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Calculation of Maximum Discharges and Water Levels of Veliki Rzav and Golijska Moravica Rivers

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Calculation of Maximum Discharges and Water Levels of Veliki Rzav and Golijska Moravica Rivers Calculation of Maximum Discharges and Water Levels of Veliki Rzav and Golijska Moravica Rivers Marko Urosev, Natasa Urosev Geographical Institute “Jovan Cvijic” SASA Belgrade, Serbia Abstract It is very important to calculate accurately maximum discharges and water levels for purposes of constructing water reservoirs and embankments for flood defense. Construction of four large reservoirs in Golijska Moravica basin is planned until 2021, according to Water management plan of Serbia. Maximum discharge of Veliki Rzav at Roge has been calculated for conditions of projecting hydrotechnical object of first class. That’s why detailed analyses of maximum discharges and water levels of Moravica and Veliki Rzav of frequency Р = 0,01; 0,1; 1%, for the 1961-2000 period, are presented in this paper. Method of series was used for calculation of maximum discharges and water levels and function of Pierson III type for construction of frequency curves. Key words: maximum discharges and water levels, frequency curves, Moravica Introduction Until recently, Golijska Moravica river basin was one of the less investigated parts of Serbia. The reason for that lays in undeveloped road network and hard, somewhat impassable terrain for research. In the works of Sretenovic (1955) and Ocokoljic (1971, 1987) some of the hydrological characteristics of Moravica and Veliki Rzav, as a part of Moravica basin, correspondingly West and Great Morava, have been analyzed. River basin of Veliki Rzav has a very high specific runoff (13,9 l/s/km2), and an excellent water quality (I class). That’s why the large part of this basin is pronounced as reservation of surface waters for future water supply for settlements (Urosev, 2006). Already, there is in function regional water supply system “Rzav”, which supplies five towns: Arilje, Pozega, Lucane, Cacak and Gornji Milanovac. Construction of four large reservoirs in Golijska Moravica basin until year 2021 is planned, according to Water management plan of Serbia from 2002. They are three reservoirs on the river Veliki Rzav (“Roge”, “Arilje” and “Orlovaca”) and one on river Nosnica at Medjurecje (“Rokci”). These reservoirs are foreseen for multipurpose exploitation, but main purpose is water supply (Group of authors, 2002). It is very important to calculate accurately maximum discharges and water levels for purposes of constructing water reservoirs and embankments for flood defense. That’s why detailed analyses of maximum discharges and water levels of Moravica and Veliki Rzav, for the 1961-2000 period, are presented in this paper. Calculation of maximum water discharges Calculation of maximum discharges must been done on the basis of current maximum discharges. If there are more than one maximum discharges in day at the river gauge, then mean daily values are used. Determination of maximum water discharges demands following criteria to data series: a) upper part of curve Q = f (H) must be constructed using measured data or extrapolated to highest water level, confirmed with more than one methods, b) there shouldn’t be any missing observations of water discharges, c) frequency of observation should secure registration of highest water level for the period of high water, d) length of observation period depends on geographical zone and usually it takes: Tundra and forests – 25, forest-steppe – 30, steppe – 40, dry steppe and desert – 50 and mountain – 40 years. In our case data series is more than 40 years (1961–2000.), therefore, it satisfies this criteria. Here we will show the calculation of maximum discharges of Veliki Rzav at Roge, because on this profile dam of the future very important water reservoir should be constructed. BALWOIS 2010 - Ohrid, Republic of Macedonia - 25, 29 May 2010 1 Method of series was used for calculation of maximum discharges and water levels and function of Pierson III type for construction of frequency curves. To construct frequency curves we need to determine parameters Qsr, Cv, Cs. When calculating maximum discharges, coefficient of skewness Cs is determined in dependence of genesis maximum discharge and is equal to: for discharges of low land rivers, snowmelt waters Cs = 2,0–2,5 Cv; for rainfall discharges of low land rivers and mountain rivers with monsoon climate Cs = 3,0–4,0 Cv and for discharges of mountain rivers – Cs = 4 Cv. Moravica and Veliki Rzav rivers are mountain rivers and therefore, for all four stations we take relation Cs = 4 Cv. The parameters of frequency curve of maximum discharges for all four stations are: 3 • st. Ivanjica – r. Moravica: Qsr.max = 75,6 m /s; Cv = 0,85; Cs = 3,40; 3 • st. Arilje – r. Moravica: Qsr.max = 125 m /s; Cv = 0,73; Cs = 2,92; 3 • st. Roge – r. Veliki Rzav: Qsr.max = 99,8 m /s; Cv = 0,57; Cs = 2,28; 3 • st. Arilje – r. Veliki Rzav: Qsr.max = 96,9 m /s; Cv = 0,51; Cs = 2,04. Ordinates of frequency curve have been calculated in table 1 with use of table “Ordinates of three parameters gamma distribution” (Lucseva, 1976). Analytical (theoretic) frequency curves of maximum discharges are constructed on half logarithmic plot of probability (figure 1). For purpose of controlling the calculation and estimation of occurrence probability of observed maximum discharges, on the frequency curve we put points of observe (empirical) maximum discharges of frequency Р%. Maximum discharges of given occurrence probability are: 3 3 3 st. Ivanjica – r. Moravica: Q0,01%=937 m /s; Q0,1%=577 m /s; Q1%=321 m /s; 3 3 3 st. Arilje – r. Moravica: Q0,01%=1250 m /s; Q0,1%=796 m /s; Q1%=465 m /s; 3 3 3 st. Roge – r. Veliki Rzav: Q0,01%=713 m /s; Q0,1%=481 m /s; Q1%=303 m /s; 3 3 3 st. Arilje – r. Veliki Rzav: Q0,01%=590 m /s; Q0,1%=412 m /s; Q1%=270 m /s. Table 1. Ordinates of frequency curve for maximum discharges of Veliki Rzav at Roge: 3 Qsr.max = 99,8 m /s; Cv = 0,57; Cs = 2,28 P% 0,01 0,1 1 5 10 20 30 50 60 70 80 90 95 99 Qp 713 481 303 206 169 133 113 85,8 75,8 66,9 56,9 46,9 39,9 28,9 Calculations of maximum water discharges are very important in designing and building of hydrotechnical objects of different class. In Russian hydrotechnical practice there are four class of objects, and for each class there is a specific calculation occurrence probability of maximum water discharges: for class I it’s Р = 0,01 %, class II – 0,1 %, class III – 0,5 % and class IV – 1 %. Classes of rivers hydrotechnical objects are established on special norms and regulations for projecting objects (Group of authors, 1972). In this case we have classes that are established in former USSR in 1972, but which are still in use today not only in Russia, but also in our country. For example, Hydrosistem “Djerdap” is dimensioned so that it can evacuate 22 300 m3/s, which has a probability of occurrence once in 10 000 years (Gavrilovic, 1988), therefore it belongs to class I. When calculating objects of this class we need to add guaranty correction ∆Qp to the calculated maximum discharge Q0,01%. This correction is invented to avoid mistake in decreasing maximum discharges, which occurs because period of hydrometric observation can’t contain all characteristic aEp changes of regime. Guaranty correction can be calculated by formula: ΔQp = Qp, where а – n coefficient that characterize hydrological knowledge of basin (а = 0,7 for rivers that are in hydrological known regions, а = 1,5 for poorly investigated territories), Ер – value which characterize variations of maximum discharges and it is determined with help of table: Cv 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 Ep = 0,01 % 0,25 0,45 0,64 0,80 0,97 1,12 1,26 1,40 1,56 1,71 1,89 2,06 BALWOIS 2010 - Ohrid, Republic of Macedonia - 25, 29 May 2010 2 Guaranty correction will be applied if it’s not more than 20 % of discharge, determined on frequency curve Qp. Final calculated maximum discharge (Q'p), that we take for projecting hydrotechnical object is calculated by formula: Q'p = Qp + ∆Qp. Figure 1. Frequency curve of maximum discharges of Veliki Rzav river at Roge Maximum discharge of Veliki Rzav at Roge has been calculated for conditions of projecting hydrotechnical object of first class. It’s well known that in future at this site dam should be constructed for the big multipurpose reservoir. Basin of Veliki Rzav river is situated in hydrological known region, therefore coefficient а = 0,7. When Cv = 0,57, Еp0,01% = 1,08; observation period is n = 31, and Q0,01% = 3 3 713 m /s. We get ∆Q0,01% = 96,8 m /s. The correction ∆Q0,01% is less then 20 % of discharge Q0,01% ΔQ ( 0 , 01% = 13,6 < 20% ), which means that data range is long enough for accurate determination of Q0 , 01% guaranteed discharge for projecting hydrotechnical object of first class. Maximum water discharge for 3 hydrotechnical object of first class on Veliki Rzav river at Roge is Q'0,01% = 713 + 96,8 = 810 m /s. Calculation of maximum water levels Estimations of maximum water levels of different frequencies are very important for planning the height of embankments for flood defense. They show us the height above sea level under which the terrain will be flooded during high waters of different frequencies. In this paper we will show the calculation of maximum water levels of frequency P = 0.1 %. As an example, the calculation for station Ivanjica on Moravica River will be presented.
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