Research ArticleComparative Study of M5 Model Tree andArtificial Neural Network in Estimating ReferenceEvapotranspiration Using MODIS Products

Armin Alipour Jalal Yarahmadi and Maryam Mahdavi

Department of Irrigation and Drainage Engineering College of Aburaihan University of Tehran PO Box 33955-159Pakdasht Tehran Iran

Correspondence should be addressed to Armin Alipour aalipourutacir

Received 29 August 2014 Accepted 18 November 2014 Published 17 December 2014

Academic Editor Ines Alvarez

Copyright copy 2014 Armin Alipour et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Reference evapotranspiration (ET119874) is one of the major parameters affecting hydrological cycle Use of satellite images can be very

helpful to compensate for lack of reliable weather data This study aimed to determine ET119874using land surface temperature (LST)

data acquired fromMODIS sensor LSTdatawere considered as inputs of twodata-drivenmodels including artificial neural network(ANN) andM5model tree to estimate ET

119874values and their results were compared with calculated ET

119874by FAO-Penman-Monteith

(FAO-PM) equation Climatic data of five weather stations in Khuzestan province which is located in the southeastern Iran wereemployed in order to calculate ET

119874 LST data extracted from corresponding points ofMODIS images were used in training of ANN

andM5model tree Among study stations three stations (Amirkabir Farabi and Gazali) were selected for creating the models andtwo stations (Khazaei and Shoeybie) for testing In Khazaei station the coefficient of determination (1198772) values for comparisonbetween calculated ET

119874by FAO-PM and estimated ET

119874by ANN and M5 tree model were 079 and 080 respectively In a similar

manner 1198772 values for Shoeybie station were 086 and 085 In general the results showed that both models can properly estimateET119874by means of LST data derived fromMODIS sensor

1 Introduction

Decline in availability of water for agriculture is one of themost serious challenges facing human life that has affectedagricultural production in some arid and semiarid regionsaround the world Determining future demands of water foragriculture section includes computation of several factorssuch as runoff groundwater precipitation and evapotran-spiration (ET) [1] ET is identified as the combination oftwo different processes including evaporation from the soilsurface and crop transpiration [2]

Accurate and reliable estimates of ET are necessary todetermine temporal variations in irrigation requirementimprove allocation of water resources and evaluate the effectof changes in land use and crop patterns on the water balance[3] Considering difficulties in direct measurement of ET [4]this parameter is estimated through reference evapotranspi-ration (ET

119874) and crop coefficient (119870

119888) for a specific crop [5]

Therefore calculation of ET119888(evapotranspiration of the given

plant) and subsequently crop water requirement as irrigationwater depend on ET

119874estimates ET

119874is defined as the rate of

ET from a reference surface in such a way that the surface isassumed to be covered with a hypothetical grass with specificcharacteristics [2] A large number of methods have beenoffered in order to model ET

119874[2 6 7] the majority of these

methods are extremely complicated and rely on weather datasuch as temperature solar radiation wind speed and airhumidity [1 8] ET119874 is principally calculated by physicallybased equations (eg Penman-Monteith (PM) equation) orby empirical relationships between meteorological variables

The FAO-Penman-Monteith (FAO-PM) method is cur-rently recommended as an accepted standard technique forcomputing ET119874 This method employs a variety of complexequations which are based on weather data including airtemperature humidity radiation and wind speed [9] Therequirement of various weather data which are not mainly

Hindawi Publishing CorporationJournal of ClimatologyVolume 2014 Article ID 839205 11 pageshttpdxdoiorg1011552014839205

2 Journal of Climatology

available in many regions is the major limitation of thismethod [10] in addition it seems that the reordered data arenot accurate enough especially in developing countries [11]

From the viewpoint of temporal and spatial variationsof climatic data weather stations density (the number ofstations per unit of area) is not generally adequate for demon-strating spatiotemporal variations Today remote sensingtechniques which gather land surface information from abroader geographic scope are known as an effective tool andmethodology for extracting the ground parameters that canbe used to estimate ET at regional scales [12] To this end inthe basins that may face shortage of measured data remotesensing data can considerably supply needed informationsuch as albedo leaf area index and land surface temperature(LST) [13] Recent advances in remote sensing techniques andenhancement of temporal spatial and radiometric resolutionof satellite images have produced a range of useful productsThese products can be widely used in various research areasespecially water and environment Many studies have beenconducted in estimating ET

119874as an important element of

hydrological cycle In this regard it can be mentioned in thestudies of Guerschman et al [14] Maeda et al [4] Yang et al[12] Cleugh et al [15] Tian et al [16] Hankerson et al [17]Li et al [18]

Recently some data-based techniques such as artificialneural networks (ANNs) support vector machine and M5model tree have been broadly utilized in solving practicalproblems Mentioned techniques can simulate processes inwhich there is not an exact solution and it is merely possibleto approach near-optimal solution [19] In these methodsa new knowledge is not produced about the process of aproblem In fact thanks to the proper recognition of theproblem process in selecting the input and output variablescaused by the use of modern regression techniques thishelps to better fit the data [20] Data-driven techniques canefficiently model nonlinear and complicated processes suchas ET that its precise calculation depends on numerousweather data and interactions between them [21]

Recently by the developing new machine learning meth-ods application of new models in the estimation of ET

119874has

been increased Kisi and Ozturk [22] studied the adaptiveneurofuzzy inference system (ANFIS) technique in estima-tion of ET

119874in Los Angeles California and showed that

it could be successfully considered in the ET119874estimation

Kisi and Cimen [23] applied SVM in modeling ET119874

incentral California and concluded that SVR model could beembedded as a module for estimating ET

119874data in hydro-

logical modeling studies Tabari et al [24] investigated thepotential of SVM ANFIS multiple linear regression (MLR)and multiple nonlinear regression (MNLR) for estimating ina semiarid highland environment in IranThey found that theSVM and ANFIS had better performance in ET

119874modeling

compared to the others Besides several studies have shownhigh performance of ANNs inmodeling ET against statisticalmethods [8 25ndash29]The substantial benefit of ANNmethodscompared to conventional methods is the ability of solvingproblems that are difficult to formalize [30] Hou et al [10]studied ANNs in simulating ET119874 values and demonstratedthat the models reflected a noticeable efficiency Landeras

et al [21] compared calculated ET119874byANN to the ET

119874values

of radiation and thermal models and declared that ANN canprovide more accurate results than empirical models

Due to the simple geometric structure of model tree andproviding fast computing set of IF-THEN rules which areeasily understandable [31] the model tree has been utilizedin different scientific studies Pal and Deswal [1] in a studyevaluated the capability of M5 model tree to model ET119874 indaily scale and the obtained results showed that M5 modeltree can be properly used in this context Rahimikhoob et al[11] conducted a study to assess the performance ofM5modeltree in reaching ET119874 values in a semiarid region of Iran bymeans of 119870119901 values of pan evaporation They asserted thatthis model shows more satisfactory performance than otherapproaches in estimating ET

119874in the study region Sattari et al

[32] compared ANN andM5 model tree in determining ET119874

and concluded that both ANNmodel andM5model tree canproperly estimate ET

119874 ANN suggested a better performance

howeverM5model tree offered simple linear regressions thatcan simply calculate ET

119874

The main aim of this study is to evaluate the ability of M5model tree and ANN model in estimating daily ET

119874using

LST values obtained from MODerate Resolution ImagingSpectroradiometer (MODIS)Terra sensor The accuracy ofcalculated ET

119874by means of M5 model tree and ANN model

has been investigated by comparing with the ET119874amounts of

FAO-PMmethod

2 Materials and Methods

21 Study Area and Data Farms of Sugarcane DevelopmentProject which are located in Khuzestan province Iranwere considered as the study area in the present researchKhuzestan province is stretched in southeastern part ofthe country with the area of approximately 63238 km2between longitudes of 47∘381015840 E to 50∘321015840 E and latitudes of29∘571015840 N to 33∘001015840 N This province is located adjoining theboundary of Iraq from the west and Persian Gulf from thesouth Khuzestan province according to deMartonne climateclassification has a semiarid climateThe average temperatureduring the winter season is nearly 914∘C and occasionally itsminimum falls down a few degrees below 0∘C The averagetemperature in the summers is approximately 312∘C whereasits maximum sometimes exceeds 50∘C Required climaticvariables in order to estimate ET119874 in this study were collectedfrom weather stations namely Amirkabir Farabi GazaliKhazaei and Shoeybie for the years of 2006 and 2007 inthe periods when satellite images existed The meteorolog-ical data consisted of daily observations of maximum andminimum temperature sunshine duration relative humidityand wind speed which have been used in estimating ET

119874by

FAO-PM equation Figure 1 illustrates the location of weatherstations in the study area

22 MODIS Images In the current study data of daytimeLST (LST

119863) and nighttime LST (LST

119873) obtained from the

MODIS sensor were used as inputs to the M5 model treeand ANN models The MODIS sensor which is on board

Journal of Climatology 3

Iran

Khuzestan

Figure 1 Location of weather stations in the study area

of the Terra and Aqua satellites is able to provide imagesin 36 spectral bands between 062 and 14385 120583m Spatialresolutions of the sensor are 250m 500m and 1 km in severalbands In the thermal-infrared (TIR) MODIS sensors have1 km spatial resolution [19] This sensor performs a range ofdaily regular observations on the sea land and atmospherein the global scale moreover it has an extensive and con-tinuous spectral and spatial coverage MODIS sensor waslaunched by the Terra and Aqua satellites in 1999 and 2002respectively These satellites both have a sun-synchronousnear polar circular orbit Terra satellite everyday crosses overthe equator from north to south while Aqua satellite hasan inverse movement from south to north United StatesNational Aeronautics and Space Administration (NASA) isresponsible for processing and providing MODIS sensorrsquosdata NASA supplies the data in a large variety of productsapplicable to land ocean and atmosphere uses [4] The dataand products of MODIS sensor are available on the NASArsquoswebsite (httpmodisgsfcnasagov)The images selected forthis study are the level three (L3) data of the MODIS sensor(MOD11A1) which are related to Terra satellite This productprovides daytime and nighttime LST data collected on a 1 kmspatial resolution and gridded in the sinusoidal projectionsystem [33] The MODIS sensor LST data is acquired fromtwo TIR channels that is 31 (1078ndash1128120583m) and 32 (1177ndash1227120583m) using the split-window algorithm [34]

A total of 428 images of the MODIS sensor associatedwith MOD11A1 production from the Terra satellite in thetime periods of 2006 and 2007 covering the study area wereretrieved from the Land ProcessesDistributedActiveArchiveCenter (LP DAAC) (httplpdaacusgsgov) Cloudless skyand fair weather were the reason for selecting these picturesChanging coordinate systems from the sinusoidal to UTM(datum WGS84) was performed using MODIS ReprojectionTool (MRT) Afterward locations of study stations were pro-jected on the images and then LST119863 and LST119873were extractedfrom the corresponding pixels of the images ExtractingLST values in the desired stations was done by means ofHawthrsquos Analysis Tools (HAT) in ArcGIS 93 software Unitof LST values extracted from the images was Kelvin so before

utilizing them as model input these values were converted toCelsius

In the present study whole LST values extracted fromMODIS images in three stations includingAmirkabir Farabiand Gazali were used to construct and train the ANN andM5model tree and two other stations Khazaei and Shoeybiewere applied to test mentioned models

23 Artificial Neural Network (ANN) ANNs are known aspowerfulmachine-learning techniques which are extensivelyused for numerical prediction and classification [35] ANNsare also operative tools to model nonlinear systems and needless amount of data as inputs than customary mathematicalapproaches [27] A neural network is based on processinga set of data that its analysis procedure has been inspiredby biological neural systems Neural networks consist of aninterconnected group of neurons placed near to each otherin layers that implement data processing through neuronsand their connections ANNs included one input layer anoutput layer and one or more hidden layers neurons of eachlayer are joined to all neurons of the previous layer by meansof weighted connections The input vectors are received byneurons of the input layer and the values can be conveyedto the next layer of processing elements across connectionsThe number of neurons in each hidden layer is determinedby the user This process continues up to the output layerANNmodeling is carried out in two stages including trainingand testing In the training stage after getting input dataneural network makes attempts to convert the inputs intodesired outputs Connecting weights of network neurons aredetermined in this stage these weights in the testing stage areexamined using various datasets

A multilayer perceptron (MLP) ANN with one inputlayer one hidden layer and one output layer was used toestimate ET119874 from LST

119863 LST119873 mean LST (LST

119872) and day

of year (DOY) data as inputs The transfer function in thenetworks was log-sigmoid for this study The accuracy ofthe networks was evaluated for each epoch in the trainingthrough mean squared error (MSE) The backpropagation(BP) algorithm was employed to train MLP neural networkLevenberg-Marquardt (LM) a second-order nonlinear opti-mization technique was usedwith an early stopping criterionto improve the network training speed and efficiency Thetarget error for the training of networks was equal to 10minus4With the specification of this target error the number ofiteration for all ANN models was placed to 1000

24 M5 Model Tree M5 model tree was introduced byQuinlan in 1992 [36] The model is established according toa binary decision tree in which there are linear regressionfunctions in the terminal node (leaf) which sets a relation-ship between independent anddependent variables [11] Tree-based models are made according to a divide-and-conquermethod for constructing a relationship between independentand dependent variables [37] The tree models can be alsoused for qualitative and quantitative data [9]

Building the M5 model tree involves two separate steps[36 38] The first one consists of dividing data into subsets

4 Journal of Climatology

X2

LM6

LM5

LM1 LM2

LM3

LM4

2 4 6 8 10

2

4

6

8

X1

Y (output)

(a)

X1X1

X2 X2

gt42le42

le35

le2 le63

le5 gt5gt35

gt2 gt63

LM6LM5

LM1

LM2 LM3

LM4

X2

(b)

Figure 2 (a) Example of M5 model tree a splitting the input space 1199091times 1199092by M5 model tree algorithm and (b) diagram of model tree with

six linear regression models at the leaves [11]

to construct the model tree The dividing criterion is basedon the standard deviation of the subset values that reach anode as ameasure of error value in that node and additionallycalculating the expected reduction in the error as a resultof testing each attribute at that node Equation of standarddeviation reduction (SDR) is given as follows [1]

SDR = SD (119879) minussum119879119894

119879times SD (119879

119894) (1)

where 119879 is defined as a set of examples that reaches the node119879119894 demonstrates the subset of examples that have the 119894th

output of the potential set and SD is the standard deviation[39] Due to branching process data in child nodes (subtreeor smaller nodes) have fewer SD than parent nodes (greaternodes) After examining all possible structures a struc-ture would be picked out that has the maximum expectederror reduction This dividing often creates a great tree-likestructure that leads to overfit structure In order to avoidoverfitting in the second step the overgrown tree is prunedand pruned subtrees are replaced with linear regressionfunctions Figure 2(a) illustrates splitting the input space1199091times 1199092(independent variables) into six linear regression

functions at the leaves (labeled LM1 through LM6) by M5model tree algorithm General form of the model is 119910 =1198860+ 11988611199091+ 11988621199092 in which 119886

0 1198861 and 119886

2are linear regression

constants Figure 2(b) shows branches relations in the formof a tree diagram [19]

25 FAO-PM Equation FAO-PM equation a physicallybased method is widely used in the calculation of ET119874 and isa reliable method in the estimation of ET119874 in various climateconditions [2 40 41] Moreover FAO proposed this equationas a standard method for estimating ET119874 Although the mostprecise method for estimating ET119874 is to employ lysimeterdata considering the absence of such data in the study regionassessment of ANN and M5 model tree performance wasmade by FAO-PMequationThe equation for estimating dailyET119874has been presented as follows [2]

ET119874=0484Δ (119877119899 minus 119866) + 120574 (900 (119879119886 + 273))1198802 (119890119904 minus 119890119886)

Δ + 120574 (1 + 0341198802)

(2)

where ET119874is the reference evapotranspiration (mmdminus1) Δ

is the slope of the saturation vapor pressure curve (kPa ∘Cminus1)at the daily mean air temperature (∘C) 119877

119899and 119866 are the net

solar radiation and soil heat flux density (MJmminus2 dminus1) 120574 isthe psychrometric constant (kPa ∘Cminus1) 119879 is the daily meantemperature (∘C) 119880

2is the mean wind speed (msminus1) 119890

119904is

the saturation vapor pressure (kPa) and 119890119886is the actual vapor

pressure (kPa) [2]In current study the daily values of Δ 119877

119899 119890119904 and 119890

119886

were calculated using the equation given by Allen et al [2]For calculation of 119877

119899 it is needed to calculate daily solar

radiation (119877119904) Allen et al [2] proposed 119877

119904to be calculated

using the Angstrom formula which relates solar radiation toextraterrestrial radiation (119877119886) and relative sunshine durationThe formula has the following form

119877119904 = (119886 + 119887119899

119873)119877119886 (3)

where 119899 and 119873 are respectively the actual daily sunshineduration and daily maximum possible sunshine duration119877119904and 119877

119886are respectively the daily global solar radiation

(MJmminus2 dminus1) and the daily extraterrestrial solar radiation(MJmminus2 dminus1) on a horizontal surface and 119886 and 119887 areempirical coefficients which depend on location The valuesof a and b coefficients are considered as default values 025and 05 respectively proposed by Allen et al [2]

26 Statistical Analyses In this study ET119874results obtained

from FAO-PM equation were utilized as reference valuesand the results achieved by ANN and M5 model tree weretaken into account as estimated values The comparisonof ANN model and M5 model tree values with FAO-PMequationwasmade using statistical indices such as coefficientof determination (1198772) root mean square error (RMSE) andmean absolute error (MAE) in addition to plotting graphsThese indices are defined as follows

1198772= (

sum119899

119894=1(119909119894 minus 119909) (119910119894 minus 119910)

radicsum119899

119894=1(119909119894 minus 119909)

2sum119899

119894=1(119910119894 minus 119910)

2

)

2

Journal of Climatology 5

y = 090x + 241

R2 = 089

Gazali

y = 086x + 182

R2 = 089

Farabi

y = 091x + 193R2 = 088

All data

y = 103x + 126

R2 = 091

Shoeybie

y = 086x + 271

R2 = 087

minus10

0

10

20

30

40

Amirkabir

y = 093x + 094R2 = 090

minus10 0 10 20 30 40

Khazaei

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

Figure 3 Scatter plot of 119879min against LST119873

RMSE = radic 1119899

119899

sum

119894=1

(119909119894 minus 119910119894)2

MAE = 1119899

119899

sum

119894=1

1003816100381610038161003816119909119894 minus 1199101198941003816100381610038161003816

(4)where 119909

119894is ET119874computed by FAO-PM 119909 denotes the average

amount of computed ET119874computed by FAO-PM 119910

119894is ET119874

computed by ANNM5 and 119910 is the average computed ET119874

amounts by last models

3 Results and Discussion

In the first stage of the study before calculating the ET119874 the

correlation between LST obtained from MODIS sensor andair temperature was determined Accordingly scatter plots ofLST values provided by MODIS images versus air tempera-ture are presented for different stations in Figures 3 and 4As it can be perceived in Figure 3 there is a high correlationbetween the LST

119873andminimum air temperature (119879min)The

greatest1198772 was observed between LST119873and119879min in Shoeybie

station which was equal to 091 the minimum1198772 was seen inthe Amirkabir station with the value of 087 Furthermore forall stations1198772 of two aforementioned parameterswas entirelyassessed at 088 In Figure 3 symmetrical and appropriatedistribution of points around the line of best fit (line 1 1)indicates a strong correlation between the two parametersIn Figure 4 relation between the LST119863 and maximum airtemperature (119879max) displays that the greatest 1198772 betweenLST119863and 119879max is related to Amirkabir and Khazaei stations

(1198772 = 091) the minimum amount of this coefficient isassociated with Gazali station (1198772 = 081) For all studystations 1198772 was generally equal to 078 Overall it can beconcluded that there is a strong relationship between thesetwo parameters The scatter of points around the line ofbest fit in the Figure 4 depicts an overestimation of LST

119863

over 119879max This overestimation is more pronounced for thetemperatures over 30∘C

For all examined datasets the correlation between LST119873

and119879min is higher compared to the correlation between LST119863and 119879max for thermal products of MODIS sensor Moreoverprevious studies concerning estimation of air temperaturehave similarly confirmed that correlation between LST119873 and119879min is greater than correlation between LST119863 and 119879max [1219]

In the second stage in order to calculate ET119874 using LSTvalues extracted from the MODIS sensor (LST119863 and LST119873)ANNmodels andM5model tree were employed In additionto LST

119863and LST

119873 two parameters including mean LST

(LST119872) and day of year (DOY) were considered as inputs

for generating model in order to increase accuracy of ET119874

estimates Thus in producing ANN model and M5 modeltree four parameters including LST

119863 LST119873 DOY and LST

119872

were taken into consideration as input and ET119874calculated

from weather data using FAO-PM equation as outputFor generating ANN model training data (whole data

of Amirkabir Farabi and Gazali stations) were applied andthe number of nodes in the hidden layer was obtained usingtrial and error method The number of nodes in the hiddenlayer was considered varying from 1 to 12 based on errorstatistical parameters a network with 3 nodes in the hiddenlayer indicated the lowest error in comparison of ET

119874values

6 Journal of Climatology

y = 105x minus 157

R2 = 081

10 20 30 40 50 60

Gazali

y = 092x + 052

R2 = 088

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

Farabi

y = 072x + 404

R2 = 091

Amirkabir

y = 078x + 516

R2 = 078

All data

y = 100x minus 199

R2 = 089

Shoeybie

y = 078x + 291

R2 = 091

Khazaei

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

LSTD (∘C)

LSTD (∘C) LSTD (∘C) LSTD (∘C)

LSTD (∘C) LSTD (∘C)

Figure 4 Scatter plot of 119879max against LST119863

y = 100x minus 001

R2 = 079

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-ANN (mmd)

Figure 5 Scatter plot of estimated ET119874using ANN against calcu-

lated ET119874by FAO-PM equation for training data

calculated by FAO-PMmethod Table 1 presents the values oferror parameters for the neural network with the structure ofthree nodes in the hidden layer In Figure 5 scatter diagramof calculated ET

119874values through ANN for all training data

has been plotted against ET119874 values obtained by FAO-PMequation As shown in Figure 3 1198772 = 079 demonstratesthat the ANN has provided an acceptable determinationcoefficient in approximating ET

119874 In this figure the points

density increases around the line 1 1 in large amounts of ET119874

that is it represents the overestimation or underestimation ofthe data that are situated in this area

y = 102x minus 015R2 = 083

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-M5 (mmd)

Figure 6 Scatter plot of estimated ET119874usingM5model tree against

calculated ET119874by FAO-PM equation for training data

Table 1 Error statistics in estimating ET119874for model tree and ANN

methods using training data

Model RMSE (mmd) MAE (mmd)ANN 140 105M5 127 096

For generating M5 model tree WEKA 37 software [42]was used considering the same data applied to the trainingANN model Algorithm 1 shows M5 model tree produced

Journal of Climatology 7

LSTn lt= 1943 LM num 1LSTms lt= 1555 LM1 Pm = 00147 lowast Tn + 01048 lowast Tms minus 00007 lowast DOY + 08963LSTms gt 1555 LM num 2

DOY lt= 2825 Pm = 00349 lowast Tn + 00312 lowast Tms + 0028 lowast DOY + 13107DOY lt= 815 LM2 LM num 3DOY gt 815 Pm = 0046 lowast Tn + 0081 lowast Tms minus 00134 lowast DOY + 39221

DOY lt= 106 LM num 4LSTd lt= 312 LM3 Pm = 00719 lowast Tn + 00642 lowast Tms minus 00088 lowast DOY + 38864LSTd gt 312 LM4 LM num 5

DOY gt 106 Pm = 00705 lowast Tn + 00073 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 46615DOY lt= 207 LM num 6

LSTn lt= 1772 Pm = 0201 lowast Tn + 00147 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 25252DOY lt= 129 LM5 LM num 7DOY gt 129 LM6 Pm = 0118 lowast Tn + 00301 lowast Tms + 00026 lowast DOY + 47479

LSTn gt 1772 LM7 LM num 8DOY gt 207 Pm = 00529 lowast Tn + 00301 lowast Tms minus 00087 lowast DOY + 6254

DOY lt= 2725 LM8 LM num 9DOY gt 2725 LM9 Pm = 00529 lowast Tn minus 00348 lowast Tms minus 00116 lowast DOY + 84773

DOY gt 2825 LM num 10DOY lt= 3115 LM10 Pm = 00328 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 3367DOY gt 3115 LM11 LM num 11

LSTn gt 1943 Pm = 01437 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 17414DOY lt= 2275 LM num 12

DOY lt= 1595 Pm = minus01076 lowast Tn + 00018 lowast Tms minus 00393 lowast DOY + 159787DOY lt= 1475 LM12 LM num 13DOY gt 1475 LM13 Pm = 00297 lowast Tn + 00018 lowast Tms + 00032 lowast DOY + 80036

DOY gt 1595 LM num 14DOY lt= 1985 Pm = 03445 lowast Tn + 00769 lowast Td + 00018 lowast Tms minus 01664 lowast DOY + 263097

DOY lt= 1675 LM14 LM num 15DOY gt 1675 LM15 Pm = 00316 lowast Tn + 00018 lowast Tms minus 0006 lowast DOY + 105743

DOY gt 1985 LM num 16DOY lt= 2165 Pm = minus00175 lowast Tn + 00018 lowast Tms + 00225 lowast DOY + 45799

DOY lt= 2065 LM16 LM num 17DOY gt 2065 LM17 Pm = minus0206 lowast Tn + 00018 lowast Tms + 00185 lowast DOY + 111645

DOY gt 2165 LM18 LM num 18DOY gt 2275 LM19 Pm = 00015 lowast Tn + 00018 lowast Tms minus 00046 lowast DOY + 96864

LM num 19Pm = 0022 lowast Tn + 00018 lowast Tms minus 00387 lowast DOY + 160569

Algorithm 1 Tree-structured regression model generated by M5 algorithm using training data

by the software and established linear regression relationsAfterward a scatter plot of estimated ET

119874by M5 model

tree versus calculated ET119874by FAO-PM equation has been

presented for training data (Figure 6) 1198772 value equal to083 indicates proper agreement The distribution of pointsaround the best fit line represents higher accuracy of thismethod in the estimation of low ET

119874values in the great

values of ET119874the error amount increases as well

The comparison of error statistics concerning developedmodels by ANN model and M5 model tree in estimatingET119874using training data can be drawn in Table 1 As seen

M5 model tree which has shown RMSE and MAE valuesrespectively equal to 127 and 096mmdminus1 has resulted inhigher accuracy than ANN in estimating ET

119874

For testing the methods of ANN andM5model tree dataof Khazaei and Shoeybie stations have been used In Figure 7the scatter plot of calculated ET

119874through two models of

ANN and M5 model tree versus FAO-PM values for thementioned stations have been shown 1198772 values associatedwith calculated ET

119874by ANN against FAO-PM equation ET

119874

values for Khazaei and Shoeybie stations were 079 and 086respectively Additionally the same 1198772 values related to M5model tree for aforementioned stations were 080 and 085respectively In both methods ET

119874values were properly

distributed around line 1 1 For smaller amounts of ET119874

there was been a better compatibility between the calculatedvalues by two models and FAO-PM values compared togreater amounts of ET

119874 In other words underestimation or

overestimation of ET119874is related towarm seasons further than

cold seasons The evolutions of calculated ET119874values over

time have been illustrated for two test stations in Figure 8As perceived in this graph the maximum amounts of ET

119874by

these twomodels were not entirely compatible with FAO-PMvaluesThis could be due to the lack of consideration of some

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

2 Journal of Climatology

available in many regions is the major limitation of thismethod [10] in addition it seems that the reordered data arenot accurate enough especially in developing countries [11]

From the viewpoint of temporal and spatial variationsof climatic data weather stations density (the number ofstations per unit of area) is not generally adequate for demon-strating spatiotemporal variations Today remote sensingtechniques which gather land surface information from abroader geographic scope are known as an effective tool andmethodology for extracting the ground parameters that canbe used to estimate ET at regional scales [12] To this end inthe basins that may face shortage of measured data remotesensing data can considerably supply needed informationsuch as albedo leaf area index and land surface temperature(LST) [13] Recent advances in remote sensing techniques andenhancement of temporal spatial and radiometric resolutionof satellite images have produced a range of useful productsThese products can be widely used in various research areasespecially water and environment Many studies have beenconducted in estimating ET

119874as an important element of

hydrological cycle In this regard it can be mentioned in thestudies of Guerschman et al [14] Maeda et al [4] Yang et al[12] Cleugh et al [15] Tian et al [16] Hankerson et al [17]Li et al [18]

Recently some data-based techniques such as artificialneural networks (ANNs) support vector machine and M5model tree have been broadly utilized in solving practicalproblems Mentioned techniques can simulate processes inwhich there is not an exact solution and it is merely possibleto approach near-optimal solution [19] In these methodsa new knowledge is not produced about the process of aproblem In fact thanks to the proper recognition of theproblem process in selecting the input and output variablescaused by the use of modern regression techniques thishelps to better fit the data [20] Data-driven techniques canefficiently model nonlinear and complicated processes suchas ET that its precise calculation depends on numerousweather data and interactions between them [21]

Recently by the developing new machine learning meth-ods application of new models in the estimation of ET

119874has

been increased Kisi and Ozturk [22] studied the adaptiveneurofuzzy inference system (ANFIS) technique in estima-tion of ET

119874in Los Angeles California and showed that

it could be successfully considered in the ET119874estimation

Kisi and Cimen [23] applied SVM in modeling ET119874

incentral California and concluded that SVR model could beembedded as a module for estimating ET

119874data in hydro-

logical modeling studies Tabari et al [24] investigated thepotential of SVM ANFIS multiple linear regression (MLR)and multiple nonlinear regression (MNLR) for estimating ina semiarid highland environment in IranThey found that theSVM and ANFIS had better performance in ET

119874modeling

compared to the others Besides several studies have shownhigh performance of ANNs inmodeling ET against statisticalmethods [8 25ndash29]The substantial benefit of ANNmethodscompared to conventional methods is the ability of solvingproblems that are difficult to formalize [30] Hou et al [10]studied ANNs in simulating ET119874 values and demonstratedthat the models reflected a noticeable efficiency Landeras

et al [21] compared calculated ET119874byANN to the ET

119874values

of radiation and thermal models and declared that ANN canprovide more accurate results than empirical models

Due to the simple geometric structure of model tree andproviding fast computing set of IF-THEN rules which areeasily understandable [31] the model tree has been utilizedin different scientific studies Pal and Deswal [1] in a studyevaluated the capability of M5 model tree to model ET119874 indaily scale and the obtained results showed that M5 modeltree can be properly used in this context Rahimikhoob et al[11] conducted a study to assess the performance ofM5modeltree in reaching ET119874 values in a semiarid region of Iran bymeans of 119870119901 values of pan evaporation They asserted thatthis model shows more satisfactory performance than otherapproaches in estimating ET

119874in the study region Sattari et al

[32] compared ANN andM5 model tree in determining ET119874

and concluded that both ANNmodel andM5model tree canproperly estimate ET

119874 ANN suggested a better performance

howeverM5model tree offered simple linear regressions thatcan simply calculate ET

119874

The main aim of this study is to evaluate the ability of M5model tree and ANN model in estimating daily ET

119874using

LST values obtained from MODerate Resolution ImagingSpectroradiometer (MODIS)Terra sensor The accuracy ofcalculated ET

119874by means of M5 model tree and ANN model

has been investigated by comparing with the ET119874amounts of

FAO-PMmethod

2 Materials and Methods

21 Study Area and Data Farms of Sugarcane DevelopmentProject which are located in Khuzestan province Iranwere considered as the study area in the present researchKhuzestan province is stretched in southeastern part ofthe country with the area of approximately 63238 km2between longitudes of 47∘381015840 E to 50∘321015840 E and latitudes of29∘571015840 N to 33∘001015840 N This province is located adjoining theboundary of Iraq from the west and Persian Gulf from thesouth Khuzestan province according to deMartonne climateclassification has a semiarid climateThe average temperatureduring the winter season is nearly 914∘C and occasionally itsminimum falls down a few degrees below 0∘C The averagetemperature in the summers is approximately 312∘C whereasits maximum sometimes exceeds 50∘C Required climaticvariables in order to estimate ET119874 in this study were collectedfrom weather stations namely Amirkabir Farabi GazaliKhazaei and Shoeybie for the years of 2006 and 2007 inthe periods when satellite images existed The meteorolog-ical data consisted of daily observations of maximum andminimum temperature sunshine duration relative humidityand wind speed which have been used in estimating ET

119874by

FAO-PM equation Figure 1 illustrates the location of weatherstations in the study area

22 MODIS Images In the current study data of daytimeLST (LST

119863) and nighttime LST (LST

119873) obtained from the

MODIS sensor were used as inputs to the M5 model treeand ANN models The MODIS sensor which is on board

Journal of Climatology 3

Iran

Khuzestan

Figure 1 Location of weather stations in the study area

of the Terra and Aqua satellites is able to provide imagesin 36 spectral bands between 062 and 14385 120583m Spatialresolutions of the sensor are 250m 500m and 1 km in severalbands In the thermal-infrared (TIR) MODIS sensors have1 km spatial resolution [19] This sensor performs a range ofdaily regular observations on the sea land and atmospherein the global scale moreover it has an extensive and con-tinuous spectral and spatial coverage MODIS sensor waslaunched by the Terra and Aqua satellites in 1999 and 2002respectively These satellites both have a sun-synchronousnear polar circular orbit Terra satellite everyday crosses overthe equator from north to south while Aqua satellite hasan inverse movement from south to north United StatesNational Aeronautics and Space Administration (NASA) isresponsible for processing and providing MODIS sensorrsquosdata NASA supplies the data in a large variety of productsapplicable to land ocean and atmosphere uses [4] The dataand products of MODIS sensor are available on the NASArsquoswebsite (httpmodisgsfcnasagov)The images selected forthis study are the level three (L3) data of the MODIS sensor(MOD11A1) which are related to Terra satellite This productprovides daytime and nighttime LST data collected on a 1 kmspatial resolution and gridded in the sinusoidal projectionsystem [33] The MODIS sensor LST data is acquired fromtwo TIR channels that is 31 (1078ndash1128120583m) and 32 (1177ndash1227120583m) using the split-window algorithm [34]

A total of 428 images of the MODIS sensor associatedwith MOD11A1 production from the Terra satellite in thetime periods of 2006 and 2007 covering the study area wereretrieved from the Land ProcessesDistributedActiveArchiveCenter (LP DAAC) (httplpdaacusgsgov) Cloudless skyand fair weather were the reason for selecting these picturesChanging coordinate systems from the sinusoidal to UTM(datum WGS84) was performed using MODIS ReprojectionTool (MRT) Afterward locations of study stations were pro-jected on the images and then LST119863 and LST119873were extractedfrom the corresponding pixels of the images ExtractingLST values in the desired stations was done by means ofHawthrsquos Analysis Tools (HAT) in ArcGIS 93 software Unitof LST values extracted from the images was Kelvin so before

utilizing them as model input these values were converted toCelsius

In the present study whole LST values extracted fromMODIS images in three stations includingAmirkabir Farabiand Gazali were used to construct and train the ANN andM5model tree and two other stations Khazaei and Shoeybiewere applied to test mentioned models

23 Artificial Neural Network (ANN) ANNs are known aspowerfulmachine-learning techniques which are extensivelyused for numerical prediction and classification [35] ANNsare also operative tools to model nonlinear systems and needless amount of data as inputs than customary mathematicalapproaches [27] A neural network is based on processinga set of data that its analysis procedure has been inspiredby biological neural systems Neural networks consist of aninterconnected group of neurons placed near to each otherin layers that implement data processing through neuronsand their connections ANNs included one input layer anoutput layer and one or more hidden layers neurons of eachlayer are joined to all neurons of the previous layer by meansof weighted connections The input vectors are received byneurons of the input layer and the values can be conveyedto the next layer of processing elements across connectionsThe number of neurons in each hidden layer is determinedby the user This process continues up to the output layerANNmodeling is carried out in two stages including trainingand testing In the training stage after getting input dataneural network makes attempts to convert the inputs intodesired outputs Connecting weights of network neurons aredetermined in this stage these weights in the testing stage areexamined using various datasets

A multilayer perceptron (MLP) ANN with one inputlayer one hidden layer and one output layer was used toestimate ET119874 from LST

119863 LST119873 mean LST (LST

119872) and day

of year (DOY) data as inputs The transfer function in thenetworks was log-sigmoid for this study The accuracy ofthe networks was evaluated for each epoch in the trainingthrough mean squared error (MSE) The backpropagation(BP) algorithm was employed to train MLP neural networkLevenberg-Marquardt (LM) a second-order nonlinear opti-mization technique was usedwith an early stopping criterionto improve the network training speed and efficiency Thetarget error for the training of networks was equal to 10minus4With the specification of this target error the number ofiteration for all ANN models was placed to 1000

24 M5 Model Tree M5 model tree was introduced byQuinlan in 1992 [36] The model is established according toa binary decision tree in which there are linear regressionfunctions in the terminal node (leaf) which sets a relation-ship between independent anddependent variables [11] Tree-based models are made according to a divide-and-conquermethod for constructing a relationship between independentand dependent variables [37] The tree models can be alsoused for qualitative and quantitative data [9]

Building the M5 model tree involves two separate steps[36 38] The first one consists of dividing data into subsets

4 Journal of Climatology

X2

LM6

LM5

LM1 LM2

LM3

LM4

2 4 6 8 10

2

4

6

8

X1

Y (output)

(a)

X1X1

X2 X2

gt42le42

le35

le2 le63

le5 gt5gt35

gt2 gt63

LM6LM5

LM1

LM2 LM3

LM4

X2

(b)

Figure 2 (a) Example of M5 model tree a splitting the input space 1199091times 1199092by M5 model tree algorithm and (b) diagram of model tree with

six linear regression models at the leaves [11]

to construct the model tree The dividing criterion is basedon the standard deviation of the subset values that reach anode as ameasure of error value in that node and additionallycalculating the expected reduction in the error as a resultof testing each attribute at that node Equation of standarddeviation reduction (SDR) is given as follows [1]

SDR = SD (119879) minussum119879119894

119879times SD (119879

119894) (1)

where 119879 is defined as a set of examples that reaches the node119879119894 demonstrates the subset of examples that have the 119894th

output of the potential set and SD is the standard deviation[39] Due to branching process data in child nodes (subtreeor smaller nodes) have fewer SD than parent nodes (greaternodes) After examining all possible structures a struc-ture would be picked out that has the maximum expectederror reduction This dividing often creates a great tree-likestructure that leads to overfit structure In order to avoidoverfitting in the second step the overgrown tree is prunedand pruned subtrees are replaced with linear regressionfunctions Figure 2(a) illustrates splitting the input space1199091times 1199092(independent variables) into six linear regression

functions at the leaves (labeled LM1 through LM6) by M5model tree algorithm General form of the model is 119910 =1198860+ 11988611199091+ 11988621199092 in which 119886

0 1198861 and 119886

2are linear regression

constants Figure 2(b) shows branches relations in the formof a tree diagram [19]

25 FAO-PM Equation FAO-PM equation a physicallybased method is widely used in the calculation of ET119874 and isa reliable method in the estimation of ET119874 in various climateconditions [2 40 41] Moreover FAO proposed this equationas a standard method for estimating ET119874 Although the mostprecise method for estimating ET119874 is to employ lysimeterdata considering the absence of such data in the study regionassessment of ANN and M5 model tree performance wasmade by FAO-PMequationThe equation for estimating dailyET119874has been presented as follows [2]

ET119874=0484Δ (119877119899 minus 119866) + 120574 (900 (119879119886 + 273))1198802 (119890119904 minus 119890119886)

Δ + 120574 (1 + 0341198802)

(2)

where ET119874is the reference evapotranspiration (mmdminus1) Δ

is the slope of the saturation vapor pressure curve (kPa ∘Cminus1)at the daily mean air temperature (∘C) 119877

119899and 119866 are the net

solar radiation and soil heat flux density (MJmminus2 dminus1) 120574 isthe psychrometric constant (kPa ∘Cminus1) 119879 is the daily meantemperature (∘C) 119880

2is the mean wind speed (msminus1) 119890

119904is

the saturation vapor pressure (kPa) and 119890119886is the actual vapor

pressure (kPa) [2]In current study the daily values of Δ 119877

119899 119890119904 and 119890

119886

were calculated using the equation given by Allen et al [2]For calculation of 119877

119899 it is needed to calculate daily solar

radiation (119877119904) Allen et al [2] proposed 119877

119904to be calculated

using the Angstrom formula which relates solar radiation toextraterrestrial radiation (119877119886) and relative sunshine durationThe formula has the following form

119877119904 = (119886 + 119887119899

119873)119877119886 (3)

where 119899 and 119873 are respectively the actual daily sunshineduration and daily maximum possible sunshine duration119877119904and 119877

119886are respectively the daily global solar radiation

(MJmminus2 dminus1) and the daily extraterrestrial solar radiation(MJmminus2 dminus1) on a horizontal surface and 119886 and 119887 areempirical coefficients which depend on location The valuesof a and b coefficients are considered as default values 025and 05 respectively proposed by Allen et al [2]

26 Statistical Analyses In this study ET119874results obtained

from FAO-PM equation were utilized as reference valuesand the results achieved by ANN and M5 model tree weretaken into account as estimated values The comparisonof ANN model and M5 model tree values with FAO-PMequationwasmade using statistical indices such as coefficientof determination (1198772) root mean square error (RMSE) andmean absolute error (MAE) in addition to plotting graphsThese indices are defined as follows

1198772= (

sum119899

119894=1(119909119894 minus 119909) (119910119894 minus 119910)

radicsum119899

119894=1(119909119894 minus 119909)

2sum119899

119894=1(119910119894 minus 119910)

2

)

2

Journal of Climatology 5

y = 090x + 241

R2 = 089

Gazali

y = 086x + 182

R2 = 089

Farabi

y = 091x + 193R2 = 088

All data

y = 103x + 126

R2 = 091

Shoeybie

y = 086x + 271

R2 = 087

minus10

0

10

20

30

40

Amirkabir

y = 093x + 094R2 = 090

minus10 0 10 20 30 40

Khazaei

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

Figure 3 Scatter plot of 119879min against LST119873

RMSE = radic 1119899

119899

sum

119894=1

(119909119894 minus 119910119894)2

MAE = 1119899

119899

sum

119894=1

1003816100381610038161003816119909119894 minus 1199101198941003816100381610038161003816

(4)where 119909

119894is ET119874computed by FAO-PM 119909 denotes the average

amount of computed ET119874computed by FAO-PM 119910

119894is ET119874

computed by ANNM5 and 119910 is the average computed ET119874

amounts by last models

3 Results and Discussion

In the first stage of the study before calculating the ET119874 the

correlation between LST obtained from MODIS sensor andair temperature was determined Accordingly scatter plots ofLST values provided by MODIS images versus air tempera-ture are presented for different stations in Figures 3 and 4As it can be perceived in Figure 3 there is a high correlationbetween the LST

119873andminimum air temperature (119879min)The

greatest1198772 was observed between LST119873and119879min in Shoeybie

station which was equal to 091 the minimum1198772 was seen inthe Amirkabir station with the value of 087 Furthermore forall stations1198772 of two aforementioned parameterswas entirelyassessed at 088 In Figure 3 symmetrical and appropriatedistribution of points around the line of best fit (line 1 1)indicates a strong correlation between the two parametersIn Figure 4 relation between the LST119863 and maximum airtemperature (119879max) displays that the greatest 1198772 betweenLST119863and 119879max is related to Amirkabir and Khazaei stations

(1198772 = 091) the minimum amount of this coefficient isassociated with Gazali station (1198772 = 081) For all studystations 1198772 was generally equal to 078 Overall it can beconcluded that there is a strong relationship between thesetwo parameters The scatter of points around the line ofbest fit in the Figure 4 depicts an overestimation of LST

119863

over 119879max This overestimation is more pronounced for thetemperatures over 30∘C

For all examined datasets the correlation between LST119873

and119879min is higher compared to the correlation between LST119863and 119879max for thermal products of MODIS sensor Moreoverprevious studies concerning estimation of air temperaturehave similarly confirmed that correlation between LST119873 and119879min is greater than correlation between LST119863 and 119879max [1219]

In the second stage in order to calculate ET119874 using LSTvalues extracted from the MODIS sensor (LST119863 and LST119873)ANNmodels andM5model tree were employed In additionto LST

119863and LST

119873 two parameters including mean LST

(LST119872) and day of year (DOY) were considered as inputs

for generating model in order to increase accuracy of ET119874

estimates Thus in producing ANN model and M5 modeltree four parameters including LST

119863 LST119873 DOY and LST

119872

were taken into consideration as input and ET119874calculated

from weather data using FAO-PM equation as outputFor generating ANN model training data (whole data

of Amirkabir Farabi and Gazali stations) were applied andthe number of nodes in the hidden layer was obtained usingtrial and error method The number of nodes in the hiddenlayer was considered varying from 1 to 12 based on errorstatistical parameters a network with 3 nodes in the hiddenlayer indicated the lowest error in comparison of ET

119874values

6 Journal of Climatology

y = 105x minus 157

R2 = 081

10 20 30 40 50 60

Gazali

y = 092x + 052

R2 = 088

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

Farabi

y = 072x + 404

R2 = 091

Amirkabir

y = 078x + 516

R2 = 078

All data

y = 100x minus 199

R2 = 089

Shoeybie

y = 078x + 291

R2 = 091

Khazaei

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

LSTD (∘C)

LSTD (∘C) LSTD (∘C) LSTD (∘C)

LSTD (∘C) LSTD (∘C)

Figure 4 Scatter plot of 119879max against LST119863

y = 100x minus 001

R2 = 079

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-ANN (mmd)

Figure 5 Scatter plot of estimated ET119874using ANN against calcu-

lated ET119874by FAO-PM equation for training data

calculated by FAO-PMmethod Table 1 presents the values oferror parameters for the neural network with the structure ofthree nodes in the hidden layer In Figure 5 scatter diagramof calculated ET

119874values through ANN for all training data

has been plotted against ET119874 values obtained by FAO-PMequation As shown in Figure 3 1198772 = 079 demonstratesthat the ANN has provided an acceptable determinationcoefficient in approximating ET

119874 In this figure the points

density increases around the line 1 1 in large amounts of ET119874

that is it represents the overestimation or underestimation ofthe data that are situated in this area

y = 102x minus 015R2 = 083

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-M5 (mmd)

Figure 6 Scatter plot of estimated ET119874usingM5model tree against

calculated ET119874by FAO-PM equation for training data

Table 1 Error statistics in estimating ET119874for model tree and ANN

methods using training data

Model RMSE (mmd) MAE (mmd)ANN 140 105M5 127 096

For generating M5 model tree WEKA 37 software [42]was used considering the same data applied to the trainingANN model Algorithm 1 shows M5 model tree produced

Journal of Climatology 7

LSTn lt= 1943 LM num 1LSTms lt= 1555 LM1 Pm = 00147 lowast Tn + 01048 lowast Tms minus 00007 lowast DOY + 08963LSTms gt 1555 LM num 2

DOY lt= 2825 Pm = 00349 lowast Tn + 00312 lowast Tms + 0028 lowast DOY + 13107DOY lt= 815 LM2 LM num 3DOY gt 815 Pm = 0046 lowast Tn + 0081 lowast Tms minus 00134 lowast DOY + 39221

DOY lt= 106 LM num 4LSTd lt= 312 LM3 Pm = 00719 lowast Tn + 00642 lowast Tms minus 00088 lowast DOY + 38864LSTd gt 312 LM4 LM num 5

DOY gt 106 Pm = 00705 lowast Tn + 00073 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 46615DOY lt= 207 LM num 6

LSTn lt= 1772 Pm = 0201 lowast Tn + 00147 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 25252DOY lt= 129 LM5 LM num 7DOY gt 129 LM6 Pm = 0118 lowast Tn + 00301 lowast Tms + 00026 lowast DOY + 47479

LSTn gt 1772 LM7 LM num 8DOY gt 207 Pm = 00529 lowast Tn + 00301 lowast Tms minus 00087 lowast DOY + 6254

DOY lt= 2725 LM8 LM num 9DOY gt 2725 LM9 Pm = 00529 lowast Tn minus 00348 lowast Tms minus 00116 lowast DOY + 84773

DOY gt 2825 LM num 10DOY lt= 3115 LM10 Pm = 00328 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 3367DOY gt 3115 LM11 LM num 11

LSTn gt 1943 Pm = 01437 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 17414DOY lt= 2275 LM num 12

DOY lt= 1595 Pm = minus01076 lowast Tn + 00018 lowast Tms minus 00393 lowast DOY + 159787DOY lt= 1475 LM12 LM num 13DOY gt 1475 LM13 Pm = 00297 lowast Tn + 00018 lowast Tms + 00032 lowast DOY + 80036

DOY gt 1595 LM num 14DOY lt= 1985 Pm = 03445 lowast Tn + 00769 lowast Td + 00018 lowast Tms minus 01664 lowast DOY + 263097

DOY lt= 1675 LM14 LM num 15DOY gt 1675 LM15 Pm = 00316 lowast Tn + 00018 lowast Tms minus 0006 lowast DOY + 105743

DOY gt 1985 LM num 16DOY lt= 2165 Pm = minus00175 lowast Tn + 00018 lowast Tms + 00225 lowast DOY + 45799

DOY lt= 2065 LM16 LM num 17DOY gt 2065 LM17 Pm = minus0206 lowast Tn + 00018 lowast Tms + 00185 lowast DOY + 111645

DOY gt 2165 LM18 LM num 18DOY gt 2275 LM19 Pm = 00015 lowast Tn + 00018 lowast Tms minus 00046 lowast DOY + 96864

LM num 19Pm = 0022 lowast Tn + 00018 lowast Tms minus 00387 lowast DOY + 160569

Algorithm 1 Tree-structured regression model generated by M5 algorithm using training data

by the software and established linear regression relationsAfterward a scatter plot of estimated ET

119874by M5 model

tree versus calculated ET119874by FAO-PM equation has been

presented for training data (Figure 6) 1198772 value equal to083 indicates proper agreement The distribution of pointsaround the best fit line represents higher accuracy of thismethod in the estimation of low ET

119874values in the great

values of ET119874the error amount increases as well

The comparison of error statistics concerning developedmodels by ANN model and M5 model tree in estimatingET119874using training data can be drawn in Table 1 As seen

M5 model tree which has shown RMSE and MAE valuesrespectively equal to 127 and 096mmdminus1 has resulted inhigher accuracy than ANN in estimating ET

119874

For testing the methods of ANN andM5model tree dataof Khazaei and Shoeybie stations have been used In Figure 7the scatter plot of calculated ET

119874through two models of

ANN and M5 model tree versus FAO-PM values for thementioned stations have been shown 1198772 values associatedwith calculated ET

119874by ANN against FAO-PM equation ET

119874

values for Khazaei and Shoeybie stations were 079 and 086respectively Additionally the same 1198772 values related to M5model tree for aforementioned stations were 080 and 085respectively In both methods ET

119874values were properly

distributed around line 1 1 For smaller amounts of ET119874

there was been a better compatibility between the calculatedvalues by two models and FAO-PM values compared togreater amounts of ET

119874 In other words underestimation or

overestimation of ET119874is related towarm seasons further than

cold seasons The evolutions of calculated ET119874values over

time have been illustrated for two test stations in Figure 8As perceived in this graph the maximum amounts of ET

119874by

these twomodels were not entirely compatible with FAO-PMvaluesThis could be due to the lack of consideration of some

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

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Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Marine BiologyJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

Journal of Climatology 3

Iran

Khuzestan

Figure 1 Location of weather stations in the study area

of the Terra and Aqua satellites is able to provide imagesin 36 spectral bands between 062 and 14385 120583m Spatialresolutions of the sensor are 250m 500m and 1 km in severalbands In the thermal-infrared (TIR) MODIS sensors have1 km spatial resolution [19] This sensor performs a range ofdaily regular observations on the sea land and atmospherein the global scale moreover it has an extensive and con-tinuous spectral and spatial coverage MODIS sensor waslaunched by the Terra and Aqua satellites in 1999 and 2002respectively These satellites both have a sun-synchronousnear polar circular orbit Terra satellite everyday crosses overthe equator from north to south while Aqua satellite hasan inverse movement from south to north United StatesNational Aeronautics and Space Administration (NASA) isresponsible for processing and providing MODIS sensorrsquosdata NASA supplies the data in a large variety of productsapplicable to land ocean and atmosphere uses [4] The dataand products of MODIS sensor are available on the NASArsquoswebsite (httpmodisgsfcnasagov)The images selected forthis study are the level three (L3) data of the MODIS sensor(MOD11A1) which are related to Terra satellite This productprovides daytime and nighttime LST data collected on a 1 kmspatial resolution and gridded in the sinusoidal projectionsystem [33] The MODIS sensor LST data is acquired fromtwo TIR channels that is 31 (1078ndash1128120583m) and 32 (1177ndash1227120583m) using the split-window algorithm [34]

A total of 428 images of the MODIS sensor associatedwith MOD11A1 production from the Terra satellite in thetime periods of 2006 and 2007 covering the study area wereretrieved from the Land ProcessesDistributedActiveArchiveCenter (LP DAAC) (httplpdaacusgsgov) Cloudless skyand fair weather were the reason for selecting these picturesChanging coordinate systems from the sinusoidal to UTM(datum WGS84) was performed using MODIS ReprojectionTool (MRT) Afterward locations of study stations were pro-jected on the images and then LST119863 and LST119873were extractedfrom the corresponding pixels of the images ExtractingLST values in the desired stations was done by means ofHawthrsquos Analysis Tools (HAT) in ArcGIS 93 software Unitof LST values extracted from the images was Kelvin so before

utilizing them as model input these values were converted toCelsius

In the present study whole LST values extracted fromMODIS images in three stations includingAmirkabir Farabiand Gazali were used to construct and train the ANN andM5model tree and two other stations Khazaei and Shoeybiewere applied to test mentioned models

23 Artificial Neural Network (ANN) ANNs are known aspowerfulmachine-learning techniques which are extensivelyused for numerical prediction and classification [35] ANNsare also operative tools to model nonlinear systems and needless amount of data as inputs than customary mathematicalapproaches [27] A neural network is based on processinga set of data that its analysis procedure has been inspiredby biological neural systems Neural networks consist of aninterconnected group of neurons placed near to each otherin layers that implement data processing through neuronsand their connections ANNs included one input layer anoutput layer and one or more hidden layers neurons of eachlayer are joined to all neurons of the previous layer by meansof weighted connections The input vectors are received byneurons of the input layer and the values can be conveyedto the next layer of processing elements across connectionsThe number of neurons in each hidden layer is determinedby the user This process continues up to the output layerANNmodeling is carried out in two stages including trainingand testing In the training stage after getting input dataneural network makes attempts to convert the inputs intodesired outputs Connecting weights of network neurons aredetermined in this stage these weights in the testing stage areexamined using various datasets

A multilayer perceptron (MLP) ANN with one inputlayer one hidden layer and one output layer was used toestimate ET119874 from LST

119863 LST119873 mean LST (LST

119872) and day

of year (DOY) data as inputs The transfer function in thenetworks was log-sigmoid for this study The accuracy ofthe networks was evaluated for each epoch in the trainingthrough mean squared error (MSE) The backpropagation(BP) algorithm was employed to train MLP neural networkLevenberg-Marquardt (LM) a second-order nonlinear opti-mization technique was usedwith an early stopping criterionto improve the network training speed and efficiency Thetarget error for the training of networks was equal to 10minus4With the specification of this target error the number ofiteration for all ANN models was placed to 1000

24 M5 Model Tree M5 model tree was introduced byQuinlan in 1992 [36] The model is established according toa binary decision tree in which there are linear regressionfunctions in the terminal node (leaf) which sets a relation-ship between independent anddependent variables [11] Tree-based models are made according to a divide-and-conquermethod for constructing a relationship between independentand dependent variables [37] The tree models can be alsoused for qualitative and quantitative data [9]

Building the M5 model tree involves two separate steps[36 38] The first one consists of dividing data into subsets

4 Journal of Climatology

X2

LM6

LM5

LM1 LM2

LM3

LM4

2 4 6 8 10

2

4

6

8

X1

Y (output)

(a)

X1X1

X2 X2

gt42le42

le35

le2 le63

le5 gt5gt35

gt2 gt63

LM6LM5

LM1

LM2 LM3

LM4

X2

(b)

Figure 2 (a) Example of M5 model tree a splitting the input space 1199091times 1199092by M5 model tree algorithm and (b) diagram of model tree with

six linear regression models at the leaves [11]

to construct the model tree The dividing criterion is basedon the standard deviation of the subset values that reach anode as ameasure of error value in that node and additionallycalculating the expected reduction in the error as a resultof testing each attribute at that node Equation of standarddeviation reduction (SDR) is given as follows [1]

SDR = SD (119879) minussum119879119894

119879times SD (119879

119894) (1)

where 119879 is defined as a set of examples that reaches the node119879119894 demonstrates the subset of examples that have the 119894th

output of the potential set and SD is the standard deviation[39] Due to branching process data in child nodes (subtreeor smaller nodes) have fewer SD than parent nodes (greaternodes) After examining all possible structures a struc-ture would be picked out that has the maximum expectederror reduction This dividing often creates a great tree-likestructure that leads to overfit structure In order to avoidoverfitting in the second step the overgrown tree is prunedand pruned subtrees are replaced with linear regressionfunctions Figure 2(a) illustrates splitting the input space1199091times 1199092(independent variables) into six linear regression

functions at the leaves (labeled LM1 through LM6) by M5model tree algorithm General form of the model is 119910 =1198860+ 11988611199091+ 11988621199092 in which 119886

0 1198861 and 119886

2are linear regression

constants Figure 2(b) shows branches relations in the formof a tree diagram [19]

25 FAO-PM Equation FAO-PM equation a physicallybased method is widely used in the calculation of ET119874 and isa reliable method in the estimation of ET119874 in various climateconditions [2 40 41] Moreover FAO proposed this equationas a standard method for estimating ET119874 Although the mostprecise method for estimating ET119874 is to employ lysimeterdata considering the absence of such data in the study regionassessment of ANN and M5 model tree performance wasmade by FAO-PMequationThe equation for estimating dailyET119874has been presented as follows [2]

ET119874=0484Δ (119877119899 minus 119866) + 120574 (900 (119879119886 + 273))1198802 (119890119904 minus 119890119886)

Δ + 120574 (1 + 0341198802)

(2)

where ET119874is the reference evapotranspiration (mmdminus1) Δ

is the slope of the saturation vapor pressure curve (kPa ∘Cminus1)at the daily mean air temperature (∘C) 119877

119899and 119866 are the net

solar radiation and soil heat flux density (MJmminus2 dminus1) 120574 isthe psychrometric constant (kPa ∘Cminus1) 119879 is the daily meantemperature (∘C) 119880

2is the mean wind speed (msminus1) 119890

119904is

the saturation vapor pressure (kPa) and 119890119886is the actual vapor

pressure (kPa) [2]In current study the daily values of Δ 119877

119899 119890119904 and 119890

119886

were calculated using the equation given by Allen et al [2]For calculation of 119877

119899 it is needed to calculate daily solar

radiation (119877119904) Allen et al [2] proposed 119877

119904to be calculated

using the Angstrom formula which relates solar radiation toextraterrestrial radiation (119877119886) and relative sunshine durationThe formula has the following form

119877119904 = (119886 + 119887119899

119873)119877119886 (3)

where 119899 and 119873 are respectively the actual daily sunshineduration and daily maximum possible sunshine duration119877119904and 119877

119886are respectively the daily global solar radiation

(MJmminus2 dminus1) and the daily extraterrestrial solar radiation(MJmminus2 dminus1) on a horizontal surface and 119886 and 119887 areempirical coefficients which depend on location The valuesof a and b coefficients are considered as default values 025and 05 respectively proposed by Allen et al [2]

26 Statistical Analyses In this study ET119874results obtained

from FAO-PM equation were utilized as reference valuesand the results achieved by ANN and M5 model tree weretaken into account as estimated values The comparisonof ANN model and M5 model tree values with FAO-PMequationwasmade using statistical indices such as coefficientof determination (1198772) root mean square error (RMSE) andmean absolute error (MAE) in addition to plotting graphsThese indices are defined as follows

1198772= (

sum119899

119894=1(119909119894 minus 119909) (119910119894 minus 119910)

radicsum119899

119894=1(119909119894 minus 119909)

2sum119899

119894=1(119910119894 minus 119910)

2

)

2

Journal of Climatology 5

y = 090x + 241

R2 = 089

Gazali

y = 086x + 182

R2 = 089

Farabi

y = 091x + 193R2 = 088

All data

y = 103x + 126

R2 = 091

Shoeybie

y = 086x + 271

R2 = 087

minus10

0

10

20

30

40

Amirkabir

y = 093x + 094R2 = 090

minus10 0 10 20 30 40

Khazaei

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

Figure 3 Scatter plot of 119879min against LST119873

RMSE = radic 1119899

119899

sum

119894=1

(119909119894 minus 119910119894)2

MAE = 1119899

119899

sum

119894=1

1003816100381610038161003816119909119894 minus 1199101198941003816100381610038161003816

(4)where 119909

119894is ET119874computed by FAO-PM 119909 denotes the average

amount of computed ET119874computed by FAO-PM 119910

119894is ET119874

computed by ANNM5 and 119910 is the average computed ET119874

amounts by last models

3 Results and Discussion

In the first stage of the study before calculating the ET119874 the

correlation between LST obtained from MODIS sensor andair temperature was determined Accordingly scatter plots ofLST values provided by MODIS images versus air tempera-ture are presented for different stations in Figures 3 and 4As it can be perceived in Figure 3 there is a high correlationbetween the LST

119873andminimum air temperature (119879min)The

greatest1198772 was observed between LST119873and119879min in Shoeybie

station which was equal to 091 the minimum1198772 was seen inthe Amirkabir station with the value of 087 Furthermore forall stations1198772 of two aforementioned parameterswas entirelyassessed at 088 In Figure 3 symmetrical and appropriatedistribution of points around the line of best fit (line 1 1)indicates a strong correlation between the two parametersIn Figure 4 relation between the LST119863 and maximum airtemperature (119879max) displays that the greatest 1198772 betweenLST119863and 119879max is related to Amirkabir and Khazaei stations

(1198772 = 091) the minimum amount of this coefficient isassociated with Gazali station (1198772 = 081) For all studystations 1198772 was generally equal to 078 Overall it can beconcluded that there is a strong relationship between thesetwo parameters The scatter of points around the line ofbest fit in the Figure 4 depicts an overestimation of LST

119863

over 119879max This overestimation is more pronounced for thetemperatures over 30∘C

For all examined datasets the correlation between LST119873

and119879min is higher compared to the correlation between LST119863and 119879max for thermal products of MODIS sensor Moreoverprevious studies concerning estimation of air temperaturehave similarly confirmed that correlation between LST119873 and119879min is greater than correlation between LST119863 and 119879max [1219]

In the second stage in order to calculate ET119874 using LSTvalues extracted from the MODIS sensor (LST119863 and LST119873)ANNmodels andM5model tree were employed In additionto LST

119863and LST

119873 two parameters including mean LST

(LST119872) and day of year (DOY) were considered as inputs

for generating model in order to increase accuracy of ET119874

estimates Thus in producing ANN model and M5 modeltree four parameters including LST

119863 LST119873 DOY and LST

119872

were taken into consideration as input and ET119874calculated

from weather data using FAO-PM equation as outputFor generating ANN model training data (whole data

of Amirkabir Farabi and Gazali stations) were applied andthe number of nodes in the hidden layer was obtained usingtrial and error method The number of nodes in the hiddenlayer was considered varying from 1 to 12 based on errorstatistical parameters a network with 3 nodes in the hiddenlayer indicated the lowest error in comparison of ET

119874values

6 Journal of Climatology

y = 105x minus 157

R2 = 081

10 20 30 40 50 60

Gazali

y = 092x + 052

R2 = 088

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

Farabi

y = 072x + 404

R2 = 091

Amirkabir

y = 078x + 516

R2 = 078

All data

y = 100x minus 199

R2 = 089

Shoeybie

y = 078x + 291

R2 = 091

Khazaei

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

LSTD (∘C)

LSTD (∘C) LSTD (∘C) LSTD (∘C)

LSTD (∘C) LSTD (∘C)

Figure 4 Scatter plot of 119879max against LST119863

y = 100x minus 001

R2 = 079

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-ANN (mmd)

Figure 5 Scatter plot of estimated ET119874using ANN against calcu-

lated ET119874by FAO-PM equation for training data

calculated by FAO-PMmethod Table 1 presents the values oferror parameters for the neural network with the structure ofthree nodes in the hidden layer In Figure 5 scatter diagramof calculated ET

119874values through ANN for all training data

has been plotted against ET119874 values obtained by FAO-PMequation As shown in Figure 3 1198772 = 079 demonstratesthat the ANN has provided an acceptable determinationcoefficient in approximating ET

119874 In this figure the points

density increases around the line 1 1 in large amounts of ET119874

that is it represents the overestimation or underestimation ofthe data that are situated in this area

y = 102x minus 015R2 = 083

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-M5 (mmd)

Figure 6 Scatter plot of estimated ET119874usingM5model tree against

calculated ET119874by FAO-PM equation for training data

Table 1 Error statistics in estimating ET119874for model tree and ANN

methods using training data

Model RMSE (mmd) MAE (mmd)ANN 140 105M5 127 096

For generating M5 model tree WEKA 37 software [42]was used considering the same data applied to the trainingANN model Algorithm 1 shows M5 model tree produced

Journal of Climatology 7

LSTn lt= 1943 LM num 1LSTms lt= 1555 LM1 Pm = 00147 lowast Tn + 01048 lowast Tms minus 00007 lowast DOY + 08963LSTms gt 1555 LM num 2

DOY lt= 2825 Pm = 00349 lowast Tn + 00312 lowast Tms + 0028 lowast DOY + 13107DOY lt= 815 LM2 LM num 3DOY gt 815 Pm = 0046 lowast Tn + 0081 lowast Tms minus 00134 lowast DOY + 39221

DOY lt= 106 LM num 4LSTd lt= 312 LM3 Pm = 00719 lowast Tn + 00642 lowast Tms minus 00088 lowast DOY + 38864LSTd gt 312 LM4 LM num 5

DOY gt 106 Pm = 00705 lowast Tn + 00073 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 46615DOY lt= 207 LM num 6

LSTn lt= 1772 Pm = 0201 lowast Tn + 00147 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 25252DOY lt= 129 LM5 LM num 7DOY gt 129 LM6 Pm = 0118 lowast Tn + 00301 lowast Tms + 00026 lowast DOY + 47479

LSTn gt 1772 LM7 LM num 8DOY gt 207 Pm = 00529 lowast Tn + 00301 lowast Tms minus 00087 lowast DOY + 6254

DOY lt= 2725 LM8 LM num 9DOY gt 2725 LM9 Pm = 00529 lowast Tn minus 00348 lowast Tms minus 00116 lowast DOY + 84773

DOY gt 2825 LM num 10DOY lt= 3115 LM10 Pm = 00328 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 3367DOY gt 3115 LM11 LM num 11

LSTn gt 1943 Pm = 01437 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 17414DOY lt= 2275 LM num 12

DOY lt= 1595 Pm = minus01076 lowast Tn + 00018 lowast Tms minus 00393 lowast DOY + 159787DOY lt= 1475 LM12 LM num 13DOY gt 1475 LM13 Pm = 00297 lowast Tn + 00018 lowast Tms + 00032 lowast DOY + 80036

DOY gt 1595 LM num 14DOY lt= 1985 Pm = 03445 lowast Tn + 00769 lowast Td + 00018 lowast Tms minus 01664 lowast DOY + 263097

DOY lt= 1675 LM14 LM num 15DOY gt 1675 LM15 Pm = 00316 lowast Tn + 00018 lowast Tms minus 0006 lowast DOY + 105743

DOY gt 1985 LM num 16DOY lt= 2165 Pm = minus00175 lowast Tn + 00018 lowast Tms + 00225 lowast DOY + 45799

DOY lt= 2065 LM16 LM num 17DOY gt 2065 LM17 Pm = minus0206 lowast Tn + 00018 lowast Tms + 00185 lowast DOY + 111645

DOY gt 2165 LM18 LM num 18DOY gt 2275 LM19 Pm = 00015 lowast Tn + 00018 lowast Tms minus 00046 lowast DOY + 96864

LM num 19Pm = 0022 lowast Tn + 00018 lowast Tms minus 00387 lowast DOY + 160569

Algorithm 1 Tree-structured regression model generated by M5 algorithm using training data

by the software and established linear regression relationsAfterward a scatter plot of estimated ET

119874by M5 model

tree versus calculated ET119874by FAO-PM equation has been

presented for training data (Figure 6) 1198772 value equal to083 indicates proper agreement The distribution of pointsaround the best fit line represents higher accuracy of thismethod in the estimation of low ET

119874values in the great

values of ET119874the error amount increases as well

The comparison of error statistics concerning developedmodels by ANN model and M5 model tree in estimatingET119874using training data can be drawn in Table 1 As seen

M5 model tree which has shown RMSE and MAE valuesrespectively equal to 127 and 096mmdminus1 has resulted inhigher accuracy than ANN in estimating ET

119874

For testing the methods of ANN andM5model tree dataof Khazaei and Shoeybie stations have been used In Figure 7the scatter plot of calculated ET

119874through two models of

ANN and M5 model tree versus FAO-PM values for thementioned stations have been shown 1198772 values associatedwith calculated ET

119874by ANN against FAO-PM equation ET

119874

values for Khazaei and Shoeybie stations were 079 and 086respectively Additionally the same 1198772 values related to M5model tree for aforementioned stations were 080 and 085respectively In both methods ET

119874values were properly

distributed around line 1 1 For smaller amounts of ET119874

there was been a better compatibility between the calculatedvalues by two models and FAO-PM values compared togreater amounts of ET

119874 In other words underestimation or

overestimation of ET119874is related towarm seasons further than

cold seasons The evolutions of calculated ET119874values over

time have been illustrated for two test stations in Figure 8As perceived in this graph the maximum amounts of ET

119874by

these twomodels were not entirely compatible with FAO-PMvaluesThis could be due to the lack of consideration of some

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

4 Journal of Climatology

X2

LM6

LM5

LM1 LM2

LM3

LM4

2 4 6 8 10

2

4

6

8

X1

Y (output)

(a)

X1X1

X2 X2

gt42le42

le35

le2 le63

le5 gt5gt35

gt2 gt63

LM6LM5

LM1

LM2 LM3

LM4

X2

(b)

Figure 2 (a) Example of M5 model tree a splitting the input space 1199091times 1199092by M5 model tree algorithm and (b) diagram of model tree with

six linear regression models at the leaves [11]

to construct the model tree The dividing criterion is basedon the standard deviation of the subset values that reach anode as ameasure of error value in that node and additionallycalculating the expected reduction in the error as a resultof testing each attribute at that node Equation of standarddeviation reduction (SDR) is given as follows [1]

SDR = SD (119879) minussum119879119894

119879times SD (119879

119894) (1)

where 119879 is defined as a set of examples that reaches the node119879119894 demonstrates the subset of examples that have the 119894th

output of the potential set and SD is the standard deviation[39] Due to branching process data in child nodes (subtreeor smaller nodes) have fewer SD than parent nodes (greaternodes) After examining all possible structures a struc-ture would be picked out that has the maximum expectederror reduction This dividing often creates a great tree-likestructure that leads to overfit structure In order to avoidoverfitting in the second step the overgrown tree is prunedand pruned subtrees are replaced with linear regressionfunctions Figure 2(a) illustrates splitting the input space1199091times 1199092(independent variables) into six linear regression

functions at the leaves (labeled LM1 through LM6) by M5model tree algorithm General form of the model is 119910 =1198860+ 11988611199091+ 11988621199092 in which 119886

0 1198861 and 119886

2are linear regression

constants Figure 2(b) shows branches relations in the formof a tree diagram [19]

25 FAO-PM Equation FAO-PM equation a physicallybased method is widely used in the calculation of ET119874 and isa reliable method in the estimation of ET119874 in various climateconditions [2 40 41] Moreover FAO proposed this equationas a standard method for estimating ET119874 Although the mostprecise method for estimating ET119874 is to employ lysimeterdata considering the absence of such data in the study regionassessment of ANN and M5 model tree performance wasmade by FAO-PMequationThe equation for estimating dailyET119874has been presented as follows [2]

ET119874=0484Δ (119877119899 minus 119866) + 120574 (900 (119879119886 + 273))1198802 (119890119904 minus 119890119886)

Δ + 120574 (1 + 0341198802)

(2)

where ET119874is the reference evapotranspiration (mmdminus1) Δ

is the slope of the saturation vapor pressure curve (kPa ∘Cminus1)at the daily mean air temperature (∘C) 119877

119899and 119866 are the net

solar radiation and soil heat flux density (MJmminus2 dminus1) 120574 isthe psychrometric constant (kPa ∘Cminus1) 119879 is the daily meantemperature (∘C) 119880

2is the mean wind speed (msminus1) 119890

119904is

the saturation vapor pressure (kPa) and 119890119886is the actual vapor

pressure (kPa) [2]In current study the daily values of Δ 119877

119899 119890119904 and 119890

119886

were calculated using the equation given by Allen et al [2]For calculation of 119877

119899 it is needed to calculate daily solar

radiation (119877119904) Allen et al [2] proposed 119877

119904to be calculated

using the Angstrom formula which relates solar radiation toextraterrestrial radiation (119877119886) and relative sunshine durationThe formula has the following form

119877119904 = (119886 + 119887119899

119873)119877119886 (3)

where 119899 and 119873 are respectively the actual daily sunshineduration and daily maximum possible sunshine duration119877119904and 119877

119886are respectively the daily global solar radiation

(MJmminus2 dminus1) and the daily extraterrestrial solar radiation(MJmminus2 dminus1) on a horizontal surface and 119886 and 119887 areempirical coefficients which depend on location The valuesof a and b coefficients are considered as default values 025and 05 respectively proposed by Allen et al [2]

26 Statistical Analyses In this study ET119874results obtained

from FAO-PM equation were utilized as reference valuesand the results achieved by ANN and M5 model tree weretaken into account as estimated values The comparisonof ANN model and M5 model tree values with FAO-PMequationwasmade using statistical indices such as coefficientof determination (1198772) root mean square error (RMSE) andmean absolute error (MAE) in addition to plotting graphsThese indices are defined as follows

1198772= (

sum119899

119894=1(119909119894 minus 119909) (119910119894 minus 119910)

radicsum119899

119894=1(119909119894 minus 119909)

2sum119899

119894=1(119910119894 minus 119910)

2

)

2

Journal of Climatology 5

y = 090x + 241

R2 = 089

Gazali

y = 086x + 182

R2 = 089

Farabi

y = 091x + 193R2 = 088

All data

y = 103x + 126

R2 = 091

Shoeybie

y = 086x + 271

R2 = 087

minus10

0

10

20

30

40

Amirkabir

y = 093x + 094R2 = 090

minus10 0 10 20 30 40

Khazaei

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

Figure 3 Scatter plot of 119879min against LST119873

RMSE = radic 1119899

119899

sum

119894=1

(119909119894 minus 119910119894)2

MAE = 1119899

119899

sum

119894=1

1003816100381610038161003816119909119894 minus 1199101198941003816100381610038161003816

(4)where 119909

119894is ET119874computed by FAO-PM 119909 denotes the average

amount of computed ET119874computed by FAO-PM 119910

119894is ET119874

computed by ANNM5 and 119910 is the average computed ET119874

amounts by last models

3 Results and Discussion

In the first stage of the study before calculating the ET119874 the

correlation between LST obtained from MODIS sensor andair temperature was determined Accordingly scatter plots ofLST values provided by MODIS images versus air tempera-ture are presented for different stations in Figures 3 and 4As it can be perceived in Figure 3 there is a high correlationbetween the LST

119873andminimum air temperature (119879min)The

greatest1198772 was observed between LST119873and119879min in Shoeybie

station which was equal to 091 the minimum1198772 was seen inthe Amirkabir station with the value of 087 Furthermore forall stations1198772 of two aforementioned parameterswas entirelyassessed at 088 In Figure 3 symmetrical and appropriatedistribution of points around the line of best fit (line 1 1)indicates a strong correlation between the two parametersIn Figure 4 relation between the LST119863 and maximum airtemperature (119879max) displays that the greatest 1198772 betweenLST119863and 119879max is related to Amirkabir and Khazaei stations

(1198772 = 091) the minimum amount of this coefficient isassociated with Gazali station (1198772 = 081) For all studystations 1198772 was generally equal to 078 Overall it can beconcluded that there is a strong relationship between thesetwo parameters The scatter of points around the line ofbest fit in the Figure 4 depicts an overestimation of LST

119863

over 119879max This overestimation is more pronounced for thetemperatures over 30∘C

For all examined datasets the correlation between LST119873

and119879min is higher compared to the correlation between LST119863and 119879max for thermal products of MODIS sensor Moreoverprevious studies concerning estimation of air temperaturehave similarly confirmed that correlation between LST119873 and119879min is greater than correlation between LST119863 and 119879max [1219]

In the second stage in order to calculate ET119874 using LSTvalues extracted from the MODIS sensor (LST119863 and LST119873)ANNmodels andM5model tree were employed In additionto LST

119863and LST

119873 two parameters including mean LST

(LST119872) and day of year (DOY) were considered as inputs

for generating model in order to increase accuracy of ET119874

estimates Thus in producing ANN model and M5 modeltree four parameters including LST

119863 LST119873 DOY and LST

119872

were taken into consideration as input and ET119874calculated

from weather data using FAO-PM equation as outputFor generating ANN model training data (whole data

of Amirkabir Farabi and Gazali stations) were applied andthe number of nodes in the hidden layer was obtained usingtrial and error method The number of nodes in the hiddenlayer was considered varying from 1 to 12 based on errorstatistical parameters a network with 3 nodes in the hiddenlayer indicated the lowest error in comparison of ET

119874values

6 Journal of Climatology

y = 105x minus 157

R2 = 081

10 20 30 40 50 60

Gazali

y = 092x + 052

R2 = 088

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

Farabi

y = 072x + 404

R2 = 091

Amirkabir

y = 078x + 516

R2 = 078

All data

y = 100x minus 199

R2 = 089

Shoeybie

y = 078x + 291

R2 = 091

Khazaei

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

LSTD (∘C)

LSTD (∘C) LSTD (∘C) LSTD (∘C)

LSTD (∘C) LSTD (∘C)

Figure 4 Scatter plot of 119879max against LST119863

y = 100x minus 001

R2 = 079

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-ANN (mmd)

Figure 5 Scatter plot of estimated ET119874using ANN against calcu-

lated ET119874by FAO-PM equation for training data

calculated by FAO-PMmethod Table 1 presents the values oferror parameters for the neural network with the structure ofthree nodes in the hidden layer In Figure 5 scatter diagramof calculated ET

119874values through ANN for all training data

has been plotted against ET119874 values obtained by FAO-PMequation As shown in Figure 3 1198772 = 079 demonstratesthat the ANN has provided an acceptable determinationcoefficient in approximating ET

119874 In this figure the points

density increases around the line 1 1 in large amounts of ET119874

that is it represents the overestimation or underestimation ofthe data that are situated in this area

y = 102x minus 015R2 = 083

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-M5 (mmd)

Figure 6 Scatter plot of estimated ET119874usingM5model tree against

calculated ET119874by FAO-PM equation for training data

Table 1 Error statistics in estimating ET119874for model tree and ANN

methods using training data

Model RMSE (mmd) MAE (mmd)ANN 140 105M5 127 096

For generating M5 model tree WEKA 37 software [42]was used considering the same data applied to the trainingANN model Algorithm 1 shows M5 model tree produced

Journal of Climatology 7

LSTn lt= 1943 LM num 1LSTms lt= 1555 LM1 Pm = 00147 lowast Tn + 01048 lowast Tms minus 00007 lowast DOY + 08963LSTms gt 1555 LM num 2

DOY lt= 2825 Pm = 00349 lowast Tn + 00312 lowast Tms + 0028 lowast DOY + 13107DOY lt= 815 LM2 LM num 3DOY gt 815 Pm = 0046 lowast Tn + 0081 lowast Tms minus 00134 lowast DOY + 39221

DOY lt= 106 LM num 4LSTd lt= 312 LM3 Pm = 00719 lowast Tn + 00642 lowast Tms minus 00088 lowast DOY + 38864LSTd gt 312 LM4 LM num 5

DOY gt 106 Pm = 00705 lowast Tn + 00073 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 46615DOY lt= 207 LM num 6

LSTn lt= 1772 Pm = 0201 lowast Tn + 00147 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 25252DOY lt= 129 LM5 LM num 7DOY gt 129 LM6 Pm = 0118 lowast Tn + 00301 lowast Tms + 00026 lowast DOY + 47479

LSTn gt 1772 LM7 LM num 8DOY gt 207 Pm = 00529 lowast Tn + 00301 lowast Tms minus 00087 lowast DOY + 6254

DOY lt= 2725 LM8 LM num 9DOY gt 2725 LM9 Pm = 00529 lowast Tn minus 00348 lowast Tms minus 00116 lowast DOY + 84773

DOY gt 2825 LM num 10DOY lt= 3115 LM10 Pm = 00328 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 3367DOY gt 3115 LM11 LM num 11

LSTn gt 1943 Pm = 01437 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 17414DOY lt= 2275 LM num 12

DOY lt= 1595 Pm = minus01076 lowast Tn + 00018 lowast Tms minus 00393 lowast DOY + 159787DOY lt= 1475 LM12 LM num 13DOY gt 1475 LM13 Pm = 00297 lowast Tn + 00018 lowast Tms + 00032 lowast DOY + 80036

DOY gt 1595 LM num 14DOY lt= 1985 Pm = 03445 lowast Tn + 00769 lowast Td + 00018 lowast Tms minus 01664 lowast DOY + 263097

DOY lt= 1675 LM14 LM num 15DOY gt 1675 LM15 Pm = 00316 lowast Tn + 00018 lowast Tms minus 0006 lowast DOY + 105743

DOY gt 1985 LM num 16DOY lt= 2165 Pm = minus00175 lowast Tn + 00018 lowast Tms + 00225 lowast DOY + 45799

DOY lt= 2065 LM16 LM num 17DOY gt 2065 LM17 Pm = minus0206 lowast Tn + 00018 lowast Tms + 00185 lowast DOY + 111645

DOY gt 2165 LM18 LM num 18DOY gt 2275 LM19 Pm = 00015 lowast Tn + 00018 lowast Tms minus 00046 lowast DOY + 96864

LM num 19Pm = 0022 lowast Tn + 00018 lowast Tms minus 00387 lowast DOY + 160569

Algorithm 1 Tree-structured regression model generated by M5 algorithm using training data

by the software and established linear regression relationsAfterward a scatter plot of estimated ET

119874by M5 model

tree versus calculated ET119874by FAO-PM equation has been

presented for training data (Figure 6) 1198772 value equal to083 indicates proper agreement The distribution of pointsaround the best fit line represents higher accuracy of thismethod in the estimation of low ET

119874values in the great

values of ET119874the error amount increases as well

The comparison of error statistics concerning developedmodels by ANN model and M5 model tree in estimatingET119874using training data can be drawn in Table 1 As seen

M5 model tree which has shown RMSE and MAE valuesrespectively equal to 127 and 096mmdminus1 has resulted inhigher accuracy than ANN in estimating ET

119874

For testing the methods of ANN andM5model tree dataof Khazaei and Shoeybie stations have been used In Figure 7the scatter plot of calculated ET

119874through two models of

ANN and M5 model tree versus FAO-PM values for thementioned stations have been shown 1198772 values associatedwith calculated ET

119874by ANN against FAO-PM equation ET

119874

values for Khazaei and Shoeybie stations were 079 and 086respectively Additionally the same 1198772 values related to M5model tree for aforementioned stations were 080 and 085respectively In both methods ET

119874values were properly

distributed around line 1 1 For smaller amounts of ET119874

there was been a better compatibility between the calculatedvalues by two models and FAO-PM values compared togreater amounts of ET

119874 In other words underestimation or

overestimation of ET119874is related towarm seasons further than

cold seasons The evolutions of calculated ET119874values over

time have been illustrated for two test stations in Figure 8As perceived in this graph the maximum amounts of ET

119874by

these twomodels were not entirely compatible with FAO-PMvaluesThis could be due to the lack of consideration of some

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

Journal of Climatology 5

y = 090x + 241

R2 = 089

Gazali

y = 086x + 182

R2 = 089

Farabi

y = 091x + 193R2 = 088

All data

y = 103x + 126

R2 = 091

Shoeybie

y = 086x + 271

R2 = 087

minus10

0

10

20

30

40

Amirkabir

y = 093x + 094R2 = 090

minus10 0 10 20 30 40

Khazaei

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

minus10

0

10

20

30

40

Tm

in(∘

C)

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)minus10 0 10 20 30 40

LSTN (∘C)

Figure 3 Scatter plot of 119879min against LST119873

RMSE = radic 1119899

119899

sum

119894=1

(119909119894 minus 119910119894)2

MAE = 1119899

119899

sum

119894=1

1003816100381610038161003816119909119894 minus 1199101198941003816100381610038161003816

(4)where 119909

119894is ET119874computed by FAO-PM 119909 denotes the average

amount of computed ET119874computed by FAO-PM 119910

119894is ET119874

computed by ANNM5 and 119910 is the average computed ET119874

amounts by last models

3 Results and Discussion

In the first stage of the study before calculating the ET119874 the

correlation between LST obtained from MODIS sensor andair temperature was determined Accordingly scatter plots ofLST values provided by MODIS images versus air tempera-ture are presented for different stations in Figures 3 and 4As it can be perceived in Figure 3 there is a high correlationbetween the LST

119873andminimum air temperature (119879min)The

greatest1198772 was observed between LST119873and119879min in Shoeybie

station which was equal to 091 the minimum1198772 was seen inthe Amirkabir station with the value of 087 Furthermore forall stations1198772 of two aforementioned parameterswas entirelyassessed at 088 In Figure 3 symmetrical and appropriatedistribution of points around the line of best fit (line 1 1)indicates a strong correlation between the two parametersIn Figure 4 relation between the LST119863 and maximum airtemperature (119879max) displays that the greatest 1198772 betweenLST119863and 119879max is related to Amirkabir and Khazaei stations

(1198772 = 091) the minimum amount of this coefficient isassociated with Gazali station (1198772 = 081) For all studystations 1198772 was generally equal to 078 Overall it can beconcluded that there is a strong relationship between thesetwo parameters The scatter of points around the line ofbest fit in the Figure 4 depicts an overestimation of LST

119863

over 119879max This overestimation is more pronounced for thetemperatures over 30∘C

For all examined datasets the correlation between LST119873

and119879min is higher compared to the correlation between LST119863and 119879max for thermal products of MODIS sensor Moreoverprevious studies concerning estimation of air temperaturehave similarly confirmed that correlation between LST119873 and119879min is greater than correlation between LST119863 and 119879max [1219]

In the second stage in order to calculate ET119874 using LSTvalues extracted from the MODIS sensor (LST119863 and LST119873)ANNmodels andM5model tree were employed In additionto LST

119863and LST

119873 two parameters including mean LST

(LST119872) and day of year (DOY) were considered as inputs

for generating model in order to increase accuracy of ET119874

estimates Thus in producing ANN model and M5 modeltree four parameters including LST

119863 LST119873 DOY and LST

119872

were taken into consideration as input and ET119874calculated

from weather data using FAO-PM equation as outputFor generating ANN model training data (whole data

of Amirkabir Farabi and Gazali stations) were applied andthe number of nodes in the hidden layer was obtained usingtrial and error method The number of nodes in the hiddenlayer was considered varying from 1 to 12 based on errorstatistical parameters a network with 3 nodes in the hiddenlayer indicated the lowest error in comparison of ET

119874values

6 Journal of Climatology

y = 105x minus 157

R2 = 081

10 20 30 40 50 60

Gazali

y = 092x + 052

R2 = 088

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

Farabi

y = 072x + 404

R2 = 091

Amirkabir

y = 078x + 516

R2 = 078

All data

y = 100x minus 199

R2 = 089

Shoeybie

y = 078x + 291

R2 = 091

Khazaei

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

LSTD (∘C)

LSTD (∘C) LSTD (∘C) LSTD (∘C)

LSTD (∘C) LSTD (∘C)

Figure 4 Scatter plot of 119879max against LST119863

y = 100x minus 001

R2 = 079

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-ANN (mmd)

Figure 5 Scatter plot of estimated ET119874using ANN against calcu-

lated ET119874by FAO-PM equation for training data

calculated by FAO-PMmethod Table 1 presents the values oferror parameters for the neural network with the structure ofthree nodes in the hidden layer In Figure 5 scatter diagramof calculated ET

119874values through ANN for all training data

has been plotted against ET119874 values obtained by FAO-PMequation As shown in Figure 3 1198772 = 079 demonstratesthat the ANN has provided an acceptable determinationcoefficient in approximating ET

119874 In this figure the points

density increases around the line 1 1 in large amounts of ET119874

that is it represents the overestimation or underestimation ofthe data that are situated in this area

y = 102x minus 015R2 = 083

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-M5 (mmd)

Figure 6 Scatter plot of estimated ET119874usingM5model tree against

calculated ET119874by FAO-PM equation for training data

Table 1 Error statistics in estimating ET119874for model tree and ANN

methods using training data

Model RMSE (mmd) MAE (mmd)ANN 140 105M5 127 096

For generating M5 model tree WEKA 37 software [42]was used considering the same data applied to the trainingANN model Algorithm 1 shows M5 model tree produced

Journal of Climatology 7

LSTn lt= 1943 LM num 1LSTms lt= 1555 LM1 Pm = 00147 lowast Tn + 01048 lowast Tms minus 00007 lowast DOY + 08963LSTms gt 1555 LM num 2

DOY lt= 2825 Pm = 00349 lowast Tn + 00312 lowast Tms + 0028 lowast DOY + 13107DOY lt= 815 LM2 LM num 3DOY gt 815 Pm = 0046 lowast Tn + 0081 lowast Tms minus 00134 lowast DOY + 39221

DOY lt= 106 LM num 4LSTd lt= 312 LM3 Pm = 00719 lowast Tn + 00642 lowast Tms minus 00088 lowast DOY + 38864LSTd gt 312 LM4 LM num 5

DOY gt 106 Pm = 00705 lowast Tn + 00073 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 46615DOY lt= 207 LM num 6

LSTn lt= 1772 Pm = 0201 lowast Tn + 00147 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 25252DOY lt= 129 LM5 LM num 7DOY gt 129 LM6 Pm = 0118 lowast Tn + 00301 lowast Tms + 00026 lowast DOY + 47479

LSTn gt 1772 LM7 LM num 8DOY gt 207 Pm = 00529 lowast Tn + 00301 lowast Tms minus 00087 lowast DOY + 6254

DOY lt= 2725 LM8 LM num 9DOY gt 2725 LM9 Pm = 00529 lowast Tn minus 00348 lowast Tms minus 00116 lowast DOY + 84773

DOY gt 2825 LM num 10DOY lt= 3115 LM10 Pm = 00328 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 3367DOY gt 3115 LM11 LM num 11

LSTn gt 1943 Pm = 01437 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 17414DOY lt= 2275 LM num 12

DOY lt= 1595 Pm = minus01076 lowast Tn + 00018 lowast Tms minus 00393 lowast DOY + 159787DOY lt= 1475 LM12 LM num 13DOY gt 1475 LM13 Pm = 00297 lowast Tn + 00018 lowast Tms + 00032 lowast DOY + 80036

DOY gt 1595 LM num 14DOY lt= 1985 Pm = 03445 lowast Tn + 00769 lowast Td + 00018 lowast Tms minus 01664 lowast DOY + 263097

DOY lt= 1675 LM14 LM num 15DOY gt 1675 LM15 Pm = 00316 lowast Tn + 00018 lowast Tms minus 0006 lowast DOY + 105743

DOY gt 1985 LM num 16DOY lt= 2165 Pm = minus00175 lowast Tn + 00018 lowast Tms + 00225 lowast DOY + 45799

DOY lt= 2065 LM16 LM num 17DOY gt 2065 LM17 Pm = minus0206 lowast Tn + 00018 lowast Tms + 00185 lowast DOY + 111645

DOY gt 2165 LM18 LM num 18DOY gt 2275 LM19 Pm = 00015 lowast Tn + 00018 lowast Tms minus 00046 lowast DOY + 96864

LM num 19Pm = 0022 lowast Tn + 00018 lowast Tms minus 00387 lowast DOY + 160569

Algorithm 1 Tree-structured regression model generated by M5 algorithm using training data

by the software and established linear regression relationsAfterward a scatter plot of estimated ET

119874by M5 model

tree versus calculated ET119874by FAO-PM equation has been

presented for training data (Figure 6) 1198772 value equal to083 indicates proper agreement The distribution of pointsaround the best fit line represents higher accuracy of thismethod in the estimation of low ET

119874values in the great

values of ET119874the error amount increases as well

The comparison of error statistics concerning developedmodels by ANN model and M5 model tree in estimatingET119874using training data can be drawn in Table 1 As seen

M5 model tree which has shown RMSE and MAE valuesrespectively equal to 127 and 096mmdminus1 has resulted inhigher accuracy than ANN in estimating ET

119874

For testing the methods of ANN andM5model tree dataof Khazaei and Shoeybie stations have been used In Figure 7the scatter plot of calculated ET

119874through two models of

ANN and M5 model tree versus FAO-PM values for thementioned stations have been shown 1198772 values associatedwith calculated ET

119874by ANN against FAO-PM equation ET

119874

values for Khazaei and Shoeybie stations were 079 and 086respectively Additionally the same 1198772 values related to M5model tree for aforementioned stations were 080 and 085respectively In both methods ET

119874values were properly

distributed around line 1 1 For smaller amounts of ET119874

there was been a better compatibility between the calculatedvalues by two models and FAO-PM values compared togreater amounts of ET

119874 In other words underestimation or

overestimation of ET119874is related towarm seasons further than

cold seasons The evolutions of calculated ET119874values over

time have been illustrated for two test stations in Figure 8As perceived in this graph the maximum amounts of ET

119874by

these twomodels were not entirely compatible with FAO-PMvaluesThis could be due to the lack of consideration of some

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

6 Journal of Climatology

y = 105x minus 157

R2 = 081

10 20 30 40 50 60

Gazali

y = 092x + 052

R2 = 088

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

Farabi

y = 072x + 404

R2 = 091

Amirkabir

y = 078x + 516

R2 = 078

All data

y = 100x minus 199

R2 = 089

Shoeybie

y = 078x + 291

R2 = 091

Khazaei

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

Tm

ax(∘

C)

Tm

ax(∘

C)T

max(∘

C)

LSTD (∘C)

LSTD (∘C) LSTD (∘C) LSTD (∘C)

LSTD (∘C) LSTD (∘C)

Figure 4 Scatter plot of 119879max against LST119863

y = 100x minus 001

R2 = 079

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-ANN (mmd)

Figure 5 Scatter plot of estimated ET119874using ANN against calcu-

lated ET119874by FAO-PM equation for training data

calculated by FAO-PMmethod Table 1 presents the values oferror parameters for the neural network with the structure ofthree nodes in the hidden layer In Figure 5 scatter diagramof calculated ET

119874values through ANN for all training data

has been plotted against ET119874 values obtained by FAO-PMequation As shown in Figure 3 1198772 = 079 demonstratesthat the ANN has provided an acceptable determinationcoefficient in approximating ET

119874 In this figure the points

density increases around the line 1 1 in large amounts of ET119874

that is it represents the overestimation or underestimation ofthe data that are situated in this area

y = 102x minus 015R2 = 083

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO-M5 (mmd)

Figure 6 Scatter plot of estimated ET119874usingM5model tree against

calculated ET119874by FAO-PM equation for training data

Table 1 Error statistics in estimating ET119874for model tree and ANN

methods using training data

Model RMSE (mmd) MAE (mmd)ANN 140 105M5 127 096

For generating M5 model tree WEKA 37 software [42]was used considering the same data applied to the trainingANN model Algorithm 1 shows M5 model tree produced

Journal of Climatology 7

LSTn lt= 1943 LM num 1LSTms lt= 1555 LM1 Pm = 00147 lowast Tn + 01048 lowast Tms minus 00007 lowast DOY + 08963LSTms gt 1555 LM num 2

DOY lt= 2825 Pm = 00349 lowast Tn + 00312 lowast Tms + 0028 lowast DOY + 13107DOY lt= 815 LM2 LM num 3DOY gt 815 Pm = 0046 lowast Tn + 0081 lowast Tms minus 00134 lowast DOY + 39221

DOY lt= 106 LM num 4LSTd lt= 312 LM3 Pm = 00719 lowast Tn + 00642 lowast Tms minus 00088 lowast DOY + 38864LSTd gt 312 LM4 LM num 5

DOY gt 106 Pm = 00705 lowast Tn + 00073 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 46615DOY lt= 207 LM num 6

LSTn lt= 1772 Pm = 0201 lowast Tn + 00147 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 25252DOY lt= 129 LM5 LM num 7DOY gt 129 LM6 Pm = 0118 lowast Tn + 00301 lowast Tms + 00026 lowast DOY + 47479

LSTn gt 1772 LM7 LM num 8DOY gt 207 Pm = 00529 lowast Tn + 00301 lowast Tms minus 00087 lowast DOY + 6254

DOY lt= 2725 LM8 LM num 9DOY gt 2725 LM9 Pm = 00529 lowast Tn minus 00348 lowast Tms minus 00116 lowast DOY + 84773

DOY gt 2825 LM num 10DOY lt= 3115 LM10 Pm = 00328 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 3367DOY gt 3115 LM11 LM num 11

LSTn gt 1943 Pm = 01437 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 17414DOY lt= 2275 LM num 12

DOY lt= 1595 Pm = minus01076 lowast Tn + 00018 lowast Tms minus 00393 lowast DOY + 159787DOY lt= 1475 LM12 LM num 13DOY gt 1475 LM13 Pm = 00297 lowast Tn + 00018 lowast Tms + 00032 lowast DOY + 80036

DOY gt 1595 LM num 14DOY lt= 1985 Pm = 03445 lowast Tn + 00769 lowast Td + 00018 lowast Tms minus 01664 lowast DOY + 263097

DOY lt= 1675 LM14 LM num 15DOY gt 1675 LM15 Pm = 00316 lowast Tn + 00018 lowast Tms minus 0006 lowast DOY + 105743

DOY gt 1985 LM num 16DOY lt= 2165 Pm = minus00175 lowast Tn + 00018 lowast Tms + 00225 lowast DOY + 45799

DOY lt= 2065 LM16 LM num 17DOY gt 2065 LM17 Pm = minus0206 lowast Tn + 00018 lowast Tms + 00185 lowast DOY + 111645

DOY gt 2165 LM18 LM num 18DOY gt 2275 LM19 Pm = 00015 lowast Tn + 00018 lowast Tms minus 00046 lowast DOY + 96864

LM num 19Pm = 0022 lowast Tn + 00018 lowast Tms minus 00387 lowast DOY + 160569

Algorithm 1 Tree-structured regression model generated by M5 algorithm using training data

by the software and established linear regression relationsAfterward a scatter plot of estimated ET

119874by M5 model

tree versus calculated ET119874by FAO-PM equation has been

presented for training data (Figure 6) 1198772 value equal to083 indicates proper agreement The distribution of pointsaround the best fit line represents higher accuracy of thismethod in the estimation of low ET

119874values in the great

values of ET119874the error amount increases as well

The comparison of error statistics concerning developedmodels by ANN model and M5 model tree in estimatingET119874using training data can be drawn in Table 1 As seen

M5 model tree which has shown RMSE and MAE valuesrespectively equal to 127 and 096mmdminus1 has resulted inhigher accuracy than ANN in estimating ET

119874

For testing the methods of ANN andM5model tree dataof Khazaei and Shoeybie stations have been used In Figure 7the scatter plot of calculated ET

119874through two models of

ANN and M5 model tree versus FAO-PM values for thementioned stations have been shown 1198772 values associatedwith calculated ET

119874by ANN against FAO-PM equation ET

119874

values for Khazaei and Shoeybie stations were 079 and 086respectively Additionally the same 1198772 values related to M5model tree for aforementioned stations were 080 and 085respectively In both methods ET

119874values were properly

distributed around line 1 1 For smaller amounts of ET119874

there was been a better compatibility between the calculatedvalues by two models and FAO-PM values compared togreater amounts of ET

119874 In other words underestimation or

overestimation of ET119874is related towarm seasons further than

cold seasons The evolutions of calculated ET119874values over

time have been illustrated for two test stations in Figure 8As perceived in this graph the maximum amounts of ET

119874by

these twomodels were not entirely compatible with FAO-PMvaluesThis could be due to the lack of consideration of some

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

Journal of Climatology 7

LSTn lt= 1943 LM num 1LSTms lt= 1555 LM1 Pm = 00147 lowast Tn + 01048 lowast Tms minus 00007 lowast DOY + 08963LSTms gt 1555 LM num 2

DOY lt= 2825 Pm = 00349 lowast Tn + 00312 lowast Tms + 0028 lowast DOY + 13107DOY lt= 815 LM2 LM num 3DOY gt 815 Pm = 0046 lowast Tn + 0081 lowast Tms minus 00134 lowast DOY + 39221

DOY lt= 106 LM num 4LSTd lt= 312 LM3 Pm = 00719 lowast Tn + 00642 lowast Tms minus 00088 lowast DOY + 38864LSTd gt 312 LM4 LM num 5

DOY gt 106 Pm = 00705 lowast Tn + 00073 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 46615DOY lt= 207 LM num 6

LSTn lt= 1772 Pm = 0201 lowast Tn + 00147 lowast Td + 00301 lowast Tms + 00003 lowast DOY + 25252DOY lt= 129 LM5 LM num 7DOY gt 129 LM6 Pm = 0118 lowast Tn + 00301 lowast Tms + 00026 lowast DOY + 47479

LSTn gt 1772 LM7 LM num 8DOY gt 207 Pm = 00529 lowast Tn + 00301 lowast Tms minus 00087 lowast DOY + 6254

DOY lt= 2725 LM8 LM num 9DOY gt 2725 LM9 Pm = 00529 lowast Tn minus 00348 lowast Tms minus 00116 lowast DOY + 84773

DOY gt 2825 LM num 10DOY lt= 3115 LM10 Pm = 00328 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 3367DOY gt 3115 LM11 LM num 11

LSTn gt 1943 Pm = 01437 lowast Tn + 00201 lowast Tms minus 00012 lowast DOY + 17414DOY lt= 2275 LM num 12

DOY lt= 1595 Pm = minus01076 lowast Tn + 00018 lowast Tms minus 00393 lowast DOY + 159787DOY lt= 1475 LM12 LM num 13DOY gt 1475 LM13 Pm = 00297 lowast Tn + 00018 lowast Tms + 00032 lowast DOY + 80036

DOY gt 1595 LM num 14DOY lt= 1985 Pm = 03445 lowast Tn + 00769 lowast Td + 00018 lowast Tms minus 01664 lowast DOY + 263097

DOY lt= 1675 LM14 LM num 15DOY gt 1675 LM15 Pm = 00316 lowast Tn + 00018 lowast Tms minus 0006 lowast DOY + 105743

DOY gt 1985 LM num 16DOY lt= 2165 Pm = minus00175 lowast Tn + 00018 lowast Tms + 00225 lowast DOY + 45799

DOY lt= 2065 LM16 LM num 17DOY gt 2065 LM17 Pm = minus0206 lowast Tn + 00018 lowast Tms + 00185 lowast DOY + 111645

DOY gt 2165 LM18 LM num 18DOY gt 2275 LM19 Pm = 00015 lowast Tn + 00018 lowast Tms minus 00046 lowast DOY + 96864

LM num 19Pm = 0022 lowast Tn + 00018 lowast Tms minus 00387 lowast DOY + 160569

Algorithm 1 Tree-structured regression model generated by M5 algorithm using training data

by the software and established linear regression relationsAfterward a scatter plot of estimated ET

119874by M5 model

tree versus calculated ET119874by FAO-PM equation has been

presented for training data (Figure 6) 1198772 value equal to083 indicates proper agreement The distribution of pointsaround the best fit line represents higher accuracy of thismethod in the estimation of low ET

119874values in the great

values of ET119874the error amount increases as well

The comparison of error statistics concerning developedmodels by ANN model and M5 model tree in estimatingET119874using training data can be drawn in Table 1 As seen

M5 model tree which has shown RMSE and MAE valuesrespectively equal to 127 and 096mmdminus1 has resulted inhigher accuracy than ANN in estimating ET

119874

For testing the methods of ANN andM5model tree dataof Khazaei and Shoeybie stations have been used In Figure 7the scatter plot of calculated ET

119874through two models of

ANN and M5 model tree versus FAO-PM values for thementioned stations have been shown 1198772 values associatedwith calculated ET

119874by ANN against FAO-PM equation ET

119874

values for Khazaei and Shoeybie stations were 079 and 086respectively Additionally the same 1198772 values related to M5model tree for aforementioned stations were 080 and 085respectively In both methods ET

119874values were properly

distributed around line 1 1 For smaller amounts of ET119874

there was been a better compatibility between the calculatedvalues by two models and FAO-PM values compared togreater amounts of ET

119874 In other words underestimation or

overestimation of ET119874is related towarm seasons further than

cold seasons The evolutions of calculated ET119874values over

time have been illustrated for two test stations in Figure 8As perceived in this graph the maximum amounts of ET

119874by

these twomodels were not entirely compatible with FAO-PMvaluesThis could be due to the lack of consideration of some

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

8 Journal of Climatology

Shoeybie

y = 097x minus 024

R2 = 086

0 5 10 15

y = 102x + 004

R2 = 079

0

5

10

15

0 5 10 15

0

5

10

15

Khazaei

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-ANN (mmd) ETO-ANN (mmd)

(a)

y = 096x minus 013

R2 = 085y = 105x minus 027

R2 = 080

Shoeybie

0 5 10 15

0

5

10

15

0 5 10 15

0

5

10

15

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

ETO-M5 (mmd) ETO-M5 (mmd)

Khazaei

(b)

Figure 7 Scatter plot of estimated ET119874using ANN and M5 model tree against calculated ET

119874by FAO-PM method (a) ANN method and

(b) M5 method

weather parameters affecting ET119874rate (eg wind speed solar

radiation and relative humidity) as inputs of ANNmodel andM5 model tree

In Table 2 error statistics of ET119874estimation by ANN and

M5 model tree have been presented for two test stationsAccording to the statistics of RMSE andMAE both methodsperformed equally well Similar results have been reportedabout close performance of ANN and M5 models in rainfall-runoff modeling [43] and river flow forecasting [44] Themain advantage ofM5model tree is that it provides the resultsin a simple and comprehensible form of regression equations[1] which can be easily used in the calculation of ET

119874

It seems generally that LST119873and LST

119863values obtained

from MODIS sensor making the use of both ANN and M5models can be properly utilized in the estimation of ET119874

4 Conclusion

In this study attempts were made to calculate ET119874using

LST values extracted from images of MODIS sensor For this

Table 2 Error statistics in estimating ET119874by ANN and M5 model

tree using testing data

Station Model 1198772 RMSE (mmd) MAE (mmd)

Khazaei ANN 079 154 114M5 080 149 112

Shoeybie ANN 086 115 090M5 085 117 090

purpose two methods of ANN and M5 model tree wereselected in order to estimate ET119874 four parameters includingLST119863 LST119873 LST119872 and DOY were considered as modelinputs and ET119874 was calculated from FAO-PM equation asmodel outputs A comparison of estimated ET119874 using eachmentioned model with the values obtained from the FAO-PM method revealed high accuracy of both methods Theaverage amounts of RSME in two test stations for ANNand M5 model tree were respectively 135 and 134mmdayAccording to the error values it can be observed that both

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

Journal of Climatology 9

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMANN

PMANN

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(a)

ShoeybieKhazaei

0 100 200 300 400

Days

0

5

10

15

0 100 200 300 400

Days

0

5

10

15

PMM5

PMM5

ETO

-PM

(mm

d)

ETO

-PM

(mm

d)

(b)

Figure 8 Time variations of estimated ET119874using ANN and M5 model tree for test statins (a) ANN method and (b) M5 method

models have shown close performance in determining ET119874

It seems that considering other significant variables affectingthe ET process such as relative humidity and wind speed (asmodel inputs) can lead to higher accuracy

Overall it can be concluded that unlike complex ANNmethod M5 model tree due to its simple structure andproviding simple regression equations is a more appropriatemethod in determining ET

119874using LST data derived from

MODIS sensorIn this paper A M5 tree model with some simple linear

regressionswas developed to estimate ET119874 usingMODIS LSTdata Considering simple linear equations and minor datarequired in the developed M5 tree model it is expected thatthis method could be an alternative to calculate ET119874 in thestudy area However this model provided acceptable resultsin the current area but it seems that its applicability in theother region of the world or the region with similar climatecondition needs more investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Pal and S Deswal ldquoM5 model tree based modelling ofreference evapotranspirationrdquo Hydrological Processes vol 23no 10 pp 1437ndash1443 2009

[2] R G Allen L S Pereira D Raes and M Smith ldquoCrop evapo-transpirationmdashguidelines for computing crop water require-mentsrdquo FAO Irrigation and Drainage Paper 56 FAO RomeItaly 1998

[3] S Ortega-Farias S Irmak and R H Cuenca ldquoSpecial issueon evapotranspiration measurement and modelingrdquo IrrigationScience vol 28 no 1 pp 1ndash3 2009

[4] E E Maeda D A Wiberg and P K E Pellikka ldquoEstimatingreference evapotranspiration using remote sensing and empir-ical models in a region with limited ground data availability inKenyardquo Applied Geography vol 31 no 1 pp 251ndash258 2011

[5] A A Sabziparvar H Tabari A Aeini and M GhafourildquoEvaluation of class a pan coefficient models for estimation ofreference crop evapotranspiration in cold semi-arid and warmarid climatesrdquo Water Resources Management vol 24 no 5 pp909ndash920 2010

[6] M E Jensen R D Burman and R G Allen ldquoEvapotranspira-tion and irrigation water requirementsrdquo ASCEM Annuals andReports on Engineering Practice no 70 ASCE New York NYUSA 1990

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

10 Journal of Climatology

[7] M Smith Report on the Expert Consultation on Revision of FAOMethodologies for Crop Water Requirements FAO Rome Italy1992

[8] M Kumar N S Raghuwanshi R Singh W W WallenderandWO Pruitt ldquoEstimating evapotranspiration using artificialneural networkrdquo Journal of Irrigation andDrainage Engineeringvol 128 no 4 pp 224ndash233 2002

[9] P Ditthakit and C Chinnarasri ldquoEstimation of pan coefficientusing M5 model treerdquo American Journal of EnvironmentalSciences vol 8 no 2 pp 95ndash103 2012

[10] Z Huo S Feng S Kang and X Dai ldquoArtificial neural networkmodels for reference evapotranspiration in an arid area ofnorthwest Chinardquo Journal of Arid Environments vol 82 pp 81ndash90 2012

[11] A Rahimikhoob M Asadi and M Mashal ldquoA comparisonbetween conventional andM5model tree methods for convert-ing pan evaporation to reference evapotranspiration for semi-arid region rdquo Water Resources Management vol 27 no 14 pp4815ndash4826 2013

[12] Y Yang S Shang and L Jiang ldquoRemote sensing temporaland spatial patterns of evapotranspiration and the responses towatermanagement in a large irrigation district of North ChinardquoAgricultural and Forest Meteorology vol 164 pp 112ndash122 2012

[13] Z Wan ldquoNew refinements and validation of the MODIS land-surface temperatureemissivity productsrdquo Remote Sensing ofEnvironment vol 112 no 1 pp 59ndash74 2008

[14] J P Guerschman A I J M van Dijk G Mattersdorf et alldquoScaling of potential evapotranspiration with MODIS datareproduces flux observations and catchment water balanceobservations across Australiardquo Journal of Hydrology vol 369no 1-2 pp 107ndash119 2009

[15] H A Cleugh R Leuning QMu and SW Running ldquoRegionalevaporation estimates from flux tower and MODIS satellitedatardquo Remote Sensing of Environment vol 106 no 3 pp 285ndash304 2007

[16] H Tian J Wen C-H Wang R Liu and D-R Lu ldquoEffect ofpixel scale on evapotranspiration estimation by remote sensingover oasis areas in north-western Chinardquo Environmental EarthSciences vol 67 no 8 pp 2301ndash2313 2012

[17] B Hankerson J Kjaersgaard and C Hay ldquoEstimation ofevapotranspiration from fields with and without cover cropsusing remote sensing and in situ methodsrdquo Remote Sensing vol4 no 12 pp 3796ndash3812 2012

[18] X Li L Lua W Yangc and G Chenga ldquoEstimation of evapo-transpiration in an arid region by remote sensingmdasha case studyin the middle reaches of the Heihe River Basinrdquo InternationalJournal of Applied Earth Observation and Geoinformation vol17 no 1 pp 85ndash93 2012

[19] S Emamifar A Rahimikhoob and A A Noroozi ldquoDailymean air temperature estimation from MODIS land surfacetemperature products based on M5 model treerdquo InternationalJournal of Climatology vol 33 no 15 pp 3174ndash3181 2013

[20] B Bhattacharya andD P Solomatine ldquoNeural networks andM5model trees in modelling water level-discharge relationshiprdquoNeurocomputing vol 63 pp 381ndash396 2005

[21] G Landeras A Ortiz-Barredo and J J Lopez ldquoComparisonof artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration esti-mation in the Basque Country (Northern Spain)rdquo AgriculturalWater Management vol 95 no 5 pp 553ndash565 2008

[22] O Kisi and O Ozturk ldquoAdaptive neurofuzzy computing tech-nique for evapotranspiration estimationrdquo Journal of Irrigationand Drainage Engineering vol 133 no 4 pp 368ndash379 2007

[23] O Kisi and M Cimen ldquoEvapotranspiration modelling usingsupport vectormachinesrdquoHydrological Sciences Journal vol 54no 5 pp 918ndash928 2009

[24] H Tabari O Kisi A Ezani and P H Talaee ldquoSVM ANFISregression and climate based models for reference evapotran-spiration modeling using limited climatic data in a semi-aridhighland environmentrdquo Journal of Hydrology vol 444-445 pp78ndash89 2012

[25] P B Shirsath and A K Singh ldquoA comparative study of dailypan evaporation estimation using ANN regression and climatebased modelsrdquoWater Resources Management vol 24 no 8 pp1571ndash1581 2010

[26] S S Zanetti E F Sousa V P S Oliveira F T Almeidaand S Bernardo ldquoEstimating evapotranspiration using artificialneural network and minimum climatological datardquo Journal ofIrrigation and Drainage Engineering vol 133 no 2 pp 83ndash892007

[27] A Rahimikhoob ldquoEstimating sunshine duration from otherclimatic data by artificial neural network for ET

0estimation in

an arid environmentrdquoTheoretical and Applied Climatology vol118 no 1-2 pp 1ndash8 2014

[28] I El-Baroudy A Elshorbagy S K Carey O Giustolisi andD Savic ldquoComparison of three data-driven techniques inmodelling the evapotranspiration processrdquo Journal of Hydroin-formatics vol 12 no 4 pp 365ndash379 2010

[29] M-B Aghajanloo A-A Sabziparvar and P HosseinzadehTalaee ldquoArtificial neural network-genetic algorithm for estima-tion of crop evapotranspiration in a semi-arid region of IranrdquoNeural Computing andApplications vol 23 no 5 pp 1387ndash13932013

[30] K P Sudheer A K Gosain and K S Ramasastri ldquoEstimatingactual evapotranspiration from limited climatic data usingneural computing techniquerdquo Journal of Irrigation andDrainageEngineering vol 129 no 3 pp 214ndash218 2003

[31] V Jothiprakash and A S Kote ldquoEffect of pruning and smooth-ing while using m5 model tree technique for reservoir inflowpredictionrdquo Journal of Hydrologic Engineering vol 16 no 7 pp563ndash574 2011

[32] M T Sattari M Pal K Yurekli and A Unlukara ldquoM5 modeltrees and neural network based modelling of ET

0in Ankara

Turkeyrdquo Turkish Journal of Engineering amp Environmental Sci-ences vol 37 no 2 pp 211ndash219 2013

[33] K Wang Z Wan P Wang et al ldquoEstimation of surface longwave radiation and broadband emissivity using moderate reso-lution imaging spectroradiometer (MODIS) land surface tem-peratureemissivity productsrdquo Journal of Geophysical ResearchD Atmospheres vol 110 no 11 pp 1ndash12 2005

[34] C Vancutsem P Ceccato T Dinku and S J Connor ldquoEval-uation of MODIS land surface temperature data to estimateair temperature in different ecosystems over Africardquo RemoteSensing of Environment vol 114 no 2 pp 449ndash465 2010

[35] K K SinghM Pal and V P Singh ldquoEstimation ofmean annualflood in indian catchments using backpropagation neural net-work andM5model treerdquoWater ResourcesManagement vol 24no 10 pp 2007ndash2019 2010

[36] J RQuinlan ldquoLearningwith continuous classesrdquo inProceedingsof the 5th Australian Joint Conference on Artificial Intelligence(AI rsquo92) pp 343ndash348 World Scientific Singapore 1992

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

Journal of Climatology 11

[37] M Pal ldquoM5 model tree for land cover classificationrdquo Interna-tional Journal of Remote Sensing vol 27 no 4 pp 825ndash831 2006

[38] D P Solomatine and Y Xue ldquoM5 model trees and neuralnetworks application to flood forecasting in the upper reach ofthe Huai River in Chinardquo Journal of Hydrologic Engineering vol9 no 6 pp 491ndash501 2004

[39] Y Wang and I H Witten ldquoInduction of model trees forpredicting continuous lassesrdquo in Proceedings of the Poster Papersof the European Conference on Machine Learning University ofEconomics Faculty of Informatics and Statistic Prague CzechRepublic 1997

[40] D Itenfisu R L Elliott R G Allen and I A Walter ldquoCompar-ison of reference evapotranspiration calculations as part of theASCE standardization effortrdquo Journal of Irrigation andDrainageEngineering vol 129 no 6 pp 440ndash448 2003

[41] P Gavilan I J Lorite S Tornero and J Berengena ldquoRegionalcalibration ofHargreaves equation for estimating reference et ina semiarid environmentrdquo Agricultural Water Management vol81 no 3 pp 257ndash281 2006

[42] I H Witten and E Frank Data Mining Practical MachineLearning Tools and Techniques with Java ImplementationsMorgan Kaufmann San Francisco Calif USA 2005

[43] D P Solomatine and K N Dulal ldquoModel trees as an alternativeto neural networks in rainfallmdashrunoff modellingrdquoHydrologicalSciences Journal vol 48 no 3 pp 399ndash411 2003

[44] S Londhe and S Charhate ldquoComparison of data-drivenmodelling techniques for river flow forecastingrdquo HydrologicalSciences Journal vol 55 no 7 pp 1163ndash1174 2010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EcosystemsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental Chemistry

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BiodiversityInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of