Flow Analysis in River Llap Gani Gashi, Florim Isuf, Shpejtim Bulliqi, Ibrahim Ramadani Faculty of Mathematics and Natural Science, University of Prishtina, Republic of Kosova [email protected] Abstract Llapi River Basin lies in north-eastern part of Kosovo. Through this river flows the water of this area which has about 950 km2. A major form of this area consists of high mountains side and valley of the Lab in between. In this part is located considerable population and water needs are necessary. From this river basin area, considerable amount of water used by Batllava reservoir to water supply the city of Pristina and the vital economy of Kosovo Energy Corporation. Rivers of Kosovo have adverse hydrological regime, of the fact that the largest amount of water, flowing in the cold season when water needs are smaller. Since 2003 in River Lab was repaired hydrometric station with new instruments. Previous data have been lost for a considerable period that represents a loss. The present paper will analyze new data that enable frequent measurement of qualitative data. The data will be analyzed according to seasons of the year, which is shown in which season is the biggest concentration of water flow. Simultaneously measured asymmetry in the distribution year to ascertain whether a normal distribution and how is this asymmetry. Key words: River Basin, River Llap, Hydrograme, Discharge, Asymmetry, Runoff Introduction The quality of space, among other heavily depends on its wealth of water. Water use depends on many factors; one of them is seasonal distribution of flows, their stability over the years. Knowledge of hydrological regime and the factors affecting it represents a prerequisite for their rational use. The study of rivers is important not only for use but also for flood protection and protection of rivers. Processing of data streams represents an important step for the recognition of their characteristics. Water levels are the basis for further processing, their conversion to discharge and their monthly fluctuation and seasonal. Study area River Basin Lab covers suitable space for housing, but also for agriculture economy. The river is part of the right site of river Sitnica which further unloaded in the river Iber and in Danube. It is part of the Black Sea basin. Stems from the Kopaonik Mountains at an altitude of about 1700m, its length until the nozzle is about 83 km. Branches of the river are mostly short, with prominent are Batllava River and River Kaqandoll. Total river flow in the basin includes 575 km length (1). The river basin has an irregular shape with about 196.8 km circumference. The lowered point is located in his river gorge in the Sitnica River with 518m altitude; in the mountains Kopaonik highest point does not exceed 1750 m. BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 1 Figure 1. Geographical position and river basin of Llap Material and methods For this paper are used the observed data from 2003 through 2011. This time period is too short for analysis, but will be compared with previous data. In the past there were two hydrometric stations in the river, in Lluzhan and Milosevo. Repaired only point in Lluzhan and so far has worked well. Hydrological studies starts with rainfall, their features in this case we lack some data. The data for measuring points were taken in the form of water levels and sample of discharge measurements. Level data were first converted to discharge and are calculated as monthly averages and minimum and maximum values. Standard deviation and coefficient of variation also represent important parameters to analyze the fluctuation in the data series. For these data will be calculated asymmetry, the rating curve and stability and classification of months according to their flow. Water levels and their converting methods in discharge In this river basin hydrometric station was refurbished and started measuring from August of 2003. The point was put in place where it existed earlier points that are located only new equipment, sensor for measuring water levels and winch for measuring the speed of water as a prerequisite for calculating the discharge. The averages of the monthly mean discharges over the years of record calculated for each month, January to December, give the general or expected pattern, the flow regime of the river (2). The water level data are given in the following table. BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 2 Table 1. Water levels record in the River Lab station Lluzhan 2003-2011 (3) Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Mean 2003 0.38 0.40 0.49 0.58 0.56 0.48 2004 0.94 1.26 1.44 1.20 0.99 0.86 0.70 0.67 0.60 0.64 0.91 0.93 0.93 2005 0.77 1.13 1.74 1.17 1.36 0.80 0.79 0.82 0.84 1.05 1.05 2006 1.00 1.24 2.01 1.63 1.29 1.02 0.88 0.85 0.81 0.83 0.84 0.84 1.10 2007 0.90 0.91 0.93 0.93 0.92 0.92 0.73 0.69 0.72 0.78 1.12 1.09 0.89 2008 0.99 0.90 1.09 0.94 0.84 0.75 0.68 0.66 0.66 0.67 0.68 0.97 0.82 2009 0.93 0.96 1.31 1.18 0.84 0.78 0.81 0.68 0.66 0.70 0.86 1.00 0.89 2010 1.15 1.77 1.65 1.60 1.12 0.92 0.85 0.79 0.80 0.83 0.93 1.28 1.14 2011 1.00 0.98 1.11 0.99 1.01 0.86 0.78 0.74 0.94 Mean 0.96 1.14 1.41 1.20 1.05 0.87 0.78 0.69 0.68 0.72 0.85 0.97 Missing data in the table lead to problems in determining the average values and their correctness. In a year 2003 is missing 7 months, in 2005 is missing 2 months, and in a year 2011 is missing the last 4 months. Due to lack since 2003 can not be taken into consideration because the measure appears to have had months to lower levels for those months that there are measurements. These water-level data through the formula Q = A * he that represents the flow curve converted to dicharge. Parameters A and e present a constant that is calculated by the method of small squares Σy − Σx ⋅ e applied to the measured levels. Constants A and e are calculated according formulas A = n (Σx)(Σy) − nΣ(xy) and e = . The calculated parameter A represents the result of inverse logarithm. (Σx)2 − nΣx2 Table 2. Table of measurement of discharge (3) Level m Nr (x) Flow m3 /(y) X=log H Y=log Q X2 XY 1 2.37 19.825 0.3738311 1.2972132 0.13975 0.484939 2 1.35 10.369 0.1306553 1.0157226 0.017071 0.13271 3 1.34 10.510 0.128076 1.0216051 0.016403 0.130843 4 1.29 4.582 0.109241 0.6610551 0.011934 0.072214 5 1.10 5.186 0.0406023 0.7148667 0.001649 0.029025 6 0.83 1.516 -0.08302 0.1806992 0.006892 -0.015002 7 0.73 1.474 -0.137272 0.1684975 0.018844 -0.02313 8 0.71 1.455 -0.149354 0.162863 0.022307 -0.024324 9 0.62 0.764 -0.211125 -0.116907 0.044574 0.024682 10 0.60 0.675 -0.224754 -0.170696 0.050514 0.038365 11 0.58 0.516 -0.238072 -0.28735 0.056678 0.06841 12 0.49 1.162 -0.314258 0.0652061 0.098758 -0.020492 amount -0.575449 4.7127753 0.485373 0.89824 BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 3 Measurements are presented in the table of flow at certain levels. In order to improve the values two of measurements had to eliminate them because their involvement in the series causes an increase in values. Those values seen that there are okay because they were contrary to the values of other members in the series. Based on calculations of the parameter value A is A = 3.1784 and e = 2.2833, hence Q = 3.1784 * H2.2833. River rating curve for Lap looks like the following graph. 3 2 2 h/m 1 1 0 0 5 10 15 20 25 m3/s Figure 2. Rating curve Data for water level were calculated with the formula Q = 3.1784 * H2.2833 and are converted to discharge, representing more practical than the water levels. After this calculations are obtained the data presented in the following section. Table 3. Monthly flow record in the River Lab Catchments 2 694 km Station :Lluzhan Mean Vol. Runoff Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec m3/s Mm3 mm 2003 0.34 0.39 0.62 0.92 0.85 2004 2.76 5.39 7.30 4.82 3.11 2.27 1.42 1.27 0.98 1.14 2.56 2.66 2.97 93.71 135 1.8 2005 1.76 4.17 11.30 4.54 6.37 1.88 4 2.02 2.15 3.59 3.96 104.67 151 2006 3.16 5.17 15.73 9.71 5.70 3.34 2.39 2.17 1.98 2.08 2.14 2.13 4.64 146.80 212 2007 2.48 2.59 2.69 2.72 2.63 2.62 1.57 1.36 1.52 1.81 4.10 3.90 2.50 78.92 114 2008 3.13 2.52 3.88 2.76 2.11 1.66 1.31 1.23 1.23 1.28 1.33 2.95 2.12 67.00 97 2009 2.68 2.90 5.84 4.60 2.16 1.80 1.96 1.30 1.24 1.41 2.26 3.18 2.61 82.55 119 2010 4.41 11.74 9.96 9.30 4.11 2.62 2.19 1.88 1.89 2.08 2.67 5.63 4.87 153.13 221 2011 3.20 3.04 4.06 3.09 3.23 2.28 1.81 1.61 2.79 BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 4 Min 1.76 2.52 2.69 2.72 2.11 1.66 1.31 0.34 0.39 0.62 0.92 0.85 2.12 Mean 2.95 4.69 7.60 5.19 3.68 2.37 1.81 1.45 1.38 1.56 2.27 3.11 3.31 103.83 149.60 Max 4.41 11.74 15.73 9.71 6.37 3.34 2.39 2.17 1.98 2.08 4.10 5.63 4.87 S.D 0.76 3.07 4.46 2.79 1.60 0.56 0.40 0.53 0.54 0.53 0.95 1.39 1.04 C.V 0.26 0.65 0.59 0.54 0.43 0.24 0.22 0.37 0.39 0.34 0.42 0.45 0.31 From the data table is determined that the average for the entire period is 3.3 m3/s, the minimum value 0.34 m3/s and the maximum average is 15.73 m3/s.