Prediction of runoff using BPNN,FFBPNN,CFBPNN algorithm in arid watershed: A case study

Abstract

Here, an endeavor has been made to predict the correspondence between rainfall and runoff and modeling are demonstrated using Feed Forward Back Propagation Neural Network (FFBPNN), Back Propagation Neural Network (BPNN), and Cascade Forward Back Propagation Neural Network (CFBPNN), for predicting runoff. Various indicators like mean square error (MSE), Root Mean Square Error (RMSE), and coefficient of determination (R ${}^{2}$ ) for training and testing phase are used to appraise performance of model. BPNN performs paramount among three networks having model architecture 4-5-1 utilizing Log-sig transfer function, having R ${}^{2}$ for training and testing is correspondingly 96.43 and 95.98. Similarly for FFBPNN, with Tan-sig function preeminent model architecture is seen to be 4-5-1 which possess MSE training and testing value 0.000483, 0.001025, RMSE training and testing value 0.02316, 0.03085 and R ${}^{2}$ for training and testing as 0.9925, 0.9611, respectively. But for FFBPNN the value of R ${}^{2}$ in training and testing is 0.8765 0.8976. Outcomes on the whole recommend that assessment of runoff is suitable to BPNN as contrasted to CFBPNN and FFBPNN. This consequence helps to plan, arrange and manage hydraulic structures of watershed.

Keywords

BPNN CFBPNN FFBPNN arid watershed runoff

1. Introduction

For managing water resources problems, it is extremely important to find convenience to potential of runoff. Runoff calculation resulting as of rainfall and loss due to permeation including atmospheric parameters is necessary for any catchment. Measuring runoff in a catchment depends on accessibility period of precipitation and runoff. Rainfall, loss due to infiltration, atmospheric factors are related among one another. This coherence is utilized for measuring runoff from observed rainfall, temperature and loss due to infiltration. Rainfall refers to water falling from atmosphere on ground. Present study focuses on examining co-relation amid rainfall and infiltration loss. Runoff from a catchment is course of water from various parts above ground level towards an exit. Intricate interactions amid precipitation and infiltration loss are needed to be understood by arrangement, plan and managing of a catchment. This can be found out by modeling hydrologic parameters.

Hsu et al. [1] applied three-layer feed forward ANN model to develop rainfall-runoff relationship at Collins watershed, Mississipi. Temporal back propagation neural network effectively demonstrates forecasting monthly rainfall-runoff model [2]. Rajurkar et al. [3] used MISO model coupled with ANN to establish daily rainfall-runoff relationship at Narmada watershed. Badrzadeh et al. [4] employed ANN, ANFIS, WNN, WNF algorithms to predict flow discharge at Casino station on Richmond River, Australia. Chiang et al. [5] Real-time recurrent learning algorithm and conjugate gradient method are utilized to predict stream flow at Lan-Yang River in Taiwan. Single neural network (SNN) and ensemble neural network (ENN) employed for providing enhanced rainfall-runoff recreation at Geum river basin [6]. Particle swarm optimization feed forward neural network (FFNN) is used to forecast rainfall-runoff relation in Sungai Bedup basin, Sarawak, Malaysia [7]. Multilayer perceptron neural network, generalized feedforward neural network, radial basis function neural network, modular neural network, and neuro-fuzzy neural network are utilized to predict rainfall-runoff relationship at four various regions around the world [8]. Shoaib et al. [9] applied wavelet-coupled artificial neural network to develop rainfall-runoff relationship. FFBPNN and radial basis function neural network models incorporated by means of discrete wavelet transform employed to predict runoff at Jinsha River basin, China [10]. Samantaray and Ghose [11] used FFBP, CFBP and Neural Network Fit techniques for simulating suspended sediment load in Mahanadi river basin, Odisha, India. Nayak et al. [12] developed Nedbør-Afstrømnings-Model, Artificial neural network and wavelet neural network models for processing rainfall-runoff relationship for Malaprabha basin in India. Nourani [13] implemented Emotional Artificial Neural Network (EANN), as a new generation of Artificial Intelligence-based models for daily rainfall runoff modeling of watersheds. Shoaib et al. [14] explored potential of wavelet coupled time lagged recurrent neural network (TLRNN) models to predict runoff with the use of rainfall data. Ghose and Samantaray [15] incorporated regression model and BPNN model for forecasting sediment concentration at various discharge and temperature conditions.

Smith and eli [16] applied BPNN for predicting maximum discharge for a river basin. Tokar and Johnson [17] used ANN algorithm for daily rainfall-runoff relationship in the Little Patuxent River basin, Maryland. Birikundavyi et al. [18] employed neural network to forecast daily stream flow at Mistassibi River Station. Raghuwanshi et al. [19] developed ANN model to predict both sediment and runoff on daily and weekly basis for minute farming catchment. Sedki et al. [20] investigated that Genetic Algorithm is applied to predict rainfall runoff relationship at Ourika catchment. Kisi et al. [21] used ANNs, Adaptive Neuro-Fuzzy Inference System (ANFIS) and Gene Expression Programming (GEP) for forecasting rainfall runoff relationship at Kurukavak watershed. BP model and Xinanjiang model are used for evaluating efficiency of rainfall-runoff model at Shanwei City watershed, China [22]. Intelligent computing tools based on fuzzy logic and ANN were utilized to predict rainfall-runoff relationship at Kranji basin, Singapore [23]. Back propagation algorithm, real-coded genetic algorithm (RGA), and self-organizing map (SOM) are applied to predict rainfall-runoff modeling at Kentucky River basin [24]. Singh and Deo [25] applied various neural networks and found RBF superior than FFBP, GRNN and ANFIS to forecast rainfall runoff modelling at Narmada river basin. Devi et al. [26] employed FFBPNN, CFBPNN, distributed time delay NN and nonlinear autoregressive exogenous network to predict rainfall at Coonoor gauging station. Karunanithi et al. [27] evaluated applicability of neural network approach utilizing cascade-correlation algorithm which can be used as an adaptive model synthesizer and also as a predictor. Goyal and Goyal [28] developed CFBPNN and FFBPNN artificial intelligence models to predict sensory feature of immediate coffee flavored sterilized drink. Filik and Kurban [29] introduced and applied a novel prospective to forecast short-term load utilizing autoregressive (AR), FFBP and CFBP models at a power system in Turkey taking utilization data of electrical energy. Khaki et al. [30] employed FFNN, Elman neural networks and CFBPNN to evaluate ground water level at Langat Basin.

The aim of present study is to predict runoff using BPNN, FFBPNN, and CFBPNN algorithm for arid watershed.

2. Study area

Kalahandi is an arid watershed of Odisha in India considered for research purposes. Kalahandi is situated amid 19.3 N and 21.5 N latitude and 82.20 E and 83.47 E longitude and dwells in south western segment of Odisha. Balangir and Nuapada district borders north, Nabarangpur, Koraput and Rayagada district to south and Kandhamal and Boudh district in east. The watershed consists of region of 8,364.89 sq. kms. Tel is the main river of Kalahandi. Topography in this region comprises of bare terrain and mountains. The area is bounded by hills. The watershed depends mostly on farming, with more than one third of the region enclosed with intense forest.

Figure 1.

Proposed study area.

3. Methodology

3.1 BPNN

Rumelhart et al. [31] established first ever neural network which was simple to use and afterwards several varieties of ANN have been projected. Neural network (NN) having multi-layer perceptron (MLP) is mainly established and broadly utilized model amid ANN models. Investigation done using ANN models illustrates potential outcomes in hydrology [32, 33, 34]. BPNN is most extensively utilized ANN to model hydrological problems and henceforth is applied in present research work. This network consists of every function of NN and has distinctive benefits like capability to map superior processing for rainfall-runoff separating with extra elasticity. As a result, NN model possessing multiple hierarchy of configuration on basis of BP arithmetic is an accepted selection in hydrological ground dealing with different intricate substantial procedures.

BPNN is characteristically a fully linked NN which includes input, hidden and output layer. Objective of training procedure is utilized for finding weights which minimizes a few inaccuracy events on a whole, for example MSE. Therefore, to train a network is in fact an unimpeded nonlinear minimization problem. A number of research people’s state that networks having solitary hidden layer can estimate any uninterrupted function to any preferred accurateness and is sufficient for majority problems related to forecasting.

3.2 FFBPN

In recent years, artificial intelligence techniques were utilized and put into application with a huge pact of success. As an information processing system, ANN comprises of several non-linear, arbitrary and dense unified processing fundamentals named neurons that are structured in sets identified as layers. Fundamental advantage of ANN models is they don’t need multifaceted character information of main procedure beneath likeness to be evidently explained in precise mathematical outline. ANN is a conventional and a well-organized way to model diverse and intricate input – output connections in predicting hydrological time series.

Amongst additional NN, FFNN utilizing BP as training algorithm is taken into consideration as very prominent training technique and frequently used to model hydrologic problems. Structure of a common three layer FFNN is revealed in Fig. 3. It is observed from Figure that this network consists of a single input layer, where data are established to model network, a single hidden layer consisting of ‘n’ neurons, where data is refined or taken care of and a single output layer, where results and consequences of specified input is formed.

Figure 2.

Architecture of BPNN.

Figure 3.

Architecture of FFBPNN.

3.3 CFBPNN

Cascade Forward neural networks are analogous to FFNN even though it comprises a weight link from input to each layer and then connected to succeeding layers. Although two-layer FFNNs could possibly be trained virtually with any input output link, FFNNs having more layers may be trained with intricate relations more rapidly. For instance, in a three layer network, layer 1 is connected to layer 2, layer 2 to layer 3, and then layer 1 to layer 3. In CFBPNN, neurons of one layer entail to compute and update weight of every layer in front This model is same as compared to FFBPNN while utilizing back propagation algorithm to update weights. In other words, the input layer has its influence on all the layers ahead.

Figure 4.

Architecture of CFBPNN.

3.4 Data preparation and processing

Precipitation, avg. temperature, infiltration loss, humidity are composed from India meteorological department and daily runoff data are collected from soil conservation department Sambalpur, India between 1986–2018. Data from 1986–2008 are utilized to train and from 2009–2018 are used to test the network. Daily data are transformed to monthly data that is utilized to develop model. Input and output data are balanced in such a way so that every data lie in a particular set prior to training. Procedure concerned in this is known as normalization so that normalized data are restricted in a range from 0 to 1. Normalization equation utilized to scale data is

$\displaystyle X_{t}=0.1+\frac{X-X_{\textit{min}}}{X_{\textit{max}}-X_{\textit{% min}}}$ (1)

Table 1

Results of BPNN at Kalahandi watershed

Model input	Transfer	Architecture	MSE		RMSE		R ${}^{2}$
	function		Training	Testing	Training	Testing	Training	Testing
Precipitation,	Tansig	4-2-1	0.000634	0.005532	0.009287	0.009317	0.9173	0.9348
average		4-4-1	0.000717	0.006853	0.001812	0.004587	0.9411	0.9568
temperature,		4-6-1	0.000287	0.001654	0.001301	0.001187	0.9525	0.9653
infiltration		4-8-1	0.000542	0.004298	0.003243	0.006201	0.8998	0.9117
loss,		4-9-1	0.000797	0.006256	0.003512	0.006498	0.8697	0.8827
humidity	Logsig	4-2-1	0.000613	0.006386	0.003324	0.007898	0.8764	0.8945
		4-4-1	0.000542	0.002932	0.003319	0.005675	0.9362	0.9587
		4-6-1	0.000742	0.003798	0.002589	0.004453	0.9327	0.9491
		4-8-1	0.000665	0.002832	0.003801	0.002987	0.9102	0.9258
		4-9-1	0.000487	0.001934	0.002592	0.004387	0.9574	0.9715
	Purelin	4-2-1	0.000923	0.003698	0.003009	0.006098	0.9018	0.9257
		4-4-1	0.000776	0.004413	0.003198	0.006765	0.8711	0.8996
		4-6-1	0.000627	0.007576	0.003489	0.008876	0.9289	0.9463
		4-8-1	0.000545	0.003018	0.002798	0.005609	0.9493	0.9609
		4-9-1	0.000898	0.007086	0.003609	0.008409	0.8391	0.8684

Figure 5.

Assessment of actual versus predicted runoff using BPNN at Kalahandi during testing phase.

Where $X_{t}=$ altered data series, $X=$ orginal input data series, $X_{\textit{min}}=$ minimum of orginal input data series, $X_{\textit{max}}=$ maximum of original input data series.

3.5 Evaluating criteria

For ascertaining finest model, criterion is R ${}^{2}$ , MSE and RMSE. For choosing perfect model for present study, provision is MSE, RMSE is supposed to be least and R ${}^{2}$ is supposed to be highest.

$\displaystyle R^{2}=1-\frac{\left[\sum^{N}_{i=1}(x^{i}_{\textit{comp}}-\bar{x}% ^{i}_{\textit{comp}})\right]^{2}}{\left[\sum^{N}_{i=1}(x^{i}_{\textit{obs}}-% \bar{x}_{\textit{obs}})\right]^{2}}$ (2) $\displaystyle\textit{MSE}=\frac{1}{N}\mathop{\sum}^{N}_{j=1}(x^{i}_{\textit{% comp}}-x^{i}_{\textit{obs}})^{2}$ (3)

where, $x^{i}_{\textit{comp}}$ and $x^{i}_{\textit{obs}}$ are the computed and actual data.

$\bar{x}^{i}_{\textit{comp}}$ and $x^{i}_{\textit{obs}}$ and are the mean values of computed and measured data

Table 2

Results of FFBPNN at Kalahandi watershed

Model input	Transfer	Architecture	MSE		RMSE		R ${}^{2}$
	function		Training	Testing	Training	Testing	Training	Testing
Precipitation,	Tansig	4-2-1	0.000234	0.001798	0.001118	0.001196	0.9327	0.9481
average		4-4-1	0.000787	0.006178	0.001498	0.004329	0.9018	0.9245
temperature,		4-6-1	0.000687	0.005609	0.009732	0.009186	0.8891	0.8978
iInfiltration		4-8-1	0.000566	0.004905	0.003885	0.006592	0.8319	0.8568
loss,		4-9-1	0.000711	0.006118	0.003906	0.006298	0.8612	0.8755
humidity	Logsig	4-2-1	0.000676	0.006298	0.003117	0.007498	0.8256	0.8429
		4-4-1	0.000656	0.002284	0.003045	0.002309	0.8488	0.8791
		4-6-1	0.000702	0.003567	0.002117	0.004198	0.8836	0.9032
		4-8-1	0.000498	0.001908	0.002009	0.004229	0.9247	0.9409
		4-9-1	0.000578	0.002852	0.004178	0.003987	0.9068	0.9211
	Purelin	4-2-1	0.000928	0.003598	0.003298	0.006109	0.8798	0.9053
		4-4-1	0.000533	0.003003	0.002587	0.005339	0.9115	0.9372
		4-6-1	0.000694	0.007187	0.003176	0.008198	0.8793	0.8911
		4-8-1	0.000717	0.004936	0.003187	0.006009	0.8506	0.8609
		4-9-1	0.000848	0.007994	0.003938	0.008299	0.8076	0.8312

Table 3

Results of CFBPNN at Kalahandi watershed

Model input	Transfer	Architecture	MSE		RMSE		R ${}^{2}$
	function		Training	Testing	Training	Testing	Training	Testing
Precipitation,	Tansig	4-2-1	0.000626	0.005398	0.009995	0.009295	0.8626	0.8897
average		4-4-1	0.000785	0.006288	0.001793	0.004438	0.8922	0.9016
temperature,		4-6-1	0.000566	0.004286	0.003167	0.006201	0.8356	0.8576
infiltration		4-8-1	0.000229	0.001995	0.001209	0.001102	0.9001	0.9123
loss,		4-9-1	0.000794	0.006285	0.003995	0.006436	0.8259	0.8458
humidity	Logsig	4-2-1	0.000665	0.006865	0.003297	0.007884	0.8257	0.8487
		4-4-1	0.000495	0.001288	0.002005	0.004403	0.8912	0.9079
		4-6-1	0.000774	0.003867	0.002296	0.004298	0.8527	0.8743
		4-8-1	0.000666	0.002296	0.003064	0.002184	0.8369	0.8579
		4-9-1	0.000598	0.002996	0.005289	0.005874	0.7998	0.8109
	Purelin	4-2-1	0.000937	0.003864	0.003184	0.006025	0.81981	0.8476
		4-4-1	0.000818	0.007298	0.003032	0.008983	0.7701	0.7853
		4-6-1	0.000665	0.007826	0.003387	0.008784	0.8529	0.8715
		4-8-1	0.000784	0.004685	0.003995	0.006711	0.7954	0.8189
		4-9-1	0.000565	0.003005	0.002943	0.005721	0.8811	0.8983

Figure 6.

Assessment of actual versus predicted runoff using FFBPNN at Kalahandi during testing phase.

Figure 7.

Assessment of actual versus predicted runoff using CFBPNN at Kalahandi during testing phase.

Figure 8.

Actual v/s simulated runoff using BPNN, FFBPNN, and CFBPNN at Kalahandi during testing phase.

4. Results and discussions

Results for BPNN are conferred below for Kalahandi. Here Tan-sig, Log-sig, and Purelin transfer function having 4-2-1, 4-4-1, 4-6-1, 4-8-1, 4-9-1 architectures are considered to compute performance. The best model architecture for Log-sig function is 4-9-1 having MSE training and testing value 0.000487 and 0.001934, RMSE training and testing value 0.002592, 0.00387 and R ${}^{2}$ training and testing value 0.9574 and 0.9715. Similarly, in case of Tan-sig function preeminent model architecture is 4-6-1 having MSE training and testing value 0.000287 and 0.001654, RMSE training and testing value 0.001301 and 0.001187 and R ${}^{2}$ training and testing value 0.9525 and 0.9653. Also for Purelin function, finest model architecture is 4-8-1 having MSE training and testing value 0.000545 and 0.003018, RMSE training and testing value 0.002798 and 0.005609 and R ${}^{2}$ training and testing value 0.9179 and 0.9019. Outcomes of transfer functions are presented in detail in table below in Table 1 and conjunctively best value of R ${}^{2}$ is accessible in Fig. 5.

Similarly for FFBPN Tan-sig function gives best value of performance, while 4-2-1, 4-4-1, 4-6-1, 4-8-1, and 4-9-1 architectures are considered. Preeminent model architecture for Tan-sig function is found to be 4-2-1 which possess MSE training and testing value 0.000234, 0.001798, RMSE training and testing value 0.001118, 0.001196 and R ${}^{2}$ for training and testing value0.9327 and 0.9481. Superlative model architecture in case of Log-sig is 4-8-1, which possess R ${}^{2}$ for training and testing 0.9247, 0.9409. The inclusive outcomes are accessible in Table 2 and performance results in context to actual versus predicted is presented in Fig. 6.

Correspondingly for CFBPNN, 4-2-1, 4-4-1, 4-6-1, 4-8-1, and 4-9-1 architectures are considered. The finest model architecture is 4-8-1 having MSE training and testing value 0.000229, 0.001995, RMSE training and testing 0.001209, value 0.001102 and coefficient R ${}^{2}$ training and testing 0.9001 and 0.9123. For Log-sig greatest model architecture is found to be 4-4-1 which possess coefficient of determination value for training and testing 0.8912, 0.9079. The detailed outcomes are available in Table 3 and actual versus predicted graph is presented in Fig. 7.

5. Simulation

Deviation of actual runoff vs. predicted runoff is shown in Fig. 8. It can be observed from outcomes that estimated peak runoffs are 149.272 mm, 141.208 mm, and 142.313 mm for BPNN, CFBPNN, and FFBPNN verses actual peak 157.29 mm for Kalahandi.

6. Conclusion

Present study aims to predict runoff taking into consideration humidity, infiltration loss, precipitation, and avg. temperature data. Three NNs are utilized for estimating daily runoff through monsoon phase taking condition for assessment as value of MSE, RMSE and R ${}^{2}$ . BPNN shows preeminent results for Tan-sig transfer function having architecture 3-7-1 and for Log-sig transfer function with 3-5-1 architecture. But for FFBPNN Tan-sig transfer function gives prominent value for architecture 4-9-1. Considering overall results, it can be observed that BPNN gives better results when compared to FFBPNN and CFBPNN having confidence limit of performance ranging about $\pm$ 10%, $\pm$ 16%. Present study will assist in water preservation, control erosion of soil and hydraulic structure design to develop the watershed. Output of current investigation signifies suitable method to estimate runoff in arid region.

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