strem flow forecasting by fuzzy logic method

STREM FLOW FORECASTING BY FUZZY LOGIC METHOD

Mesut ÇİMEN Kemal SAPLIOĞLU [email protected], [email protected] Süleyman Demirel University, Department of Civil Engineering, 32260, ISPARTA

ABSTRACT

Water structures are build on the streams which collect water from catchments, and while their dimensions are arranged, discharge at the stream section must be known. However, according to the size of catchment basin, on an average 3-4 flowobservation station can be situated on a stream. This limit can be occurred a problem to determine maximum discharge for a water structure built anywhere on the stream. On these areas where there is no station, stream flow can only be estimated by using some methods. This problem is solved by General Directorate of State Hydraulic Works (DSI) and different water construction designers by taking into consideration drainage area of two sections (both measured and unmeasured). In this study, in a stream between two observation station a fuzzy flow estimation model has set up for predicting the downstream - flow values from the upstream - flow values. Hence, the rational and fuzzy method developed in this study has been investigated for stream flows. Keywords: Stream Flow, Fuzzy Logic, Rational Method, Köprüçay River INTRODUCTION

In recent years, growing population and changing living conditions have caused increasing demand for water, thus resulting in more and bigger problems about hydrology and hydraulics. Therefore, it is of great importance in view of time and economical aspects that such engineering structures as bringing water, irrigation and storing water should be planned and dimensionized properly. In order to achieve proper planning and dimensioning, evaluated data is important. However, data

RIVER BASIN FLOOD MANAGEMENT

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needed for the region to be planned either does not exist or is not sufficient. For a cross section which has insufficient or no measurement, process-driven or datadriven models are usually used to obtain the flow data [Wang, 2006]. Process-driven models can be viewed in two groups as runoff-run out model and low flow model. Run-off models are the ones that are based on physical facts of the problem and constituted with combination of some experimental equations. There are many studies on this subject. For instance, Pitman model [Pitman, 1973], developed in 1973 for prediction of flow, and run-off model on a monthly series basis, carried out in South Africa by Hughes [2004], are among these studies. Low flow recession models are the ones constituted to predict the flow that may occur in streams in dry seasons. Tallaksen (1995) summarizes in his study the models created for this subject. Second group of studies used for prediction of stream flows is evaluated datadriven models. These models are more useful in that they can be applied easily and stay away from complicated mathematical models. Among most frequently used of these models are regression models, time serial models, artificial neural network (ANN) and fuzzy logic (FL). Regression models, involved in data-driven models, are among the models which are frequently used for prediction of stream flows. Its advantage lies in that it is quite simple and applicable. Graphical techniques made by Linsley et.al [1975] can be regarded as among the first regression models. Later on, multiple regression model developed by Zuzel et.al [1975] and Smith’s non-parametrical regression model are notable studies carried out on this subject. Another important study within data-driven models is time serial models. Most frequently used ones of this kind of models are ARMA, AR, ARIMA, PARMA and SARIMA models. For nonseasonal series ARMA model, for seasonal models ARIMA and SARIMA, and as a periodical ARMA model PARMA are used. Applications of these three types of models cover a large place in literature [McKerchar and Delleur, 1974; Thompson et.al, 1985]. One of the most frequently used methods among data-driven methods is studies conducted with ANN which has become so popular in the last fifteen years. These studies are quite suitable studies for non-linear studies. Many researchers have made use of ANN for prediction of flow (Markus, 1997; Maier and Dandy, 2000; Hsu et.al, 1995). The most popular of ANN types is backward spreading algorithm. This method is widely used for predicting stream flows. The method used for predicting a flow in a stream in our country is the rational method which is conducted by General Directorate of State Hydraulic Works (DSI) and also widely used throughout the world. This method makes use of the terms of

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INTERNATIONAL CONGRESS ON RIVER BASIN MANAGEMENT

drainage area that is in source of the cross section where the prediction of flow will be made, intensity of rainfall and coefficient of drainage area flow. In this method, it is accepted that there is no storing in the drainage area used [Maidment, 1992].

Q = CiA

(1)

Where C is a constant as the ruoff coefficient of the drainage basin, I is the intensity of rainfall and A is the area of drainage basin. The study is carried out on two separate cross sections of a stream and if hydro meteorological characteristics of the basin are similar, then the coefficient, C, can be regarded as equal. Besides, if rainfall quantities of drainage areas of the two cross sections bear similar characteristics, rainfall intensities can be regarded equal as well. In this way, the flow, Q2, at a stream cross section whose rate of flow is unknown can be calculated with the help of known values as following:

Q2 =

A2 Q1 A1

(2)

In this study, considering two stream gauging stations, Fuzzy Logic method will be used in order to predict flow values at a station by making use of the values of the other station. For this reason, daily flow rates of the station, where the measurement will be realized, at certain times, t and t-1, are entered as input values and by doing so, the other station’s flow rates at the time of t are tried to be calculated. 2. STUDY FIELD AND METHOD

The stream examined in this study is Köprüçay River situated in the waters of Middle Mediterranean Sea in Turkey. Köprüçay stream emanates from the western skirts of Mount Anamas and follows its course towards south. Firstly, Oluk Köprü spring joins this stream, later on Kocadere from west and branches of Sağır from east join the stream. The stream, passing through Serik plain, flows into Mediterranean Sea. Köprüçay stream is approximately 156 kilometres long and possesses a basin area of 1498 km2 (Figure 1). Yearly rainfall amount of this stream is 3.2x10 m3 and it is one of the most important rivers in the region. The stream gauging station at the very source of Köprüçay is Bolasan (919) gauging station. Bolasan is a settlement situated in 25 kilometres away from the source of Köprüçay. Drainage basin, as far as stream gauging station, is 1538 km2 and minimum base flow observed there is 0 m3/sc. Beşkonak stream gauging station is at a distance of 40 km from the source of Köprüçay stream, and the area covered by its drainage basin as far as to the station is 1980 km2. This drainage basin forms nearly 80% of Köprüçay basin. Reported amount


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of minimum base flow is 28,8 m3/s. Average rainfall height for both Bolasan and Beşkonak basins is 1500 mm, and also vegetation and geological structures bear resemblances [Feasibility Report, 1983].

MEDITERRNIAN SEA Figure 1. Köprüçay Stream Basin and Gauging Station (EIE, 2006)

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In this study, by using data of Bolasan stream gauging station which is situated on Köprüçay River, data of Beşkonak gauging station which is situated 15 km downstream of Bolasan are tried to be predicted. Daily flow data of the years 1987 and 1988 are taken into consideration in the study. Making use of the daily flow rates in Beşkonak on days of t-1 and t (the previous day and that day), predictions of flow rates in Beşkonak stream gauging station on t day are tried to be realized by using fuzzy logic. Early information on principles of fuzzy logic was put forward by Zadeh [1965] and though it was thought in the beginning that it did not comply with scientific principles, it asserted itself by an application made by Mamdani and Assilian in 1975. Fuzzy logic basically occurs as an expression of indefiniteness. While classical mathematical methods are not much proper for incomplete and undefined models, fuzzy logic system can modelize qualitative sides of man’s knowledge and approach processes without using delicate and quantitative analysis. Today it can be applied to almost all branches of engineering as well. Main reasons for using fuzzy logic methods are that there is no definiteness in solving hardly any problems, and determining the solution of problems in which a lot of parameters are used is extremely difficult [Şen, 2000]. Based on the stream gauging made in Bolasan and Beşkonak stream gauging stations, fuzzy sub-groups of flow rates of these two stations are shown in Figures 2 and 3. Fuzzy sub-groups formed for both stations are made by making use of frequency curves of flows at stations. 1

2

3

4

5

15

29

6

7

8

9

1

0

0.6. 0.8 6.6

94

53

136

330

Discharge, Q (m³/sn)

Figure 2. Fuzzy Subsets for Discharges of Bolasan Gauging Station 1

2

3

4

5

6

68

89

120 Debi, Q (m³/sn)

7

8

9

1

0 30 35 38 49

177

230

Figure 3. Fuzzy Subsets for Discharges of Beşkonakn Gauging Station

500

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3. DISCUSSIONS

Making predictions for discharges at Beşkonak gauging station which is situated in downstream of Bolasan gauging station by using recorded flow data of Bolasan gauging station which is situated in the very source of Köprüçay stream makes up the content of this study. Dily hydrograph of both stations are given in Figure 4. When this figure is viewed, it can be concluded that inclinations of flows measured in both Bolasan and Beşkonak stream gauging stations coincide with each other.

450 400 Beşkonak Bolasan

350 300 250 200 150 100 50 0 25.25.Eyl.86 Sep.86

03.Oca.87 03. Jan.87

13.Nis.87 22.Tem.87 30.Sep.87 30.Eki.87 07.Feb.88 07.Şub.88 13. Apr.87 22.Jul.87

17.May.88 25.Aus.88 25.Ağu.88 17.May.88

Figure 4. Daily Hydrographs for Bolasan ve Beşkonak Gauging Stations

With the use of correlation given in equation 2, which is also used for development studies of some water sources in our country, discharge rates of Beşkonak gauging station have been calculated. Relation between these calculated rates and measured flow rates is given in Figure 5. According to this figure a linear relation has been observed between discharges which are measured at Beşkonak gauging station and discharges which are predicted by equation 2. In this relation, determination coefficient has been found as R2=0,9514, maximum error as -0,369, and total error as 13,08. However, when the 1:1 line straight line between measurement and predicted values is considered, it is seen that predicted rates are lower than the measured rates in general. The fact that right side of the equation given by equation 2 should be exponential can be regarded as the solution problem. This property has been ignored in the study.

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450

Estimated Discharge (m³/s) Tahmin Edilen Debi, Q (m³/sn)

400 350 300 250 200

y = 0,9013x R2 = 0,9514

150 100 50 0 0

50

100

150

200

250

300

350

400

450

Measuremed Discharge, Q(m³/s) Ölçülen Debi, Q (m³/sn)

Figure 5. Scatter Plot of Observed and Estimated Discharges by the Rational Method for Beşkonak Gauging Station

In this study, with the help of fuzzy logic sub-groups shown in Figures 2 and 3, flow rates at Beşkonak gauging station have been calculated through the flow rates at Bolasan gauging station on t-1 and t days. Measured and predicted flow data are given in Figure 5. Determination coefficient of the relation obtained through the agency of this method is R2=0,9656, maximum error is 0,30 , and total error is 5,08. A little difference has taken place between the 1:1 line and curves of regression line, and it has been observed that predicted discharge rates spread out regularly around this line. 450

Estimated Discharge (m³/s) Tahmin Edilen Debi, Q (m³/sn)

400 350 300 250

y = 0,9821x R2 = 0,9656

200 150 100 50 0 0

50

100

150

200

250

300

350

400

450

Measuremed Ölçülen Discharge, Debi, Q(m³/s) Q (m³/sn)

Şekil 6. Scatter Plot of Observed and Estimated Discharges by the Fuzzy Logic Model for Beşkonak Gauging Station

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4. RESULTS

In view of the values obtained, it has been observed that the model, which has been created with fuzzy logic method and which owns 2 inputs (Bolasan gauging station discharges on days of t-1 and t), 1 output (discharges of Beşkonak gauging station on t day) and 9 sub-groups for each, provides better results than rational method. It has also been observed that fuzzy model in which there are 275 days without rainfall on average provides nearly correct results for observed peak discharges as well. Nevertheless, it is necessary that this study should be more realistic and feasible by involving other flows that have been ignored in this study. Besides, it is thought for the following studies that runout coefficients and rainfall intensity should be considered in a more delicate way throughout the basin and be involved in the model. As a result, flow rates of Beşkonak gauging station can be calculated through the flow rates of Bolasan stream gauging station by means of this study.

5. REFERENCES

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McKerchar, A.I., Delleur, J.W., 1974. Application of seasonal parametric linear stochastic models to monthly flow data. Water Resources Research, 10, 246-255 Pitman, W.V., 1973. A mathematical model for generating river flows from meteorological data in South Africa. Report no. 2/73, Hydrological Research Unit, University of the Witwatersrand, Johannesburg, South Africa. Smith, J.A., 1991. Long-Range Streamflow Forecasting Using Nonparametric Regression. Water Resources Bulletin, 27(1), 39-46. Şen, Z, 2000. Mühendislikte bulanık (fuzzy) mantık ile modelleme prensipleri, Su Vakfı, İstanbul. Tallaksen, L.M., 1995. A review of baseflow recession analysis. Journal of Hydrology, 165, 349-370. Thompson, R.M., Hipel, K.W., Mcleod, A.I., 1985. Forecasting quarter-monthly river flow. Water Resources Bulletin, 21(5), 731-741. Wang, W, 2006 ., Stochasticity, Nonlinearity and Forecasting of Streamflow Processes PhD Thesis.Hohai University. Zadeh, L., 1965. Fuzzy algorithms. Information and control. 12, no. 2, pp.94-102. Zuzel, J.F., Robertson, DL., Rawls, W.J., 1975. Optimizing long – term streamflow forecast. Journal of soil and water conservation, 30 (2), 76-78.