Akım ölçümü olmayan kuruyan akarsular için debi süreklilik çizgisi modeli

Abstract

Debi süreklilik çizgisi, akarsu akımlarının değerlendirilmesinde yaygın bir şekilde kullanılmaktadır. Debi süreklilik çizgisi; taşkın kontrolü, düşük akım ve kuraklık çalışmaları, su kaynakları ve hidroelektrik santralların planlanması ve işletilmesi, yağmur suyu drenaj sistemlerinin tasarımı gibi birçok hidrolojik çalışmada kullanılmaktadır. Ayrıca hidrolojik havzalarda akım tahmini ve eksik akım verilerinin tamamlanması gibi konularda debi süreklilik çizgisinden yararlanılmaktadır. Debi süreklilik çizgisi kullanılarak akarsudaki taşkın veya düşük akım gibi uç debiler ile yıllık ortalama akım belirlenebilmektedir. Ancak her havzada yeterli uzunlukta gözlem olmadığından ve hatta bazı havzalarda hiç gözlem bulunmadığından havzanın meteorolojik, topografik ve morfolojik karakteristikleri yardımıyla debi süreklilik çizgisi elde edilebilir. Debi süreklilik çizgisi ile ilgili modeller, matematiksel, istatistiksel, stokastik, grafik ve diğer modeller şeklinde sınıflandırılabilir. Ayrıca yıllık, aylık ve günlük akımlar kullanılarak debi süreklilik çizgisi elde edilebilir. Seçilecek zaman aralığı çalışmanın amacıyla ilişkilidir. Bu çalışma akım ölçümü olmayan kuruyan akarsularda debi süreklilik çizgisi ile ilgilidir. Akarsularda kuruma oranı zaman aralığı küçüldükçe artmaktadır. Yani aynı bir akarsuda yıllık ve hatta aylık zaman ölçeğinde sürekli akan bir akarsu günlük zaman ölçeğinde kuruyan akarsu niteliği taşıyabilir. Bu çalışmada geliştirilen debi süreklilik çizgisi modeli boyutsuzlaştırma, normalleştirme, kuruma noktası, normal kuantillerin hesabı, boyutsuz kuantillerin ters dönüşümü, ortalama debi ve boyutlu kuantillerin hesabı adımlarından oluşmaktadır. Kuruma noktası, kuruyan bir akarsuda debi süreklilik çizgisinin yatay ekseni kestiği aşılma yüzdesini ifade etmektedir. Kuruma noktası ve ortalama debi tahmininde havza karakteristiklerinden yararlanılmıştır. Model ile elde edilen debi süreklilik çizgileri değerlendirme ölçütleri kullanılarak incelenmiştir. Havza karakteristiklerinin hesabında hidrolojik çalışmalarda ve taşkın alanlarının belirlenmesinde MERIT DEM verisi ile çalışılmıştır. Bu veri sayesinde coğrafi bilgi sistemleri yazılımında havza karakteristikleri ve havzanın alansal yağışı hesaplanmıştır. Uygulamada Seyhan, Ceyhan, Meriç ve Gediz havzalarından seçilen ve olabildiğince insan müdahalesinden uzak Akım Gözlem İstasyonları (AGİ) seçilmiştir. Müdahaleli AGİ'lerde yeteri kadar uzun olması koşuluyla müdahele öncesi veriler değerlendirmeye alınmıştır. Yıllık debi süreklilik çizgisi uygulaması için Seyhan ve Ceyhan havzaları üzerinde gerçekleştirilmiştir. Çalışmanın konusu olan kuruyan akarsular ele alındığında Seyhan havzasından seçilen AGİ'lerin günlük zaman ölçeğinde bile kurumadığı belirlenmiş, bu nedenle aylık debi süreklilik çizgisi uygulamasına Ceyhan havzası ile devam edilmiştir. Günlük debi süreklilik çizgisi uygulamasında ise Ceyhan havzasının yanı sıra Meriç ve Gediz havzaları da kullanılmıştır. Ortalama debi tahmininde sonuçlar kabul edilebilir mertebededir. Benzer şekilde kuruma noktası hesabında da başarılı sonuçlar elde edilmiştir. Model sonuçlarının değerlendirilmesinde determinasyon katsayısı, ortalama karesel hatanın karekökü, ortalama mutlak hata gibi değerlendirme ölçütleri kullanılmıştır. Bunun yanında debi süreklilik çizgisini yüksek, orta ve düşük akımlar olarak üç parçaya ayırarak değerlendiren değerlendirme ölçütlerinden de yararlanılmıştır. Debi süreklilik çizgisi güven aralıkları, her bir gözlem yılına ait debi süreklilik çizgileri yardımıyla belirlenmiştir. Kuruyan akarsuların debi süreklilik çizgisi nispeten çok yeni olup çalışmalar genellikle belli bir aşılma yüzdesindeki debi değerini tahmin etmeye dayanmaktadır. Akım ölçümü olmayan havzalarda kuruyan bir akarsuyun debi süreklilik çizgisinin kuruma noktası yağış ve havza karakteristiklerine bağlı bir regresyon denklemi ile hesaplanmıştır. Günümüz coğrafi bilgi sistemleri ve uydu teknolojisi sayesinde hesaplanabilen havza karakteristikleri ile akım ölçümü olmayan kuruyan akarsularda debi süreklilik çizgisinin elde edilmesi, böylelikle bu akarsuların su potansiyellerinin en iyi şekilde değerlendirilmesi gelecekte mümkün görülmektedir.

A flow duration curve is used to determine the discharge of a certain time percentage (quantile) in hydrological basins. It can simply be obtained by sorting the observed streamflow time series in the ascending order and plotting it against its corresponding duration. In a gauged basin, it is obtained by sorting the observed flow from the largest to the smallest, and plotting against the corresponding exceedance probability. At ungauged basins where no data exists the need for developing empirical methods emerges. Flow duration curves are useful tools for characterizing hydrological regimes and flow variability. They are widely used in the determination of the upper extreme events (floods) as well as in the calculation of low-flow characteristics of streams. The urban storm water modelling, environmental flow allocation and the determination of hydropower potential and water availability at ungauged sites are all performed by using flow duration curves. Flow duration curve-related studies started as early as the first half of the 20th century for producing weekly flow duration curves. Due to the importance of water resources, flow duration curves have always been studied in the water-related development and planning projects for which extensive hydrological engineering practice is needed. Therefore, there are quite high number of studies in the literature based on a wide range of methodologies such as regression equations, probabilistic and empirical approaches, analytical and statistical methods, and soft computational techniques applied at individual gauging stations or used at regional scale. Flow duration curve models were established using regression equations based on morphological characteristics such as drainage area and elevation of the hydrological basin. Flow duration curve at ungauged basins were estimated by regression equations between the mean flow and the drainage area, and precipitation over the hydrological basin. Probability distribution functions have also widely been used in the flow duration curve literature as well as the analytical and statistical methods. Recently, soft computational techniques such as artificial neural networks, gene expression programming and geostatistical methods have also been applicable extensively in the flow duration curve literature. Not all hydrological basins are properly gauged. Therefore, regional flow duration curves have been studied for many cases aiming at transferring information at gauged sites to ungauged sites. In regional flow duration curves, morphological characteristics of the hydrological basin are used solely or they are combined with the parameter of the probability distribution function. For the ungauged basins, regression equations using the drainage area as an input has always been valuable. Methodologies used for the flow duration curves of ungauged basins consider also the dominant landscape and climate characteristics and also the karstic and non-karstic structure of the hydrological basin. A regional model for the estimation of the dimensionless flow duration curve in sites with no or limited data has a higher importance due to the generalization ability of the dimensionless flow duration curve. This study aims at developing flow duration curve models for ungauged basins. Flow duration curves are obtained at annual, monthly and daily time scales. The flow duration curve models are based on empirical regression equations between the annual mean flow and the hydrological basin characteristics such as precipitation, slope, basin relief, basin area and drainage density. Steps of the method proposed for the flow duration curve of ungauged intermittent river basins are composed of following steps: •Nondimensionalization: Annual mean flow time series of each gauging station is nondimensionalized by dividing with the long-term mean streamflow of the gauging station. •Normalization: The dimensionless annual mean flow is transformed to fit normal distribution using a proper transformation. •Calculation of cease-to-flow proportion: An empirical model is proposed which accommodates the drainage area of basin, annual precipitation, basin relief, topographical slope, and the drainage density. This step exists only in the daily flow duration curve model. •Calculation of the normalized quantiles: The mean value and standard deviation of the normalized streamflow time series are calculated. •Back transformation of the dimensionless quantiles: For the known transformed quantiles, any quantile of a given exceedance probability can be derived by inverse transformation. •Calculation of annual mean flow: An empirical model is proposed, which accommodates the drainage area of the basin, annual precipitation, basin relief, topographical slope and the drainage density to calculate the annual, monthly and daily mean flow of each hydrological basin. Log-linear regression equations are preferred. •Calculation of dimensional quantiles: Discharge at any exceedance probability for an ungauged basin is calculated by multiplying the transformed dimensionless quantile with the empirically calculated mean value of the discharge from the hydrological basin. Four river basins were used for the case studies which are Seyhan and Ceyhan river basins in the Mediterranean region, Gediz river basin in the Aegean region and Meriç river basin in Thrace. Seyhan and Ceyhan river basins are considered for the annual flow duration curve model while the Seyhan river basin has been excluded in the monthly flow duration curve model for which the Ceyhan river basin is used solely. Finally, for the daily flow duration curve model, Gediz and Meriç river basins were taken for the application of the model. Data from the Seyhan and Ceyhan river basins are used for the annual flow duration curve model. In total, 109 gauging stations were used, 20 of which were selected for the validation of the model while the remaining 89 were used for the calibration. At monthly time scale, data from 42 gauging stations in the Ceyhan river basin are considered. When the daily time step is considered for the model, number of gauging stations has increased to 48. In total, 1792 station-year annual flow data were used for the modelling; 1452 station-years for calibration and 340 station-years for validation. The total number of data has increased to 13944 station-month and 407340 station-day, for the monthly and daily time steps, respectively. It should be emphasized that gauging stations on the tributaries not on the main river are studied with the sake of limiting anthropogenic activities on the rivers. The developed models were evaluated at the annual, monthly and daily time steps. Evaluation of the models were checked by the performance criteria such as determination coefficient, root mean square error and mean absolute error. However, due to the great variability between the higher and lower ends of the flow duration curves, it has not been possible to apply one single performance metric to the whole flow duration curve. Therefore, performance metrics called BiasFLV and BiasFHV were also used to check the models. At annual scale, the dimensionless flow duration curve obtained from the model was fitted to the observation at the calibration and validation stages appropriately. A regression equation was established between the mean flow of the basin and the product of the basin area and precipitation as one single variable. The equation estimated quite well the mean flow for all basins. The annual flow duration curves were mainly found proper for the basins. However, the annual flow duration curve estimated higher flow in a couple of basins with lower flow. Owing to the aim of the study that intermittent rivers are interested, Seyhan River basin was excluded as this particular basin has no intermittent flow at all at monthly time scale. The same methodology as the annual flow duration curve model was applied. The regression between the mean flow of the basin was constructed again with the product of the basin area and precipitation as one single variable. Results show a very good performance between the observed and estimated mean flows of the rivers. As for the flow duration curves, it was observed that higher and middle segments of the flow duration curve were fitted quite good. However, the lower segment of the flow duration curve is usually overestimated. At the daily scale, only intermittent rivers of the Ceyhan, Meriç and Gediz river basins were used. Flow duration curves of intermittent rivers take into account also the cease-to-flow point which was formulated as a regression model considering the basin area, precipitation, basin relief, slope, and drainage density as independent variables. Better results were obtained for the estimated mean flow values compared to the mean flow at the annual and monthly time scales. Results in terms of flow duration curves are particularly good in river basins with higher intermittency. A flow duration curve model is presented in this study at annual, monthly and daily time scales as an effort to make a contribution to the existing flow duration curve literature. The model accommodates an empirical regression model that counts not only on the drainage area of the hydrological basin as usual but also precipitation, slope, basin relief and drainage density as additional independent variables to calculate the annual mean flow. Although the model may have a low performance in some particular stations deviating from the average hydrological behavior of the basin, higher performance might be expected with empirical models better approaching the observed mean flow. This is the key issue of the flow duration curve development methodology to be further analyzed. Results of the application are finally found such promising that the model can be considered a good foundation for the development of flow duration curves at ungauged intermittent river basins at annual and shorter time intervals such as monthly and daily.