Utilizing RBF-NN and ANFIS Methods for Multi-Leadahead Prediction Model of Evaporation from Reservoir

Mohammed Falah Allawi1 & Ahmed El-Shafie2,1

Received: 27 May 2016 /Accepted: 24 July 2016 /Published online: 28 July 2016# Springer Science+Business Media Dordrecht 2016

Abstract Evaporation as a major meteorological component of the hydrologic cycleplays a key role in water resources studies and climate change. The estimation ofevaporation is a complex and unsteady process, so it is difficult to derive an accuratephysical-based formula to represent all parameters that effect on estimate evaporation.Artificial intelligence-based methods may provide reliable prediction models for severalapplications in engineering. In this research have been introduced twelve networks withthe RBF-NN and ANFIS methods. These models have applied to prediction dailyevaporation at Layang reservoir, located in the southeast part of Malaysia. The usedmeteorological data set to develop the models for prediction daily evaporation rate fromwater surface for Layang reservoir includes daily air temperature, solar radiation, panevaporation, and relative humidity that measured at a case study for fourteen years. Theobtained result denote to the superiority of the RBF-NN models on the ANFIS models. Acomparison of the model performance between RBF-NN and ANFIS models indicatedthat RBF-NN method presents the best estimates of daily evaporation rate with theminimum MSE 0.0471 , MAE 0.0032, RE and maximum R2 0.963.

Keywords Radial basis function neural network (RBF-NN) . Adaptive neuro-fuzzy inferencesystem (ANFIS) . Evaporation rate . Reservoir

Water Resour Manage (2016) 30:4773–4788DOI 10.1007/s11269-016-1452-1

* Mohammed Falah Allawimohmmd.falah@gmail.com

1 Civil and Structural Engineering Department, Faculty of Engineering and Built Environment,Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia

2 Department of Civil Engineering, Faculty of Engineering, University Malaya, Jalan Universiti,Wilayah Persekutuan Kuala Lumpur, 50603 Kuala Lumpur, Malaysia

1 Introduction

1.1 Background

Evaporation is a major meteorological component of the hydrologic cycle plays a keyrole in water resources studies and climate change. The accurate estimation of theevaporation, one of the main parameters of the hydrological cycle, is vital for variousfields of study such as hydrologic water balance, water resources planning and improv-ing water usage. It is commonly stored water by many structures such as dams, but thereare approximate to half from these water may be lost due to the evaporation phenomenaleading to a huge waste of our resources.

In additional, the reservoir storage is fundamental for developing reliable watersupplies and is a main component of the river system water budget. The water level inwater reservoirs fluctuates greatly over time with the difference in water use andhydrologic conditions that range from severe multiple-year droughts to floods. Watersurface evaporation typically represents a major component of the reservoir waterbudget. Therefore, the estimating of evaporation rate from the reservoir is a hard taskespecially there are a number of factors affecting the evaporation process, like theclimate and physiography of the water body and its surroundings.

There are empirical approaches available for estimating evaporation like (direct methodsinclude the application of (class A pan, class U pan) and indirect methods such as Penman –Monteith, Priestley-Taylor and others types of measurement), however, their accuracy is notsatisfactory because the evaporation is a complex and unsteady process. Therefore it is difficultto an accurate physical-based formula to appear all the physical meaning involved.

In order to the researchers proposed other advanced methods consider nonlinear and non-stationary characteristic of the natural data such as artificial neural network and adaptiveneuro-fuzzy inference system that have been successfully utilized in many field in waterresource suck as stream flow (Kişi 2008; Singh and Cui 2015; El-Shafie et al. 2009; Sanikhaniand Kisi 2012), water quality (Heddam 2016; Heddam et al. 2016; Kontos and Katsifarakis2012), operation and planning reservoir (Spiliotis 2014; Cervarolo et al. 2012), sediment (Afanet al. 2015), water level ( Hipni et al. 2013), evapotranspiration (El-Shafie et al. 2013; El-Shafie et al. 2014), evaporation (Eslamian et al. 2008; Keskin and Terzi 2006; Kişi 2009a; Kişi2009b; Moghaddamnia et al. 2009; Piri et al. 2009; Samui 2011; Sudheer et al. 2002; Tabariet al. 2010; Terzi and Erol Keskin 2005).

Kişi (2009a) compared between three different neural network techniques (multi-layer perceptron’s (MLPS), radial basis neural networks (RBNNs) and generalizedregression neural networks (GRNNs)) to estimate evaporation. The researcher is foundthe RBNN and MLP could be employed successfully to model evaporation processusing the available climate data.

Samui (2011) investigated the potential of least square support vector machine (LS-SVM)for prediction of evaporation losses from Anand Sagar reservoir, India. Tabari et al. (2010)estimated daily pan evaporation using ANN methods and multivariate non-linear regressionmethods in the semi-arid region of Iran.

Eslamian et al. (2008) utilized SVM and ANN models for estimation of pan evaporationused consider effect many meteorological variables like humidity, solar radiation, air temper-ature, precipitation and wind speed. Guven and Kişi (2011) compared between ANN modelwith linear genetic programming to predict daily pan evaporation.

4774 Allawi M.F., El-Shafie A.

1.2 Problem Statement

It is known that the evaporation process is complex where the effect of many physicalparameters the value evaporation. The empirical methods are unable to consider all parametersfor estimate evaporation, therefore the accuracy of these methods are not acceptable. On theother hand, these methods incapable of estimating evaporation rate when obscene some datalike (wind speed, relative humidity, sun shine and air temperature). Thus, It necessary findmethod have the ability to estimate values of evaporation in the case of losses one or morefrom these parameters. Different studies were carried out in order to compare and evaluateevaporation methods or calculate of required parameters in limited data conditions around theworld. On the other hand, there are many studies looked for to find the suitable methods toestimate evaporation in case miss some data that effect on evaporation process. In order, thereis no clear unanimity on which methods are best to employ lacking important long termmeasured data like (Air temperature, Relative humidity, Wind speed, Radiation) as in the casein some reservoir in Malaysia.

In this context, there is a critical need to assess more reasonable scenarios for estimatingevaporation rate under conditions of lost some of the measured data. In this article have beeninvestigated which method (RBF-NN and ANFIS) have the ability to estimate evaporation forhigh accuracy in under these conditions.

1.3 Objectives

The main objective of the current research is applying Radial Basis Function neural Network(RBF-NN) and adaptive neuro-fuzzy inference system (ANFIS) models and examine theirpotential to achieve the consistent and reliable accuracy level for evaporation prediction.Twelve networks have been used to investigate perform the proposed models. Comprehensivecomparative analysis has been evaluated and discussed on the results achieved. The remainderof the article is organized in the following manner. Section 2 gives the description of the casesstudies and data collection. Section 3 expresses the methodology part. Application and analysispresented in section 4. Finally, section 5 is the conclusion.

2 Case Study

The Layang reservoir is located in the Johor region. Johor is located in the southern region ofpeninsular Malaysia. Johor region has a river called Johor river, Johor river is originated fromits source of Sungai Linggui/Sayong in the upstream before merging to Sungai Johor andflows down southeast to estuarine of Johor Straits. Downstream major tributaries are SungaiTiram and Sungai Lebam (DID). The highest elevation in the basin based on the availableDEM is 600-m and the lowest point is 4 m. The Layang reservoir located on the one of thebranch Johor River as shown in Fig. 1. The total drainage basin for both Layang reservoir is50.5 Km2.

For the purposes of this study, daily meteorological parameters. The data sample consistedof 14 years (1975–1988) of daily records air temperature (T, 0C), mean relative humidity(Rh,%) ,solar radiation (RS) and pan evaporation ( PE, mm). The input architecture for twomethods considers all these parameters as input to find evaporation rate. The mean monthly foreach parameter are presented in Table 1.

Utilizing RBF-NN and ANFIS for evaporation prediction 4775

3 Methodology

3.1 Radial Basis Function Neural Network (RBF-NN)

The ANNs have become an attractive computational tool because the ANNs methods have thecapability to work well even when the training sets contain noise and measurement errors.ANNs can recognize the relation between the input and output parameters without explicitphysical consideration and also can adapt to solutions over time to retrieve changing circum-stances. The network model of the multi-layer perceptron architecture is based on units, which

Fig. 1 The Layang Reservoir at Johor River Basin

Table 1 Monthly means of the main climate variables during 1975–1988

Month Tmax (°C) Tmean (°C) Tmin (°C) Rh (%) RS (MJ m−2/day) PE (mm)

January 31.5 26.5 22.2 78 12.3 1.5

February 32.1 27.3 22.4 75 15.2 0.9

March 34 28.5 23 77 18.2 1.58

April 33 25.8 24 76 21.6 2.54

May 31.9 25.3 23.8 83 27.5 3.34

June 31.7 26.8 23.2 82 30.4 4.6

July 31.3 29.7 22 79 26.2 4.1

August 30.9 28.9 22.2 73 28.1 3.2

September 30.5 26.3 21.6 72 25.5 2.6

October 29.8 25.5 21 79 19.5 1.75

November 30.4 24.7 20.3 81 14.5 1.3

December 29.5 23.8 20.5 80 11.8 0.75

4776 Allawi M.F., El-Shafie A.

compute a non-linear function of the scalar product of the input vector and the weight vector.An alternative architecture of ANN is one in which the distance between the input vector and acertain prototype vector determines the activation of a hidden unit. This architecture is knownas a radial basis function neural network (RBF-NN) (El-Shafie et al. 2014).

Radial basis function Neural network (RBF-NN) was originally proposed by Broomheadand Lowe (1988). The RBF-NN method consists of an input layer, a single hidden layer with aradial basis activation function, and a linear output layer. The connection between input layerspace and output layer space by a non-linear transformation, while between the hidden layerspace and output layer space by linear transformation function. The most commonly used isthe Gaussian, which in its one-dimensional representation takes the following Eq. 1

φ x;μð Þ ¼ ex−μk k∧22d2 ð1Þ

Where μ is the center of the Gaussian function (mean value of x) and d is the distance(radius) from the center of φ(x, μ), which gives a measure of the spread of the Gaussian curve.Gaussian radial function behavior to the input data (see Fig. 2). Clearly, the larger the spreadvalue the less sensitivity of radial basis function to the input data. The number of radial basisfunctions inside the hidden layer depends on the complexity of the mapping to be modeled andnot on the size of the data set (Haykin 1999; Ripley 1996).

The length of input data set, the location of neurons and determination of other trainingparameters are quite important during the training of RBNN. The location of the first centermay be chosen from the training data set, and the standard deviation r (i.e. width) of the j theneuron is;

σ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffid2maxjþ 1

sð2Þ

jr ¼1

2

X k

i¼1Eobs−Tnetð Þ2 ð3Þ

Where, d max is the maximum distance between training data set, Tnet is the response of thenetwork, Eobs is observation value (Here the observation values are pan evaporation). Thetraining process continues until this error reaches an acceptable value. The advantages ofutilizing RBF-NN are MLP-NN can have many layers of weights with a relatively complex

(a) (b) (c)

Fig. 2 RBFNN with three levels of spread. a Normal spread. b Small spread. c Large spread

Utilizing RBF-NN and ANFIS for evaporation prediction 4777

pattern of connectivity. Several activation functions can be used within the samenetwork. However, RBFNN has a more simple architecture that consists of two layersof weights in which the first layer contains the parameters of the basis functions andthe second layer forms linear combinations of these basis functions to generate waterquality parameter the output. The unique architecture of the RBFNN has the advan-tage of a fast training procedure when compared to multi-layer perceptron ANN. Thesecond advantage is parameters of the multi-layer perceptron ANN (biases andweights) are determined simultaneously during the training procedure with supervisedtraining techniques. On the other hand, RBFNN is typically trained in two stages withthe parameters of the basis functions being first determined by unsupervised learningtechniques using the input data alone. The weights at the second layer are found byfast linear supervised methods.

3.2 Adaptive Neuro Fuzzy Inference System (ANFIS)

A neural-fuzzy model is an effective approach for modeling nonlinear systems likeevaporation data due to the combination of fuzzy logic systems and advantage ofneural systems. The neuro-adaptive learning techniques provide a method for thefuzzy modeling procedure to gain information about a dataset, in order to computethe membership function parameters which allow the associated fuzzy inferencesystems to track the given input-output data (Jang 1993).

ANFIS is a composition of the neural network and Zadeh’s fussy system (zadeh1965) which uses the potential of ANN to learn from input-output data. The generalstructure of the ANFIS includes two (x,y) inputs, with each one having two mem-bership functions, and one output. It has five layers with several types of nodes. For afirst-order Sugeno fuzzy model, a common rule set with two fuzzy if-then rules isdefined as (Eq.4 and 5).

Rule 1 : if x is x1 and y is y1 then f 1 ¼ p1χþ q1yþ r1 ð4Þ

Rule 2 : if x is x2 and y is y2 then f 2 ¼ p2χþ q2yþ r2 ð5ÞWhere xi and yi (i = 1,2) are the membership functions, related to x,y inputs, as well as the

output parameters are pi, qi, and ri (I = 1,2). The following are the nodes descriptions whichhave the same function in each layer.

Layer 1 square nodes in this layer generate the membership grades of crisp input variables.The output of each node will be defined by

E1i ¼ μAi xð Þ For i ¼ 1; 2 ð6Þ

E1i ¼ μBi yð Þ For i ¼ 3; 4 ð7Þ

Where x or y are the inputs of node i, and Ai, Bi are the linguistic fuzzy set associated, (low,high) specified the shape of membership (μAi, μBi).

Different shapes of membership functions (MFs) with different classes of parameters aredefined. The adaptive fuzzy interface systems is an influence by these shapes. The main reason

4778 Allawi M.F., El-Shafie A.

for their popularity for specifying fuzzy sets is smoothness of Generalized-Bell and Gaussianfunctions. The bell shape function is defined by (Eq. 8 and 9)

μAi ¼1

1þ xþciai

��� ���2bið8Þ

μAi ¼1

1þ x�ciai

��� ���2bið9Þ

Where a,b and c are the parameters of the bell-shape membership function that change theshape of the membership function.

Layer 2 Every node in this layer multiplies the incoming signals and sends the productwhich represents the firing strength of a rule (Eq. 10).

E2i ¼ wi ¼ μAi xð ÞμBi yð Þ For i ¼ 1; 2 ð10Þ

Layer 3 The function of this layer is to calculate the weight of firing strength for ith node tothe sum of all rules firing strength (Eq.11).

E3i ¼ ϖi ¼ ωiX

ωi

For i ¼ 1; 2 ð11Þ

Layer 4 Every node in this layer is a square node with a node function (Eq.12)

E4i ¼ ϖi f i ¼ ϖi pixþ qiyþ rið Þ For i ¼ 1; 2 ð12Þ

Where ϖi is the output of layer 3, and (pi, qi, ri) is the parameters set referred to asconsequence or as consequent parameters (Eq.5).

Layer 5 The single node in this layer is the output note which computes the overall outputof summing all incoming signals (Eq.13).

E5i ¼

Xwi f iXwi

ð13Þ

3.3 Model Evaluation

The performance of a model is evaluated based on the comparison between the actual valuesand predicted values. The prediction of each model is evaluated utilizing the mean square error(RMSE), relative error (RE %), correlation of coefficient (R2) and mean absolute error (MAE).Formulas for estimating MSE, RE %, R2, and MAE are given as follows:

R2 ¼X n

t¼1E0 tð Þ−E�0 tð Þ

� �Es tð Þ−E�s tð Þ

� �h iffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX n

t¼1E0 tð Þ−E�0 tð Þ

� �2X n

t¼1Es tð Þ−E�s tð Þ

� �2r ð14Þ

Utilizing RBF-NN and ANFIS for evaporation prediction 4779

MSE ¼ 1

N

Xn

t¼1

E0 tð Þ−Es tð Þð Þ2 ð15Þ

RE ¼ E0 tð Þ−Es tð ÞE0 tð Þ

� �*100 ð16Þ

MAE ¼ 1

N

X n

t¼1E0 tð Þ−Es tð Þj j ð17Þ

Where E0 (t), Es(t), Ê0 (t), Ês (t) are the observed evaporation values, simulated evaporationvalues, mean observed evaporation, mean simulated respectively; n is the number of obser-vations or time periods over which the errors are simulated.

3.4 Model Structure

In this article have been applied two methods namely: Radial Basis Function Neural Network(RBF-NN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) to predict the pan evapo-ration. In fact, PE, Tmean, RS and RH data were collected daily over the 14 years between 1975and 1988 at Layang Reservoir, Malaysia. These data were used to train, validate and test theproposed model. Actually, the data splitting into to these three stages in order to evaluate theproposed model. The training session is for building the model, the test session is consideredfor the initial examination of the model performance using unseen dataset. On the other hand,the validation session is considered to evaluate the consistency of the model performance withanother unseen data input set. It can be observed from the data collected during 14 years thatthe model experienced all possible pattern the pan evaporation, which substantiates thereliability of the proposed model accuracy.

The model structure is organized using daily data for each month individually. To achievethe desired prediction accuracy, twelve RBF-NN and ANFIS architectures have been devel-oped (1 per month). Daily Tmean, RS, RH and PE values for the 12 years from 1975 to 1986were used to train 12 networks. The performance and reliability of RBF-NN and ANFISmodels were examined with the data actual for the year 1987 (validation phase). The capabilityof the developed RBF-NN and ANFIS models were further verified for the year 1988 (testphase). Figure 3 shows the architecture of the RBF-NN and ANFIS methods, including aninput layer, output layer and hidden layer. The input layer consists of 4 neurons thatcorresponding to the actual Tmean, RS, RH, and PE. The output layer consist of 1 neuron(corresponding to the predicted evaporation rate).

4 Result and Discussion

Several methods were used to examine the best performance. The selection of the bestmodel in each method was based on the amount error between actual values andpredict during the test period (1 year) for each month. This section provides a detaileddescription and analysis of the proposed methods when applied to evaporation rate

4780 Allawi M.F., El-Shafie A.

from reservoir. It should be noticed that the utilized data for the case study iscontinuous and there is some missing data during the period of study.

The performance criteria for RBF-NN and ANFIS methods are shown in Table 2, whichwere designed to prediction monthly evaporation. According to the result, the lower value ofMSE and MAE was reached with RBF-NN method (June model) while May model achievedwas the high correlation of coefficient (R2) reached 0.963. On the other hand, the better modelby using ANFIS method is June model. It has a lower value of MSE and MAE (0.0986 and0.0078) respectively over the test period. In addition, the model for May obtained the highvalue of correlation of coefficient (R2) reached 0.928.

Fig. 3 The architecture of the RBF-NN and ANFIS

Utilizing RBF-NN and ANFIS for evaporation prediction 4781

Tab

le2

The

performance

criteria(M

SE,M

AEandR2)values

fortwomethods

RBF-NN

ANFIS

Training

Validation

Testing

Training

Validation

Months

MAE

MSE

R2

MAE

MSE

R2

MAE

MSE

R2

MAE

MSE

R2

MAE

MSE

R2

MAE

MSE

R2

January

0.228

0.0929

0.88

0.13

0.032

0.85

0.2572

0.2023

0.927

0.217

0.091

0.87

0.175

0.035

0.82

0.2854

0.2536

0.892

February

0.151

0.057

0.92

0.125

0.032

0.928

0.1013

0.0164

0.933

0.142

0.062

0.88

0.153

0.037

0.85

0.1852

0.0288

0.901

March

0.114

0.027

0.97

0.084

0.013

0.92

0.1331

0.0327

0.906

0.162

0.074

0.923

0.124

0.022

0.875

0.1923

0.0651

0.875

April

0.165

0.054

0.965

0.147

0.037

0.955

0.1816

0.0488

0.94

0.182

0.072

0.912

0.182

0.039

0.918

0.2024

0.0767

0.912

May

0.164

0.051

0.929

0.163

0.058

0.934

0.1343

0.0269

0.963

0.172

0.053

0.891

0.165

0.061

0.925

0.1752

0.0475

0.928

June

0.206

0.07

0.897

0.211

0.072

0.918

0.0471

0.0032

0.922

0.301

0.091

0.865

0.284

0.077

0.932

0.0986

0.0078

0.852

July

0.228

0.092

0.885

0.19

0.059

0.858

0.2605

0.0848

0.877

0.245

0.012

0.891

0.21

0.061

0.832

0.2827

0.0977

0.836

August

0.209

0.077

0.90

0.229

0.076

0.92

0.2121

0.0645

0.925

0.213

0.079

0.88

0.236

0.082

0.912

0.2642

0.0868

0.879

Septem

ber

0.169

0.051

0.906

0.145

0.04

0.957

0.1526

0.0348

0.957

0.173

0.057

0.872

0.166

0.051

0.934

0.1844

0.0531

0.918

October

0.141

0.04

0.91

0.099

0.024

0.875

0.1002

0.0176

0.913

0.172

0.063

0.902

0.102

0.028

0.882

0.1354

0.0397

0.862

Novem

ber

0.116

0.032

0.96

0.102

0.02

0.918

0.1134

0.0286

0.85

0.145

0.038

0.935

0.109

0.04

0.912

0.1568

0.0495

0.805

Decem

ber

0.099

0.027

0.97

0.115

0.072

0.959

0.2010

0.0569

0.868

0.104

0.033

0.956

0.166

0.077

0.943

0.3112

0.0985

0.836

4782 Allawi M.F., El-Shafie A.

In order to evaluate the proposed methods, two different figures are presented. Figure 4(a,b)show the observed versus the predict values of the evaporation for the May model, Fig. 4a byusing RBF-NN method, Fig. 4b by using ANFIS method. This fig. Presents the detail of theobserved and prediction evaporation for the testing period.

The simulation between actual values for pan evaporation with predict that provided byRBF-NN and ANFIS methods for June is presented in Figure 4 (c, d). Figure 4c describe thematching time series for June using RBF-NN. On the other hand, the performance for ANFISto predict evaporation values shown in Fig. 4d. It could be noticed that the proposed modelscould provide prediction values of the evaporation. The examined models exhibit a remarkablegoodness in term of matching between the observed and prediction evaporation. For assess-ment of the effectiveness of the data-driven models, it seems reasonable to investigate thelinear relationship between the observed and prediction time series for the testing period.

The scatter form shows in Fig. 5 between of the pan evaporation value with the predictedevaporation value for all models using RBF-NN. It is observed the May model better thananother models, where recorded highly R (0.964). Figure 6 shows the scatter plot betweenactual and predicted evaporation for 12 models using ANFIS. Clearly from this figure that theMay model recorded highly R reached to (0.928). It can be observed that the RBF-NNapproach was the ability to obtain high accuracies if compare with the ANIFS method.

One of the most important performance indicators in this research is a relative error. Therelative error demonstrates the percentage of the difference between observed and predicteddata. Relative error (%RE) for all models over testing period have been calculated by theformula (15). Table 2 showed details for the distribution error over the test period where thereis three zone have been presented in Table 2 namely, first zone the error between predict valueswith the actual values less than 5 %, second zone ARE between 5 % and 10 % while in thethird zone the relative error recorded more than 10 % between predict and observe. Clearly, thebest three models that by using RBF-NN method were June, May and October models. Thefirst model is model June who recorded 53.33 % from its values within the first zone. The Maymodel obtained 20 % from its values within the first zone. The results indicator that theOctober model recorded high percentage in the first zone (56.66 %). On the other hand, thesemodels were recorded in the second zone 40 % for model June, 76.66 % for model May and

Fig. 4 Evaporation prediction using RBF-NN and ANFIS methods for May and June

Utilizing RBF-NN and ANFIS for evaporation prediction 4783

23.34 % for model October. It observed from those results that the May and June modelrecorded approximately (96.6 and 93 %) respectively from its values got on error less than10 % while October model appear 80 % from its values over test period got on the errorbetween predict and actual values less than 10 %.

From another side, ANFIS method obtains a good result where the percentage was formodel May, June, and October within the first zone are 13.34, 40 % and 43.34 % respectively.

Fig. 5 Scatter plots between predicted and actual for the testing phase by ANN method

Fig. 6 Scatter plots between predicted and actual for the testing phase by ANFIS method

4784 Allawi M.F., El-Shafie A.

Furthermore, the indicate results that these models got on percentage 56.67 %, 33.34 %and 13.34 % from the total of its values (30 days) within the second zone. In order to,observed that there are 70 %, 73.34 % and 63.68 from values of model May, June andOctober respectively were obtained on error less than 10 % between actual and predict.Figure 7 present the relative error between predict and actual through test period forthese models for each method.

4.1 RBF-NN Model versus ANFIS Model

To compare the RBF-NN to existing modeling techniques, we compared the prediction error ofthe RBF-NN with the prediction error from ANFIS models. Table 2 shows the comparison ofthe performance of the RBF-NN to the ANFIS models using the correlation of coefficient (R2),mean square error (MSE), relative error (RE %), and mean absolute error (MAE) werecalculated from (Eq. 13,14,15 and 16) respectively as indicators for performance each method.It is obvious that the RBF-NN model outperformed the ANFIS models.

Scatter plots are illustrated in Fig. 5 and Fig. 6 for all models using two methods. It can benoticed that all models that proved successful that reach values of R higher that 70 %, whichsuggests that the proposed methods could provide prediction values of evaporation stronglycorrelated with the actual evaporation values. It is clear from Figs. 5 and 6 performance forRBF-NN method better than performance ANFIS method.

Finally, to have a whole comparison among all the investigated methods namely,RBF-NN and ANFIS with a comprehensive detailed analysis, the distribution error hasbeen examined over the testing phase period. Table 3 illustrates the accomplished resultsfor each month using two methods. It can be seen that in general all models performedwell by RBF-NN. In particular, the residual error for the testing phase remarkablyimproved using the established model RBF-NN. According to Table 3, the error per-centage less than (+10,-10) for approximately 93 % from the test period for the bestmodel who the May model using RBF-NN approach. This reveals that a high level ofaccuracy could be obtained with artificial neural network method. On the other hand, amodel for May by ANFIS method recorded 73 % from total its values through a testingphase on error less than 10 %. These results noticed that the RBF-NN method has highaccuracy if compared with the ANFIS method.

Fig. 7 The error distribution for BF-NN and ANFIS during testing st

Utilizing RBF-NN and ANFIS for evaporation prediction 4785

5 Conclusion

In this study have been used two methods namely, RBF-NN and ANFIS to predict evaporationrate from water surface for the Layang reservoir at Malaysia. In order to achieve the desirableprediction accuracy, twelve RBF-NN and ANFIS architecture were used developed (one foreach month). Daily pan evaporation and metrological data for a period of fourteen years, 1975to 1987 were utilized to training and validation networks. The performance and the reliabilityof the RBF-NN and ANFIS models were examined using the evaporation data monitored forthe year 1988.

Comparison analysis has been developed between the proposed RBF-NN model andANFIS model. Twelve networks were employed for the input-output pattern of the RBF-NNand ANFIS model architecture to optimize the accuracy level. According to the result that theRBF-NN model outperformed the ANFIS model and achieved reliable performance, includinglow MAE, MSE, and high R2 result.

This research has managed to integrated different analytical and modeling methods for eachmonth that would prove to be useful for a various establishment that is directly shared in thewater resource management. In additional, the techniques were used in this paper could form abasis for a more effective decision-making process on the part of the policymakers in order tohelp improve and maintain the water resources management especially in hydrology.

Although, the proposed model provides the suitable flexibility to fit the evaporationphenomenon procedure and achieved relatively good accuracy, the model showed somedrawback for the peak values. In this context, a need to explore a new method for evaporationprediction is crucial. Offering an high-order function with the effective nonlinear processwould be more reliable for better evaporation prediction model. In addition, such model couldprovide an explicit function for such complex prediction stochastic parameter. Therefore, it isrecommended in future research for developing evaporation prediction model to introduce amethod with highly nonlinear polynomial functions that can be provided an accurate predic-tion of an explicit mathematical function.

Table 3 The error distribution percentage between actual and predicted values during test phase

ANN ANFIS

Month ARE 5 % 5 % ARE 10 % ARE 5 % 5 % ARE 10 %

Percentage Percentage Percentage Percentage

January 26.66 6.66 16.67 10

February 20 26.66 13.34 23.34

March 40 30 33.34 33.34

April 36.66 40 26.67 36.67

May 20 76.66 13.34 56.67

June 53.33 40 40 33.34

July 33.33 53.33 30 40

August 46.66 33.33 36.67 26.67

September 43.33 33.33 33.33 30

October 56.66 23.34 43.34 13.34

November 40 26.67 30 16.67

December 40 33.33 33.34 30

4786 Allawi M.F., El-Shafie A.

The AI method, in general, experienced several drawbacks while applying morespecifically for natural phenomenon such as evaporation. While developing AI method,in some case, there is a need to investigate the raw data and develop appropriate pre-processing for the raw data in order to detect the noise in the data. In addition, the AImethod should be integrated with a proper optimization method for re-adjusting theinternal structure parameters of the method used. Finally, for few types of AI methodssuch as Multi-Layer Perceptron Artificial Neural Network (MLP-ANN) and AdaptiveNeuro-Fuzzy Inference System (ANFIS), due to the complexity of their internal archi-tecture, there is a need to randomly select few parameters and then examine the results,in case of low accuracy, several trial and error procedure have to be carried out in orderto achieve the acceptable level of accuracy.

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