Sakarya havzası akarsularının düşük akım debilerine en uygun dağılımın araştırılması /
Yazar: YAVUZ SELİM SERTBAŞ
Danışman: PROF. DR. ATIL BULUT
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1996
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Akarsular = Streams ; Akım dağılımı = Flow distribution ; Sakarya Havzası = Sakarya Basin ; Su mühendisliği = Water engineering

Özet:
Bu çalışmada Sakarya Havzası' ndaki düşük akım debi gözlemlerine en iyi uyan olasılık dağılımı araştırmıştır. Bu amaçla Sakarya Havzasında yeterli gözlem uzunluğuna sahip dört akarsu ele alınmıştır. Çalışmada iki parametreli dağılımlar ve 1, 3, 7, 10, 14, 30, 60, 90, 120, 150, 273 günlük düşük akım debileri kullanılmıştır. Düşük akım hidrolojisinde debi süreklilik çizgisinin önemi ve kullanımına değinilmiştir. Olasılık dağılımı olarak Norrnal(N), Lognormal (LN2) ve Weibull (W2) kullanılmıştır. Bu dağılım fonksiyonlarının karşılaştırılmasında X2 (ki-kare), Kolmogorov-Smirnov (K-S) gibi testlerden daha hassas olduğu bilinen Olasılık Çizgisi Korelasyon Katsayısı (PPCC) testi kullanılmıştır. Bu çalışmanın sonunda W2 dağılımının Sakarya Havzası için N ve LN2' ye göre üstün bir performans gösterdiği açıkça görülmüştür. Düşük akım hidrolojisinde kullanılan Weibull dağılımı ile parametre tahmin yöntemleri verilmiştir. W2 dağılımı ile çeşitli dönüş aralıkları için bu dönüş aralıklarına karşı gelen düşük akım debileri hesaplanmış; Çeşitli aşılma olasılıkları için debi gidiş çizgileri yardımıyla bu aşılma olasıklanna sahip düşük akım debilerinin W2 dağılımıyla dönüş aralıkları elde edilmiştir. vııı

Abstract:
River discharges can get low values in some period of the year and even they get dry especially in semi-arid regions. This usually occurs during the summer months in which irrigation has primary importance. Low-flow frequency analysis is used in the water quality management applications including the wasteload allocations and discharge permits, and in siting treatment plants and sanitary landfills. Low-flow statistics are also used in the water- supply planning to determine allowable water transfers and withdrawals. If the flow decreases under a certain low flow values, it has a direct effect on the aquatic life of the surface flow under consideration. Other applications of the low-flow frequency analysis include determination of minimum downstream release requirements from the hydropower, water-supply, cooling plants and other facilities. From the foregoing explanations, it can be seen that low flow hydrology is an important subject to be examined under a different discipline of hydrology. In this study, it was attempted to find out the best fitted probability distribution function to the low-flows of Sakarya Basin on the Middle Anatolian part of Turkey. For this purpose, daily flows of the selected 4 stations having the possible longest record were used. By the stations selection it is also considered whether the stations are located before or after the reservoir or the site. By the station selection its location with respect to the nearest reservoir or the habitation is also taken into consideration. These 4 stations are; Porsuk Çayı-Beşdeğirmen, before Porsuk Dam having record of 53 years, Porsuk Çayı-Eskişehir, after Eskişehir City having record of 19 years, Sakarya Nehri-Kargi, before Adapazarı City having record of 37 years, Sakarya Nehri-Doğançay before Sanyar Dam having record of 3 1 years. In the examining low-flows, different duration days (D-day) of flows were taken into consideration. For instance, in calculating 3-day flow of N year of observations, mean value of three days of flows was calculated and exceedance probabilties were determined. By the help of flow duration curve of a D-day flow, one can find out the percentage of time during which specified discharges are equaled or exceeded during the period of record. ixAlso frequency curves are used in low-flow analysis. While the flow duration curve is concerned with the proportion of time during which a flow is exceeded, the flow frequency curve shows the proportion of years when a flow is exceeded, or equivalently the average interval in years that the river falls below a given discharge.In this study minima of 1, 3, 7, 10, 14, 30, 60, 90, 120, 150 and 273 days were extracted from the mean daily flow time series. In U.S.A 7-day 10-year low-flow value is accepted as a low-flow criteria. Some researchers accept 7-day 2-year flow as a low-flow criteria, also. The parameters of low-flows were estimated for each station. These parameters are the mean x, standard deviation Sx, coefficient of variation Cvx, skewness coefficient C^ and kurtosis Ks. Using Probability Weighted Moments (PWM) L-moments are computed, L-moment ratios are defined as L-coefficient of variations, L- coefficient of skewness, X3, and L- coefficient of kurtosis, X4. It is investigated which probability distiribution function is suitable for the low- flow values of the considered stations. For the study Normal distribution (N), Lognormal distribution (LN2) and the Weibull distribution (W2) were used. Various methods are used for the parameters of the probability distributions. The parameters of Normal distribution are the mean x and standard deviation Nonnormally distributed variables can be adjusted to the normal distribution by means of a suitable distribution. One of these transformation methods is computing the logarithms (y = Lnx). In this case, logaritmic mean y and standard deviation Sy will be the parameters of the 2-parameter lognormal (LN2) distribution. Extreme Value Type HI distribution (Weibull, W2) was commonly used as low-flow distribution function. Parameter estimations of Weibull distribution were accomplished by the help of L-moments and probability weighted moments (PWM). L-moments and Probability Weighted Moments (PWM) are analogous to ordinary moments in that their purpose is to summarize theoretical probability distributions and observed samples. L-moments can also be used in parameter estimation. The simplest approach to describing L-moments is by first defining probability weighted moments because L-moments are linear functions of PWMs which may be defined by fir =E\x[Fx(x)Y where pr is the rth order PWMs and Fx(x) is the cumulative distribution function of x.For r = 0, Po will be equal to the mean of the low-flows, and the probability weighting moments (PWM's) will be calculated as follows: fi'~lfp' N-\ A=Z y=i (N-j) *U) H-2 A=Z J=l (N-JM-j-l). N(N-lXN-2)j *U) Af-3 (N-MN-j-lW-j-2) L N(N-lXN-2)(N-3) J *0) x(j ): are the lowflow values on the j'th row of the arranged sample. To calculate the " PWM" at any level the genarel definition below can be used *0) Using the " PWM's the values of the first four L-moments can be calculated as follows: X2 = 2P!-p0X3 = 6P2-6P!+Po X4 = 20p3-3032+1231-po L-moments sample estimators can be obtained by PWMs from the general recursion ^-S^(-1} ill- J The L-moment ratios are defrned as below, K r2 = - ; L-coefScient of variation; X r3 =-; L-skewness; K r, =- ; L-Kurtosis; 4 V Probability Plot Correlation Test (PPCC), which is known to be more powerful than X2 (chi-square), and K-S (Kolmogorov-Smirnov) tests, was used to test the suitability of the foregoing distribution functions. The test statistic is the correlation coefficent r which measures and evaluates the linearity between the ordered observations Xi and the inverse value of the hypothesized cumulative distribution function Mi (Statistic medians) : Z(x,-x)(Mf-M) r=-^= E(*,-*)2(M-M)2 i=l in which x is the mean of the observed values. XllF(.) is the cumulative probability and p; is the value calculated from the unbiased plotting position equation for different distribution functions. The inverse of the standard normal distribution is calculated by Mt =4.9l[/f4-(l-jR)0-14] in which pi values are defined as, Pi=l-(0.5) l/n i=l Pi = (1-0.3175) /(n+0.365) i=2,, n-1 Pi = (0.5) l/n i=n PPCC test statistic is calculated using the equation simultaneously. If the calculated PPCC value is higher than the given values for a selected significance level, the observed values are accepted as normally distributed. The same procedure can be applied to the logaritmically transformed observed values for lognormal distribution. The cumulative distribution function of W2 is, F(x)=l-exp|-(- -)j and the return period is calculated by the formula; T = F(x) PPCC test statistics is calculated by r between Xi and xniMt =F;\pi)=\np+^\n[-\n{\-pi)\ values, p; unbiased plotting positions can be calculated by /-0.44 Pr n + 0.12 a an P parameters of W2 distribution can be estimated by Probability Weighted Moments, ln(2) ",T 0.5772^ a = ~, ^=exp(i,>(hlx)+ ) Lkl, (tax) a in which Li, q^ is the mean of the Lnx series, and L2, $&$ is L2 - moment of lny series. In the examining the PPCC test results it is seen seen that the number of the correlation coefficient, r, values for all stations which can not be accepted at the 5% level of significance is fourteen for Normal distribution (Porsuk Çayı-Beşdeğirmen 120-150-273, Sakarya Nehri-Doğançay 273, Sakarya Nehri-Kargı 273, Porsuk Çayı- Estrişehir 1-3-7-10-14-30-60-90-273), fourteen for Lognormal distribution (Porsuk Çayı-Beşdeğirmen 1-3-30, Sakarya Nehri-Doğançay 3-7-10-14-30-60-90-120, Sakarya Nehri-Kargı 1, Porsuk Çayı-Eskişehir 1-3) and four for Weibull distribution (Porsuk Çayı-Beşdeğirmen 1-3, Sakarya Nehri-Kargı 273, Porsuk Çayı-Eskişehir 1- 90). The result of this study can be summarized as below: 1) Considering these results it can concluded that the two parameter Weibull (W2) distribution is the most suitable distribution. 2) In the study it is possible to realize the reliable estimation of the low-flows having the desired return period using the Weibull (W2) distribution. For this aim after obtaining a (scale) and J3 (location) parameters. F(x) is found using the desired return period value (T) and finally corresponding low-flow value (x) is determined. So the low-flow value (x) is found for the desired return period (T). The results are presented in Table 6.1., Table 6.2., Table 6.3., Table 6.4. 3) Drawing the flow duration curve, Q90, Q95, Q99 values and the corresponding return periods are obtained in a reliable manner. These values are presented in Table 6.5., Table 6.6., Table 6.7., Table 6.8. The flow duration curve graphics are enclosed in the part of Annexes. xiv4) With previously realized studies it has been shown beforehand that the Weibull (W2) distribution, which is found in this study as the most suitable distribution for the low-flows in the Sakarya Basin, is also very suitable for the low-flows in Thrace region. But the continuation of the studies is necessary to investigate the suitabilility of this distribution for the whole of Turkey. Also with the increase of the observed years and the number of stations it will be possible to obtain more reliable results. xv