August 2012, P.P. 673 685 www.cafetinnova.org ! "! $ * )+ , $, ) %& ' ( +- . ! ! "# # ) , /0+ % )0 , $ % & )*)+,) ( -# . 12* &# ' .( , ( ( 3 4 This paper deals with the prediction of hydrologic behavior of the runoff for the one of the largest discharge carrier International River, Brahmaputra, located in Assam (India) at the Pandu station, by using daily time unit. The flow regime dominated by high data non stationary and seasonal irregularity due to Himalayan climate fallout. The influence of data preprocessing through wavelet transforms has been investigated. For this, the main time series of flow data were decomposed to multiresolution time series using discrete wavelet transformations. Then these decomposed data were used as input to Artificial Neural Network (ANN) for multiple lead time flow forecasting. Various types of wavelets were used to evaluate the optimal performance of models developed. The forecasting accuracy of the models has been tested for multiple lead time upto 4 days using different decomposition levels. The performance of the proposed hybrid model has been evaluated based on the performance indices such as root mean square error (RMSE), coefficient of efficiency (CE) and mean relative error (MRE).The results shows the better forecasting accuracy by the proposed combined hybrid model over the single ANN model in hydrological time series forecasting. / "# 5 % & % 0 % 4 Hydrology system is influenced by many factors such as weather, land cover, infiltration, evapotranspiration, so it includes the good deal of stochastic dependent component, multi time scale and highly non linear characteristics. Hydrologic time series are often non linear and non stationary. Inspite of high flexibility of Artificial Neural Network (ANN) in modelling hydrologic time series, sometimes signals are highly non stationary and exhibits seasonal irregularity. In such situation, ANN may not be able to cope with non stationary data if pre processing of input and/or output data is not performed (Cannas et al.,2006). Pre processing data referes to analysing and transforming input and output variables in order to detect trends, minimise noise, underline important relationship and flatten the variables distribution in a time series. These analysis and transformations help the model learn relevant patterns. Data Pre processing techniques, which facilitates stabilisation of the mean and variance, and seasonality removal, are often applied to remove non stationarity in data used to build soft computing models. Most of the researchers using ANN prefer using Feed Forward Back Propagation (FFBP) algorithm. But major disadvantages of FFBP are slow convergence, often trapped in local minima, weak extrapolator and $$ 1 2 . unable to cope up with high non linearity and non stationary data series. To minimize these limitations, Wavelet transformation attached with ANN as data preprocessing technique can be adopted to achieve higher forecasting accuracy and consistency in multi lead time ahead (Deka and Prahlada,2012). non stationary time series can be decomposed into certain number of stationary time series by wavelet transform (WT). Then different single prediction methods are combined with wavelet transform to improve the prediction accuracy. In most of the hybrid models, WT is used as data preprocessing technique. The wavelet transformed data aid in improving the model performance by capturing helpful information on various resolution levels. Due the above mentioned advantages of WT, it has been found that the hybridization of wavelet transformation with other models like ANN, FL, ANFIS, linear models, etc., improved the results significantly than the single regular model (Prahlada and Deka, 2011). Wavelet theory (Mallat, 1989) is first developed in the end of 1980s of last century. Now a days, it has been applied in many fields, such as signal process, image compression, voice code, pattern recognition, hydrology, earthquake investigation and many other non linear science fields. #02050405 Copyright ©2012 CAFET INNOVA TECHNICAL SOCIETY. All rights reserved. PARESH CHANDRA DEKA, LATIFA HAQUE and ANIRUDDHA GOPAL BANHATTI Wensheng and Ding (2003), carried out a multi time scale prediction of ground water level at Beijing and daily discharge of Yangte River Basin at China using Hybrid Model of Wavelet Neural Network. The proposed WLNN model focused on improving the precision and prolonging the forecasting time period. Kim and Valdes (2003) developed nonlinear model for drought forecasting based on a conjunction of wavelet transforms and neural networks in the Conchos river basin in Maxico. The results indicate that the conjunction model using dyadic wavelet transform significantly improves the ability of neural network in forecasting.B. Cannas et al. (2005) modelled the river flow forecasting one month ahead with Neural Networks and Wavelet Analysis using monthly runoff data for the Tirso Basin, Italy. For the non stationary and seasonal irregularity of runoff time series, the best results were obtained using data clustering and discrete Wavelet Transform combination. Tests showed that neural networks trained with pre processed data showed better performance. Zhou et al(2008)developed monthly discharge predictor corrector model based on wavelet decomposition using 52 years records of monthly discharge at Yichang station of Yangtse river The decomposed times series data were used as input to ARMA model for prediction which improves the prediction accuracy. Y.R. Satyaji Rao et al. (2009) carried out modelling using Hydrological Time Series data adopting Wavelet Neural Network for four west flowing rivers in India .The results of daily Streamflow and monthly Groundwater level series modelling indicated that the performances of WNN Models are more effective than ANN Models. A rainfall runoff modelling using Wavelet ANN approach was carried out by Nourani et al., (2009), for predictions of runoff discharge one day ahead of the Ligvanchai watershed at Tabriz, Iran. The daily rainfall and runoff time series for 21 years were used. The time series were decomposed upto four levels by using Haar, Daubechies (db2), Symlet (sym3) and Coiflet (coif1). The Study showed that both short and long term runoff discharges could be predicted considerably with higher merit of Haar wavelet in comparison with the others. They also recommended that Wavelet Transform could be used for trend analysis in watersheds. Another Intermittant streamflow forecasting model was developed by Kisi,O. (2009)called neurowavelet (NW) model combining two methods discrete wavelet transform (DWT) and artificial neural network (ANN), for 1 day ahead forecasting. The new subtime series having high correlation coefficient were used as input to the ANN model. The NW model was found to be much better than the ANN in high flow estimation. The test results showed that the DWT could significantly 6 increase the accuracy of the ANN model in modelling intermittent streamflows. Many works related to sediment load estimation were alsoreported in the literature using wavelet transformations (T. Rajaee et al.,2010, Kisi,O.2010, Rajaee, T., and et al. 2011) Shiri and Kisi, (2010), examined the performance of short term and long term streamflow forecasting using a wavelet and neuro fuzzy conjunction model to investigate the daily, monthly and yearly streamflow of Derecikviran station on Filyos River in the Western Black Sea region of Turkey using 31 years of streamflow data. The results obtained showed that the neuro fuzzy (NF) and wavelet neuro fuzzy (WNF) models increased the accuracy of the single NF models especially in forecasting yearly streamflow. The effects of various decomposition level of wavelet in flow forecasting performance was investigated by Adamowski, J., and Sun, K. (2010) in non perennial rivers in semi arid watersheds at lead times of 1 and 3 days for two different rivers in Cyprus. The discrete trous wavelet transform was used to decompose flow time series data into 8 levels wavelet coefficients which are used as inputs to Levenberg Marquardt artificial neural network models to forecast flow. WA ANN model provided more accurate results than regular ANN. Further,wavelet combined with Genetic programming and ANFIS were also reported in very recent literature in streamflow forecasting and rainfall runoff modeling(Kisi and Shiri,2011; Nourani et al.,2011). In fact, in general, and in Brahmaputra basin in particular, runoff time series consists of high non linearity and non stationary, and neural network models may not be able to cope with these two different aspects if no pre processing of the input and/or output data is performed. In this study, wavelet transforms and neural networks have been applied to predict the hydrologic behavior of the runoff for the Brahmaputra basin located in Assam (India) at Pandu (Guwahati) station by using daily flow data. Wavelet analysis is used to pre process the data to be fed to a traditional multilayer perception (MLP) neural network. 7 %& % & 4 The Brahmaputra is the fourth largest river in the world in terms of average discharge at mouth, with a flow of 19,830 cumec. The hydrologic regime of the river responds to the seasonal rhythm of the monsoons and to the freeze thaw cycle of the Himalayan snow. The rainy season (May to October) accounts for 82% of the mean annual flow at Pandu. The station Pandu is located near Guwahati city of Assam, India. The discharge is highly fluctuating in nature. Discharge per unit drainage area in International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 Discrete Wavelet Ann Approach in Time Series Flow Forecasting A Case Study of Brahmaputra River 6 the Brahmaputra Basin River is among the highest of major rivers of the world. At Pandu, the Brahmaputra yields 0.0306 cumecs per sq.km and the mean annual flood discharge is 51,156 Cumecs. The maximum discharge being 61,000 Cumecs and the minimum being 2432 Cumecs for Pandu Station.The study area (station Pandu) is shown in figure 1 below. 8 9 % #& % %4 2. Root Mean Square Error, $ ∑ (4 − 3 ) 2 =1 = $ 3. Mean relative error, (%) Most of the previous studies were carried out using selective type of wavelet attached with one wavelet for the same data point. Also the optimal level of decomposition in a particular type of wavelet is the difficulty in proper combination selection. Again the forecasting accuracy for higher lead time is not well documented so far. Keeping all this point of view, in this paper an attempt has been made to investigate the potential and applicability of Hybrid Model by combining Wavelet and ANN with objectives to address the above mentioned scenarios using time series data. Development of various combined models for selective input scenarios for Multistep Lead Time and their performance evaluation has also been carried out. = 1 $ $ ∑ 4 −3 4 =1 × 100 Where, X=observed values, Y=predicted values, N = total number of values, and x 5 4 4 The objectives of this paper are to examine how successfully Wavelet Transform have been used in hydrologic problem. The focus of this work for hydrologists in practicing field. In this study, Discrete Wavelet Transform and Neural Networks has been applied for multistep lead time predictions. Daily discharge data is collected for 20 years for the period from 1980 1999. Statistical analysis and Data Normalization of data has been done to analyze the pattern and the type of data. Out of total available data,2/3 of data set used for training and 1/3 of data set used for testing in MATLAB PACKAGE using ANN and Wavelet Tool. The data statistics for both training and testing are given below which contains minimum, maximum, mean, standard deviation (Sd) and skewness coefficient. It is obvious from the table that the extreme values of the available data are in the training set. When classifying the data into training and testing subsets, it is essential to check that the data represents the same statistical population. It was earlier observed that high skewness coefficient has a considerable negative effect on ANN performance. The table 1 shows the statistical behavior of the observed available time series flow data which reveals the large variation in data at the station Pandu. Prediction is made using 1 day, 2 days, 3 days and four days lead time. The Performance of ANN and Hybrid Wavelet ANN Model is analyzed by the performance indices like Coefficient of Efficiency (CE), Root Mean Squared Error (RMSE), and Mean Relative Error (MRE). * ' % 4 1. Coefficient of Efficiency, # 85 ' 67 & & 8 " :4 Artificial Neural Networks are mathematical inventions inspired by observations made in the biological systems. ANN has gained popularity among Hydrologist in recent decades due to its large array of application in the field of Engineering and research. The purpose of ANN is mapping function i.e., mapping an input space to an output space. ANN has excellent flexibility and high efficiency in dealing with nonlinear and noisy data in Hydrological modeling. Some of the advantages of using ANN Tool are Input Output mapping, Self adaptive, Real Time Operation, Fault Tolerance and Pattern Recognition. ANN is a massively parallel distributed processor made International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 PARESH CHANDRA DEKA, LATIFA HAQUE and ANIRUDDHA GOPAL BANHATTI up of simple processing units, which has a natural prosperity for strong experimental knowledge and making it available for use. A typical ANN consists of a number of nodes that are organized according to a particular arrangement. It consists of “Neurons” which are interconnected computational elements that are arranged in a number of layers which can be single or multiple. Each pair of neurons is linked and is associated with weights.ANN are trained by adjusting the values of these connection weights between network elements. The weighted inputs in each layer are processed from neurons in the previous layer and transmit its output to neurons in the next layer. A transfer function/activation function is used to convert a weighted function of input to get the output. Usually non linear sigmoidal activation functions are 2 * 9 % $== 9 9 = 2 87 4 The term wavelet means small wave. The smallness refers to the condition that the function is of finite length. The wave refers to the condition that it is oscillatory. The term mother implies that the functions used in the transformation process are derived from one main function, the mother wavelet. A mother wavelet that is continuously differentiable with compactly supported scaling function and high vanishing moments. 875 ' used as reported in the literature which was also adopted in this study. The inputs to the ANN model were normalized and kept within the range of 0.1 to 0.9. The learning rate and momentum coefficient are influential parameters which controls the convergence rate but to optimize them for best output .Here,both the parameters were kept with constant 0.4 and 0.6 respectively throughout the network structure for various number of hidden neurons. The basic structure of ANN is shown in figure 2 below. In this study,various ANN models were developed using various input combinations for multiple leadtime.The input combinations were consists of lagged data upto past four days.The output was kept as single flow variable for multiple leadtime. % # ;$ < 17520.11 11011.62 0.59 2432 61015 4 More, technically, a wavelet is a mathematical function used to divide a given function or continuous time signal into different scale components. The wavelet 6 6 # # ;$ < 18897.3 10306.13 0.64 5539 54100 ;$ < 17904.94 10836.02 0.59 2432 61015 $$ transform of a signal is capable of providing time and frequency information simultaneously, hence providing a time frequency representation of the signal. Usually one can assign a frequency range to each scale component. Each scale component can then be studied with a resolution that matches its scale. To do this, the data series is broken down by the transformation into its “wavelets”, that are “scaled” and “shifted” version of the mother wavelet (Nason and Von Sachs, 1999). A Wavelet analysis is a set of building blocks to build or represent a signal or function. Wavelet analysis has become a common tool for analyzing localized variations of power within a time series. Wavelet analysis gives information both time and frequency International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 Discrete Wavelet Ann Approach in Time Series Flow Forecasting A Case Study of Brahmaputra River 6 domain of the signal. Wavelet transformed data of original time series improves the ability of a predicting model by capturing useful information on various resolution levels (Kim and Valdes 2003).The signal and corresponding wavelet is shown in figure 3 for better understanding of concept. & 1 ' ;$ <4 The Continuous Wavelet Transform (CWT) of a signal x(t) is defined as follows: CWTxψ (τ,s) = (1) Where‘s’ is the scale parameter, ‘Ƭ’ is the translation parameter and the ‘*’ denote the complex conjugate. Here, the concept of frequency is replaced by that of scale, determined by the factor ‘s’ ψ (2) is the transforming function and it is called mother wavelet. ' ; <4 The Discrete Wavelet Transform (DWT) allows one to reduce the computation time and it is considerably simpler to implement than CWT. High pass and low pass filters of different cutoff frequencies are used to analyze the signal separating the signal at different scales. The signal is passed through a series of high pass filters to analyze the high frequencies, and it is passed through a series of low pass filters to analyze the low frequencies. y[n] = (x*g) [n] = ylow[n] = yhigh[n] = ..(4) ..(5) The time series after wavelet decomposition allows one to have a look at the signal frequency at different scales. The discrete wavelet transform allows reducing computation time than CWT. High pass and low pass filters of different cutoff frequencies are used to separate the signal at different scales. The scale is changed by upscaling and downscaling operations (Cannas et.al, 2005). 877$ 878 The DWT of a signal x is calculated by passing it through a series of filters. First the samples are passed through a low pass filter with impulse response g resulting in a convolution of the two. (3) 0 / The time series is decomposed into one containing its trend (the approximation) and one containing the high frequencies and the fast events (the detail). The filtering procedure is repeated every time some portion of the signal corresponding to some frequencies is removed and the outputs giving the detail coefficients (from the high pass filter) and approximation coefficients (from the low pass) are obtained depending on the chosen decomposition level. It is important that the two filters are related to each other and they are known as a quadrature mirror filter. Figure 4 shows the low scale and high scale concept of signal and wavelet. The resolution of the signal, which is a measure of the amount of detail information in the signal, is changed by the filtering operations, and the scale is changed by upsampling and downsampling (subsampling) operations. Subsampling a signal corresponds to reducing the sampling rate, or removing some of the samples of the signal. Upsampling a signal corresponds to increasing the sampling rate of a signal by adding new samples to the signal. The decomposition process can be iterated, with successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution components. This is called the wavelet decomposition tree (Figure 5). "& & International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 PARESH CHANDRA DEKA, LATIFA HAQUE and ANIRUDDHA GOPAL BANHATTI 1 Most of the wavelets used in discrete wavelet transform are fractal in nature. They are expressed in terms of a recurrence relation so that to see them we must do several iterations. Wavelets are mathematical functions that were developed by scientists working in several different fields for the purpose of sorting data by frequency. Translated data can then be sorted at a resolution which matches its scale. Studying data at different levels allows for the development of a more complete picture. Both small features and large features are discernable because they are studied separately. Unlike the discrete cosine transform, the wavelet transform is not Fourier based and therefore wavelets do a better job of handling discontinuities in data.The Different Wavelets used are Haar, Daubechies wavelets, Coiflet which were described briefly in the following section4 3 4 The Daubechies wavelets are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support. With each wavelet type of this class, there is a scaling function (also called father wavelet) which generates an orthogonal multiresolution analysis. The Daubechies wavelets have surprising features such as intimate connections with the theory of fractals. Daubechies wavelets are widely used in solving a broad range of problems, e.g. self similarity properties of a signal or fractal problems, signal discontinuities, etc. The Daubechies wavelets are not defined in terms of the resulting scaling and wavelet functions; in fact, they are not possible to write down in closed form. This wavelet type has balanced frequency responses but non linear phase responses. Daubechies wavelets use overlapping windows, so the high frequency coefficient spectrum reflects all high 6 > % frequency changes. Therefore Daubechies wavelets are useful in compression and noise removal of audio signal processing. , 4 The Haar wavelet operates on data by calculating the sums and differences of adjacent elements. The Haar wavelet operates first on adjacent horizontal elements and then on adjacent vertical elements. After each transform is performed the size of the square which contains the most important information is reduced by a factor of 4. The next step in the image compression process is quantization. In Haar wavelet, the basic functions are scaled and translated versions of a "mother wavelet” ψ(t). The Haar wavelet transform has a number of advantages such as it is conceptually simple, fast, memory efficient, since it can be calculated in place without a temporary Array and it is exactly reversible without the edge effects that are a problem with other. $ ' 4 Coiflets are discrete wavelets designed by Ingrid Daubechies, at the request of Ronald Coifman, to have scaling functions with vanishing moments. The wavelet is near symmetric, their wavelet functions have N / 3 vanishing moments and scaling functions N / 3 − 1, and has been used in many applications using Calderón Zygmund Operators. Both the scaling function (low pass filter) and the wavelet function (High Pass Filter) must be normalized by a factor 1/ .The wavelet coefficients are derived by reversing the order of the scaling function coefficients and then reversing the sign of every second one.The various type of wavelet used in the study are shown in figure 6. International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 Discrete Wavelet Ann Approach in Time Series Flow Forecasting A Case Study of Brahmaputra River 6 %# ,&3 % " :4 The hybrid model consists of a three layer feed forward perceptron structure so that the first layer is the wavelet neurons unit with the inputs runoff time series sub signals obtained via a wavelet transform. In the proposed approach, the runoff signals are firstly decomposed into sub signals with different scales .i.e. a large scale sub signal and several small scale sub signals in order to obtain temporal characteristics of the input time series. For a given time series, the time series corresponding to a(t)(i.e. Qa(t)) is approximation sub signal(large scale) of the original signal and jth detailed sub signal(small scale) is identified by j(i.e. Qj(t)) where j are decomposition levels of the runoff(Q(t)) time series. The wavelet decomposition of non stationary time series into different scales provides an interpretation of the series structure and extracts the significant information about its history, using few coefficients. % $ Lag time flow data # These reasons make this technique attractive to researchers for time series analysis of non stationary signals (Nason and Von Sachs, 1999). This study deals with some irregular mother wavelets such as Haar,db 2(Daubechies wavelet of order2), and coif1 which are illustrated in figure 6.The network architecture that yielded the best results in terms of determination coefficient and root mean square error on the training and verifying steps may be determined through trial and error process. The time series data before going through the network are usually normalized between 0 and 1 as sigmoidal activation function was used in the study. ) % 4 In the first stage, a multilayer perceptron (MLP) feed forward ANN model with raw data was used to model the daily flow at multistep lead time. Here, testing results are shown in table 2. & 2 23 3 1 0 ' % 1 day ahead 2 days ahead 3 days ahead 4 days ahead Each MLP was trained with 2 to 15 hidden neurons in a single hidden layer and scheme of Levenberg Marquardt back propagation was used as the training algorithm. No significant improvements in the model performance were observed when the number of hidden neurons was increased from a threshold. The training was stopped at the stage where the error in the validation data set begins to rise. Hence, overfitting the training data is avoided and the model generalization capacity was kept intact. At this stage, model efficiency [CE] reveals unsatisfactory performance. This may be 12 13 14 13 % )9 + ; 8? < $+ 9)+ @ 1584 2213 2691 3460 0.87 0.85 0.83 0.78 4.34 6.39 8.16 8.62 due to significant fluctuations of the data around the mean value. In the second step, preprocessed data were fed to the ANN model to improve the model accuracy using the discrete wavelet transform. Here, the influence of used mother wavelet type as well as decomposition level on the model efficiency has been investigated. The time series were decomposed to various levels for three kinds of wavelet transforms such as Haar, db 2 and Coif1 .The results of this study are presented in table 3 for all the cases. International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 6> PARESH CHANDRA DEKA, LATIFA HAQUE and ANIRUDDHA GOPAL BANHATTI % & 9 1 $ 0 ;) 9 . % & 1 day ahead 2day ahead 3 day ahead 4 day ahead 5 899.88 503.49 8 >> 8>> >6 867.43 726.87 869.88 860.23 8 876.09 >68 1135.47 DB 2 COIF1 HAAR DB 2 COIF1 HAAR DB 2 COIF1 HAAR DB 2 COIF1 HAAR 7 853.85 895.45 > > 5 861.04 907.09 >77 86 896.28 870.52 8 5 6 1062.21 914.01 >7 68 For multilevel sub signals, which are used as input neurons, the attached weights by ANN will be different at various decomposition levels. Usually higher weights are applied to the worthy level of the data or signals. The validation time series of level 6 decomposition by db 2 wavelet are shown in figure 6 after reconstructed via trained ANN. Analyzing the table 3 results, it is clearly observed that in validation phase, level 1,2,3,4,5 and 6 decomposition give relatively similar performance but difficult to draw a conclusive inference. Increasing the lead time, model efficiency slightly decreased due to higher level lead to large number of parameters in complex non linearity for ANN. Each parameters produces error in forecasting data and net errors leads to decreasing performance. This is not too much 2 9 % ANN WLNN & NON LINEAR HYBRID 7 5% & % 1584.42 309.88 The combined model performing better in lead time than single ANN model as observed from the table 4.Figure 7 below shows how the original signal is reconstructed and the formation of Daubacheis wavelet tree. Also, various decomposition levels of db 2 is shown in figure 8 with details and approximations. (Here x axis is time in days, y axis is flow in cumecs) Where s is full signal(flow);a1,a2,a3,a4,a5,a6 are approximations;d1,d2,d3,d4,d5,d6 are details The testing performance results of MRE for both ANN and combined model are also shown in figure 9 to visualise the error variations for different leadtime 8 861.74 55 527.13 883.14 956.50 >6 861.13 843.85 890.91 914.09 928.27 > 5 8 +< 906.52 891.62 5 55 >58 934.71 408.16 1406.98 866.58 >6 5 8> 8 570.24 863.26 871.53 505.62 867.02 895.75 >5 5 8 5 466.56 862.91 886.96 881.81 > 5 6 880.56 87 494.98 895.75 938.74 >> >> 895.18 845.93 > 8 457.04 65 7 836.78 significant in all the levels which may be considered as optimal decomposition level for the data set. The decomposition level more than 6 leads to low efficiency as not included in the result table. As observed in the data, there are sharp upward and downward jumps in the time series because of several factors such as rainfall, landslides, hydraulic failure. The structure of DB 2 wavelet, which is similar to signal, could capture the signal features such as peaks can be able to deliver high efficiency. This phenomenon may guide the selection of wavelet type. To evaluate the ability of proposed model, various comparisons have been made as presented in table 4. 9 0 % # )9 +; < 7% & % 8% & % 2213 2691 408.16 441.52 % & % 3460 461.92 forecast. It can be confirmed that WLNN model outperformed ANN model for all the leadtime forecast considered in the study. The performance of hybrid model for high peak flow as well as low flow are presented for one day ahead forecasting in figure 10 for the year 1999.The proposed model output is in close agreement with observed flow .The ANN model also performs in a similar way with hybrid model for one day ahead flow forecasting. But for the higher lead time such as 4th day lead time, hybrid model performance is observed better than ANN model results as shown in figure 11. International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 6>5 Discrete Wavelet Ann Approach in Time Series Flow Forecasting A Case Study of Brahmaputra River & 1 % International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 6>7 PARESH CHANDRA DEKA, LATIFA HAQUE and ANIRUDDHA GOPAL BANHATTI , 6" & / 6" ; : # # < , / 0 = > ) : 8 International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 : 8 6>8 Discrete Wavelet Ann Approach in Time Series Flow Forecasting A Case Study of Brahmaputra River 7 9 efficiency in validation set because of the time series may have different long, intermediate and short trends. The hybrid model involved in effective training of time series data but also considers the influence of each sub signal by magnifying its weights relatively (Noorani et.al, 2009). From the results, it is observed that the accuracy for hybrid model is improved and the better estimation of peaks reflects in the figure 10 and figure 11.It is to be mentioned that capturing the flood peaks along with the transition is very important in any river flood modeling. The major difference of these two methods is related to training procedure. The process leads to decrease model 7 0 % & < # 6# <???8 International Journal of Earth Sciences and Engineering ISSN 0974 5904, Vol. 05, No. 04, August 2012, pp. 673 685 PARESH CHANDRA DEKA, LATIFA HAQUE and ANIRUDDHA GOPAL BANHATTI 7 6 $ 4 In this study, wavelet transform was used to decompose the runoff time series of Brahmaputra river basin so as to provide multiscale features of data or signal. These decomposed signals (sub signals) were used as input to ANN model to forecast runoff for multistep lead time. This proposed model has shown much improvement in forecasting than single ANN model which used undecomposed data as inputs. The proposed model has shown the capacity to simulate non linear behavior of the phenomenon more accurately than single ANN model. Analyzing the data preprocessing using wavelet transformation showed that the best results were obtained with DWT, at level 2 3 to predict runoff values as output. For multiple lead time forecasting, the proposed model outperformed single ANN model as lead time increases. The trend, fluctuations, seasonality, jumps components in the time series understood in a better way by the model due to the wavelet transformation. Overall, these results reveal the potentiality of combining data clustering and use of DWT in runoff forecasting. Further, the effect of wavelet type on model performance was investigated using three different types of wavelet transforms. The results show the high quality performance of db 2 in comparing with others. Normally, runoff time series peaks which is similar to single peaked db 2 wavelet provides better > # @ & 6# 6> <???8 approximation of sharp events exists in daily discharge records. Also, the increase in decomposition level may not be efficient in forecasting ability. Hence; an optimum level may be selected considering length of the data. In order to complete current study, it is suggested to use present strategy for other stations in the basin using weekly and monthly flow data as different signal characteristics and also including other time series variables like rainfall, temperature, evapotranspiration. Due to wavelet capabilities, the trend of basin hydrological behavior can be analyzed more effectively for which long term quality and continuous data will be required. : " %# 4 The authors greatly acknowledged the Water resources deptt. Govt.of Assam, India for providing necessary data for the analysis. Authors also thanked the deptt. 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