki (3). Najpomembnejša je izbira pravega modela, s katerim simuliramo pojav, Delo, Ljubljana, Znanje za razvoj, 2. 3. 1994.

Rajar R., Četina M., Matematično modeliranje v hidrotehniki (4). Z modeli lahko predvidimo in napovemo tudi posledice poplav in ekoloških nesreč, Delo, Ljubljana, Znanje za razvoj, 9. 3. 1994.

Rajar, R. The Role of Physical Models, Mathematical Models and Field Measurements in Water Pollution Problems, 4th International Conference Water Pollution, Bled, Slovenia, June 1997.

Rajar, R., Žagar, D., Širca, A., Horvat, M., Three-dimensional modelling of mercury cycling in the Gulf of Trieste, The Science of the Total Environment, 260 (2000), pp.109-123

Žagar Dušan Žagar, Gregor Petkovšek, Rudi Rajar, Nataša Sirnik, Milena Horvat,Antigoni Voudouri, George Kallos, Matjaž Četina. (2007) Modeling of mercury transport and transformations in the water compartment of the Mediterranean Sea, Marine Chemistry, 107,2007.

ŽAGAR, Dušan, KNAP, Ana, WARWICK, John J., RAJAR, Rudolf, HORVAT, Milena, ČETINA, Matjaž. Modelling of mercury transport and transformation processes in the Idrijca and Soča river system. Sci. total environ.. [Print ed.], 2005, vol. XX, no. X, 15 str.

The literature will be distributed to the students.

Significant publications and references:

Rajar. R, Žagar, D.: Transport of Sediments and Radionuclides from Mururoa Lagoon into the Ocean. Chapter 3.2 in the international study: The Radiological Situation at the Atolls of Mururoa and Fangataufa, Technical Report, by International Advisory Committee, 1998., pp29-38.

Četina, M., Rajar, R., Povinec, P. (2000). Modelling of Circulation and Dispersion of Radioactive Pollutants in the Japan Sea. Oceanologica Acta. Vol.23. No.7. pp 819-836.

Rajar, R., Žagar, D., Širca, A., Horvat, M., Three-dimensional modelling of mercury cycling in the Gulf of Trieste, The Science of the Total Environment , 260 (2000), pp.109-123

Rudi Rajar, Dušan Žagar, Matjaž Četina, Hirokatsu Akagi, Shinichiro Yano, Takashi Tomiyasu, Milena Horvat(2004). Application of three-dimensional mercury cycling model to coastal seas. Ecological Modelling, 171, 139-155.

Yano, S., Tada, H., Oshikawa, H., Nakamura, T., Akagi, H., Matsuyama, A., Tomiyasu, T., Rajar, R. and Horvat, M.(2003): Field Measurement of Sediment Transport in Minamata Bay, Proceedings of Coastal Engineering , JSCE, Vol.50, pp.1006-1010.(in Japanese)

Tomiyasu, T, Matsuyama, A., Eguchi, T., Fuchigami, Y., Oki, K., Horvat, M., Rajar, R., Akagi, H (2006). Spatial variation of mercury in sediment of Minamata Bay, Japan. Sci. Total Environ. 368,283-290.

Rajar, R., Četina, M.: Hydrodynamic and Water Quality Modelling: An experience. Ecological Modelling, No. 101 (1997), pp. 195-207.

Rajar, R., Četina, M., Širca, A., Hydrodynamic and Water Quality Modelling: Case Studies. Ecological Modelling, No. 101. (1997), pp. 209-228.

Horvat, M., Covelli, S., Faganeli, J., Logar, M., Mandič. V., Rajar, R., Širca, A., žagar, D. 1999, Mercury in contaminated coastal environments; a case study: the Gulf of Trieste. The Science of the Total Environment, 237/238, 43-56.

Rajar Rudi Rajar, Dusan Zagar, Matjaz Cetina, Milena Horvat, Gregor Petkovsek (2007), Mass balance of mercury in the Mediterranean sea. Marine Chemistry, 107, p. 89-102.

Rajar, R., Zagar, D., Cetina, M., Akagi, H., Yano, S., Tomiyasu, T. Horvat M. (2004a). Application of three-dimensional mercury cycling model to coastal seas, Ecological Modelling 171, pp. 139–155.

RAJAR, Rudolf, ŽAGAR, Dušan, ČETINA, Matjaž, AKAGI, Hirokatsu, YANO, Shinichiro, TOMIYASU, Takashi, HORVAT, Milena. Application of three-dimensional mercury cycling model to coastal seas. Ecol. model. [Print ed.], 2004, letn. 171, št. 1/2, str. 139-155.

RAJAR, Rudolf, ŽAGAR, Dušan, ŠIRCA, Andrej, HORVAT, Milena. Three-dimensional modelling of mercury cycling in the Gulf of Trieste. Sci. total environ.. [Print ed.], 2000, vol. 260, str. 109-123.

Širca, A., Rajar, R., Harris, R.C., Horvat, M. 1999, Mercury transport and fate in the Gulf of Trieste (Northern Adriatic)- a two dimensional modelling approach. Environmental Modelling & Software, 14, 645-655.

Yano, S., Tada, H., Oshikawa, H., Nakamura, T., Akagi, H., Matsuyama, A., Tomiyasu, T., Rajar, R. and Horvat, M.(2003): Field Measurement of Sediment Transport in Minamata Bay, Proceedings of Coastal Engineering , JSCE, Vol.50, pp.1006-1010.(in Japanese)

Žagar Dušan Žagar, Gregor Petkovšek, Rudi Rajar, Nataša Sirnik, Milena Horvat,Antigoni Voudouri, George Kallos, Matjaž Četina. (2007) Modeling of mercury transport and transformations in the water compartment of the Mediterranean Sea, Marine Chemistry, 107,2007.

ŽAGAR, Dušan, KNAP, Ana, WARWICK, John J., RAJAR, Rudolf, HORVAT, Milena, ČETINA, Matjaž. Modelling of mercury transport and transformation processes in the Idrijca and Soča river system. Sci. total environ.. [Print ed.], 2005, vol. XX, no. X, 15 str.

Examination:

• Seminar (Students will have to elaborate some exercises of environmental modeling)
• oral or written exam

Students obligations:

Seminar presentation and exam.

Links: