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
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 694 km2 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. Standard deviation value ranges from 4.46 to 0.40 that shows the months during this period changes. Reliable indicator is the coefficient of variance ranging from 0.22 until 0.59, this value is not so high. According to the coefficient of variance can be concluded that the months during this period no highlighted differences. Differences are less pronounced in February March and April. The value of the flow amount of rainfall respectively derived ranges from 97 up to 221 mm, which is very low value. For this pond does not have data for precipitation to calculate the coefficient of the flows. Even from previous studies in this basin observed decrease of the flow quantity. According to old data in the period 1951/70 the flow was 162 mm. Small amount of leakage is explained by the high turnout of working lands that affect this value is greatly reduced. According to the literature soils that are deep ploughing can absorb even 95% of rainfall (4). According to meteorological data of 1948/78 the average amount of rainfall in the catchments area does not exceed 700 mm (3).
8 7 6 5 4
Q m3/s Q 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12
Figure 3. Graph of discharge in period 2003-2011 If we analyze the flow chart notice a simple performance of discharge during the year. Month with the highest average flow is March to 6 m3/s, and a gradual decline until the month of September with 1.38 m3/s. From September begins a gradual increase until March, the flow is characterized by a one maximum and a one minimum. In order to be classified according to their months own will show the flow curve. Curve is a mathematical model showing the distribution of its sustainability and its time, but with multiple frequencies will appear around the average value.
BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 5 18
16
14
12
10
Q m3/s Q 8
6
4
2
0 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Figure 4. Flow duration curve Cumulative values of all levels who are going to divide the months in following groups: 0-10% very wet, humid 10-35%, 35-65% normal month, 65-90% dry months and over 90 are very dry (5).
Table 4. Classification of the periods by discharges Freque Cumulative Intervals m3/s ncy frequency % Very wet 15.73-5.84 9 To 10 Average wet 5.84- 3.04 24 10.1-35 average 3.04- 2.08 28 35.1-65 Average dry 2.08-1.27 24 65.1-90 Very dry 1.27-0.34 10 above 90.1 Total 95
During this period the wet months are those who flow over 5.84 m3/s and the total is 9. Months those are wet, dry and average frequency approximately equal participation of 24 to 28. While many dry months are those who flow below 2.27 m3/s. based on this criterion and the average values for this period may classify the months in the following table. Table 5. Classification of months according to humidity
Category Month Very wet Mar, Average wet Feb, Apr, Dec, may Average Jan, Jun, Nov, Average dry Jul, Aug, Sep, Oct, Very dry
BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 6 For the whole period as seen any month is not too dry, too wet is considered only in March. Moderately wet months are February, April, December and May. Water Use in warm and vegetation period, except the month of May and June which is mid July and August are considered moderately dry.
Analysis of the distribution Use of the normal distribution is of great importance for the analysis of various problems. Normal distribution represents the theoretical distribution. Natural phenomena usually have a normal distribution with a small asymmetry, but members of the series should be as long. Short time series may have high asymmetry with the fact that extreme values may have greater influence (6). During statistical analysis has important way of data processing. Arithmetic mean, standard deviation and coefficient of variation have difference if calculated from the annual monthly flow. Mean flow derived from months is 3.31, if calculated from yearly means is 3.17. The most pronounced changes show the standard deviation of 1.4 and 2.5. Through normal distribution will arrange the flow rate in this period. Arithmetic mean is 3.31, standard deviation is SD = 2.5. Values over 1 m3 are if from value 1 discount arithmetic average and the result divide by standard deviation, we find Z value. x − xm 1− 3.31 7.60 Z = = = = −0.901 , xm-arithmetic mean, z value for normal distribution -0.90 is SD 2.5 2.5 0.3159 for the left side and have to add the right side of the value 0.5. In addition to collect 0.3159 with 0.5 left sides and the right side under the normal distribution emerges 0.8159, 1000-.8159 = .1841. This shows that 18.4% of inflows are below 1 m3/s, while 81.6% are over 1 m3/s. The amount of flow over 5 m3/s will be 25.7% and under 5 m3 / s 74.3%. Between 10 m3/s and 3.31 of the series included 49.5%. Over 10 m3/s are 0.5% below 10 m3 / s 99.5%. Value between minus and plus one standard deviation (0.61 and 5.73) were 88.5% for months. Values between plus and minus 2 standard deviations are 91.5 % months, respectively 87 months. Asymmetry (SKEW-NESS) in this distribution can measure with the Pearson coefficient of asymmetry by dividing the arithmetic mean with median and difference of them by dividing with standard deviation (6). Result from this calculation range from +1 to -1, if the value is zero, then the distribution is symmetric. For discharges by months will have the coefficient of asymmetry: x − Me 3.31 − 2.52 0.66 Sk = = = = 0.25 SD 2.56 2.56
Discussion Calculation of the normal distribution by months for short series does not give good results. The reasons are that there is high value to the arithmetic average and their participation is small. This affects the arithmetic average minus 2, 3 and 4 standard deviations have negative values and not be at all frequencies. To calculate normal distribution the values must be stabilized and the series is long, the arithmetic average median and standard deviation must calculate from annual averages rather than monthly ones. Discharge is a function of rainfall, with the importance it would be that the in paper be presented their quantity, the layer of snow and their durability. At the same time temperatures are also important which affect in the amount of evaporation and melting of snow and stay.
BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 7 Conclusion On the basis of processing statistics in this paper can reach some conclusions. The formula for converting the flow is level is Q = 3.1784 * H2.2833. Average flow for the period analyzed is 3.31 m3/s. The fluctuation between maximum and minimum range is from 0.34 m3/s and 15.73 m3/s. Variation values of the months are not very significant and range from 0.22 to 0.65. Value of flow in the river is classified as very low because the range from 97 to 221 mm. In the middle continental climate conditions this value is low because the average rainfall in the catchments revolve is around 700mm. In the flow chart presented a maximum in March and the minimum that appears in September. From the flow duration curve months are classified from moderately dry to wet. In the asymmetry analysis has found that very small positive asymmetry value of 0.25. While under normal distribution t seen that 18.4% of inflows are below 1 m3/s and the rest over it. Over 5 m3/s is 25.7%, the rest are below this value.
References (1) R. Pllana, Hydrology of River Llap, Buletini 7, Prishtinë, 309-323(1981). (2) Sh. M. Elizabetth, Hydrology in Practice, third edition, (1994), (3) Ministry of Environment and Spatial Planning, Hydro meteorological Institute, Kosova. (4) D. Dukič D. (1984), Hidrologija Kopna, Beograd, školska Knjiga, (1984). (5) V. Jevdevič. Hydrology, part I (in Serbian), Beograd, (1956). (6) A. Pushka, Kuantitative Methods in Geography, Prishtina, (1981).
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