Trend Analyses of River Dragacina Runoff for Identification of the Water Availability and Accounting for Water Needs

This study aimed to analyze the available amount of water in the Dragaçina River to meet the different water needs in the Municipality of Suhareka. The water problems in this city are more pronounced, especially in the vegetation period of July–September, where the area is significantly affected by drought. The Dragacina River carries about 10 hm3 of water per year, and affected neither by urbanism nor massive deforestation of the basin. However, there are no multi-year measurements of inflows for this river, whether they are average, maximum or minimum ones. Therefore, the study is based on several multi-annual monthly rainfall measurements and some characteristics of the Dragaçina River Basin. Knowing the average annual flow coefficient η = Peff / Pbruto it is possible to convert these precipitations to Peff [mm] flow and then to monthly flow. The inputs for other years from 1983/84 onwards are obtained by simulating time series. Then, for such inflows, the probability distribution functions of small waters are assigned and the usable volume balance is carried out. Assuming an average annual withdrawal from the reservoir QAmin mes. = 0.63 × Qmes. which should be constant throughout the years, then the length of the critical period will be 0.13 years or approximately 48 days, for PH = 95%. Starting from the initial acquired volume of 1 hm3 it is possible to achieve 95% < PH < 99%. Therefore, it follows from this analysis that this river can provide a significant amount of water for the needs of the Municipality of Suhareka.


INTRODUCTION
The municipality of Suhareka is located in the southern part of the Republic of Kosovo, has an area of 361.78 km 2 and a population of about 88126 inhabitants (Municipal Development Plan Suhareka 2020-2028). To the northeast of Suhareka lies the Dragaçina River, the basin of which has an area of 39.6 km 2 and mainly mountain vegetation cover that protectes it from the erosion process. The main tributaries of Dragacina are the tributary that originates in the village of Budakovë at an altitude of 1120 m and the tributary that comes from the village of Greiçec, as well as a series of other smaller streams that feed this river. For this reason, the Dragacina port is more suitable for accumulation, which would enable a more rational use of water in this area.

Analysis and simulation of feeds
From Kosovo Hydro Meteorological Institute, it was only possible to obtain monthly rainfall data for a period of about 80 years for the city of Suhareka, but only a time series of 30 years is marked, while in other years there are disconnections of measurements for various reasons. Since the Dragacina River flow measurements are unavailable and taking into account that the average annual flow coefficient is η = 0.362 (Yaraslov Černi Institute, 1983), then the rainfall must be converted to the flow according to the expression P eff. = 0.362 · P bruto . Table 1 gives the monthly rainfall for 30 full years at the Suhareka hydrometric station.
The average annual flow coefficient P eff / P bruto = η = 0.362 shows that on average 36.2% of the total water is falling into the pond flows. The regional analysis of the average water flow provides Trend Analyses of River Dragacina Runoff for Identification of the Water Availability and Accounting for Water Needs Laura Kusari 1 , Lavdim Osmanaj 1* , Samir Bungu 1 , Premton Thaqi 1 , Venera Hajdari 1 an opportunity to approximately determine the average flow in the places where no measurements have been made (Husno Hrelja, Inženjerska Hidrologija, 2007). Therefore, the average inflows for the years given in Table 1 will be determined according to the following expression: Separating Q m. from eq. (1) as well as assuming that P eff = Η * P bruto we obtain: The year 1988 was historically quite a dry year and this is thought to have been the result of two events: the explosion of the Chernobyl nuclear power plant (1986) and the explosion of Supernova A (February 23, 1987). Therefore, an assessment of time series homogeneity is considered necessary. Thus, the year 1988 was used as the year in which a change in the flow regime could have occurred and for this reason it is necessary to simulate the inflows from 1983/84 until today.
The statistical parameters for equation (4) are defined as: • average flow: • variance: • autocorrelation coefficient: If the monthly feeds are not normally distributed, then the values of (t i ) need to be transformed. Considering the coefficient of the historical time series asymmetry (C s ), the following transformation of the size (t) normally distributed to the size (t g ) of the Gamma distribution is recommended: where: t g -random Gamma distribution numbers (0.1, C g ), C sj -coefficient of asymmetry of the month j.
On the basis of what was said above, for the series of 30-year monthly feeds, the following statistical parameters written in Table 2 were obtained.
Taking the initial inflow of September as the average, i.e. μ 0 = 0.3515 and applying equation (4) the inflow values for the respective months are obtained.
For these 30 years, the time series and the simulated one have these results as in the following graphs.
The dependence between them has also been tested through the statistical test of Durbin-Watson (Bașkent Universitesi, Istatistiksel formüller ve tablolar, 2005), where the null hypothesis is laid as: where: To test the homogeneity of the long time series, it was divided into two subcategories: (N 1 ) before the show and (N 2 ) after the change. Thus, the homogeneity of the available series was checked by testing the statistical significance between the means (z-test) or between the standard deviations (variances) (F-test or Fischer test). In the following, the fi rst N 1 = 34 (1954 / 55-1987 / 88) and the second subseries N 2 = 33 (1988 / 89-2020 / 21) were taken. The authors hypothesized the testing of statistical signifi cance between averages: From which: Since z ≤ z cr , then the null hypothesis was accepted, i.e., below the 5% probability level there is no statistically significant difference. Similarly, the possible differences between the variances can be tested; the null hypothesis is as follows: From which: Since F = 1.355 ≤ F cr = 2.019, then the null hypothesis below the significance level α = 0.05 is accepted which means that there is no statistically significant difference between the variances.

Statistical analysis of low waters
The period in which the precipitation deficit occurs (in relation to any expected value) is known as drought. Since the lack of precipitation in the observed basin affects the reduction of river inflows and the decrease of the groundwater level, hydrological drought occurs, which means a longer period of time with low waters, with the river flowing significantly more smaller than the average flow (Husno Hrelja, Inženjerska Hidrologija, 2007). In other words, a meteorological drought causes hydrological drought or small waters. Discharges below (0.15-0.5) Q avg are estimated approximately for the low water area (Ulrich Maniak, Hydrologie und Wasserwirtschaft, 2010). In our climatic zone there are periods with little water lasting from several weeks to 3 months, mainly from July to September.
Statistical analysis of low waters is usually based on the analysis of a series of minimum annual inflows with a certain duration (Δt = 7, 10, 14, 20, 30,… days). These series should be statistically sufficient in length and of satisfactory quality. If the statistical hypotheses are satisfied, then a satisfactory theoretical distribution is defined, where in small waters the Pearson III distribution, the log-Pearson III distribution, the extreme III-Weibull distribution and the Galton distribution are satisfactorily applied.

Annual extremes method
In the statistical analysis of the extreme values of the hydrological series, and consequently of the minimum annual inflows, the method of annual extremes was most often used. This method is based on the analysis of annual values (one data per year) over a multi-year period. The purpose of the analysis is to determine the probability of occurrence, namely the function of distributing the probability of minimum annual inflows. The probability distribution function F p F(Q) = P[Q ≤ Q m ] or ϕ(Q) = P[Q > Q m ] is a complete distribution characteristic. This means that all results of a random variable (Q) can be obtained from the probability distribution function F(Q) respectively ϕ(Q).
The values of the minimum annual inflows of a given return period (T) are determined by the equation: For this purpose, the series of minimum annual inflows (an extreme value per year) is taken, simulated from 1988/89 to 2020/21 (N = 33 years) and with duration Δt = 30 days. The statistical parameters of this group are calculated and an empirical probability distribution for the previously adjusted sample of the random variable is determined according to Weibull.
Some theoretical probability distribution functions, which serve to calculate the largest absolute differences between the empirical and theoretical probability distributions were selected. These include: Gaussian, Galton, Gumbel, Pearson, and log-Pearson distributions. All these theoretical probability distribution functions fit satisfactorily with the empirical distribution according to Kolmogorov's test, satisfying the condition d max < c below the 5% probability level, respectively P (d < c) = 1-α. However, the function that has a lower value of: or higher value of [1 -F(λ)], has a better fit of the empirical probability distribution function with the theoretical distribution. Therefore, based on the latter, the theoretical probability distribution functions of Pearson III and log-Pearson III have lower values of F(λ), but since the theoretical log-Pearson distribution is defined for any x > 0 (y = log(x)), it was also chosen as the final theoretical distribution of probability.
The probability density function for the Gamma 3-parametric distribution (Pearson III distribution) is as follows: where, the three parameters of the function are: α -form parameter; β -scale parameter; x 0 -position parameter.
The corresponding cumulative probability distribution function is: The characteristic statistical moments of the distribution are: • Coefficient of asymmetry: Using the frequency factor for this distribution K p = f (Cs; T) the flow for the respective return period was calculated: If the logarithms of the variable X have a Pearson III distribution, then the variable X is said to follow the log-Pearson III distribution. Therefore, in equations (16), (17) and (20) the transformations were applied y = ln (x) or y = log (x), x > 0, so that the flow is: The value of the random variable (x) for the corresponding return period will be: There is great practical interest in defining the boundaries within which, with a certain probability, a population distribution function can be found, provided that the type of this function is known. In other words, the confidence intervals of the probability distribution function, the parameters of which are estimated on the basis of the group, must be determined. For this purpose, empirical methods will be used, assuming a normal x T event distribution function, a confidence interval with a security factor of 1 -τ.
where: x T d and x T g are the lower and upper limits of the confidence interval, respectively, which are defined using the following expressions: • Lower limit of confidence interval: • Upper limit of confidence interval: where: z 1-τ/2 -is the value of the standardized normal variable for the selected security factor (confidence level) of 1-τ⁄2; SG T -represents the standard estimation error, which according to this empirical method, for a random variable of a given period of return T, is calculated using the following expression: where: S -is the standard deviation based on the series (group), δ T -is a function of the frequency factor (K) and a certain number of statistical moments, depending on the applied theoretical distribution function.
The standard estimation error for the log-Pearson III SG T (y) distribution (y = logx), can be calculated according to the same equations as for the Pearson III distribution (Husno Hrelja, Inženjerska Hidrologija, 2007), but including the logarithmic group values (Sy, Csy). The standard estimation error thus defi ned for the logarithmic group SG T (y) is converted to the standard error of the group (without calculation) SG T (x), through the equation: Finally, we can written the confi dence intervals for log-Pearson III distribution function: The selected theoretical probability distribution function (log-Pearson III) together with the corresponding empirical function as well as the 95% confi dence interval limits are graphically presented in Figure 3.

Aspect of low water management
From the point of view of water use and protection, the following two management regimes are especially important: a) Minimum water management (Q vm ) and b) Guaranteed ecological minimum (Q em ).
Guaranteed ecological fl ow should always be provided in the water fl ow for the survival and normal development of the fl ora and fauna in it. It enters management tasks as a constraint, as opposed to minimum water management as a management variable.
Dorđević and Dašić propose to determine Q em : 1. In the extra-vegetative period (October-March), Q em is selected based on the relation: where: Ǭ g represents the average multi-year watercourse fl ow, while Q 95% -is the average minimum monthly fl ow with 95% certainty.
In the vegetation period (April-September), Q em is selected by the conditions: where: Q 80% -is the average minimum monthly fl ow with 80% certainty.
For Ǭ g = 0.366 m 3 / s and for Q 80% and Q 95% read in Figure 4, analogous to the graph in Figure 3, the following can be obtained: • For the extra-vegetative period Q em = 37 l / s, • For the vegetation period Q em = 55 l / s. The feed defi ned by the relations above is also consistent with the expression used in France and Austria: If the infl ow amount is above the discharge amount, a surplus is displayed, while a defi cit exists if at any time the total discharge exceeds the  curve. It is more convenient to choose the average fl ow as the reference value, which corresponds to the curve connecting the start and end point of the cumulative curve. The sum of successive surpluses and defi cits gives the size of the usable volume of the dam for the respective successive wet or dry periods. The required volume size for the entire period under review is the largest value of the amount of surplus and subsequent defi cit. At the end of each fi lling phase, the tank volume indicates the highest fi lling level during this period.
On the basis of the above, infl ows of three consecutive typical years are taken, the average of which corresponds to about 0.34 m 3 / s, and the usable volume of the reservoir is examined.
total infl ow. In addition to the defi cit, its duration also plays a role, for which there is no longer a complete planned supply. Defi cits in individual years are taken accordingly as the maximum difference between the cumulative input and output curves. The following graphs show the cumulative curves (Jasna Plavšić & Zoran Radić, Inženjerska hidrologija-rešeni zadaci, 2015) for a characteristic year and another extremely dry year (1967/68), whereas discharges in 8 months are taken from 200 l / s, while in other 4 months from 150 l / s without counting here Q em in the respective periods.
As it can be seen from the graphs in Figures  5 and 6, the cumulative curve is presented in the orthogonal coordinate system as an ascending   (Maniak, 2010) Here, the average is set as ∑(Q × ∆t) / (3 × 12), respectively 31.93725 / 36 = 0.8871 hm 3 / month and represents a continuous discharge for each month. The parallel displacement of the cumulative discharge curve is done because an initial volume is needed to cover the maximum defi cit, which in this case is D = 0.89 hm 3 . This volume may be required only in extremely dry periods.
The usable volume for this 3-year period will be: Acquiring an initial volume of 1 hm 3 and that from eq. (36) V ≤ N we obtain the usable volume of the reservoir V sh. = 4.5 hm 3 .
The following graph gives the relevant downloads along with Q em . for a dry hydrological year like that of 1967/68 (the Jaroslav Černi Institute in this year had organized measurements of daily river infl ows for 9 consecutive months, respectively October-August).

Volume based on the theory of probability of infl ows and reservoir fi llings
If a degree of compensation α is to be guaranteed, the volume required for the critical period nkr. taken as: where: Q n,p -is the sum of the n-year input with a probability of stagnation P u , which is defi ned as: