Calculation of Maximum Discharges and Water Levels of Veliki and Rivers

Marko Urosev, Natasa Urosev Geographical Institute “Jovan Cvijic” SASA Belgrade,

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 , 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: , 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.

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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. – 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

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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.

Maximum water levels are determined by frequency curves of annual maximum levels. If the maximum water levels are observed in different phase of water regime, then the calculation is done separately (Lucseva, 1976).

In order to construct empirical frequency curve, water levels must be rearrange in decreasing manner. Everything is done as in maximum discharges. On the half logarithmic plot we put empirical points and construct flattering curve.

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Method of series is used for construction of analytical frequency curve of maximum water levels, which is recommended for calculation when there is no significant deviation of points from flattered empirical curve in its upper part. Determining of parameters of analytical frequency curve (Hsr, Cv и Cs) is done in similar way as in calculations of annual discharges. Parameters for all four stations are:

• st. Ivanjica – r. Moravica: Hsr = 159 cm; Cv = 0,45; ECv = 12,3 %; • st. Arilje – r. Moravica: Hsr = 191 cm; Cv = 0,30; ECv = 15,4 %; • st. Roge – r. Veliki Rzav: Hsr = 180 cm; Cv = 0,23; ECv = 14,8 %; • st. Arilje – r. Veliki Rzav: Hsr = 132 cm; Cv = 0,37; ECv = 16,0 %.

If the error is ECv = 10–15 %, then the length of data set is considered to be acceptable. In our case ECv satisfies this condition.

In table 2 ordinates of analytical frequency curve of maximum water levels have been calculated with different relations: Cs = 2Cv, Cs = 3Cv и Cs = 4Cv. Method of selection of relation Cs/Cv is used because errors of Cs are big.

Table 2. Ordinates of analytical frequency curve for maximum water levels of Moravica at Ivanjica: Hsr. = 159 cm; Cv = 0,45; 1961–2000

P (%) Cs Parameter 0,01 0,1 1 5 10 20 30 40 4Cv Hp 714 563 409 301 253 205 176 155 3Cv Hp 643 518 391 297 255 211 182 161 2Cv Hp 569 472 371 292 255 214 188 167 P (%) Cs Parameter 50 60 70 80 90 95 99 99,9 4Cv Hp 139 125 113 102 92 86 81 80 3Cv Hp 143 128 113 99 84 75 62 56 2Cv Hp 148 132 115 98 77 62 40 23

Frequency curves of maximum levels are presented on the figure 2. Analytical frequency curve, which has better match with upper part of empirical curve, is selected. For station Arilje on Moravica river best match is when Cs = 2Cv, while for other stations that relation is Cs = 4Cv. That’s how we get levels of given frequency for all four stations:

• st. Ivanjica – r. Moravica: H0,1% = 563 cm; • st. Arilje – r. Moravica: H0,1% = 418 cm; • st. Roge – r. Veliki Rzav: H0,1% = 363 cm; • st. Arilje – r. Veliki Rzav: H0,1% = 386 cm.

To get absolute value of water levels, i.e. to find height above sea level under which the terrain will be flooded during flood of frequency Р = 0,1 %, we need to add value of water level to the quota ”0” of water gauging station:

• st. Ivanjica – r. Moravica: H0,1% = 451,42 m above sea level; • st. Аrilje – r. Moravica: H0,1% = 330,87 m above sea level; • st. Roge – r. Veliki Rzav: H0,1% = 393,63 m above sea level; • st. Arilje – r. Veliki Rzav: H0,1% = 331,25 m above sea level.

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Figure 2. Frequency curve of maximum water levels of Moravica river at Ivanjica

Conclusion To satisfy needs for water we must work on regulation and protection of water resources. To achieve this it’s necessary to enable rational use of available water resources combined with construction of some reservoirs, which are well checked; then to build waste water treatment plants for protection of available water, as well as their reuse; to establish integrated water management on larger river basins, which can achieve rational regulation, protection and use of water resources (Urosev, 2007).

The problem of droughts and floods that occur on Veliki Rzav can be solved by construction of reservoirs, in particular reservoir “Arilje” on profile Svrackovo, which will regulate seasonal changes in water flow. On photos 1 and 2 the example of flood and low water at Sevelj, near Arilje, is presented.

Photo 1. Veliki Rzav at Sevelj during Photo 2. Veliki Rzav at Sevelj during low flow November 2009 flood (photo by Otasevic G.) period (summer 2006) (photo by Urosev M.)

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In last two years during summer months there was a problem with deficit of water for the regional water supply system “Rzav”, which made five towns with around 122 000 inhabitants vulnerable. Shortage in water occurred because of small discharges of Veliki Rzav River, caused by drought. This point out the necessity of construction water reservoirs in Veliki Rzav basin, as it was planned in project. In year 2008 there were intensified efforts on securing funds for construction of reservoir “Arilje” on profile Svrackovo.

On the other hand, in November of 2009 major flood occurred on Veliki Rzav river. This flash flood occurred after heavy rain showers of strong intensity. On November 7th the daily apsolute maximum of precipitation for this month was recorded – 90.1 mm on the meteorological station , which is in a drainage area of Veliki Rzav. This caused the rapid passage of the flood wave. Floods that occur in the spring during high water rise slowly and decline even more slowly. That’s why the land is under water for a longer period, while in this case water withdrew in river beds after only one day.

Unfortunately, until now we don’t have any data on this event. Eyewitnesses say that the size of this flood was similar to one back in 1965, maybe even greater. So far, the largest water discharge of Veliki Rzav river at Arilje was recorded in 1965 and it was 260 m3/s, which corresponds in this calculation to the occurrence once in one hundred years. Only when we get data on recorded water levels and flow of the November 2009 flood, we can say what her probability of occurrence was.

Therefore, it’s very important that these hydrological objects are accurately dimensioned, i.e. to calculate maximum discharges of different frequencies with given accuracy. Analysis presented in this paper are example how calculation of maximum discharges and water levels, for the purposes of projecting reservoir and the height of embankment for flood defense, needs to be done.

Reference

Gavrilovic Lj., 1988: Hydrology in spatial planning (in Serbian). Belgrade. Group of authors, 1972: Guidance on the definition of the calculated hydrological characteristics (in Russian), SN 435-72. Leningrad, Gidrometeoizdat. Group of authors, 2002: Basis of Water Management of Republic of Serbia (in Serbian). Official Gazette, 2002, No.11. Lucseva A., 1976: Practical Hydrology (in Russian). Leningrad, Gidrometeoizdat. Ocokoljic M., 1971: The relationship between surface and underground runoff in the basin of the Zapadna Morava (in Serbian). Faculty of Geography, MA thesis, Belgrade. Ocokoljic M., 1987: The height of water zoning in the basin of the Morava and some aspects of their protection (in Serbian). Special Editions of Serbian geographical society vol. 64th, Belgrade. Sretenovic Lj., 1955: Water Regime of Moravica and possibilities of its water use (in Serbian). Proceedings of the Faculty of Geography, vol. II, pp. 6 - 27, Belgrade. Urosev М., 2006: Water quality in Golijska Moravica river basin (in Serbian). Bulletin of the Serbian geographical society, 86 (1), pp. 55 - 60, Belgrade. Urosev М., 2007: Basin of Golijska Moravica - hydrological analysis (in Serbian). Special edition of the Geographic Institute "Jovan Cvijić, SASA, vol. 69, Belgrade. ***(1961-2000): Hydrological yearbooks. Republic Hydrometeorological Service of Serbia, Beograd.

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