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Turkish J. Eng. Env. Sci.29 (2005) , 9 20.c TUB ITAK

Daily River Flow Forecasting Using Articial Neural Networks andAuto-Regressive Models

Ozgur K IS I Istanbul Technical University, Faculty of Civil Engineering,

Istanbul-TURKEY

Received 01.07.2003

Abstract

Estimating the ows of rivers can have a signicant economic impact, as this can help in agriculturalwater management and in providing protection from water shortages and possible ood damage. Thispaper provides forecasting benchmarks for river ow prediction in the form of a numerical and graphicalcomparison between neural networks and auto-regressive (AR) models. Benchmarking was based on 7 and4-year periods of continuous river ow data for 2 rivers in the USA, the Blackwater River and the Gila River,and a 2-year period of streamow data for the Filyos Stream in Turkey. The choice of appropriate articialneural network (ANN) architectures for hydrological forecasting, in terms of hidden layers and nodes, wasinvestigated. Three simple neural network (NN) architectures were then selected for comparison with theAR model forecasts. Sum of square errors (SSEs) and correlation statistic measures were used to evaluatethe models performances. The benchmark results showed that NNs were able to produce better resultsthan AR models when given the same data inputs.

Key words: Streamow forecasting, Neural networks, Auto-regressive models.

Introduction

Many of the activities associated with the planningand operation of the components of a water resourcesystem require forecasts of future events. For thehydrologic component, there is a need for both shortterm and long term forecasts of streamow eventsin order to optimize the system or to plan for fu-ture expansion or reduction. Many of these sys-tems are large in spatial extent and have a hydro-metric data collection network that is very sparse.These conditions can result in considerable uncer-tainty in the hydrologic information that is available.Furthermore, the inherently non-linear relationshipsbetween input and output variables complicate at-tempts to forecast streamow events. There is thusa need for improvement in forecasting techniques.Many of the techniques currently used in model-ing hydrological time series and generating syntheticstreamows assume linear relationships amongst the

variables. The 2 main groups of techniques includephysically based conceptual models and time seriesmodels. Techniques in the former group are specif-ically designed to mathematically simulate the sub-processes and physical mechanisms that govern thehydrological cycle. These models usually incorpo-rate simplied forms of physical laws and are gen-erally nonlinear, time-invariant, and deterministic,with parameters that are representative of water-shed characteristics (Hsu et al ., 1995) but ignorethe spatially distributed, time-varying, and stochas-tic properties of the rainfallrunoff (RR) process.

Kitanidis and Bras (1980 a,b) state that concep-tual watershed models are reliable in forecasting themost important features of the hydrograph. How-ever, the implementation and calibration of such amodel can typicallypresent various difficulties (Duanet al ., 1992), requiring sophisticated mathematicaltools (Sorooshian et al ., 1993), signicant amountsof calibration data (Yapo et al ., 1996), and some de-

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gree of expertise and experience with the model (Hsuet al ., 1995). The problem with conceptual modelsis that empirical regularities or periodicities are notalways evident and can often be masked by noise.

In time-series analysis, stochastic models are t-ted to one or more of the time-series describing the

system for purposes that include forecasting, gener-ating synthetic sequences for use in simulation stud-ies, and investigating and modeling the underlyingcharacteristics of the system under study. Mostof the time-series modeling procedures fall withinthe framework of multivariate autoregressive movingaverage (ARMA) models (Raman and Sunilkumar,1995).

ANNs have been successfully applied in a num-ber of diverse elds, including water resources. Inthe hydrological forecasting context, recent experi-ments have reported that ANNs may offer a promis-ing alternative for R-R modeling (Smith and Eli,1995; Shamseldin, 1997; Tokar and Johnson, 1999),streamow prediction (Zealand et al ., 1999; Changand Chen, 2001; Sivakumar et al ., 2002; Kisi, 2004;Cigizoglu and Kisi (in press)) and reservoir inowforecasting (Saad et al ., 1996; Jain et al ., 1999). Re-cently, Coulibaly et al . (1999) reviewed the ANN-based modeling in hydrology over the last years, andreported that about 90% of experiments make exten-sive use of the multi-layer feed-forward neural net-works (FNN) trained by the standard backpropaga-tion (BP) algorithm (Rumelhart et al ., 1986).

The main purposes of this paper are to ana-lyze and to discuss stochastic modeling of time se-ries using FNN and traditional modeling techniques.There are many parameters (precipitation, evapo-transpiration, ground water, initial moisture contentof soil etc.) that affect the next day runoff. Al-though it is possible to identify sophisticated mod-els taking into consideration the hydrological andhydro-meteorological variables such as precipitation,runoff, temperature and evaporation, it is economi-cally preferable that a model that simulates the owvariations on the basis of past discharge records beavailable to the decision maker, whether administra-tor, local authority or technical operator. Therefore,only the past discharge records were used as inputsin the present study. The FNN and AR models areapplied to forecast daily river ow for 3 rivers, theBlackwater River and Gila River in USA and theFilyos Stream in Turkey. The results are comparedand conclusions are presented.

Articial Neural Networks

General

The human brain contains billions of interconnectedneurons. Due to the structure in which the neu-rons are arranged and operate, humans are able to

quickly recognize patterns and process data. AnANN is a simplied mathematical representation of this biological neural network. It has the ability tolearn from examples, recognize a pattern in the data,adapt solutions over time, and process informationrapidly. The application of ANNs to water resourcesproblems is rapidly gaining popularity due to theirimmense power and potential in the mapping of non-linear system data.

A water resources system may be nonlinear andmultivariate, and the variables involved may havecomplex interrelationships. Such problems can beefficiently solved using ANNs. The processes that in-volve several parameters are easily amenable to neu-rocomputing. Among the many ANN structures thathave been studied, the most widely used networkstructure in the area of hydrology is the multilayer,feed-forward network. The remaining discussion isfocused on such networks.

An ANN consists of a number of data processingelements called neurons or nodes, which are groupedin layers. The input layer neurons receive the inputvector and transmit the values to the next layer of processing elements across connections. This processis continued until the output layer is reached. This

type of network in which data ows in one direction(forward) is known as a feed-forward network. TheANN theory has been described in many books, in-cluding the text by Rumelhart et al. (1986). Theapplication of ANNs has been the subject of a largenumber of papers that have appeared in the recentliterature. Therefore, to avoid duplication, this sec-tion will be limited to main concepts.

A 3-layer, feed-forward ANN is shown in Figure1. It has input, output, and hidden middle layers.Each neuron in a layer is connected to all the neu-rons of the next layer, and the neurons in one layerare not connected among themselves. All the nodeswithin a layer act synchronously. The data passingthrough the connections from one neuron to anotherare multiplied by weights that control the strength of a passing signal. When these weights are modied,the data transferred through the network changes;consequently, the network output also changes. Thesignal emanating from the output node(s) is the net-works solution to the input problem.

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used to estimate AR coefficients. The maximum en-tropy method (MEM, or Burg algorithm) is an alter-native way to estimate AR coefficients. The modelthat gives the maximum correlation and the mini-mum sum of square errors (SSE) was selected. TheAR(5) and AR(2) were found appropriate for theBlackwater. For the Gila River and Filyos Stream,however, the AR(2) model gave the best results.

Case study

The ow data of the 2 stations operated by the U.S.Geological Survey (USGS) and the data of the Dere-cikviran Station operated by the Turkish General Di-rectorate of Electrical Power Resources Survey andDevelopment Administration (EIE) were used in thestudy. The locations of these stations are illus-trated in Figures 2 and 3. The 1 st station (USGS

Station No: 02047500, datum of gauge is 9.45 mabove sea level) is on the Blackwater River near Den-dron in Virginia, the 2 nd station (USGS Station No:09442000, datum of gauge is 1017 m above sea level)is on the Gila River near Clifton in Arizona, the 3 rdstation (EIE Station No: 1335, datum of gauge is 1m above sea level) is on the Filyos Stream in Turkey.The drainage areas at these sites are 761 km 2, 10386km2 and 133300 km 2 , respectively.

For the 1 st station, the data for October 01 1990to September 30 1996 (6 water years) were chosen forcalibration, and data for October 01 1996 to Septem-ber 30 1997 (1997 water year) were chosen for val-idation, arbitrarily. For the 2 nd station, the datafor October 01 1995 to September 30 1998 (3 wateryears) were used for calibration, and data for Octo-ber 01 1998 to September 30 1999 (1999 water year)

Figure 2. The locations of the stations operated by the USGS.

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Figures 10, 11 and 12 show the extent of thematch between the measured and predicted dailyriver ow values by ANN and AR models in termof a scatter diagram. The R 2 performances of ANNmodels are slightly better than those of AR models.

The relative SSE difference between the 5 th ANNcombination and the AR(5) model in the calibrationperiod for the Blackwater River is 20% that betweenthe 2 nd ANN combination and the AR(2) model incalibration period for the Gila River is 42% and that

between the 3 rd ANN combination and the AR(2)model in the calibration period for the Filyos Streamis 16%. Since the linearity in the Blackwater Riverand the Filyos Stream is much higher than that in theow data of the Gila River (see Table 1), the relativeSSE difference between the 2 methods for these riversis much lower than the value for the Gila River. Inother words, the performances of the AR and ANNmodels are closer to each other for the 1 st and 3 rdrivers whose auto-correlations are quite high.

0 50 100 150 200 250 300 350Day

Observed

ANN

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40

30

20

10

0

R i v e r

f l o w

( m 3 / s )

Figure 4. Observed and computed (ANN model) ows for the Blackwater River, validation period (01 October 1996-30September 1997; 1997 water year).

0 50 100 150 200 250 300 350Day

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60

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40

30

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0

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f l o w

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ObservedAR(5)

Figure 5. Observed and computed (AR model) ows for Blackwater River, validation period (01 October 1996-30 Sep1997; 1997 water year).

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0 30Day

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f l o w

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90 120 150 180 210 240 270 300 330 36060

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Figure 6. Observed and computed (ANN model) ows for the Gila River, validation period (01 October 1998-30 Septem-ber 1999; 1999 water year).

0 30Day

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f l o w

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90 120 150 180 210 240 270 300 330 36060

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Figure 7. Observed and computed (AR model) ows for the Gila River, validation period (01.October1998-30.September1999; 1999 water year).

0

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0 50 100 150 200 250 300 350Day

observedANN

R i v e r

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Figure 8. Observed and computed (ANN model) ows for Filyos Stream-Validation period.

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R2 = 0.900ANN

0

100

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0 200 400 600observed

p r e

d i c t e

d

R2 = 0.890AR(2)

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Figure 12. Scatterplots comparing predicted and observed ows for validation data of Filyos Stream.

Conclusions

The potential of ANN models for simulating the hy-drologic behavior of streamow has been presented inthis study. The greatest difficulty lay in determiningthe appropriate model inputs for such a problem. Al-though ANNs belong to the class of data-driven ap-proaches, it is important to determine the dominantmodel inputs, as this reduces the size of the networkand consequently reduces the training times and in-creases the generalization ability of the network for

a given data set.The results obtained with ANNs for 1-day ahead

forecasts are better than those reached in the ARmodels and conrm the ability of this approach toprovide a useful tool in solving a specic problem inhydrology, that of streamow forecasting. The re-sults suggest that the ANN approach may provide asuperior alternative to the AR models for developinginputoutput simulations and forecasting models insituations that do not require modeling of the inter-nal structure of the watershed.

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