Artificial neural network simulation for prediction of suspended sediment concentration in the River Ramganga, Ganges Basin, India

Author’s Accepted Manuscript Artificial neural network simulation for prediction of suspended sediment concentration in the River Ramganga, Ganges Basin, India Mohd Yawar Ali Khan, Fuqiang Tian, Faisal Hasan, Govind Joseph Chakrapani www.elsevier.com/locate/ijsrc

PII: DOI: Reference:

S1001-6279(17)30323-2 https://doi.org/10.1016/j.ijsrc.2018.09.001 IJSRC194

To appear in: International Journal of Sediment Research Received date: 8 October 2017 Revised date: 21 June 2018 Accepted date: 18 September 2018 Cite this article as: Mohd Yawar Ali Khan, Fuqiang Tian, Faisal Hasan and Govind Joseph Chakrapani, Artificial neural network simulation for prediction of suspended sediment concentration in the River Ramganga, Ganges Basin, India, International Journal of Sediment Research, https://doi.org/10.1016/j.ijsrc.2018.09.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Artificial neural network simulation for prediction of suspended sediment concentration in the River Ramganga, Ganges Basin, India Artificial neural network simulation for prediction of suspended sediment concentration in the River Ramganga, Ganges Basin, India Mohd Yawar Ali Khana, c, *, Fuqiang Tiana, Faisal Hasanb, Govind Joseph Chakrapanic a

Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China

b

Department of Mechanical Engineering, Aligarh Muslim University, Aligarh 202002, India

c

Department of Earth Sciences, Indian Institute of Technology Roorkee, Roorkee 247667, India

Mohd Yawar Ali Khan (Corresponding Author) Postdoctoral Research Fellow Institute of Hydrology and Water Resources Department of Hydraulic Engineering, School of Civil Engineering Tsinghua University, Beijing 100084, China Email: [email protected]

Fuqiang Tian Associate Professor, Vice Director, Institute of Hydrology and Water Resources, Department of Hydraulic Engineering, School of Civil Engineering Tsinghua University, Beijing 100084, China Email: [email protected]

Faisal Hasan Associate Professor, Department of Mechanical Engineering, Z.H. College of Engineering and Technology, Aligarh Muslim University, Aligarh – 202002, India Email: [email protected] Govind Joseph Chakrapani Professor, Department of Earth Sciences, Indian Institute of Technology, 1

Roorkee – 247667, India Email: [email protected]

Abstract The relation between the water discharge (Q) and suspended sediment concentration (SSC) of the River Ramganga at Bareilly, Uttar Pradesh, in the Himalayas, has been modeled using Artificial Neural Networks (ANNs). The current study validates the practical capability and usefulness of this tool for simulating complex nonlinear, real world, river system processes in the Himalayan scenario. The modeling approach is based on the time series data collected from January to December (2008-2010) for Q and SSC. Three ANNs (T1-T3) with different network configurations have been developed and trained using the Levenberg Marquardt Back Propagation Algorithm in the Matlab routines. Networks were optimized using the enumeration technique, and, finally, the best network is used to predict the SSC values for the year 2011. The values thus obtained through the ANN model are compared with the observed values of SSC. The coefficient of determination (R2), for the optimal network was found to be 0.99. The study not only provides insight into ANN modeling in the Himalayan river scenario, but it also focuses on the importance of understanding a river basin and the factors that affect the SSC, before attempting to model it. Despite the temporal variations in the study area, it is possible to model and successfully predict the SSC values with very simplistic ANN models. Keywords: ANN; Water discharge; Suspended sediment concentration prediction; Ramganga River; Himalayas

2

1. Introduction The transport mechanism of sediment in a river system is a complex, nonlinear process which involves the interplay of geological and hydrological parameters varying in space and time. Knowledge of sediment transport along with estimation and prediction of sediment concentration has implications in managing water resources, land use, territorial hazards, and damage to engineering structures resulting from the morphological evolution of the river bed. However, no direct or indirect empirical model developed for evaluating this process has gained universal acceptance (Abrahart et al., 2008) and there is a growing need for development of minimalist experiential approaches that are responsive to catchment characteristics, climatic factors, and antecedent conditions. The development of the sediment rating curve, which is by far the most conventional method of estimation of sediment concentration, is seen to result in under prediction (Asselman, 2000; Walling & Webb, 1988). Several mathematical corrections have been applied to the basic linear regression equations to overcome this problem and nonlinear regression equations have also been developed (Crowder et al., 2007; Holtschlag, 2001). Many studies have indicated the potential advantage of Artificial Neural Networks (ANNs) in sediment modeling (Abrahart & White, 2001; Cigizoglu, 2001a, 2001b, 2004; Cigizoglu & Kisi, 2006; Himanshu et al., 2017a, 2017b; Jain, 2001; Kaur et al., 2003; Kisi, 2005; Nagy et al., 2002; Sarangi & Bhattacharya, 2005; Yadav et al., 2016a, 2016b, 2018). The technique of using ANNs to model discharge values has been recently applied by Tsakiri et al. (2014) for Schoharie Creek, New York, U.S. Further, predictions based on ANN models forcomputing the concentration of suspended sediment are seen in studies by Wang et al. (2008), Rajaee et al. (2009), and others. In the past, studies have tackled river flow modeling using ANN too (Kisi, 2004). Modeling of river discharge (Q) using ANN has also been attempted earlier for the Tasik Chini catchment in 3

Malaysia (Jaafar et al., 2010). ANN modeling for flow forecasting has also been undertaken in earlier research by Dawson et al. (2002) for the Yangtze River in China. There is a consistent issue of the necessity of point by point geographical and morphometric information in the use of routine models, while it is realized that a river network covers an unlimited territory composed of numerous watersheds and sub-basins, where an entire arrangement of data may not be accessible. In such a case, ANN presents a viable, easy to use, method for speedy simulations and predictions with low data necessity and without altogether sacrificing model accuracy (Li & Gu, 2003). Understanding the Suspended Sediment Concentration (SSC)-Q relation in the Himalayan context with an ANN technique can be quite interesting and challenging. Here, the rivers carry large sediment loads draining through a great range of relief and climate, active tectonic zones, and easily erodible rocks (Hasnain & Thayyen, 1999). In the past, ANNs have generally been applied in modeling geo-hydrological variables using continuous time series data of long duration. In the current study, an effort has been made to predict variation in the SSC with Q using ANNs for the Ramganga River (Fig. 1), Ganges Basin, based on the data obtained from the Central Water Commission (CWC), Government of India. The problem has high significance as till now no study on sediment prediction for Ramganga River has been done. Fig. 1. Map of the Ramganga River basin.

2. Artificial Neural Networks (ANNs): Overview An ANN is a data driven, self-adaptive, flexible numerical structure with an interlinked assembly of simple processing units known as artificial neurons, which are arranged in an architecture inspired by the human brain (ASCE, 2000a, 2000b). An ANN predicts the output of a process by training with a set of known inputs and outputs whereby it ‘learns’ and extracts the relation between them. It then tries to bring the predicted output closer to the observed output by an 4

internal network adjustment. Learning algorithms, which are mathematical versions of simple “If-then” ideas, are used, the most commonly used algorithm being the Feed Forward Back Propagation (FFBP) algorithm, which has been used in the current study too. Physical understanding into the issue being examined can prompt better selection of input variables for appropriate mapping. This selection will help in staying away from loss of data that may come about if key input variables are overlooked and furthermore forestall incorporation of wrong input sources that have a tendency to confound the training procedure (Kumar, 2004). The working and internal structure of an ANN has very often been discussed in detail (Hassoun, 1995; Hertz et al., 1991; Tettamanzi & Tomassini, 2001). In the areas of hydrology and water resources, a complete review on the application of ANNs is provided by the ASCE Task Committee in “Application of ANNs in Hydrology” (ASCE, 2000a, 2000b), Maier and Dandy (2000), and Dawson and Wilby (2001). In the last two decades, ANNs have been most commonly applied for modeling the rainfall-runoff processes (Chang & Chen, 2001; Gautam et al., 2000; Hall & Minns, 1993; Hsu et al., 1995; Minns & Hall, 1996; Rajurkar et al., 2004; Reddy, 2003; Sajikumar & Thandaveswara, 1999; Shamseldin, 1997; Shoaib et al., 2014; Smith & Eli, 1995; Sudheer, 2005; Tayyab et al., 2017; Tokar & Johnson, 1999; Wu & Chau, 2011; Zhang & Govindaraju, 2003). The current surge of enthusiasm for the estimation of SSC is also related to the present necessity for effective and efficient models that can be utilized to assess the potential effect of ecological change: modeling past, present, and future sediment development is an imperative segment in such endeavors (Abrahart et al., 2008). Rai and Mathur (2008) developed a FFBP algorithm with Gradient Descent and Bayesian regularization automation for calculation of incident based temporal variation of sediment yield. They compared the results with a linear transfer function 5

model and found ANN to perform better in calculation of runoff sedimentographs and hydrographs. Firat and Güngör (2009) used the Adaptive Neuro Fuzzy Inference System (ANFIS) approach to construct a monthly sediment forecasting system in the Great Menderes Basin in Turkey. They compared their results with ANNs and Multilayer Perceptron approaches and found the ANFIS to be more reliable and accurate. Kisi (2010) has applied the Neuro Wavelet technique by combining an ANN and a discrete wavelet transform for modeling the daily SSC-Q relation in the Tongue River in Montana. An increase in estimation accuracy was found with this technique. Sinnakaudan et al. (2006) have developed a new total bed material load equation that is applicable for rivers in Malaysia using multiple linear regression analysis. In a recent study by Boukhrissa et al. (2013),the performance of rating curves and ANN have been compared for sediment load prediction in the Kebir catchment of Algeria. Such a study would help to understand and estimate reservoir sedimentation. Lagos-Avid and Bonilla (2017) developed a model to predict the particle size distribution (PSD) of eroded soil using an ANN. Ghose (2018) predicted daily sediment yield during monsoons in small watersheds of southeast India using FFBP and the radial basis neural network (RBNN) algorithms of ANN. An ANN is formed by a group of simple processing units called neurons, which bind together to form a complex structure. This is a replication of the processing and transmission of information in humans. The complete account of the back propagation algorithm and subsequent development of the working equation has been summarized by Schmidhuber (2014). In Fig.2 a typical ANN topology is shown, which consists of an input layer, an output layer, and a few hidden layers which serve as processing layers in between the other two layers. These algorithms involve a learning stage, which is established by a gradient search, reaching optimality through the lowest sum of squares. The learning happens through analysis of input-output pairs of data 6

from the training dataset. In the back propagation algorithm, the output is first calculated using the input data, matched with the target values and the associated errors are fed back into the network to update the algorithm. The optimal network configuration develops by adjusting the number of hidden layers and the neurons associated with them. A general enumeration technique may be applied to decide the optimal number of hidden layers to arrive at the appropriate network topology. Fig. 2. The structure of the artificial neural networks.

The following notation is used to explain the back-propagation algorithm for a single neuron: E

squared error

t

target output

y

actual output

n

number of input units to a neuron

xi

ith input example/data-set to a neuron

net

weighted sum to a neuron

wi

ith weight to a neuron

winew

ith updated or new weight to a neuron

b = x0w0

bias value to a network layer

φ(z)

activation function

ρ

learning rate.

The weighted sum on any neuron is calculated as n

net   wi xi i 0

where w0 x0 represents the bias value to the layer. 7

(1)

The activation function is used to calculate the real output of any neuron as y = φ (net)

(2)

In general, any nonlinear, differentiable activation function is used. A commonly used activation function is the logistic function, and this function has been used for the current study:

 ( z) 

1 1  e z

(3)

The gradient descent method is used by the back-propagation algorithm with the purpose of minimizing the error, which is computed as

1 E  (t  y) 2 2 The derivative,

(4)

E , which characterizes the change in the error with respect to weights is wi

calculated, this is done for the purpose to minimize the error and can be done by applying the chain rule as

E dE dy net  wi dy dnet wi where

(5)

dy dE stands for the change in the error with respect to the output; stands for the output dnet dy

change with respect to the weighted sum; and

net stands for change in the weighted sum values wi

with respect to change in weights. The values of these derivatives can be calculated as

net  xi (6) wi

8

Since, y 



1 1  e net

(7)

dy d  1      y y  1 (8) dnet dnet 1  e net 

dE d  1    t  y  2   t  y dy dy  2 

(9)

On substituting these values in Eq. 5 the following is obtained:

E dE dy net   t  y  y y  1xi wi dy dnet wi

(10)

In the current study a dissimilar activation function is applied, and its derivative would replace the y(y-1) term. An appropriate value for the step size or learning rate, ρ, must be used in the gradient descent technique while updating the weight, wi. The step size parameter, ρ, is important as lower values can cause a delayed convergence, whereas higher values can lead to incorrect convergence. After learning is completed for the current iteration, the change in weight Δwi is computed as

wi   

wi

new

E    y  t  ( z )' xi wi

(11)

 wi  wi

(12)

The process of updating these weights during the training phase of the ANN continues until the algorithm arrives at a predefined stoppage criterion. This stoppage criterion may either be a set number of epochs or a threshold error value.

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3. Study area The Ramganga River originates from the Dudhatali Range at an elevation of about 2926 m in the Gairsain village of the Chamoli district in Uttarakhand state of India. In the Himalayan region, it flows a distance of about 158 km before it enters the Ganges Flood Plains and flows about another 484 km before its confluence with the Ganges River at the district Farrukhabad of Uttar Pradesh (Daityari & Khan, 2017; Khan et al., 2016b, 2016d, 2017; Khan & Tian, 2018). The Ramganga basin has a catchment area of about 22,685 km2 (Khan, 2019), which is about 8 percent of the whole catchment area of the Ganges River basin (Ray, 1998). 3.1. Physiography and relief Ramganga River originates in the Kumaon Himalayas in Uttarakhand. In the middle and outer Himalayas, the shape of the river is horseshoe like as it flows through the mountain range, a part of which also comprises of the Shivalik Hills. Steep hills and deep and narrow valleys are common in the catchment area of the river (CWC, 2012). 3.2. Climatic situation The catchment area of the river undergoes three distinct seasons over the year–summer, monsoon, and winter. The season of winter is dominant from November, following a short spell of autumn from mid-October, a period characterized by a sudden, drastic drop in temperature. Figure

3

(a)

shows

the

temporal

temperature

variations

in

the

study

(www.indiawaterportal.org). Fig. 3. (a) Average monthly temperature and (b) Average monthly rainfall at Bareilly (www.indiawaterportal.org).

3.3. Rainfall

10

area

Figure 3 (b) shows the onset of the monsoon, which starts by mid-June and is prevalent up to September or even up to mid-October. In the current study, it is seen that May/June to October/November encompasses the monsoon season, and, therefore, define the pre-Monsoon and post-Monsoon periods, respectively. Infrequent showers are observed during the months of winter (www.indiawaterportal.org). The catchment area receives about 1000 mm of rainfall annually on average (CWC, 2012). 3.4. Drainage In general, the observed drainage in the catchment area follows a sub-dendritic pattern and is relief excessive. The catchment area also is categorized by a number of winter and spring snowfalls, especiallyin the high mountains, which feed the river all year long, making the river perennial. Forests cover about half of the catchment area of the river, followed by about 30 percent of the area under terrace farming.The area remaining ismostly composed of waste land and grazing pastures (CWC, 2012). The river network of the Ramganga River before its confluence with the Ganges River and its intricate features, including the stream orders are shown in Fig.4. This map of the catchment area of the river was prepared using the Shuttle Radar Topography Mission-Digital Elevation Model (SRTM-DEM) 30 m resolution data in the software Arc GIS with the help of the spatial analyst tool, and it also shows the ordering of the streams by the Strahler (1952) method. The method stated by Strahler (1952) says that the order of a stream increases only when streams of the same order meet, which leads to a conclusion that the intersection of two different order streams would result in the order of the higher order stream, rather than create a stream with an order higher than the constituent streams. Fig. 4. Drainage map of the Ramganga River basin (Strahler’s numbers are shown). 11

3.5. Geology of Ramganga River The catchment area of the river coincides with two major lithotectonic zones - the SubHimalayas and Lesser Himalayas. The Sub-Himalayasare composed of sandstone, siltstone, clays, and boulders, which characterize molasse sediment of mid-Miocene to Pleistocene age. Moving on to the Lesser Himalayas, they consist of an unfossiliferous sequence of low- to highgrade meta-sediment of Paleozoic to Mesozoic age. In the catchment area of the river, the most important lithologies can be listed down as the following: (1) calcareous shales and siltstones (Blaini/Infrakrol formations); (2) quartzites (Nagthat and Sandra formations); (3) low-grade metamorphics (phyllites, slates, and schists); (4) limestones (Krol and Deoband formations); and (5) high-grade metamorphics (granite gneisses) (Gupta & Joshi, 1990). The river travels about 158 km in the Himalayas before emerging out into the GangesFlood plains, characterized mainly by alluvial soils. A foreland basin, linked to theextension of the Himalaya orogenic belt is observed. The Quaternary lithostratigraphic sequence established in the ascending order comprises (1) Varanasi Older Alluvium with two facies, i.e. sandy facies and silt clay facies, (2) Ganga/Ramganga Terrace Alluvium, and (3) Ganga/Ramganga Recent Alluvium, the latter two constitute the Newer Alluvium (Khan & Rawat, 1990). 3.6. Factors affecting sediment load The main controlling factors for sediment load (which is the product of discharge and sediment concentration) are relief, tectonic disturbances, lithology, and rainfall (Chakrapani, 2005; Khan et al., 2016c; Khan & Chakrapani, 2016; Panwar et al., 2016). The Himalaya region, in general, is prone to violent crustal movements responsible for high erosion rates (Valdiya, 1998). The steep channel gradients result in higher hydraulic efficiency, higher stream energy per unit area, and greater sediment transport competence (Kale, 2003). Tectonics are active in the area owing 12

to the presence of deep seated weak zones and high seismicity (Seismic zone IV). Landslides, caused due to high magnitude rainfall events not only add a tremendous amount of sediment to the river, but also block the river with debris resulting in massive floods when these blockages fail. The river drains through easily erodible lithologies like quartzites, dolomitic limestones, and metabasic formations. Rainfall in the monsoon season leads to huge water flows, which account for a considerable amount of the annual water flow and subsequently high sediment discharges. Also the summer months experience more supraglacial melting, which increases discharge and the competence of the river resulting in greater sediment transport. The contribution of humans to erratic changes in sediment discharge can be seen in the form of haphazard developmental activities like unplanned construction, mountain-toe cutting for road construction, mining activities, and deforestation. All these factors account for the temporal and spatial changes in concentration of sediment in the Ramganga River basin. 4. Methodology 4.1. Data description and analysis In the current study, high frequency (daily) time series data for SSC in mg/L (output) and Q inm3/s(input) during the period of January 2008 to December 2010have been used for modeling. Daily Q and SSC data covering the entire period under study were made available by CWC, Government of India. Basic statistical analysis of the data was done to bring out the internal structure of the data, such as trends, variation, and autocorrelation. Statistical parameters like mean, median, mode, standard deviation, and skewness have been used to study the data shape, symmetry, and dispersion (Table 1). The following three different networks were developed based on the available data sets:

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Network T1: St= f(Qt); where the Q as Qt and SSC as St from only the last year (2010) were used to derive the ANN model. Network T2: St,St-1= f(Qt,Qt-1); where the Q as Qt, Qt-1and SSC as St, St-1 from only the last two years (2009 and 2010) were used to derive the ANN model. Network T3: St, St-1,St-2 = f(Qt,Qt-1, Qt-2); where the Q as Qt, Qt-1, Qt-2 and SSC as St, St-1, St-2from the last three years (2008, 2009, and 2010) were used to derive the ANN model. Table 1 Descriptive statistics of the data used in the study.

Statistical parameters Mean Median Mode Standard deviation Range Maximum Minimum Skewness Kurtosis

Network T1 Based on just last year’s data (2010) 420 55066 57 281 56 271 1014 188127 8493 1831610 8497 1831619 4 9 5 6 27 44

Network T2 Based on last two year’s data (2009-2010) 270 31721 64 624 56 271 746 136382 8493 1831610 8497 1831619 4 9 6 8 53 87

Network T3 Based on last three year’s data (2008-2010) 261 29802 71 869 56 271 642 115901 8493 1831610 8497 1831619 4 9 7 9 65 113

The high separation among the mean, median, and mode in all cases suggests that the data are not normally distributed. The values of the standard deviation are high for both variables, connoting that the data are widely scattered and not based on the mean. The value of the skewness for both variable simplies that the data are skewed to the right of the mean and nonsymmetrical. The values of the kurtosis for all the data are more than three, proposing leptokurtic or level dispersion where the majority of values are not focused to the mean. Pre-analysis of the data clearly shows that there is a direct relation between SSC and Q (Fig. 5). Thus, the input used in ANN modeling is just the Q values rather than some time domain data as has been done by some researchers in the past (Khan et al., 2016a). 14

Fig. 5. Plot showing the relation between SSC and Q in the Ramganga River at Bareilly (note: the normalization procedure is defined by Eq.13).

4.2. Networks development As is apparent from Fig. 5 there is an inherent style in the time series data of the river flow, notwithstanding the uncertainty. Moreover, an autocorrelated time series is predictable, probabilistically, because the future values depend on current and past values. Exploiting this fact, three ANNs{(Qt);(Qt,Qt-1);(Qt, Qt-1, Qt-2)} were developed using the ANN application in MATLAB (R2013a) to model the daily Q-SSC relation at Bareilly in the Ramganga River basin. ANN networks with varying numbers of hidden layer neurons were trained with one year, two years, and three years. Various networks with one input layer, one hidden layer and one output layer were tested. An enumeration technique is applied to determine the optimum number of hidden layers neurons. The Levenberg-Marquardt Back Propagation Algorithm using a nonlinear log-sigmoidal transfer function in the hidden layer and a pure linear function in the output layer was applied. The normalization of the data is important so that the range of the input for each variable should lie in between 0and 1. The procedure of normalization was carried out after collecting the data of each variable viz, SSC and Q by using the following equation:

X norm 

X i  X min X max  X min

(13)

where Xmin is the minimum value of the variable; Xnorm is the normalized value of the observed variable, Xi; and Xmax is the maximum value of the variable. Training and validation sets were selected by the ANN tool box itself. High R2 values on the order 0.9 and above were obtained which ensures that proper training has been done (Table 2).

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Table 2 Networks characteristic and performance (note: R2 is the coefficient of determination and MSE is the mean square error). Network T1 St+1= f(Qt) (2010) Network R2 MSE topology 1-1-1 0.9832 0.00105

Network T2 St+1= f(Qt, Qt-1) (2009-2010) Network R2 MSE topology 1-1-1 0.9657 0.00094

Network T3 St+1 = f(Qt, Qt-1, Qt-2) (2008-2010) Network R2 MSE topology 1-1-1 0.9801 0.00819

1-2-1

0.9961

0.00045

1-2-1

0.9893

0.00047

1-2-1

0.5412

0.00792

1-3-1

0.996

0.00049

1-3-1

0.9935

0.00077

1-3-1

0.8468

0.00152

1-4-1

0.9986

0.00049

1-4-1

0.9834

0.00054

1-4-1

0.979

0.00047

1-5-1

0.9888

0.00117

1-5-1

0.9946

0.00043

1-5-1

0.851

0.00179

1-6-1

0.9983

0.00043

1-6-1

0.9775

0.00101

1-6-1

0.9864

0.00044

1-7-1

0.9974

0.00063

1-7-1

0.9908

0.00083

1-7-1

0.9013

0.00785

1-8-1

0.9985

0.0004

1-8-1

0.9685

0.00062

1-8-1

0.9496

0.00082

1-9-1

0.9931

0.00049

1-9-1

0.9399

0.00091

1-9-1

0.9081

0.00402

1-10-1

0.9982

0.00836

1-10-1

0.9851

0.00046

1-10-1

0.9816

0.00046

After training, the network was presented with the Q value data for the year 2011 and the SSC values so obtained were compared with the observed SSC values. The percentage of data used in the training and testing were 75% and 25%, respectively. Regression plots were created between targets (observed) and output (ANN predicted) values for training and testing data subsets for all the networks (Figs.9, 10, and 11). 5. Results and discussion The networks have been evaluated on the basis of the error between the observed and predicted values (MSE). Figures 6 to 8 shows the results for various network topologies with hidden layer neurons varying between1 to 10.The optimum network was selected on the basis of minimum MSE values (Table 2). In the current case, for the network involving Qt, the best network topology was 1-8-1 with an MSE value of 0.00040, for the network involving Qt, Qt-1, the best 16

network topology was 1-5-1 with an MSE value of 0.00043, and for the network involving Qt, Qt-1, and Qt-2, the best network topology was 1-6-1 with an MSE value of 0.00044. For each of the above three topologies the R2 values obtained were 0.99, 0.99, and 0.98, respectively. Further the regression plots obtained for each data set for the three networks have been shown in Figs. 9, 10, and 11.The performance plots (Figs. 6-8), though show some degree of error, but the trends for all the three networks followed the trends which were actually observed at gaging sites for the SSC values. The regression equations along with coefficient of correlation (R2) obtained for the outputs against the targets values for training, validation, test, and overall data sets for the networks T1, T2 and T3using ANN are presented (Table 3). Table 3 Regression equations obtained for the modeled networks. Network

Data set

Regression equation

R2 Value

T1

Training

Output=0.98*Target+0.0022

0.99

Validation

Output=0.92*Target+0.0044

0.98

Test

Output=0.96*Target+0.0023

0.98

All

Output=0.98*Target+0.0023

0.99

Training

Output=0.9*Target+0.005

0.99

Validation

Output=0.83*Target+0.0046

0.99

Test

Output=0.87*Target+0.0052

0.99

All

Output=0.88*Target+0.005

0.99

Training

Output=0.96*Target+0.0035

0.98

Validation

Output=0.94*Target+0.0028

0.98

Test

Output=0.96*Target+0.0035

0.98

All

Output=0.96*Target+0.0034

0.98

T2

T3

From the plots obtained (Figs. 6-8), it is observed that the most recent data, i.e. Qt is the best predictor for SSC for the year 2011. This is evident from the fact that the least MSE value (0.00040) was observed when the input fed to the network was just the previous year (2010), i.e.

17

Qt data for the Q. Also in any general time series problem the immediate previous year’s data are much more relevant to future prediction rather than data pertaining to much older years. Fig. 6. Plots showing the variation between observed and ANN predicted SSC values for 2011 for the ANN model derived for network T1 with different neurons in the hidden layer (1N to 10N, where N represents the number of neurons in the hidden layer). Fig. 7. Plots showing the variation between observed and ANN predicted SSC values for 2011 for the ANN model derived for network T2 with different neurons in the hidden layer (1N to 10N, where N represents the number of neurons in the hidden layer). Fig. 8. Plots showing the variation between observed and ANN predicted SSC values for 2011 for the ANN model derived for network T3 with different neurons in the hidden layer (1N to 10N, where N represents the number of neurons in the hidden layer). Fig. 9. Regression plots for training, validation, and test data sets for network T1 (note: training indicates the output obtained when only the training data set is used as input to the trained network, Validation means a random data set selected from the training set as input (validation data set is always a subset of training data set). The test set implies that when a trained network is fed with an unknown data set or one which is not a part of training data. All includes combining the training, validation, and test data sets).

This finding is all the more important because even when the network was fed with a smaller training data set (Qt) better ANN values for predicted SSC were obtained for the next year as compared to the data used for Qt, Qt-1 and Qt, Qt-1, Qt-2. Fig. 10. Regression plots for training, validation, and test data sets for network T2 (note: training indicates the output obtained when only the training data set is used as input to the trained network, Validation means a random data set selected from the training set as input (validation data set is always a subset of training data set). The test set implies that when a trained network is fed with an unknown data set or one which is not a part of training data. All includes combining the training, validation, and test data sets). Fig. 11. Regression plots for training, validation, and test data sets for network T3 (note: training indicates the output obtained when only the training data set is used as input to the trained network, Validation means a random data set selected from the training set as input (validation data set is always a subset of training data set). The test set implies that when a trained network is

18

fed with an unknown data set or one which is not a part of training data. All includes combining the training, validation, and test data sets).

This study productively shows the efficiency of using an ANN algorithm to model the relation between Q and SSC for a river in India. ANNs can be applied to predict water level and Q values for ungaged sites too. Moreover, if the training process for the ANN is based comprehensive data prediction for any time series data may be attempted for sites that are not easily accessible. 6. Conclusions This is the first work ever done on SSC prediction for the Ramganga River which is one of the important rivers in the Ganges River basin. The study gained vital significance in the aftermath of the recent avalanche resulting from a cloud burst in 2013 in the Uttarakhand region of the Himalayas in which sediment and debris mainly were responsible for changing river routes, thus, leading to the loss of flora and fauna. Though this modeling is very simple in the sense that the models are based only on the Q data, this work will definitely serve as a basis to develop better models taking into account many other contributing factors. However, the following are the conclusions drawn from the current work: 1). In all the topologies tested, the nature of the predicted values almost matches the trend of the observed values obtained from the gaging site. 2). For the present problem, a network topology of 1-8-1 for network T1 successfully predicted the SSC values corresponding to the Q data. 3). The most recent data (t-1) turned out to be the major contributor for prediction problems in this case as compared to past data (t-2) which is likewise the main feature of any time series information.

19

Acknowledgements The authors thank the Council for Scientific and Industrial Research (CSIR), New Delhi, India, for giving a research fellowship. The Central Water Commission, Lucknow, Government of India is thanked for sympathetically giving the information important to the current work. The authors gratefully acknowledge the comments of the reviewers and the editor, which enormously improved the presentation of the final manuscript.

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Tables Table 1 Descriptive statistics of the data used in the study.

Statistical parameters Mean Median Mode Standard deviation Range Maximum Minimum Skewness Kurtosis

Network T1 Based on just last year’s data (2010) 420 55066 57 281 56 271 1014 188127 8493 1831610 8497 1831619 4 9 5 6 27 44

Network T2 Based on last two year’s data (2009-2010) 270 31721 64 624 56 271 746 136382 8493 1831610 8497 1831619 4 9 6 8 53 87

Network T3 Based on last three year’s data (2008-2010) 261 29802 71 869 56 271 642 115901 8493 1831610 8497 1831619 4 9 7 9 65 113

Table 2 Networks characteristic and performance (note: R2 is the coefficient of determination and MSE is the mean square error). Network T1 St+1= f(Qt) (2010) Network R2 MSE topology 1-1-1 0.9832 0.00105

Network T2 St+1= f(Qt, Qt-1) (2009-2010) Network R2 MSE topology 1-1-1 0.9657 0.00094

Network T3 St+1 = f(Qt, Qt-1, Qt-2) (2008-2010) Network R2 MSE topology 1-1-1 0.9801 0.00819

1-2-1

0.9961

0.00045

1-2-1

0.9893

0.00047

1-2-1

0.5412

0.00792

1-3-1

0.996

0.00049

1-3-1

0.9935

0.00077

1-3-1

0.8468

0.00152

1-4-1

0.9986

0.00049

1-4-1

0.9834

0.00054

1-4-1

0.979

0.00047

1-5-1

0.9888

0.00117

1-5-1

0.9946

0.00043

1-5-1

0.851

0.00179

1-6-1

0.9983

0.00043

1-6-1

0.9775

0.00101

1-6-1

0.9864

0.00044

1-7-1

0.9974

0.00063

1-7-1

0.9908

0.00083

1-7-1

0.9013

0.00785

30

1-8-1

0.9985

0.0004

1-8-1

0.9685

0.00062

1-8-1

0.9496

0.00082

1-9-1

0.9931

0.00049

1-9-1

0.9399

0.00091

1-9-1

0.9081

0.00402

1-10-1

0.9982

0.00836

1-10-1

0.9851

0.00046

1-10-1

0.9816

0.00046

Table 3 Regression equations obtained for the modeled networks. Network

Data set

Regression equation

R2 value

T1

Training

Output=0.98*Target+0.0022

0.99

Validation

Output=0.92*Target+0.0044

0.98

Test

Output=0.96*Target+0.0023

0.98

All

Output=0.98*Target+0.0023

0.99

Training

Output=0.9*Target+0.005

0.99

Validation

Output=0.83*Target+0.0046

0.99

Test

Output=0.87*Target+0.0052

0.99

All

Output=0.88*Target+0.005

0.99

T2

T3

Training

Output=0.96*Target+0.0035

0.98

Validation

Output=0.94*Target+0.0028

0.98

Test

Output=0.96*Target+0.0035

0.98

All

Output=0.96*Target+0.0034

0.98

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55