Indian Journal of Geo Marine Sciences Vol. 47 (12), December 2018, pp. 2369-2381
Development of hydrolprocess framework for rainfall-runoff modeling in the river Brahmaputra basin
Satanand Mishra1*,C. Saravanan2, V. K. Dwivedi3 & J. P. Shukla4
1,4Water Resource Management and Rural Technology Group, CSIR-Advanced Materials and Processes Research Institute, Bhopal- 462064, India.
2Computer Centre, National Institute of Technology, Durgapur-713209, India.
3Dept. of Civil Engineering, National Institute of Technology, Durgapur-713209, India.
[E-mail: snmishra07@gmail.com]
Received 23 February 2017; revised 02 June 2017
The developed new Hydrolprocess is a combination of clustering, regression analysis and Artificial Neural Network (ANN) which gives the complete result of data analysis, discovering pattern, and prediction of hydrological parameters for the catchment. Hydrological parameters such as rainfall, river water level, discharge, temperature, evaporation, and sediment has been observed with respect to time. Monthly rainfall and runoff data from 1990 to 2010 of Brahmaputra river basin has been taken for the classification, clustering and development of the ANN model. Developed ANN models have been able to predict runoff with great accuracy. Performance of the model on the basis of correlation coefficient (R), root mean-square error (RMSE), and percentage error have been computedas0.98, 4.5 and 3.5 respectively.
[Keywords:— Feed Forward Backpropagation Algorithm, Multilayer Perceptron, Artificial Neural Network, Supervised Learning, Unsupervised Learning, Error tolerance Factor].
Introduction
Data mining is a new powerful technology that helps in extracting hidden predictive information as a future trends and behaviors from large databases and thus facilitating decision makers to make proactive, knowledge-driven decisions1. The time series data mining is commonly covered under classification, clustering, similarity analysis sequential pattern mining, forecasting, summarization, anomaly detection (Interestingness Detection), and segmentation. Runoff forecasting is a classical hydrological problem falls under the Hydrological time series analysis2,3. The ability to build a successful predictive model depends on past data.
Data mining is subjected to learn from past success and failures and will be able to predict what will happen in future4. Data mining, also popularly referred to as Knowledge Discovery from Database (KDD), is defined as Discovery of comprehensible, important and previously unknown rules or anything that is useful and non-trivial or unexpected from our collected data5. Clustering is a job of assigning a set of objects into groups called clusters. Clustering is among one of the unsupervised learning methods. Its goal is to identify structure in an unlabeled data set by
objectively organizing data into homogeneous groups where the within- group-object similarity is minimized and the between-group-object dissimilarity is maximized2.Among all clustering algorithms, K- means clustering is the most commonly used clustering algorithm with the number of clusters K, specified by the user6. K-means clustering is more useful for finding spherical-based clusters capability in small- to medium-sized databases7. Dynamic time warping (DTW) algorithm is used for comparing two time series. The distance between the two series is computed, after stretching, by summing the distances of individual aligned elements. DTW is an algorithm for measuring optimal similarity between two time data sequences8-17.
ANNs are artificial intelligence-based computational tools that can mimic the biological processes of a human brain. They do not require detailed knowledge of internal functions of a system in order to recognize relationships between inputs and outputs18. A neural network (NN) comprises large number of neuron. Neurons are simple processing input elements. On the other hand, in a recurrent network additional weighted connections are used to feed previous activations back to the
network19. The structure of a feed-forward ANN is shown in Figure 1.
An important step in developing an ANN model is the determination of its weight matrix through training. There are primarily two types of training mechanisms, supervised and unsupervised. A supervised training algorithm requires an external teacher to guide the training process. The primary goal in supervised training is to minimize the error at the output layer by searching for a set of connection strengths that cause the ANN to produce outputs that are equal to or closer to the targets. A supervised training mechanism called back-propagation training algorithmis normally adopted in most of the engineering applications20. Another class of ANN models that employ an ‘unsupervised training method’ is called a self-organizing neural network21. The approaches used for runoff forecasting cover a wide range of methods from completely black-box models to very detailed conceptual models22.
The daily runoff forecasting models based on artificial neural network has become quite important to deliver sustainable use and effective planning and management of water resources23.In recent years, the
ANN technique has become increasingly popular in hydrology and water resources among researchers and practicing engineers alike. This popularity can be gauged by the plethora of studies that have dealt with the application of ANNs in hydrology and water resources24-27. Many studies have demonstrated that the ANNs are excellent tools to model the complex rainfall–runoff process and can perform better than the conventional modelingtechniques28-30.
The neural network approach is advantageous over other techniques used for pattern recognition in various aspects. The performance and efficiency of the network can be increased using feedback information obtained from the difference between the actual and the desired result. This information will then be used to adjust the interconnections between the neurons at the input layer in order to match the actual result with the desired one. Additionally, the algorithms defined under this technique have self- organizing, self-adaptive characteristics enhancing the efficiency of the pattern recognition system. A new framework for analyzing time series data called Time Series Data Mining (TSDM) is introduced in this study. This framework adapts and innovates data mining concepts to analyzing time series data3,12. Materials and Methods
The site Panchratna (Latitude 26o 11’ 55" and Longitude 900 34’ 38”) of the river Brahmaputra, located in the district of Goalpara in the state of Assam shown in Figure 2 is selected for the study.
The length of the river upto the site is 2562 Km. The
Fig. 1 — Structure of feed-forward ANN
Fig. 2 — River basin catchment
MISHRA et al.: FRAMEWORK FOR RAINFALL-RUNOFF MODELING 2371 catchment area upto the site measures 468790 sq km.
The site is located on the left bank of river. The type of site is HO (Hydrological Observation). The Panchratna sites comes under Goalpara district experiences a tropical monsoon climate and the main seasons in the town are summers, winters and the monsoon. Summers in Goalpara are quite mild, and winters here are also moderate. The region experiences good amount of rainfall throughout the year. Summers in the town of Goalpara are during March, April and May. These three months will experience moderately high temperatures, and the maximum temperature in the region during this time found that around thirty degrees (30 °C). Minimum temperature found that around twenty two degrees (22 °C). Monsoon months in Goalpara are June, July, August, September and Octoober. Rainfall during this time will be quite heavy, and temperatures are moderate too. Humidity thus rises during this time. Winters in Goalpara are during the months of October, November, December, January and February.
During this period, the maximum temperature ranges around twenty three degrees (23 °C). The minimum temperature found around twelve degrees (12 °C) during the winter. The average maximum temperature is 30°C and minimum temperature is 15°C, recorded during the Pre monsoon period in the Goalpara. Average humidity percentage is recorded as 82% during the months from January to May.The river basin catchment of the study area is shown in Figure 2.
In this study, for the study, daily discharge and water level data for the entire year were taken from 1990 to 2010. Daily water level, river discharge data, rainfall data of the concerning catchment, sediment and daily maximum and minimum temperature data has been collected from the Central water commission, Indian metrological department’s web sites and some other resources from 1990 to 2010. The data is collected from the Central Water Commission, Ministry of Water Resources, and Government of India. Real time observation on 24 × 7 round o'clock basis has been setup.
For the complete study of hydrological real time series a Hydrolprocess framework is developed using data mining techniques. In this algorithm,two clustering algorithms k-meansand agglomerative hierarchicalclustering are used for finding the clusters and patterns in the hydrological data.Dynamic Time Warping Algorithm (DTW) applied and discovered similarities and dissimilarities within the clusters. For
the study of flood waves, risingcoefficients hasbeen calculated during onset of monsoon and recession coefficients during the recession of floods. A distance measure algorithm to achieve discharge process clustering, hydrological period segmentation, discharge process similarity search and discharge process pattern discovery3,11,12,13. The proposed algorithm for hydrological real time observations and real time knowledge extraction is termed as Hydrolprocess, which is shown below:
1. To select a data set.
2. To find out statistical parameters Qmean,Qmax,, Qrange,, Qstd.
3. To standardize the data using Z score
4. To apply K means clustering and find out number of clusters.
5. To apply Dynamic Time Warping Algorithm (DTW) and find out similarities and dissimilarities.
6. To apply Agglomerative Hierarchal Clustering (AHC) algorithms and find out patterns.
7. To calculate rising and recession coefficients during the high floods
8. To develop Forecasting model and predict the future parameters.
9. To evaluate performance measures and compare the results with different models outcomes.
10. To correlate performance with causal effects 11. To apply the model for the whole river basin 12. End the process
The Hydrolprocess is a combination of data analysis and model development. In this proposed Hydrolprocess, for the data analysis clustering techniques with similarity search and for the model development,regression analysis and ANN have been incorporated. For the data analysis, k-means clustering, AHC and regression analysis XLSTAT 2013 and MS Excel 2007 software has been used. For the ANN backpropagation simulator has been used.
The simulator is designed according to the rainfall - runoff model development.
Figure 3 shows the monthly statistics of standardized discharge data. It covers Maximum, Minimum, Range, Average and Standard Deviation.
The whole standardized data is categorized in three clusters known as pre-monsoon, monsoon, and post-monsoon
A neural network model is a powerful tool used for various real life applications like time series
prediction, sequence detection, data filtering, pattern recognition and other intelligence tasks as performed by the human brain. There are various approaches defined under neural network for pattern recognition and depending upon the type of learning mechanism applied to generate the output from the network, the appropriate aaproach is selected. The learning has been categorised as supervised learning in which the desired result is known to the system i.e., the system is trained with the priory information available to obtain the desired result. If in case the computed result does not match the desired result, then the difference between the two is determined which is used to modify the external parameter required to generate the correct result. The most popular supervised neural network model is multilayer perceptron(MLP) which can be used when prior knowledge of the relationships between inputs and targets are known31-32.
The other type of learning is reinforcement learning in which the behaviour of the network is predicted based on the feed back from the background envioronment though practically, supervised and unsupervised learning rules are more commonly followed for implementation of the network design.
For the training and validation of the ANN the whole data is recycled in four groups for the better analysis and developemnet of the model.
In this study, Multilayer perceptron (MLP) neural network was used. MLP is most important neural network. It uses linear combination function in input layer to compute single output from multiple real valued inputs and then apply nonlinear activation function on generated output. MLP-BPA (multilayer
perceptron trained with back propagation algorithm) having property to work as a good classifier for linear as well as non linear datasets. This algorithm mainly performs two tasks very effectively that is classification and forecasting by the help of data mining implementation tool. To implement this algorithm an experiment setup developed. Back propagation simulator, a data mining tool is developed for classification and prediction task.
Back propagation simulator is an easy to use neural network development tool for Microsoft Windows. In this proposed algorithm we are having following steps:
The results of any model application depend upon the quality of input data. Modeling has to be carried out for a variety of purposes including river basin planning, hydrologic design of projects and, flood forecasting and monitoring. ANN models are built using input and output observations without detailed understanding of the complex physical laws governing the process under investigation. For this research, discharge, water level data, rainfall, temperature, evaporation and sediment data were collected from the Panchratna monitoring station located at the Brahmaputra River Basin from Central Water Commission, Ministry of Water Resources, and Govt. of India. The data has been observed on daily basis by monitoring sites. Observed data is changed to monthly basis mean data by taking mean of daily basis data in excel format. At initial point, data set have 2 input parameters comprises of twelve months (January to December) discharge-Rainfall data of twenty one consequent years that is from 1990-2010.
The data set contain 252 exemplars for the years 1990
Fig. 3 — Monthly statistic of discharge process of river Brahmaputra at Panchratna HO site
MISHRA et al.: FRAMEWORK FOR RAINFALL-RUNOFF MODELING 2373 through 2010. These exemplars are used for model
training and validation. 80% data is used for training, 20% data is used for validation phase. After testing input parameter data set we then further narrowed down the data to create each forecast. The output from the model is the runoff at the time step t, Qt. out of 21 years data, four sets of data have been used to make several combination of year keeping in view the highest peaks of hydrographs. The combination of data is as follows:
All set of data have good results. The studies demonstrate the applicability of ANN approach in developing effective non-linear models of rainfall runoff process without the need to explicitly representing the internal hydraulic structure of the watershed.
The input data is pre-processed through unsupervised wavelet filter analysis, which presents as in-built function in backpropagation simulator through which all data get normalized.
Multilayer perceptron network (MLP) is constructed and choose back propagation algorithm as a training algorithm. Multilayer perceptron network (MLP) is most important neural network. It uses linear combination function in input layer to compute single output from multiple real valued inputs and then apply nonlinear activation function on generated output. The general structure of MLP is given in Figure 1.
The first layer is called input layer, which have input neuron. Each input neuron represents an input data. Second layer is called hidden layer. MLP may have more than one hidden layer. The last layer is called output layer, which have output neurons.
Output neurons consist of the predicted value.
Mathematically this is represented as:
Y = φ (∑ ) ... (1)
where Widenotes the vector of weights, Xi is the input received at node (i =1, 2...n), b is the bias, y is the output and φ is the activation function33. MLP can be used where we have little knowledge of relationship between inputs and targets.
After model construction, the next step is to train the model with training data set using back propagation Algorithm. It is a supervised learning method, i.e., a teacher is required to calculate the desired output for any input in the training set. The goal of any supervised learning algorithm is to find a function that best maps a set of inputs to its correct
output. As the algorithm's name implies, the errors propagate backwards from the output nodes to the input nodes. Since this algorithm is based on the supervised learning approach, therefore the desired result is already known to the network. We then calculate the error of each neuron, which is computed – desired output. This error is then back propagate to change the weights in such a way that the error will get smaller. In order for the hidden layer to serve any useful function, multilayer networks must have non-linear activation functions for the multiple layers.
Back propagation algorithm requires that the activation function used by the artificial neurons be differentiable. This algorithm operates in either of the 2 modes: Online mode in which each propagation is followed immediately by the weight adjustment and batch mode in which the weight updates take place after various consecutive propagations.
A neural network that uses the error back propagation algorithm is said to be a BP network, whose learning process consists of the feed-forward and feed- backward33-34. Each sample signal in the feed-forward process is applied by the sigmoid function
... (2)
Which provides an output in the range 0< f(x)
<135before it is passed to next layer. If the output layer does not produce the desired value, then the errors will be fed back from the outputs to the inputs through the network, and the weights of nodes in each layer will be changed along the way. The algorithm repeats in this way until the error values are sufficiently small. The back propagation algorithm uses method of gradient decent to minimize the error function in weight space. The learning rate isa constant used in error back-propagation learning that affects the amount of weight update. The smaller the learning rate, the more steps it takes to get to the stopping criterion. The learning rate should ideally be decreased as training progresses, since the network weights tend to approximate the desired function more closely as training continues. Network learning is very slow; if the step size is small, and step size is too large then it can oscillate. The Momentum provides the gradient descent with some inertia, so that it tends to move along a direction that is the average estimate for down. The amount of inertia is dictated by the momentum parameter, the higher the momentum, more it smoothes the gradient estimate.
The major benefit over step component is the ability
to break out the problem of local minima that a Step component might get caught in. If the value of momentum parameter is high then oscillation may occur. The momentum parameter is the same for all weights of the attached component.
The performance of each model for both testing and training data are evaluated by using the root mean-square error (RMSE), and correlation coefficient (R) which is widely implemented for evaluating effective results of time series forecasting.
The performance of model can be evaluated in terms of several characteristics. Root mean square error (RMSE) and coefficient of correlation (R) are the numerical performance indicators used to compare the models. They are defined as follows:
Coefficient of correlation (R) = ∑
∑ ∑ ... (3)
RMSE = ∑ ... (4)
where, K is the number of observations; t is the observed data; y is computed data; T= t- ̅ where ̅ is the mean of observed data; and Y = y - where is the mean of the computed data.
On the basis of model evaluation result, the best model with lower MAE and MSE is used for future forecasting. Obtained results can be used effectively over present traditional and conventional techniques.
To get the optimized structure for the neural network model, several combinations of inputs were trained, but best one is: rainfall (t-2), rainfall (t-1) and rainfall (t). In this case the output neuron is runoff (t).
It was found that the best convergence is achieved for the above combination with error tolerance, the learning parameter, neurons in hidden layer and
number of cycles. The coefficient of correlation, root means square error and weights for the best trained network structure were frozen to evaluate the trained network. The weights for the best trained network structure were collected from the training module of the back propagation simulator. The monthly rainfall and runoff data were normalized and the data set of input vector was prepared according to the best trained neural network structure. The runoff was computed using this network and the weight vector for this trained network structure. The computed runoff values were denormalized and compared with the observed runoff values.
In the back propagation simulator for the four set of data as given in Table 1 are Input Combination, Error Tolerance, Learning Parameter, no. of layers for networks, Maximum Cycles for Simulation, and no of neurons for input, hidden and output layers are given in the Table 2.
Where abbreviation stands for:
IC: Input Combination, ET: Error Tolerance, LP:
Learning Parameter, NLN: No. of layers for networks, MCS: Maximum Cycles for Simulation, R:
Coefficient of correlation, RMSE: Root Mean Square Error, DC: coefficient of determination
Result and Discussion
The Figure 4 shows the pattern received from k –means process. During the pre-monsoon period the
Table 1 — ANN Training and Validation Sets
Set Training Validation
ANN - I 1990-2004 2005-2010
ANN - II 1996-2010 1990-1995 ANN - III 1990-1995 and 2002-2010 1996-2001 ANN - IV 1990-2001 and 2008-2010 2002-2007 Table 2 — ANN Model calibration and validation parameters
ANN Model Calibration & Validation Input Option : 3,4,5
Data Set MODEL IC ET LP Cycles NLN Neurons
Input Hidden Outputs
SET1 ANN1(1) 3 0.004 0.1 300 3 3 4 5
ANN1(2) 3 0.009 0.2 400 3 3 4 5
SET2 ANN2(1) 3 0.006 0.2 400 3 3 4 5
ANN2(2) 3 0.008 0.1 350 3 3 4 5
SET 3 ANN3(1) 3 0.006 0.2 400 3 3 4 5
ANN3(2) 3 0.008 0.1 350 3 3 4 5
SET 4 ANN4(1) 3 0.4 0.8 250 3 3 4 5
ANN4(2) 3 0.3 0.5 300 3 3 4 5
graphs show graph show monsoon p pattern. The among the r from the da and validates
Table 3 segmentation the refine pa
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Fig. 4 —
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K FOR RAINFA
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Clas 199 199 199 199 199 199 200 200
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ALL-RUNOFF M
Table 3 — k –m ss 1 Class 2 91 1993 92 2000 94 2001 95 2005 96 2007 97 2008 02 2009 06
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MODELING
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1998 2004
s conducted lly found th for identify inguish betw ery cluster is all period. T
presented by usters.
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1999 2003
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segmentation 7 shows th
2375
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2010
umbers of lt of few egories or discharge esented in
in each he objects
n of data e pattern
Table 4 — AHC - Class segmentation
CLASS 1 CLASS 2 CLASS 3
1991 1993 2004 1992 1998 2010 1994 1999
1995 2000 1996 2003 1997 2005 2001 2006 2002 2007 2009 2008
received by AHC. The received patterns have been very close proximity.
Table 5 shows the node statistics of AHC tree in which given the detail description of node, level, weight , objects, left son and right son of the tree of the runoff clusters.
Figure 6 shows a bar graph of the distance values.
It chooses the number of clusters by finding a jump in the increasing pattern shown in this bar chart.
Figure 7 shows the runoff pattern after the agglomerative hierarchical clustering where three patterns of river discharge are visualised which are very fine and having very close aproximity within the patterns.
The back propagation algorithms repeats the procedure of weight adjustments until the error is reduced to the negligible amount and reaches the error tolerance range. This techniques approach is better in performance over other techniques due to high accuracy rates for complex pattern recognition, adaptive learning as well as better tolerance factor to fault even though more time may be required to train the network for very complex patterns. The actual
Fig. 6 — Levels bar Chart
Fig. 7 — Discharge pattern received by AHC for the river Brahmaputra at Panchratna site
MISHRA et al.: FRAMEWORK FOR RAINFALL-RUNOFF MODELING 2377 output vector as well as the expected output vector is provided in the result.txt file which shows the discrepancy between the two in order to perform the weigh updations on the interconnections. In the four set of data as given in Table 1 run in the ANN simulator and find out best fitted 8 models. The Input parameters which are required for the model are given in the Table 2. Out of 8 models only one SET1 DATA, ANN1(1) trainings, validation and correlation graphs have given from Figure 8 to Figure11.
Here, Figure 8 shows the ANN Set1 (1) Calibration (Discharge Prediction)-Observed Vs Computed and Figure 9 shows ANN Set1 (1) Validation (Discharge Prediction)-Observed Vs Computed through developed ANN model. Figure 10 shows correlation of ANN Set 1(1) between Calibration
Table 5 — Node statistics of AHC tree
Node Level Weight Objects Left son Right son
39 66.076 20 20 35 38
38 40.896 11 11 36 37
37 19.929 9 9 33 34
36 15.949 2 2 14 20
35 13.109 9 9 28 32
34 12.633 6 6 29 31
33 10.417 3 3 8 23
32 8.643 6 6 27 30
31 7.156 2 2 15 16
30 6.177 3 3 5 24
29 6.145 4 4 21 25
28 5.044 3 3 11 26
27 3.490 3 3 2 22
26 2.422 2 2 12 19
Fig. 8 — ANN Set1 (1) Calibration (Discharge Prediction)-Observed Vs Computed
Fig. 9 — ANN Set1 (1) Validation (Discharge Prediction)-Observed Vs Computed
Observed V shows corr Validation-O
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Fig. 13
MISHRA et al.:
Table 6 — R2 0.98 0.97 0.99 0.95 0.98 0.96 0.98 0.97
Fi
3 — Average mo
: FRAMEWORK
PERFORMAN Model ca RMS 5.6 5.09
4.6 5.24
5.3 5.46 4.63 5.0
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K FOR RAINFA
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SE %
6 9 6
4 3
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ALL-RUNOFF M
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%Error 3.5 3.7 4.7 4.9 3.6 3.8 4.7 4.0
nce Bar Graph
f Panchratna site
MODELING
MODEL Mode R2
0.99 0.95 0.98 0.96 0.97 0.95 0.96 0.97
e from 1990 to 2
el Validation RMSE
4.91 4.23 5.25 4.17 5.6 5.15 5.56 4.67
010
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in the form of bar charts. Primary axis shows the rainfall in mm.
As shown in Figure 13, a typical hydrographs shows a rising limb, a crest segment and a recession limb. The rising limb BC has a well defined point of rise B followed by increasing water level. The crest segment CF contains the peak water level within it, and from E it is the recession limb with decreasing water level. The segment AB is called the approach segment which indicates the base flow in the river prior to the storm.
The rain fall bar chart shows that during the peak of water level the rainfall was high. When rainfall was started rising the water level is started rising automatically. On the peak the maximum rainfall shows. When rainfall was started declined the water level started down.
The Figure 3 shows monthly statistic of discharge process, figure 4 shows discharge pattern received by k means clustering, Figure 7 shows discharge pattern received by AHC, figure 8 shows ANN Set1 (1) calibration (discharge prediction)-observed versus computed, figure 9 shows ANN set1 (1) validation (discharge prediction)-observed versus computed.
These figures are compared with Figure 13, the peak of all the hydrological parameters results are matches in similar time. The rising of water level, discharge and rainfall are the same time started and recession graphs of discharge, rainfall and water level have very closed similarities. Since the discharge pattern received by k means and AHC, monthly statistic of discharge process have very close similarities. The result of ANN models have very close similarities of received patterns by k-means and AHC. These results and patterns also compared with Figure 13 and it is found that all figures have very close similarities of each other. It is observed that the discharge pattern is very similar to the hydrographs and rain fall bar graphs. When rain fall is high, water level is high and the same time discharge is also high and vice versa. Therefore, the models results and received patterns by K-means & AHC have very close similarities. The casual effects also validate models results and patterns.
Thus the proposed Hydrolprocess shows the complete study of data analysis and model development for hydrological real time rainfall-runoff process for the Panchratna sites on river Brahmaputra.
The proposed Hydrolprocesss applied whole basin and to be given better performance.
Conclusion
Since the observation has been made on real time basis, therefore, the time series is proposed as a Hydrological Real Time Series and the mining of the knowledge from the proposed hydrological time series is proposed as a Hydrological Real Time Series Data Mining.Prediction for river stage flow can be obtained by generating the relationship between training length and performance parameters. Proper selection for solution algorithm could help to increase the model accuracy. The best performance of ANN for flow prediction heavily depends on not only the length of the data set but also whether the most significant patterns are included or not.
Acknowledgements
Authors thanks the Central Water Commission, Ministry of Water Resources for providing Water Level, Discharge and Sediment data.
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