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Predicting daily pan evaporation by soft computingmodels with limited climatic dataSungwon Kima, Jalal Shirib, Vijay P. Singhc, Ozgur Kisid & Gorka Landerase

a Department of Railroad and Civil Engineering, Dongyang University, Yeongju, Republicof Koreab Water Engineering Department, Faculty of Agriculture, University of Tabriz, Tabriz, Iranc Department of Biological and Agricultural Engineering & Zachry Department of CivilEngineering, Texas A & M University, College Station, TX, USAd Department of Civil Engineering, Architecture and Engineering Faculty, Canik BasariUniversity, Samsun, Turkeye NEIKER, Basque Institute of Research and Agricultural Development, Alava, BasqueCountry, SpainAccepted author version posted online: 24 Jul 2014.

To cite this article: Sungwon Kim, Jalal Shiri, Vijay P. Singh, Ozgur Kisi & Gorka Landeras (2014): Predictingdaily pan evaporation by soft computing models with limited climatic data, Hydrological Sciences Journal, DOI:10.1080/02626667.2014.945937

To link to this article: http://dx.doi.org/10.1080/02626667.2014.945937

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Publisher: Taylor & Francis & IAHS Press

Journal: Hydrological Sciences Journal

DOI: 10.1080/02626667.2014.945937

Predicting daily pan evaporation by soft computing models

with limited climatic data

Sungwon Kim1*

, Jalal Shiri2, Vijay P. Singh

3, Ozgur Kisi

4, Gorka Landeras

5

1Associate Professor, Department of Railroad and Civil Engineering, Dongyang University,

Yeongju, Republic of Korea

2Water Engineering Department, Faculty of Agriculture, University of Tabriz, Tabriz, Iran

3Caroline & William N. Lehrer Distinguished Chair in Water Engineering and Distinguished

Professor, Department of Biological and Agricultural Engineering & Zachry Department of

Civil Engineering, Texas A & M University, College Station, Texas, USA

4Department of Civil Engineering, Architecture and Engineering Faculty, Canik Basari University,

Samsun, Turkey

5NEIKER, Basque Institute of Research and Agricultural Development, Alava, Basque Country,

Spain

* Corresponding author: Phone: 82-54-630-1241; Fax:82-54-637-8027; Email:

swkim1968@dyu.ac.kr

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Accurate prediction of daily pan evaporation (PE) is important for monitoring,

surveying, and management of water resources as well as reservoir management and

evaluation of drinking water supply systems. This study develops and applies soft

computing models to predict daily PE in a dry climate region of south-western Iran. Three

soft computing models, namely multilayer perceptron-neural networks model (MLP-

NNM), Kohonen self-organizing feature maps-neural networks model (KSOFM-NNM),

and gene expression programming (GEP), were considered. Daily PE was predicted at two

stations using temperature-based, radiation-based, and sunshine duration-based input

combinations. Results obtained by the temperature-based 3 (TEM 3) model produced the

best results for both stations. The Mann-Whitney U test was employed to compute the

rank of different input combination for hypothesis testing. Comparison between the soft

computing models and multiple linear regression model (MLRM) demonstrated the

superiority of MLP-NNM, KSOFM-NNM, and GEP over MLRM. It was concluded that

the soft computing models can be successfully employed for predicting daily PE in south-

western Iran.

Key Words: soft computing models, pan evaporation, Mann-Whitney U test, limited

climatic data, multiple linear regression

Evaporation is the process of conversion of liquid water to water vapor. Evaporation

from free water surface depends on energy supply, difference in vapor pressure between

the surface and atmosphere, and exchange of surface air with the surrounding atmospheric

air (Penman 1948). Evaporation from the land surface consumes about 61 percent of total

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global precipitation (Chow et al. 1988), and hence it is an important component of the

hydrological cycle and its quantitative study is one of the important issues in water

resources engineering. Nevertheless, the continuous hydrological simulation models often

need at least the input data of precipitation and evaporation (Kay and Davies 2008). Pan

evaporation (PE) is widely used to estimate evaporation from lakes and reservoirs (Finch

2001).

Both direct and indirect methods have been employed to estimate evaporation. Direct

methods, such as evaporation pans, have also been used and compared to estimate

evaporation by other methods (Choudhury 1999, Vallet-Coulomb et al. 2001). The most

widely used pan is the U.S. Weather Bureau Class A pan, which is 21 cm in diameter,

25.5 cm deep, and mounted on a timber grid 15 cm above the soil surface. The pan

coefficient is a function of the type of pan and the size and state of the upwind buffer zone

and defines the ratio of the amount of evaporation from a large body of water to that

measured from an evaporation pan. It ranges from 0.35 to 0.85 for different conditions

(Allen et al. 1998). Indirect methods for estimating evaporation are based on different

climatic variables, but some of these techniques require data which cannot be easily

obtained (Rosenberry et al. 2007).

During the past decade, a variety of soft computing models have been developed and

applied for the estimation of evaporation (Bruton et al. 2000, Sudheer et al. 2002, Terzi

and Keskin 2005, Keskin and Terzi 2006, Kisi 2006, 2009, Tan et al. 2007, Kim and Kim

2008, Tabari et al. 2009, Chang et al. 2010, 2013, Guven and Kisi 2011, Shiri et al. 2011,

Shiri and Kisi 2011, Kim et al. 2012, 2013, Kisi et al. 2012, Shiri et al. 2013). In this

study, soft computing models, including multilayer perceptron-neural networks model

(MLP-NNM), Kohonen self-organizing feature maps-neural networks model (KSOFM-

NNM), and gene expression programming (GEP), have been applied to predict daily PE

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from available climatic data.

-

- support

vector machines neural networks model (SVM-NNM), and constructed credible

monthly PE data from the disaggregation of yearly PE data.

KSOFM-NNM transforms an input of arbitrary dimension into a one or two

dimensional discrete map subject to a topological (neighborhood preserving) constraint.

The feature maps are computed using the Kohonen unsupervised learning. The output of

SOFM can be used as input to a supervised classification neural network, such as MLP.

Chang et al. (2010) proposed a self-organizing map (SOM) neural network to assess the

variability of daily evaporation based on meteorological variables. They demonstrated that

the topological structures of SOM could yield a meaningful map to present clusters of

meteorological variables and the networks could well estimate daily evaporation.

GEP employs a parse tree structure for the search of solutions. This technique has the

capability for deriving a set of explicit formulations that rule the phenomenon and

describe the relationship between independent and dependent variables using various

operators. Shiri and Kisi (2011) investigated the capabilities of GEP to improve the

accuracy of daily evaporation estimation and demonstrated that the proposed GEP

performed quite well in modeling evaporation from climatic data.

Although there have been many soft computing models, their applications for predicting

evaporation have been limited. The present study investigates the capabilities of MLP-

NNM, KSOFM-NNM, and GEP, and conventional multiple linear regression model

(MLRM) for predicting daily PE.

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Used data

Daily climatic data of two automated weather stations, Ahwaz station (latitude 31◦20'N,

longitude 48◦40'E, elevation 22.5 m above mean sea level) and Izeh station (latitude 31◦

51'N, longitude 49◦52'E, elevation 767 m above mean sea level), operated by the

Khozestan Meteorological Organization (KMO) in Iran, were used in this study. The

distance between Ahwaz and Izeh stations is about 205 km. Figure 1 shows the location of

weather stations in south-western Iran. The basic data of Ahwaz and Izeh stations

consisted of seven years (2002-2008) of daily records of mean air temperature (T), mean

wind speed (U), sunshine duration (SD), mean relative humidity (RH), and pan

evaporation (PE) as well as computed extraterrestrial radiation (R).

The cross-validation method provides a rigorous test of neural networks skill (Dawson

and Wilby 2001). It involves dividing the available data into three sets: a training set, a

cross-validation set, and a testing set. The training set is used to fit the connection weights

of neural network model, the cross-validation set is used to select the model variant that

provides the best level of generalization, and the testing set is used to evaluate the chosen

model against unseen data. In this case, the first five years of data (71.4% of the whole

data set, 2002-2006) were used to train MLP-NNM, KSOFM-NNM, and GEP, and the

remaining two years data (2007-2008) were used to cross-validate (14.3% of the whole

data set, 2007) and test (14.3% of the whole data set, 2008) MLP-NNM, KSOFM-NNM,

and GEP, respectively. The reason for this partition is that one full seasonal cycle was

used for training, cross-validation, and testing. This also ensures the statistical properties

of training, cross-validation and testing data sets to be of similar order (Jain et al. 2008).

Tokar and Johnson (1999) suggested that the data length has less effect than the data

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quality on the performance of a neural networks model. Sivakumar et al. (2002) suggested

that it is imperative to select a good training data from the available data series. They

indicated that the best way to achieve a good training performance seems to be to include

most of the extreme events, such as very high and very low values, in the training data.

Table 1 shows statistical parameters of the data used during the study period. In table 1,

Xmean, Xmax, Xmin, Sx, Cv, Csx, SE, 25th

percentile, 75th

percentile, and 90th

percentile denote

the mean, maximum, minimum, standard deviation, coefficient of variation, skewness

coefficient, standard error, 25th

percentile, 75th

percentile, and 90th

percentile values of

each variable, respectively. In both stations, the pan evaporation shows high variation (see

Cv values in Table 1), whereas the extraterrestrial radiation has the lowest variation among

other weather variables. The mean wind speed and sunshine duration data show high

skewed distributions for both stations. Figure 2 shows the time series of daily pan

evaporation and temperature values for both stations during the study period.

Multilayer perceptron-neural networks model (MLP-NNM)

MLP-NNM has an input layer, an output layer, and one or more hidden layers between

input and output layers. Each of the nodes in a layer is connected to all the nodes of the

next layer, and the nodes in one layer are connected only to the nodes of the immediate

next layer (Haykin, 2009). In this study, MLP-NNM is trained with the QuickProp

backpropagation algorithm (BPA) which is a training method that operates much faster in

the batch mode than the conventional BPA (NeuroDimension, 2005). It has the additional

advantage that it is not sensitive to the learning rate and the momentum. Results of the

output layer for the temperature-based model (i.e., TEM 3) can be written as

1

1k

22

1j

21ji1kj2 )B)BX(t)W(ΦW(ΦPE(t) (1)

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where i, j, k = the input, the hidden, and the output layers, respectively; PE(t)= the current

PE (mm/day) at Ahwaz and Izeh stations; )(Φ1

= the linear sigmoid transfer function of

the hidden layer; )(Φ2

= the linear sigmoid transfer function of the output layer; Wkj= the

connection weights between hidden and output layers; Wji= the connection weights

between input and hidden layers; X(t) = the time series data of input nodes comprising 7

inputs corresponding to T(t-3), T(t-2), T(t-1), T(t), PE(t-3), PE(t-2), PE(t-1); 1

B = the bias

in the hidden layer; and2

B = the bias in the output layer. Figure 3 shows the structure of

MLP-NNM based on TEM 3 (7-22-1) developed in this study.

Kohonen self-organizing feature maps-neural networks model (KSOFM-NNM)

KSOFM-NNM performs mapping from a continuous input space to a discrete output

space, preserving the topological properties of the input nodes (Kohonen 1990, 2001,

Principe et al. 2000, Hsu et al. 2002, Lin and Chen 2005, 2006, Chang et al. 2007, Lin and

Wu 2007, 2009). KSOFM-NNM consists of four layers, that is, the input layer, the

Kohonen layer, the hidden layer, and the output layer. The input layer is composed of n

input nodes, each connected to all nodes of the Kohonen layer. The Kohonen layer

consists of [n1 X n1] matrices. In this study, KSOFM-NNM classifies each input node and

determines to which node in the hidden layer it must be routed for predicting daily PE of

the output layer.

The mathematical description of KSOFM-NNM is as follows. Let Wji represent the

connection weights between the input and Kohonen layers of KSOFM-NNM. The

Euclidean distance between the input and the Kohonen nodes can be written as

n

1i

2

jiij)Wx(d (2)

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where i, j = the input and the Kohonen layers, respectively; and dj = the Euclidean distance

between the input and the Kohonen nodes. The distance to each of the Kohonen nodes is

computed and the node, c, which has the smallest distance, is selected, i.e. dc=min(dj), for

all the Kohonen nodes.

The connection weights between the input and the Kohonen layers of KSOFM-NNM

are carried out using unsupervised training. The connection weights, Wji, are initialized to

randomly select values for unsupervised training. They are then adjusted so that the nodes

which are in the topological neighborhood function Λc of node c, which was determined to

be closest to the current input node, are moved towards the input node using an iterative

adjustment rules. The connection weights can be written as

)]1m(Wx)[m()1m(W)m(Wjijjiji if j ∈ Λc (m)

)1m(W)m(Wjiji otherwise (3)

where m = the training iteration; Λc= the size of a neighborhood around the winner node c;

and η(m) = the step size at the training iteration m. This procedure is applied several times

to the whole data of input nodes.

The hidden layer can receive the results calculated from Sj and the connection weights

between the Kohonen and hidden layers, which can be written as

5

1j

jkjk SWU (4)

where k = the hidden layer; Wkj = the connection weights between the Kohonen and the

hidden layers; Sj = the results calculated from dj and the Kohonen layer; and Uk = the

results calculated from Sj and the connection weights between the Kohonen and the hidden

layers. The output layer can receive the results calculated from Uk and the connection

weights between the hidden and output layers. The results of the output layer based on

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TEM 3 can be written as

)B)BSW(ΦW(ΦPE(t) 21

22

1k

jkj1

1

1l

lk2 (5)

where PE(t)= the current PE (mm/day) at Ahwaz and Izeh stations; )(1

= the linear

sigmoid transfer function of the hidden layer; )(2

= the linear sigmoid transfer function

of the output layer; B1 = the bias in the hidden layer; B2 = the bias in the output layer; and

Wlk = the connection weights between the hidden and the output layers. Figure 4 shows

the structure of KSOFM-NNM based on TEM 3 (7-[5 X 5]-22-1) developed in this study.

Gene expression programming (GEP)

GEP is a genetic algorithm (GA), as it uses populations of individuals, selects them

according to fitness, and genetic variation using one or more genetic operators (Ferreira

2006). One of the strengths of GEP over other soft computing models is its capability to

produce explicit formulations (model expression) of the relationship that rules the physical

phenomenon. However, there are also some problems regarding a GEP application. For

example, in some cases, the program size (depth of parse tree) starts growing which leads

to producing a nested function (bloat phenomenon). To overcome this weakness, one

should employ some penalization of complex models (limitation of the depth of the parse

tree) to produce parsimonious relations.

The procedure to predict daily PE (dependent variable) using the various input

combinations (independent variables) is as follows. (1) Select a fitness function; (2)

choose a set of terminals T and a set of functions F to create chromosomes; (3) choose the

chromosomal architecture; (4) choose the linking function; and (5) choose the genetic

operators. Figure 5 shows equations using mathematical functions and the parse trees. In

this study, the GeneXpro program (Ferreira 2001) was applied for predicting daily PE.

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Performance statistics

The performance of soft computing models was evaluated using four different standard

statistical criteria: the coefficient of correlation (CC), the root mean square error (RMSE),

the scatter index (SI) (Shiri and Kisi 2011), and the Nash-Sutcliffe efficiency (NS) (Nash

and Sutcliffe 1970, ASCE 1993). CC, a measure of the accuracy between predicted and

observed PE, is generally used for comparisons of alternative models. According to

Legates and McCabe (1999), the correlation coefficient (CC) alone should not be used to

evaluate the goodness-of-fit of model simulations, since the standardization inherent in

CC as well as its sensitivity to outliers yields high CC values even when the model

performance may not be good. Therefore, additional statistical measures (e.g., RMSE and

NS) should be applied to evaluate the model performance. RMSE is a measure of the

residual variance and can be defined as the square root of the average value of the squares

of the differences between predicted and observed PE values. SI is the dimensionless

RMSE and is expressed as a percentage mean of observed PE. NS, a dimensionless

measure, is the coefficient of efficiency and can be used to indicate the relative assessment

of the model performance (Nash and Sutcliffe 1970). NS is one of the most widely used

criteria for calibration and evaluation of hydrological models with the observed data

(Gupta et al. 2009). Table 2 shows mathematical expressions of the statistical criteria.

Selection of Input Nodes and Data Normalization

The input nodes for soft computing models were selected, based on the serial

correlation of daily PE and the cross correlation between (1) daily PE and T (temperature-

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based), (2) daily PE and R (radiation-based), and (3) daily PE and SD (sunshine duration-

based). T

- (1) daily

PE and T, (2) daily PE and R, and (3) daily PE and SD were calculated. -

ach input combination

was selected, based on the lag-time for T, R, and SD corresponding to the lag-time of PE,

a

minmax

mini

normYY

YYY

where for the specific node normY = the normalized dimensionless data,

iY = the observed

data, min

Y = the minimum data, and maxY = the maximum data.

Performance of MLP-NNM

Cross-validation performance was used to overcome the overfitting problem for MLP-

NNM, KSOFM-NNM, and GEP using cross-validation data. In the literature, this method

has often been applied for training (Haykin 2009). After training and cross-validation of

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soft computing models, MLP-NNM, KSOFM-NNM, and GEP were tested by determining

whether the model meets the objectives of modeling within some preestablished criteria or

not.

-

- - -

- -

Table

4 also shows the test statistics of each MLP-NNM in terms of CC, RMSE, SI, and NS for

both stations. From table 4, it can be observed that TEM 3 produced the best results

among other input combinations for both stations. Table 4 also reveals that increasing the

lag-time intervals from 1 day to 3 days for temperature-based, radiation-based, and

sunshine duration-based input combinations increases the model accuracy to some extent.

Figure 7(a)-(f) compares observed and predicted PE values for the optimal MLP-NNM

during the test period for both stations. The superiority of TEM 3 over RAD 3 and SUN 3

is clearly seen from figure 7(a)-(f).

Performance of KSOFM-NNM

-

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-

- - - -

Table 5 also shows the test statistics of each KSOFM-NNM in terms of CC,

RMSE, SI, and NS for both stations. From table 5, it can be observed that TEM 3

produced the best results among other input combinations for both stations. Table 5 also

reveals that increasing the lag-time intervals from 1 day to 3 days for temperature-based,

radiation-based, and sunshine duration-based input combinations increases the model

accuracy to some extent. Figure 8(a)-(f) compares observed and predicted PE values for

the optimal KSOFM-NNM during the test period for both stations. As found for MLP-

NNM, the better accuracy of TEM 3 can be clearly seen from figure 8(a)-(f) for both

stations.

Performance of GEP

The various forms of GEP were developed using the same input combinations as for

MLP-NNM and KSOFM-NNM. A step-by-step procedure of GEP predicting daily PE is

as follows: The first step was the selection of the appropriate fitness function which may

take various shapes. For mathematical applications, one usually applies small relative or

absolute errors to discover a good and applicable solution (Ferreira 2001). According to

the MLP-NNM and KSOFM-NNM, the optimal input combination (TEM 3) was used

with the default function set of GeneXpro for the selection of one of the fitness functions.

The second step consisted of choosing the set of terminals and the set of functions to

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create chromosomes. In the current problem, the terminal set included the various input

combinations. The study examined the various combinations of these parameters as input

variables for GEP to evaluate the degree of effect of each of these variables on the daily

PE values at designated time steps. A set of preliminary model runs was carried out to test

the performances of models with these function sets and one was selected to use in the

next stage of study. All of these procedures were performed for GEP based on TEM 3 by

using the RRSE fitness function and addition linking function. Table 6 shows the

preliminary selection of basic functions and linking functions using the SI index for both

stations. From comparison of various GEP operators listed in table 6, it can be concluded

that the F5 function set surpassed all of the other four structures.

The third step was to choose the chromosomal architecture. The length of head, h=8,

and three genes per chromosomes were employed, which are the commonly used values in

the literature (Ferreira 2001). The fourth step was to choose the linking function, which

should be chosen as "addition" or "multiplication" for algebraic sub trees (Ferreira, 2001).

It can be also concluded from table 6 that addition linking function surpasses all of the

other three linking functions. The final step was to choose the genetic operators.

Table 7 shows the test statistics of each GEP in terms of CC, RMSE, SI, and NS for

both stations. From table 7, it can be observed that TEM 3 produced the best results

among other input combinations for both stations. Table 7 also reveals that increasing the

lag-time intervals from 1 day to 3 days for temperature-based, radiation-based, and

sunshine duration-based input combinations increased the model accuracy to some extent.

Figure 9(a)-(f) compares observed and predicted PE values for the optimal GEP during the

test period for both stations. From the fit line equations and CC values given in figure

9(a)-(f), it is clear that TEM 3 performed better than did RAD 3 and SUN 3. Comparison

of tables 4, 5, and 7 revealed that KSOFM-NNM slightly outperformed MLP-NNM and

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GEP, but differences between the results of the three approaches were not significant and

three of them may be considered as alternative tools for predicting daily PE. Figure 10(a)-

(f) shows observed and predicted PE values of MLP-NNM, KSOFM-NNM, and GEP for

optimal input combination (TEM 3) during the test period for both stations.

The Mann-Whitney U test, one of the tests for homogeneity analyses, was performed to

compare observed and predicted PE values to evaluate the confidence level of soft

computing models. It is a nonparametric alternative to the two-sample t test for two

independent samples and can be used to test whether two independent samples have been

taken from the same population (McCuen 1993, Kottegoda and Rosso 1997, Ayyub and

McCuen 2003, Singh et al. 2007). The critical value of z statistic was computed for the

level of significance. If the computed value of z statistic is greater than the critical value of

z statistic, the null hypothesis, which is if the two independent samples are from the same

population, should be rejected and the alternative hypothesis should be accepted.

Table 8 shows the results of the Mann-Whitney U test between observed and predicted

PE values for the test data of soft computing models, including TEM3, RAD3, and SUN3.

The critical value of z statistic was computed as z0.05 =1.960 for the 5 percent (5%) level of

significance. Since the computed values of z statistic for both stations were not significant,

the null hypothesis, which is if the two independent samples are from the same population,

was accepted for the soft computing models of both stations.

Performance of MLRM

The test statistics of MLP-NNM, KSOFM-NNM, and GEP were compared with those

of MLRM. Table 9 shows the test statistics of optimal MLRM in terms of CC, RMSE, SI,

and NS for both stations. In parallel with the test statistics of MLP-NNM, KSOFM-NNM,

and GEP, it can be seen from table 9 that TEM 3 performed better than did RAD 3 and

SUN 3 for both stations. Comparison of tables 4, 5, 7 and 9 revealed that there are slight

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differences between the soft computing models and MLRM. It can be also concluded from

tables 4, 5, 7, and 9 that MLP-NNM, KSOFM-NNM and GEP performed slightly better

than did MLRM. Figure 11(a)-(f) compares observed and predicted PE for the optimal

MLRM during the test period for both stations. Comparison of figures 7-11 indicates the

superiority of soft computing techniques over MLRM.

- - - -

-

- - -

- -

- - -

TEM 3 whose inputs are

T(t-3), T(t-2), - - - - produces the best results among

other input combinations for both stations. The prediction accuracy of soft computing

models is found to increase with increasing lag-time intervals for input combinations.

KSOFM-NNM slightly outperforms MLP-NNM and GEP, but differences between the

results of the three approaches are not significant. The Mann-Whitney U test is performed

to compare observed and predicted PE values for the testing data of soft computing

models, including TEM3, RAD3, and SUN3. The computed values of z statistic for both

stations are not significant for the training data. The null hypothesis, which is if the two

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independent samples are from the same population, is accepted for both stations.

C

- -

-

- -

ASCE Task Committee on Definition of Criteria for Evaluation of Watershed Models.,

1993. Criteria for evaluation of watershed models. Journal of Irrigation and

Drainage Engineering, 119 (3), 429-442.

Allen, R.G., Pereira, L.S., Raes, D. and Smith, M., 1998. Crop evapotranspiration

guidelines for computing crop water requirements, FAO Irrigation and Drainage,

Paper No. 56, Food and Agriculture Organization of the United Nations, Rome.

Ayyub, B.M. and McCuen, R.H., 2003. Probability, statistics, and reliability for

engineers and scientists 2nd

Edition. Taylor & Francis, Boca Raton, FL.

Bruton, J.M., McClendon, R.W. and Hoogenboom, G., 2000. Estimating daily pan

evaporation with artificial neural networks. Transactions of American Society of

Agricultural Engineers, 43 (2), 491-496.

Chang, F.J., Chang, L.C., Kao, H.S. and Wu, G.R., 2010. Assessing the effort of

meteorological variables for evaporation estimation by self-organizing map neural

network. Journal of Hydrology, 384 (1-2), 118-129.

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

13:

50 1

6 A

ugus

t 201

4

Accep

ted M

anus

cript

18

Chang, F.J., Chang, L.C. and Wang, Y.S., 2007. Enforced self-organizing map neural

networks for river flood forecasting. Hydrological Processes, 21 (6), 741-749.

Chang , F.J., Sun, W. and Chung, C.H. 2013. Dynamic factor analysis and artificial

neural network for estimating pan evaporation at multiple stations in northern

Taiwan. Hydrological Sciences Journal, DOI:10.1080/02626667.2013.775447.

Choudhury, B.J., 1999. Evaluation of empirical equation for annual evaporation using

field observations and results from a biophysical model. Journal of Hydrology,

216(1–2), 99–110.

Chow, V.T., Maidment, D.R. and Mays, L.W., 1988. Applied Hydrology. McGraw-Hill,

NY.

Dawson, C.W. and Wilby, R.L., 2001. Hydrological modelling using artificial neural

networks. Progress in Physical Geography, 25(1), 80–108.

Ferreira, C., 2001. Gene expression programming: a new adaptive algorithm for solving

problems. Complex Systems, 13 (2), 87-129.

Ferreira, C., 2006. Gene expression programming: mathematical modeling by an

artificial intelligence 2nd

Edition. Springer, Berling, Heidelberg, NY.

Finch, J.W., 2001. A comparison between measured and modeled open water evaporation

from a reservoir in south-east England. Hydrological Processes, 15, 2771-2778.

Gupta, H.V., Kling, H., Yilmaz, K.K. and Martinez, G.F., 2009. Decomposition of the

mean squared error and NSE performance criteria: Implications for improving

hydrological modeling. Journal of Hydrology, 377 (1-2), 80-91.

Guven, A. and Kisi, O., 2011. Daily pan evaporation modeling using linear genetic

programming technique. Irrigation Science, 29 (2), 135-145.

Haykin, S., 2009. Neural networks and learning machines 3rd

Edition, Prentice Hall, NJ.

Hsu, K., Gupta, V.H., Gao, X., Sorooshian, S. and Imam, B., 2002. Self-organizing linear

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

13:

50 1

6 A

ugus

t 201

4

Accep

ted M

anus

cript

19

output map (SOLO): An artificial neural network suitable for hydrologic

modeling and analysis. Water Resources Research, 38 (12), 1302, doi:

10.1029/2001WR000795.

Jain, S.K., Nayak, P.C. and Suhheer, K.P., 2008. Models for estimating

evapotranspiration using artificial neural networks, and their physical

interpretation. Hydrological Processes, 22, 2225-2234.

Kay, A.L. and Davies, H.N., 2008. Calculating potential evaporation from climatic data:

A source of uncertainty for hydrological climate changes impact. Journal of

Hydrology, 358, 221-239.

Keskin, M.E. and Terzi, O., 2006. Artificial neural networks models of daily pan

evaporation. Journal of Hydrologic Engineering, 11 (1), 65-70.

Kim, S. and Kim, H.S., 2008. Neural networks and genetic algorithm approach for

nonlinear evaporation and evapotranspiration modeling. Journal of Hydrology,

351 (3-4), 299-317.

Kim S., Kim, J.H. and Park, K.B., 2009. Statistical learning theory for the disaggregation

of the climatic data. Proceedings of 33rd

IAHR Congress 2009, IAHR, Vancouver,

Canada, 1154-1162.

Kim S., Shiri, J. and Kisi, O., 2012. Pan evaporation modeling using neural computing

approach for different climatic zones. Water Resources Management, 26 (11),

3231-3249.

Kim S., Shiri, J., Kisi, O. and Singh, V.P., 2013. Estimating daily pan evaporation using

different data-driven methods and lag-time patterns. Water Resources

Management 27(7), 2267-2286.

Kisi, O., 2006. Daily pan evaporation modeling using a neuro-fuzzy computing

technique. Journal of Hydrology, 329 (3-4), 636-646.

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

13:

50 1

6 A

ugus

t 201

4

Accep

ted M

anus

cript

20

Kisi, O., 2007. Evapotranspiration modeling from climatic data using a neural computing

technique. Hydrological Processes, 21, 1925-1934.

Kisi, O., 2009. Modeling monthly evaporation using two different neural computing

technique. Irrigation Science, 27 (5), 417-430.

Kisi, O., Pour-Ali Baba, A. and Shiri, J., 2012. Generalized neurofuzzy models for

estimating daily pan evaporation values from weather data. Journal of Irrigation

and Drainage Engineering, 138(4), 349-362.

Kohonen, T., 1990. The self-organizing map. Proceeding of the IEEE, 78 (9), 1464-1480.

Kohonen, T., 2001. Self-organizing maps, Springer-Verlag, NY.

Kottegoda, N.T. and Rosso, R., 1997. Statistics, probability, and reliability for civil and

environmental engineers. McGraw-Hill, Singapore.

Kumar, M., Raghuwanshi, N.S., Singh, R., Wallender, W.W. and Pruitt, W.O., 2002.

Estimating evapotranspiration using artificial neural networks. Journal of

Irrigation and Drainage Engineering, 128 (4), 224-233.

Legates, D.R. and McCabe, G.J., 1999. Evaluating the use of goodness-of-fit measures in

hydrologic and hydroclimatic model validation. Water Resources Research, 35

(1), 233-241.

Lin, G.F. and Chen, L.H., 2005. Time series forecasting by combining the radial basis

function network and the self-organizing map. Hydrological Processes, 19 (10),

1925-1937.

Lin, G.F. and Chen, L.H., 2006. Identification of homogeneous regions for regional

frequency analysis using self-organizing map. Journal of Hydrology, 324 (1-4), 1-

9.

Lin, G.F. and Wu, M.C., 2007. A SOM-based approach to estimating design hyetographs

of ungaged sites. Journal of Hydrology, 339 (3-4): 216-226.

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

13:

50 1

6 A

ugus

t 201

4

Accep

ted M

anus

cript

21

Lin, G.F. and Wu, M.C., 2009. A hybrid neural network model for typhoon-rainfall

forecasting. Journal of Hydrology, 375 (3-4), 450-458.

McCuen, R.H., 1993. Microcomputer applications in statistical hydrology. Prentice Hall,

Englewood Cliffs, NJ.

Nash, J.E. and Sutcliffe, J.V., 1970. River flow forecasting through conceptual models,

Part 1 – A discussion of principles. Journal of Hydrology, 10 (3), 282-290.

NeuroDimension Inc., 2005. Developers of NeuroSolutions V5.01: Neural Network

Simulator, Gainesville, FL.

Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass,

Proceedings of the Royal Society of London. Series A. Mathematical and Physical

Sciences, 193, 120-146.

Principe, J.C., Euliano, N.R. and Lefebvre, W.C., 2000. Neural and adaptive systems:

fundamentals through simulation, Wiley, John & Sons, Inc., NY.

Rosenberry, D.O., Winter, T.C., Buso, D.C. and Likens, G.E., 2007. Comparison of 15

evaporation methods applied to a small mountain lake in the northeastern USA.

Journal of Hydrology, 340 (3-4), 149-166.

Shiri, J., Dierickx, W., Pour-Ali Baba, A., Neamati, S. and Ghorbani, M.A., 2011.

Estimating daily pan evaporation from climatic data of the state of Illinois, USA

using adaptive neuro-fuzzy inference system (ANFIS) and artificial neural

network (ANN). Hydrology Research, 42 (6), 491-502.

Shiri, J. and Kisi, O., 2011. Application of artificial intelligence to estimate daily pan

evaporation using available and estimated climatic data in the Khozestan Province

(Southwestern Iran). Journal of Irrigation and Drainage Engineering, 137 (7),

412-425.

Shiri, J., Marti, P. and Singh, V.P., 2013. Evaluation of gene expression programming

Dow

nloa

ded

by [

Uni

vers

ity o

f N

ebra

ska,

Lin

coln

] at

13:

50 1

6 A

ugus

t 201

4

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ted M

anus

cript

22

approaches for estimating daily pan evaporation through spatial and temporal data

scanning. Hydrological Processes, doi: 10.1002/hyp.9669.

Singh, V.P., Jain, S.K. and Tyagi, A., 2007. Risk and reliability analysis: a handbook for

civil and environmental engineers. ASCE Press, Reston, VA.

Sivakumar, B., Jayawardena, A.W. and Fernando, T.M.K.G., 2002. River flow

forecasting: use of phase-space reconstruction and artificial neural networks

approaches. Journal of Hydrology, 265, 225-245.

Sudheer, K.P., Gosain, A.K. and Ramasastri, K.S., 2003. Estimating actual

evapotranspiration from limited climatic data using neural computing technique.

Journal of Irrigation and Drainage Engineering, 129 (3), 214-218.

Sudheer, K.P., Gosain, A.K., Rangan, D.M. and Saheb, S.M., 2002. Modeling

evaporation using an artificial neural network algorithm. Hydrological Processes,

16, 3189-3202.

Tabari, H., Marofi, S. and Sabziparvar, A.A., 2009. Estimation of daily pan evaporation

using artificial neural network and multivariate non-linear regression. Irrigation

Science, 28 (5), 399-406.

Tan, S.B.K., Shuy, E.B. and Chua, L.H.C., 2007. Modeling hourly and daily open-water

evaporation rates in areas with an equatorial climate. Hydrological Processes, 21

(4), 486-499.

Terzi, O. and Keskin, M.E., 2005. Evaporation estimation using gene expression

programming. Journal of Applied Sciences, 5 (3), 508-512.

Tokar, A.S. and Johnson, P.A., 1999. Rainfall-runoff modeling using artificial neural

networks. Journal of Hydrologic Engineering, 4(3), 232-239.

Vallet-Coulomb, C., Legesse, D., Gasse, F., Travi, Y. and Chernet, T., 2001. Lake

evaporation estimates in tropical Africa (Lake Ziway, Ethiopia). Journal of

Dow

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by [

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Hydrology, 245(1–4), 1–18.

Table 1 Statistical parameters of the data used during the study period (2002-2008) Station Data Unit Xmean Xmax Xmin Sx Cv Csx SE 25th

Percentile

75th

Percentile

90th

Percentile

Ahwaz T

U

SD

RH

R

PE

◦C

m/sec

hr

%

MJ/m2

mm

26.53

5.24

8.69

41.86

19.04

8.88

42.50

33.00

13.20

93.50

33.76

26.00

5.20

0.00

0.00

9.00

0.00

0.00

9.61

2.51

3.48

19.00

6.69

5.72

0.36

0.48

0.40

0.45

0.35

0.64

-0.23

1.54

-1.18

0.54

-0.22

0.47

0.19

0.05

0.07

0.38

0.13

0.11

17.60

3.00

7.40

25.00

12.76

3.80

35.80

7.00

11.20

56.00

25.04

13.15

38.20

8.00

12.00

69.00

27.31

17.40

Izeh T

U

SD

RH

R

PE

◦C

m/sec

hr

%

MJ/m2

mm

21.40

5.49

8.65

40.95

19.06

7.20

39.50

30.00

13.50

96.00

31.77

26.40

1.50

0.00

0.00

0.00

2.34

0.01

9.00

2.75

3.66

20.87

7.04

5.02

0.42

0.50

0.42

0.51

0.37

0.70

-0.04

0.83

-1.09

0.38

-0.21

0.56

0.18

0.05

0.07

0.41

0.14

0.10

13.20

4.00

7.10

22.50

12.64

2.80

29.90

7.00

11.30

58.50

25.31

11.71

33.10

8.00

12.30

70.80

27.94

14.16

Statistical Index Equation

CC n

1i

2yi

n

1i

2

yi

n

1i

yiyi

]u(x)y[n

1]u(x)[y

n

1

]u(x)y][u(x)[yn

1

RMSE n

2i i

i 1

1[ y (x)- y (x)]

n

SI y

u

RMSE

NS n

1i

2yi

n

1i

2ii

]u(x)[y

(x)]y(x)[y

1

(x)yi = the observed PE (mm/day); (x)yi= the predicted PE

(mm/day); yu = mean of the observed PE (mm/day); yu =

mean of the predicted PE (mm/day); and n = total number

of the daily PE considered.

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Table 3 Input combinations of MLP-NNM, KSOFM-NNM, and GEP

Classification Expression Input Combination

Temperature-Based

TEM 1 T(t-1), T(t), PE(t-1)

TEM 2

TEM 3

T(t-2), T(t-1), T(t), PE(t-2), PE(t-1)

T(t-3), T(t-2), T(t-1), T(t), PE(t-3), PE(t-2), PE(t-1)

Radiation-Based

RAD 1 R(t-1), R(t), PE(t-1)

RAD 2

RAD 3

R(t-2), R(t-1), R(t), PE(t-2), PE(t-1)

R(t-3), R(t-2), R(t-1), R(t), PE(t-3), PE(t-2), PE(t-1)

Sunshine Duration-Based

SUN 1 SD(t-1), SD(t), PE(t-1)

SUN 2

SUN 3

SD(t-2), SD(t-1), SD(t), PE(t-2), PE(t-1)

SD(t-3), SD(t-2), SD(t-1), SD(t), PE(t-3), PE(t-2), PE(t-1)

-

Station Input

Combination

Structure

Statistics Criteria

CC RMSE

(mm)

SI NS

Ahwaz

TEM 1 3-45-1 0.889 2.541 0.291 0.791

TEM 2 5-30-1 0.286 0.797

TEM 3 7-22-1 2.417 0.277 0.811

RAD 1 3-45-1 0.883 2.655 0.304 0.772

RAD 2 5-30-1 0.295 0.785

RAD 3

SUN 1

7-22-1

3-45-1

2.549

2.685

0.292

0.308

0.790

0.767

SUN 2 5-30-1 2.667 0.305 0.770

SUN 3 7-22-1 2.596 0.297 0.781

Izeh

TEM 1 3-45-1 1.712 0.231 0.887

TEM 2 5-30-1 1.710 0.231 0.887

TEM 3 7-22-1 1.646 0.222 0.895

RAD 1 3-45-1 1.793 0.242 0.876

RAD 2 5-30-1 1.739 0.235 0.883

RAD 3

SUN 1

7-22-1

3-45-1

1.720

1.905

0.232

0.257

0.886

0.856

SUN 2 5-30-1 1.803 0.243 0.874

SUN 3 7-22-1 1.778 0.240 0.878

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Table 5 Statistical results of the testing performance of KSOFM-NNM

Station Input

Combination

Structure

Statistics Criteria

CC RMSE

(mm)

SI NS

Ahwaz

TEM 1 3-[5X5]-45-1 0.895 2.487 0.285 0.800

TEM 2 5-[5X5]-30-1 0.273 0.816

TEM 3 7-[5X5]-22-1 2.380 0.273 0.816

RAD 1 3-[5X5]-35-1 2.504 0.287 0.797

RAD 2 5-[5X5]-30-1 2.480 0.284 0.800

RAD 3

SUN 1

7-[5X5]-22-1

3-[5X5]-45-1

2.457

2.644

0.281

0.303

0.804

0.774

SUN 2 5-[5X5]-30-1 2.549 0.292 0.790

SUN 3 7-[5X5]-22-1 2.513 0.288 0.796

Izeh

TEM 1 3-[5X5]-45-1 1.790 0.242 0.876

TEM 2 5-[5X5]-30-1 1.715 0.231 0.886

TEM 3 7-[5X5]-22-1 1.590 0.215 0.902

RAD 1 3-[5X5]-45-1 1.921 0.259 0.857

RAD 2 5-[5X5]-30-1 1.848 0.249 0.868

RAD 3

SUN 1

7-[5X5]-22-1

3-[5X5]-45-1

1.696

2.149

0.229

0.290

0.889

0.822

SUN 2 5-[5X5]-30-1 1.871 0.252 0.865

SUN 3 7-[5X5]-22-1 1.772 0.239 0.879

Table 6 Preliminary selection of basic functions and linking functions using SI index

Definition SI

Ahwaz Izeh

F1

F2

F3

F4

F5

, , ,

, , , , ln,ex

, , , , 3√,√,x

2,x

3

, , , , ln,ex ,

3√,√, x2,x

3

, , , , ln,ex ,

3√,√, x2,x

3sin x, cos x,

arctgx

0.36

0.40

0.34

0.31

0.28

030

0.32

0.28

0.28

0.23

Linking Function

Addition 0.28 0.23

Multiplication 0.30 0.26

Subtraction 0.30 0.30

Division 0.32 0.33

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Table 7 Statistical results of the testing performance of GEP

Station Input

Combination

Statistics Criteria

CC RMSE

(mm)

SI NS

Ahwaz

TEM 1 0.894 2.494 0.283 0.799

TEM 2 0.279 0.809

TEM 3 2.429 0.278 0.809

RAD 1 2.517 0.288 0.795

RAD 2 2.474 0.283 0.802

RAD 3

SUN 1

2.456

2.698

0.281

0.309

0.805

0.764

SUN 2 2.616 0.300 0.778

SUN 3 2.542 0.291 0.791

Izeh

TEM 1 1.718 0.232 0.886

TEM 2 1.701 0.230 0.888

TEM 3 1.657 0.224 0.894

RAD 1 1.775 0.240 0.878

RAD 2 1.756 0.237 0.881

RAD 3

SUN 1

1.747

1.902

0.236

0.257

0.882

1.364

SUN 2 1.817 0.245 1.312

SUN 3 1.778 0.240 1.302

Table 8 Results of the Mann-Whitney U test Station Model Input

Combination

Level of

Significance

Mann-Whitney U test

Critical

z Statistic

Computed

z Statistic

Null

Hypothesis

Ahwaz

MLP-NNM

TEM3

RAD3

SUN3

0.05

0.05

0.05

1.960

1.960

1.960

-0.381

-0.311

-0.205

Accept

Accept

Accept

KSOFM-NNM

TEM3

RAD3

SUN3

0.05

0.05

0.05

1.960

1.960

1.960

-0.251

-0.768

-0.162

Accept

Accept

Accept

GEP

TEM3

RAD3

SUN3

0.05

0.05

0.05

1.960

1.960

1.960

-0.235

-0.117

-0.432

Accept

Accept

Accept

Izeh

MLP-NNM

TEM3

RAD3

SUN3

0.05

0.05

0.05

1.960

1.960

1.960

-0.516

-0.182

-0.708

Accept

Accept

Accept

KSOFM-NNM

TEM3

RAD3

SUN3

0.05

0.05

0.05

1.960

1.960

1.960

-0.356

-1.463

-0.790

Accept

Accept

Accept

GEP

TEM3

RAD3

SUN3

0.05

0.05

0.05

1.960

1.960

1.960

-0.080

-0.125

-0.081

Accept

Accept

Accept

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Table 9 Statistical results of the testing performance of MLRM

Station Input

Combination

Statistics Criteria

CC RMSE

(mm)

SI NS

Ahwaz

TEM 3 2.441 0.280 0.807

RAD 3 2.554 0.293 0.788

SUN 3 2.648 0.303 0.773

Izeh

TEM 3

RAD 3

SUN 3

1.658

1.758

1.804

0.224

0.237

0.243

0.894

0.881

0.874

Figures Captions

Figure 1 Location of weather stations in south-western Iran

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Figure 2 Daily pan evaporation and temperature values during the study period (2002-2008)

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Figure 3 Structure of MLP-NNM based on TEM 3 (7-22-1)

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- - - -

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Figure 7 Comparison of observed and predicted PE values for the optimal MLP-NNM (Testing

data)

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Figure 8 Comparison of observed and predicted PE values for the optimal KSOFM-NNM (Testing

data)

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Figure 9 Comparison of observed and predicted PE values for the optimal GEP (Testing data)

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Figure 10 Observed and predicted PE values for the optimal input combination (TEM 3, 2002-

2008)

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Figure 11 Comparison of observed and predicted PE values for the optimal MLRM (Testing data)

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