İstanbul Boğazı su seviyesi değişimleri hibrit dalgacık-matematiksel tahmin modelleri
Hybrid wavelet- mathematical models for water level prediction Bosphorus Strait
Yazar: ELİF KARTAL
Danışman: PROF. DR. ABDÜSSELAM ALTUNKAYNAK
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Hidrolik ve Su Kaynakları Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: Mühendislik Bilimleri = Engineering Sciences

Özet:
İstanbul Boğazı, kontrol ettiği su kütleleri Karadeniz ve Marmara Denizi ile yüksek etkileşim içerisindedir. Karadeniz'in Marmara Denizi ile ve dolayısıyla açık denizler ile tek bağlantısı olan kanal, komşu su kütlelerinin hidrodinamik davranışını üzerinde yönetici mekanizma olmasının yanında hazneler arası her türlü (organik, inorganik) taşınımında rol oynar. Bununla birlikte, Boğaz boyunca görülen su seviyesindeki salınımlar doğrudan komşu denizlerdeki hidrometeorolojik koşullardan etkilenmektedir. İstanbul Boğazı su seviyesi değişimleri; rüzgar, haznelerdeki pozitif su bütçesi, gelgit gibi çok sayıda zorlayıcı fiziksel sürecin etkisiyle oluşur. Su seviyesini oluşturan bileşenlerin frekans aralıklarının çok geniş ölçekte değişmesi ve etkenler arasındaki doğrusal olmayan ilişkiler, güvenilir ve doğru sistem analizlerinin ortaya konulmasını ayrıca bu analizleri taban alan kuvvetli tahmin modellerinin kurulmasını zorlaştırır. Seviye değişimlerine ait her türlü bilgiyi yalnızca zaman alanında temsil edebilen zaman serilerine dayanan tahmin modelleri, durağan olmayan boğaz sisteminde geçmiş-gelecek ilişkilerini stokastik yaklaşımlarla tanımlamakta yetersiz kalabilir. Tahmin modellerinin öngörü kabiliyetini arttırmak amacıyla girdi veri kümesinin işlenmesi ve yöntemlerin analiz edebileceği alt bileşenlere ayrılması yaygın kullanılan bir tekniktir. Bu çalışmada bir veri işleme tekniği olarak dalgacık dönüşümü ve farklı tahmin algoritmalarını kullanan hibrit dalgacık-matematiksel tahmin modelleri oluşturulmuştur. Matematiksel tahmin yöntemlerinin farklı su seviyesi zaman serileri üzerindeki analiz-tahmin başarısı değerlendirilmiş, ayrıca önişlem aracı dalgacık dönüşümünün hibrit modellerdeki olumlu katkısı incelenmiştir.
İstanbul Boğazı'nın Karadeniz ve Marmara Denizi sınırlarındaki su seviyesi zaman serileri, ayrık dalgacık dönüşümü ve 4 farklı tahmin yöntemi kullanılarak modellenmiştir. Geliştirilen hibrit dalgacık-matematiksel tahmin modelleri aracılığıyla ileri zamanlı, 1 hafta sonrasına kadar, muhtemel seviye değerleri elde edilmiştir. Boğazdaki su seviyesi değişimlerini oluşturan farklı bileşenlerin etkilerini değerlendiren ve değerlendirmeler ışığında gelecekteki davranışını öngörebilen modellerin matematiksel temelleri; modern yöntemlerden bulanık mantık, destek vektör makineleri, k-en yakın komşuluk ve klasik yöntemlerden çoklu doğrusal regresyon algoritmalarına dayandırılmıştır. Kuzey ve güney girişlerinde toplanan 15 aylık günlük seviye ölçümlerinin %60'lık kısmı eğitim verisi olarak, geriye kalan kısmı matematiksel modellerin tahmin başarısının sınandığı test verisi olarak kullanılmıştır. Tüm yöntemler, hem günlük seviye değerleri zaman serilerine hem de dalgacık dönüşümü vasıtasıyla ayrıştırılmış su seviyesi bileşenlerine uygulanmıştır.  
Çalışmada öncelikle her model için en verimli girdi kümesi sayısı 1 gün sonrası tahminlerine göre belirlenmiş ve en uygun girdi sayısı kümesi tüm tahmin adımlarında muhafaza edilmiştir. Matematiksel modellerin ve hibrit dalgacık-matematiksel modellerin analiz ve öngörü yeteneği; ortalama hata karesi (OHK) ve Nash-Sutcliffe etkinlik katsayısı (NSE) başarı kriterleri temel alınarak değerlendirilmiştir. Belirtilen başarı ölçütleri göz önünde bulundurulduğunda, ilave dalgacık dönüşümü aşamasının tüm matematiksel modellerde, tahmin edilebilir zaman adımını ve tahmin başarısını arttırdığı gözlemlenmiştir.

Abstract:
Bosphorus, which is located at the northern side of Turkish Strait system, is the only waterway of Black Sea to Marmara and thereby Mediterranean Sea. Because of the singularity, it has vital importance not only for Turkey, but also for other countries at this region. For that reason, water flows of Bosphorus is studied for many purposes such as water quality analysis, underwater construction structures, shore management projects and transportation planning. Hydrodynamic behaviour at Bosphorus and consequence of effecting forces on water level fluctuation is still a live topic in recent studies.
The main component affecting the Bosphorus stratified flow is the water level difference between Black Sea and Mediterranean Sea. Flow condition of Bosphorus and water level fluctuation are affected by hydrometeorological conditions of Mediterranean Sea and Black Sea. Water level fluctuations at Bosphorus with short period are occurred as a result of tide and atmospheric pressure difference. Positive water budget in Black sea during the annual period is the main part of seasonal component of sea level. Because of the discharge from rivers, precipitation input more than evaporation loss in the Black Sea basin, water level rise occurs at the northern side of Bosphorus. The change of Tuna River's mass flow rate in annual period which is the most important water resource feeding for Black Sea reflect on the Bosporus water level that controls Black Sea water mass. The water level is relatively higher at the northern entrance than the southern entrance of the Bosphorus. 
Even the flow conditions and the components effecting water level is well known, it is not simple to model complex Bosphorus system with high sensibility. In addition to physical properties like complex geometry, irregular bathymetry and also uncertainties of forcing effects on water motion are factors that get difficult the system analysis. Another problem encountered in strait modelling studies is that there is inadequate of data. In the complex system modelling, extensive and continuous observation data set have crucial role with calibration and installation purposes. Although there are no regular, continuous measurement recordings through Bosphorus or seaside boundaries, collecting data established occasionally within the scope of large-scale projects involving the Bosphorus guided the researchers to analyse hydrodynamic.
Within the scope of the Marmaray underwater tunnel project, measurements of current, meteorology and sea level were collected from the measurement stations established in the northern and southern part of the Bosphorus. The measurement studies conducted between 2004 and 2005 were used in many research especially analysing current conditions of the strait. Some models aim to decompose physical components on level changes based on 15-month level records. There are time series of level changes recorded during 15-months in hour intervals at both the northern and southern entrances of strait. Forecasting models based on time series that can only represent time domain may be insufficient to define past-future relationships. In order to increase predictive ability of prediction models, it is a common technique to prepare the input data set according to the method, to process it and to subdivide it into the subcomponents that the methods can analyse. In this study, discrete wavelet transform was used as a data processing technique. The effect of the pre-treatment tool on the model performance was investigated through different estimation methods and different water level time series.
The water-level oscillations of the Bosphorus occur with the combination of many complex physical process frequencies varying in time. In order to develop a suitable model that defines the internal structure of the series, it is necessary to carefully collect and examine the past observations of a time series. The prediction-based estimation models are constructed based on the general character of the current measurement values and the connection of each value with the past values. The success and sensitivity of the models are related to the selection of the appropriate method. In recent years, in order to increase the accuracy of serial-method compatibility and thus the estimation accuracy of models, the use of hybrid models in which data processing techniques and several methods are common and becoming widespread. However, the highly variable hydrological and meteorological conditions of the adjacent seas make the complex physical properties of the Bosphorus obstruct to resolve in the region and to predict future behaviour depending on the analysis. Spectral analysis methods are a useful tool for obtaining the hidden information of different overlapping components among the measurements recorded over time. Fourier analysis is a classical spectral analysis method used to differentiate water level oscillations. However, the Fourier method obtained by the infinite repetition of the constant period sinus and cosine functions is often inadequate to define the hydrological time series showing non-stationary oscillations. The wavelet transformation developed from the Fourier analysis method is an alternative spectral analysis tool as the periods of physical processes that determine the water level oscillations in the Bosphorus vary between periods and decades.
The water level time series in the Black Sea and the Sea of Marmara  entrence of Bosphorus are modelled by a method that bases combination  wavelet transform and different estimation algorithms. The developed hybrid models were used to predict possible level values until 1 week later. Simulation of time series are performed to product new samples according to system determination based past observation values Predicted samples were compared with the existing observation values. Predictions were obtained by modern methods of fuzzy logic, support vector machines, k-nearest neighbour algorithms and multiple linear regression models from classical methods. 60% of the 15-day daily level measurements collected at the north and south entrances of the Bosphorus were evaluated as training data, and the remaining data set was used to test the future success of the methods. In this study, daily water level measurements obtained in the preliminary research studies of the Marmaray tube passage project that will connect the two continents under the sea were used. The wavelet technique, used as pre-treatment tools, has been transformed into spectral bands used as input for estimation methods.
The estimation models are evaluated into two groups as mathematical prediction models using input original time series and hybrid wavelet-mathematical prediction models using input wavelet subseries.  The difference between the two groups consists in the preparation of the estimation method of the data. The same estimation methods were used in both data groups. In hybrid models, estimation process were applied to each component of water level components involving  different spectral information separated by wavelet transform. Each band was individually estimated and water level predictions were obtained as addition predicted bands cumulatively. 
The sensitivity of the methods to the number of inputs was examined and the most appropriate input set for the method was applied to the models by keeping them constant in all estimation time steps. The number of the most efficient input sets for each model is determined according to the 1-day forecast for each model. For both data groups, the most appropriate number of inputs determined in the one lag time prediction are kept in all estimation steps.
The analyse capability and prediction performance of models in original time series and wavelet band series were evaluated on the basis of success criteria using mean square errors (HKO) and Nash-Sutcliffe efficiency coefficient (NSE).Considering the mentioned success criteria, it was observed that additional wavelet transformation phase increased predictable time step and estimation success in all methods.
Acceptable accuracy estimates for 1 lag time were obtained using the mathematical prediction models. However, as the time step elapsed, the number of days between inputs and outputs increased, it is observed that the methods had difficulty in analysing the temporal connections between water levels. Level oscillations of many different frequency components are pre-treated with wavelet transform and pre-treated to equal frequency bands. Four methods used in raw (unprocessed) level values models were also applied to wavelet bands with homogeneous frequency information, and their contribution to the estimation accuracy of the conversion process was examined. Wavelet decomposition process enhance the predictable sea level lag time form one day to one week at the entrance of the Black Sea and the and 5 days at the entrance of Marmara Sea. The wavelet band series used the input as an input, while the predicted success of the Marmara Sea entry was a more powerful tool in predicting one day ahead compared to the Black Sea input models, but it was not able to maintain its sensitivity for the subsequent time steps and remained behind the Black Sea models. In the time series in the northern and southern boundaries, all methods were able to predict the post-one-day level values without wavelet transform support. 
The predictive values of these methods were compared and it was noted that the k nearest neighboring method remained behind other methods. The reason for the long-term success in the Marmara border is that it has a higher variance compared to the Black Sea. Considering that all methods have a higher success rate in high-band bands, it can be suggested that the effect reducing the predictive success at the southern entrance is dominated by small-period components in the series.
The Istanbul Strait system models needs a large measurement network to obtain higher accurancy. On the other hand, hybrit mathematical time series prediction models can described as powerful tolls  future prediction. The observation values of the different items to be obtained will contribute to the better analysis of the water mobility in the Bosphorus and to make more accurate decisions in the project design works in the region. In further studies, spectral wavelet bands and water level forcing effects relations can be investigates as another subject.