Akış Hidrografı Tahmin Modelleri

Abstract

Mühendislik açısından yağış akış süreci su çevriminin en önemli bileşenidir ve muhtemel yağışlardan meydana gelebilecek akışın tahmin edilmesi su kaynaklarıyla ilgili projelerin temelidir. Bu nedenle bir çok fiziksel ve data temelli model yağış akış sürecinin simülasyonu için geliştirilmiştir. Akış hidrografı, bir havzanın veya herhangi bir hidrolojik sistemin bir fırtınadan oluşan akış miktarının zamanla değişimini göstermektedir. Bu çalışmada akış hidrografının üç temel bileşeni yani toplam dolaysız yüzey akışı, pik debi, ve akış süresi incelenmeye alınmıştır. Bu üç parametre farklı tasarım amaçlarına göre mühendisler tarafından ele alınabilir. Bu bağlamda NAM/MIKE BASIN, SWMM parametrik modelleri ve HEC-HMS modeli kapsamında bulunan Clark, Snyder ve SCS birim hidrograf metotlarının yanısıra Kök seçimi matematiksel birim hidrograf yöntemi 1990-1995 yılları arasında Cascina Scala (Kuzey Pavia, İtalya) havzasında meydana gelen 5 ayrı fırtınanın modellenmesi için kullanılmıştır. NAM/MIKE BASIN ve SWMM parametrk modelleri havzanın fiziksel ve hidrolojik parametrelerini kullanarak yağış akış sürecinin matematiksel modelini sağlamaktadırlar. Bu modeller kapsamında yağış akış sürecine bağlantılı olan buharlaşma, sızma, evapotranspirasyon, yeraltı suyu, iç akım, yüzey akımı v.s. gibi tüm fiziksel olayların simülasyona dahil edilmesinden dolayı, modelleme için çok sayıda parametrenin belirlenmesi gerekmektedir ki genellikle tüm bu parametrelerin belirlenmesi olası değildir. Bu durum yağış akış verilerine dayanan farklı kalibrasyon yaklaşımlarından faydalanarak giderilmiştir. Buna karşılık HEC-HMS modelinin birim hidrograf yöntemleri daha az fiziksel parametrenin gerektiği ve daha çok data temmeli olan modellerdir. Ayrıca Kök seçimi birim hidrograf metodu kapsamında sadece akış verilerini kullanarak bir havzanın birim hidrografı elde edilebilir. Modellerin tahmin sonuçları RMSE ve CE istatistiksel ölçütlere göre değerlendirilmiştir. Toplam dolaysız yüzey akışı parametresi açısından en iyi tahmin NAM/MIKE BASIN modeline aittir (RMSE=2,26 mm ve CE=0,84). Bu modeli SWMM modeli RMSE=2,91 ve CE=0,73 ile takip etmektedir. Ancak tüm birim hidrograf yöntemlerin tahmini kabuledilebilir seviyede olmamıştır ki bu durum RMSE değerinin yaklaşık 6 mm ve CE değerinin sıfırdan düşük olmasıyla kanıtlanmıştır. Dikkat edilmesi gereken hususlardan biri de kullanılan tüm modellerin uygun pik debi tahmini yapamamalarıdır. Bu durum sıfırın altında CE değerleri ile gözlemlenmiştir. Hidrograf süresi tahmininde Clark ve Kök seçimi birim hidrograf yöntemleri ve SWMM parametrik modelleri iyi tahmin sergilerken diğer modellerin tahmini CE değerinin sıfırdan düşük olduğunu göz önünde bulundurarak kabuledilebilir seviyede değildir.

Rainfall-induced runoff process is the most important component of hydrological cycle that is used in the design of water structures, flood control and design of urban drainage systems. Runoff hydrograph is a graph that shows runoff variation versus time for a given rainfall event. Modeling rainfall-runoff process is a difficult task due to non-linearity and uncertainties. In addition, other physical parameters such as infiltration, evapotranspiration, soil type, soil wetness and land use conditions are required for determining this process. Rainfall-runoff models can be classified as physically based models and data driven models. Physically-based models are based on mathematical relationships between rainfall, physical parameters of the catchment and runoff. The Rational method was proposed by Mulvany (1850) as the first physical model in order to compute flood peak discharge by taking time of concentration as the basis of the model. Furthermore, analytical probabilistic or design storm approach has been used to estimate the peak discharge for design purposes. Recently, classical rational models were developed using perturbation theory where fuzzy logic model results compared with extended classical rational models. The unit hydrograph is the unit response function of a linear hydrologic system and was first proposed by Sherman (1932). It is defined as a direct runoff resulting from 1 unit of excess rainfall generated uniformly over the drainage area at a constant rate for an effective duration. Unit hydrograph theory was based on some assumptions. The intensity of the excess rainfall and the base time of the direct runoff hydrograph should remain constant and the excess rainfall should be uniform over the whole watershed. Many researchers investigated unit hydrograph theory and synthetic unit hydrographs such as Snyder (1938) and SCS (1972) were proposed as methods of derivation of unit hydrograph. Black box models have been also introduced for the prediction of runoff by formulating the response of catchment linearly or nonlinearly. Fuzzy Unit Hydrograph where Nash cascade parametric form of the unit hydrograph was used were introduced. Fuzzy logic models are based on linguistic expressions which are used for construction of fuzzy IF-THEN rules depending on expert knowledge or available data. ANN model is a black box model which simulates rainfall-runoff process in situations where explicit knowledge of the internal hydrologic process is not available. Despite all of these new developments, there has not been a comprehensive study for evaluating the comparative performance of physically based models like SWMM and NAM/MIKE BASIN and data driven models such as Clark, Snyder, SCS and Root selection method. This study was, therefore, initiated to compare the performance of various methods developed for establishing runoff hydrograph. In this study, HEC-HMS, SWMM and MIKE BASIN/NAM Rainfall-Runoff models and also Root selection method were used for estimating runoff hydrograph from rainfall events in Cascina Scala urban catchment in Italy. These models are physically-based black box models which use the catchment’s physical parameters such as area and slope, curve number, Manning roughness coefficient, and percentage impervious layers and hydrologic parameters and mathematical methods of drivation of unit hydrograph. The physical parameters are required in order to determine the catchment’s response of runoff for a given rainfall event numerically. Runoff hydrographs were calculated using the aforementioned models and the model results were compared with observed hydrograph. The specific objectives of this study were, i) to estimate rainfall-induced runoff using NAM/MIKE BASIN Rainfall-Runoff model ii) to produce runoff hydrograph by employing the NAM/MIKE BASIN Rainfall-Runoff model, and iii) to evaluate the estimation performance of NAM/MIKE BASIN and SWMM parametric models compared to the methods of unit hydrograph in terms of estimation of runoff hydrograph. The results of these models were compared by considering estimated and observed rainfall-induced runoff peak discharge, time to peak and discharge duration of the hydrographs. The comparison was based on the root mean squared error (RMSE) and the coefficient of efficiency (CE) between the observed event data and estimation results. Five storms, which were observed during the period between 1990 and 1995 in Cascina Scala watershed, were modeled using HEC-HMS, SWMM, NAM/MIKE BASIN, and Root-Selection method approaches. The total runoff, peak discharge and the discharge duration results are given below. Total runoff It is clearly seen that results of all unit hydrograph approaches (Clark, Snyder, SCS, and root selection) are not satisfying compared to SWMM and NAM/MIKE BASIN models. Estimated values by all approaches of the unit hydrograph model were found to be larger than the observed values. This conclusion is drawn based on the larger RMSE values (approximately 6.00 mm) and smaller CE values (lower than zero) of results than the other results. Considering the assumptions of the unit hydrograph theory, the storm selected for analysis should be of short duration and the catchment should be relatively small. Long duration storm rainfalls may result in unexpected errors in the estimation of runoff hydrographs. MIKE BASIN/NAM model parameters were determined by trial-and-error process. Five main parameters were selected for calibration. For storm 104, which is chosen for calibration, the estimated total runoff value is exactly equal to the observed value. However, overestimation was observed for long-duration storms, where as underestimation was seen for short duration storms. Consequently, the best estimation was observed using NAM model based on statistical models, which are RMSE is 2.26 mm and CE is 0.84. Wang and Altunkaynak (2012) performed a similar study in the same catchment using the same storm event data. The authors applied storm events using SWMM approach and compared their results with a Fuzzy logic model. They concluded that fuzzy logic model prediction results outperformed total runoff event data compared to SWMM model. But, only total runoff was predicted from total rainfall by the fuzzy logic model and time variable hydrograph components could not be generated. In this study, the same calibration values from the study by Wang and Altunkaynak (2012) were used. However, the results are not found to be similar and a better simulation was observed after changing the time intervals of input rainfall time series from one minute to 10 minutes. As a result, RMSE decreasedfrom 3.85 to 2.91 mm. Likewise, results for large storm rainfall-induced runoff were overestimated in SWMM model. Peak Discharge It was observed that SWMM and NAM/MIKE BASIN approaches tend to underestimate the peak discharge values, while HEC-HMS’s SCS unit hydrograph methods overestimated the peak discharge values. As a result, the estimation results of these models are not satisfying based on the criteria of RMSEs and CEs. Discharge Duration The SCS and Root selection methods revealed the best estimations for discharge duration. This is because there is a good agreement between the estimated and observed discharge durations considering statistical criteria, where RMSEs were found to be 22.87 min and 25.44 min and CEs were found to be 0.88 and 0.85 respectively. RMSE and CE values for SWMM model results were found to be 35 min and 0.72, respectively. However, the other models did not reveal satisfying estimation results. As a result it can be interpreted that the performances of parametric models in term of total direct runoff are better than of those unit hydrograph methods. It can be explained by the number of physical and hydrological parameters that are used for simulation of rainfall-runoff proccess. On the other hand all models were used in this thesis did not excuted a good fit in term of peak discharge where is the most important parametre for designing water structures and flood control projects. The calibration of parametric models in this study was done considering to the total direct runoff and the peak discharge was second priority. So depend on purpose of study calibration can be done in order to obtain a good performance of estimation of desired parameter.