Transactions on Ecology and the Environment vol 14, 1997 WIT Press, ISSN

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1 Determination of water quality in Yugoslav part of the River Danube (99-995) by the method of multiobjective iterative compromise optimization (MICO) J. Krizan University ofnovi Sad, YUEEE TEMPUS center, Trg Dositeja Obradovica 6, 2000 Novi Sad, Yugoslavia Abstract This paper contains elaborated state of water quality in Yugoslav part of the Danube, during period of observation (99-995), and atypical river ecosystem exposure to pollutants. One fifth (59 km) of entire length of the Danube (2860 km) flows through Yugoslavia. This fact undoubtedly emphasizes the importance of the water quality situation in Yugoslavia on the entire Danube ecosystem. Yugoslavia's exposure to UN sanction resulted in suspension in production in almost every field of economic production and that caused decrease of pollutant input in Yugoslav part of the Danube's ecosystem. The method of MICO can be represented as a mathematical algorithm. It is designed to select the most optimal solution based on decision maker's preference toward various observed criteria. It proved to be successful in determining the most optimal solution for problems regarding to the electric currency distribution, dam building, civil engineering, etc. In order to maintain satisfying water quality decision maker should know the influence that different categories of polluters make on water quality on specific site. The average annual data of concentration and flow rate for chosen parameters of water quality (Oz, BOD^, phosphates, nitrates, lead, cadmium, chromium, copper etc.) in the characteristics monitoring stations were compared with method of MICO from influence that different categories of polluters (agriculture, population, industry, energy generation, transport) make on the river ecosystem. The method of MICO selects those most endangered sights by the specific polluters. The general conclusion is that amount of pollution rises along the river together with the increase of flow rate and with the decrease in concentration of pollution in river. The decrease in concentration can be explained with dilution. The method of MICO could be successfully used for sound management of the water quality in river basins.

2 578 Water Pollution Introduction Water natural selfpurification is a complex cooperation of physical, chemical and biological processes. Existence of neither one of these processes is impossible without cooperation with others, Physical, chemical and biological processes lead to organic matter mineralization only if waste water is diluted enough with clean water in recipient and if the part of waterflow is long enough so that these processes could be done. When these conditions do not exist then natural selfpurification must be transmitted from recipient to waste water treatment plant. One fifth (59 km) of entire length of the Danube (2860 km) flows through Yugoslavia (Figure ). Ecological, economical and political interactions between countries in the same region are essential for successful management of environmental quality, because natural environment does not know the borders that different nations drove between themselves to divide them. This paper contains elaborated state of Yugoslavia's part of the Danube water quality under the UN sanctions and atypical river ecosystem exposure to pollutants. Water quality The Danube's water quality is analyzed through influence that agriculture, population, energy generation (by incineration), industry and transport make on it. Determining the Danube's water quality regarding to chosen specific parameters is done for characteristics monitoring stations with the method of multiobjective iterative compromise optimization []. Compromise programming Compromise programming is based on the idea of the "ideal point" as the reference point in the criteria functions space. Suppose that the optimal solution x*i, i.e. f*i exists, according to i-th criterion f *=max xex then we call the vector F*=(f *,...,f*n) the ideal solution for the multicriteria optimization (MCO) problem. If there is a solution x* e X for which F(x*) = F*, then all criteria functions have maximal values for the same solution, so that x* could be adopted as the optimal solution of the problem MCO. However, such a solution rarely belongs to the admissible set X, so that we have to search for the admissible solution which is the closest to the ideal solution in the criteria space. The solutions which are closest to ideal, according to the adopted distance measure, is called the compromise solution.

3 Legend. I crgiiaultuial le.qi.on H< iitu rliia station Figure : Hydrological map of Yugoslav part of the Danube

4 580 Water Pollution As the distance measure from the ideal point the following metric is usually used: Lp(F*, F)={ Iffi*-f,(x)]P}; < p < This metric represents the distance between the ideal point and the point F(x) in the criteria space. In order to underline the dependence from the parameter p, the metric is denoted as R(F(x),p). This metric is actually the additional criterion for the MCO by the compromise programming, and is called here the function of compromise programming. The solution x+(p) X, by which the minimum of R(F(x),p) is achieved, is called the compromise solution of the MCO problem, with the parameter p. In the criterion space the compromise solution is F(p)=(fi(x+(p)),...,fn(x+(p))). The minimum achieved R~*~(p) for the compromise solution x (p) is the total aberration, and f i - f i (x+(p)) the i-th individual compromise n aberration. The fj (x*(p)) represents the total benefit of the solution x~*~ (p). Instead of the function R(F(x),p), for <p < the function n R'(F(x), p)= s [fi* - fj(x)]p could be used; as R(F(x),p) is increasing function of R'(F(x),p), so that the minimum of both functions is achieved for the same solution x~*~(p). Multiobjective iterative compromising optimization (MICO) The method of MICO can be represented as a mathematical algorithm. It is designed to select the most optimal solution based on decision maker's preference toward various observed criteria. It proved to be successful in determining the most optimal solution for problems regarding to the electric currency distribution, dam building, civil engineering, etc. In order to maintain satisfying water quality decision maker should know the influence that different categories of polluters make on water quality on specific site. The average annual data of concentration and flow rate for chosen

5 Water Pollution 58 parameters of water quality (O?, BOD^, phosphates, nitrates, lead, cadmium, chromium, copper etc.) in the characteristics monitoring stations were compared with method of MICO from influence that different categories of polluters (agriculture, population, industry, energy generation, transport) make on theriverecosystem. The method of MICO selects those most endangered sights by the specific polluters. Symbols used in method of multiobjective iterative compromising optimization: n J fjj wj v i j Qj - number of criteria - number of alternatives for multiobjective ranking - value of criteria function i and alternative j - weight criteria function i - satisfying most criteria strategy weight - criterion's serial number, i =,..., n - alternative's serial number, j =,..., J - measure for multiobjective ranking Multiobjective iterative compromising optimization developed by S. Opricovic is done with the Qj - measure for multiobjective ranking shown with following relation: Qj = v QSj + (-v) QRj where are: QSj = (Sj - S*) / (S" - S*) QRj = (Rj - R*) / (R" - R*) Sj = I wj (fj* -f j) / (fj* - If) (for p = ) Rj = max wj (f * -f j) / (f;* - fj") (for p = ~) i fi* = max fy ; fj" = min fij ; i =,..., n J j Best values of metrics Sj and Rj are: S* = min Sj ; R* = min Rj j j

6 while the worst are: Water Pollution S" = max Sj J R = max Rj J It is supposed that alternative aj is better than ak judging by criterion i, and if fij > fik then in method of multiobjective iterative compromising optimization Qj < Qk [4]. Computer program VIKOR is developed on the basis of this equations. This program is tested and applied on solving many optimization problems. It is adequate for the purpose of selecting monitoring stations with the lowest and with the highest concentration and flow rate of different pollutants in water because it is iterative, it's weight of criteria function can be changed and adjusted to decision maker's needs and it is possible to choose between the total benefit and maximal individual benefit. When the parameter v > 0.5 then total benefit is increased, but also maximal individual distance from the ideal value is decreased. When the parameter v < 0.5 then single (individual) benefit has the advantage over total benefit. Table. presents the influence of different categories of polluters on the river ecosystem []. The higher mark (weighting factor) presents the greater influence of that polluter on the selected parameter of water quality. TABLE. INFLUENCE OF DIFFERENT CATEGORIES OF POLLUTERS ON SELECTED PARAMETERS OF WATER QUALITY Polluter All equally Agriculture and Population Energy generation (by incineration) Industry Transport 02 BOD; Parameters of water quality Nitrates Phosphates Pb Cr Cu The Table 2. presents the monitoring stations with the lowest and with the highest concentration of pollution in the Yugoslav part of the Danube from the point of view of influence that different polluters make on water quality. It is obvious from Table 2. that concentration of various pollutants is highest in upstream part of the Danube and that it is lowest in the downstream part of the Danube that flows through Yugoslavia.

7 Water Pollution TABLE 2. LIST OF MONITORING STATIONS WITH THE LOWEST AND WITH THE HIGHEST CONCENTRATION OF POLLUTION RANGED BY INFLUENCE THAT DIFFERENT POLLUTERS MAKE ON WATER QUALITY Polluter All equally Agriculture and Population Energy generation (by incineration) Industry Transport Lowest concentration of pollutants Radujevac, 0.0 % Tekija, 8.9% Radujevac Radujevac, 0.4 % Tekija, 2.2 % Radujevac, Tekija,. % Radujevac, 9.8 % Smederevo,.4% Highest concentration of pollutants Novi Sad Bezdan, 4.6 % Apatin,.6 % Novi Sad, 22.6% Novi Sad, 6.9 fc Apatin,. % Bezdan, 26. %? Novi Sad Novi Sad The Table. presents the monitoring stations with the lowest and with the highest annual flow rate of different pollutants in the Yugoslav part of the Danube from the point of view of influence that different polluters make on water quality. When we also take into the consideration the flow rate in the Danube and calculate the annual load of specific parameters of water quality than situation changes drastically. The fact that is the monitoring station with highest annual flow rate of observed pollutants can be explained with its geographic position. Since it is situated immediately downstream from the big polluters such as the river Sava, city of Belgrade and therivertamis. The strength of selfpurification is easily seen from the Table. where the 's downstream monitoring station Tekija is in the first and second position (evaluated by influence that various polluters make on the Danube water quality) on the scale of lowest annual flow rate of pollution. When in the Tables 2. and. under certain polluter several monitoring stations are listed that mean that the first alternative from compromising rank list is not significantly better from the following alternatives and that all of them should be taken under the consideration. The percentage represents how much is that alternative better from the following alternative in the rank list.

8 Water Pollution TABLE. LIST OF MONITORING STATIONS WITH THE LOWEST AND WITH THE HIGHEST FLOW RATE OF POLLUTION RANGED BY INFLUENCE THAT DIFFERENT POLLUTERS MAKE ON WATER QUALITY Polluter All equally Agriculture and Population Energy generation (by incineration) Industry Transport Lowest annual flow rate of pollutants Tekija, 0.9 % Apatin, 0.5 % Zemun, 5.8 % Bezdan,. % Smederevo,.2% Apatin,. % Tekija, 0. % Zemun, 6. % Apatin, 2.8 % Tekija, 0.7 % Bezdan,.0% Apatin, 8. % Tekija,.8 % Zemun, 5.6 % Apatin, 7. % Tekija, 2.0 % Bezdan,.8 % Zemun, 6.7 % Highest annual flow rate of pollutants When "all equally" is found among polluters in Table,2,. it means that individual effects of different categories of polluters are neglected and all parameters of water quality are equally taken into consideration when determining the absolutely best or worst site on river i.e. the lowest and highest concentration and flow rate of pollutants. Conclusion Amount of pollution rises along the river together with the increase of flow rate and with the decrease in concentration of pollution in river. In the times that come we should devote ourselves to inquiring and monitoring parameters that define phenomena of dynamically balanced processes in this mighty river's ecosystem. On the basis of analyzed data it is possible to conclude that improvement in quality of Yugoslav part of the Danube has occurred during period of observation, The method of MI CO could be successfully used for sound management of the water quality in river basins.

9 Water Pollution 585 References. Environmental Programme for the Danube Rive Basin, Danube integrated environmental study, report phase, Haskoning, Royal Dutch Consulting Engineers and Architects, Hydrological annual reports for 99, 992, 99, 994 year.. Krizan, J., Miloradov, M., Vojinovic-Miloradov, M. Kvalitet vode na jugoslovenskom delu Dunava (99-995), pp , Proceeding of 25th conference actual problems in water protection-zastita voda 96, Ulcinj, Yugoslavia, Opricovic, S. Visekriterijumska Optimizacija, Naucna Knjiga, Beograd, Yugoslavia, 986.