Akış hidrografı tahmin modelleri
Estimation of runoff hydrograph
Yazar: MUSTAFA NURI BALOV
Danışman: DOÇ. DR. ABDÜSSELAM ALTUNKAYNAK
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Hidrolik ve Su Kaynakları Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
Mühendislik açısından yağış akış süreci su çevriminin en önemli bileşenlerindendir.  Muhtemel yağışlardan meydana gelebilecek akışın tahmini su kaynaklarının projelendirilmesinde önemli yere sahiptir. Bu nedenle bir çok fiziksel ve veri tabanlı yağış akış modelleri 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 olan toplam dolaysız yüzey akışı, pik debi, ve akış süresi incelenmiştir. Bu üç parametre farklı tasarım amaçlarına göre ele alınabilir. Bu bağlamda NAM/MIKE BASIN, SWMM parametrik modelleri ve HEC-HMS modeli kapsamında bulunan Clark, Snyder ve SCS birim hidrograf metotları ile birlikte Kök seçimi matematiksel birim hidrograf yöntemi 1990-1995 yılları arasında Cascina Scala (Kuzey Pavia, İtalya) havzasında meydana gelen 5 ayrı fırtınanın mo-dellenmesi için kullanılmıştır.
NAM/MIKE BASIN ve SWMM parametrik yaklaşımları havzanın fiziksel ve hidrolojik parametrelerini kullanarak yağış akış sürecini modellemektedir. Bu modeller kap-samında yağış akış sürecine bağlantılı olan buharlaşma, sızma, evapotranspirasyon, yeraltı suyu, iç akım, yüzey akımı vs. gibi tüm fiziksel olayların simülasyona dâhil edilmesinden dolayı, modelleme için çok sayıda parametrenin belirlenmesi gerekmektedir. Genellikle bu parametrelerin tamamının belirlenmesi mümkün olmayabilir. Bu durumda yağış akış verilerine dayanan farklı kalibrasyon yaklaşımlarından faydalanılmıştır. Buna karşılık HEC-HMS modelinin birim hidrograf yöntemleri daha az fiziksel parametrenin gerektiği ve daha çok veri tabanlı modellerdir. Ayrıca kök seçimi birim hidrograf metodu kapsamında sadece akış verilerini kullanarak bir havzanın birim hidrografı elde edilebilir. 
Modellerin tahmin sonuçları hataların karesinin ortalamasının karekökü (RMSE) ve Verim Katsayısı (CE) istatistiksel ölçütlere göre değerlendirilmiştir. Toplam dolaysız yüzey akışı parametresi açısından en iyi tahmin sonucu NAM/MIKE BASIN modeline aittir (RMSE=2,26 mm ve CE=0,84). Bu model sonucundan sonra aniyi tahmini SWMM modeli RMSE=2,91 ve CE=0,73 vermiştir. Ancak tüm birim hidrograf yön-temlerinin tahmin sonuçları kabul edilebilir seviyede olmamıştır. RMSE değerinin yaklaşık 6 mm ve CE değerinin sıfırdan düşük olması bu durumu teyit etmektedir.  Dikkat çekici diğer bir sonuçta kullanılan tüm modellerin uygun pik debi tahmini yapamamalarıdır. CE değerlerinin sıfırın altında olması da bu durumu teyit etmektedir. Hidrograf süresi tahmininde Clark ve Kök Seçimi birim hidrograf yöntemleri ve SWMM parametrik modeller iyi tahmin gösterirken diğer modellerin tahmini kabul edilebilir seviyede değildir.

Abstract:
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 were compared with extended classical rational models. 
The unit hydrograph is the unit response function of a linear hydrologic system and was firstly 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 assump-tions. The intensity of the excess rainfall and the base time of the direct runoff hy-drograph should remain constant and the excess rainfall should be uniform over the whole watershed. Many researchers investigated unit hydrograph theory and synthet-ic unit hydrographs such as Snyder (1938) and SCS (1972) which 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, no 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 have been conducted so far. 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 mod-els 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, hydrologic parameters and mathematical methods of derivation of unit hydro-graph. 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 hydro-graph.
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 rather 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 un-expected 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, whereas underestimation was seen for short duration storms. Consequently, the best estimation was observed using NAM model based on statistical models, in which 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 the 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 decreased from 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, other models did not reveal satisfying estimation results.
As a result, it can be interpreted that the performances of parametric models in terms of total direct runoff are better than those of unit hydrograph methods. It can be explained by the number of physical and hydrological parameters that are used for simulation of rainfall-runoff process. On the other hand, all models were used in this thesis did not execute a good fit in terms of peak discharge, which is the most important parameter for designing water structures and flood control projects. The study calibration can be done in order to obtain a good performance of estimation of desired parameter. The calibration of parametric models in this study was done considering the total direct runoff and the peak discharge.