comparison of modelling ann and elm to estimate solar radiation over turkey using noaa satellite...

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Comparison of modelling ANN and ELMto estimate solar radiation over Turkeyusing NOAA satellite dataMehmet Şahin a

a Engineering Faculty, Siirt University , Siirt , 56100 , TurkeyPublished online: 19 Aug 2013.

To cite this article: Mehmet ahin (2013) Comparison of modelling ANN and ELM to estimate solarradiation over Turkey using NOAA satellite data, International Journal of Remote Sensing, 34:21,7508-7533, DOI: 10.1080/01431161.2013.822597

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International Journal of Remote Sensing, 2013Vol. 34, No. 21, 7508–7533, http://dx.doi.org/10.1080/01431161.2013.822597

Comparison of modelling ANN and ELM to estimate solar radiationover Turkey using NOAA satellite data

Mehmet Sahin*

Engineering Faculty, Siirt University, Siirt 56100, Turkey

(Received 29 May 2012; accepted 22 June 2013)

In this study, solar radiation (SR) is estimated at 61 locations with varying climaticconditions using the artificial neural network (ANN) and extreme learning machine(ELM). While the ANN and ELM methods are trained with data for the years 2002 and2003, the accuracy of these methods was tested with data for 2004. The values formonth, altitude, latitude, longitude, and land-surface temperature (LST) obtained fromthe data of the National Oceanic and Atmospheric Administration Advanced Very HighResolution Radiometer (NOAA-AVHRR) satellite are chosen as input in developing theANN and ELM models. SR is found to be the output in modelling of the methods.Results are then compared with meteorological values by statistical methods. UsingANN, the determination coefficient (R2), mean bias error (MBE), root mean square error(RMSE), and Willmott’s index (WI) values were calculated as 0.943, −0.148 MJ m−2,1.604 MJ m−2, and 0.996, respectively. While R2 was 0.961, MBE, RMSE, and WIwere found to be in the order 0.045 MJ m−2, 0.672 MJ m−2, and 0.997 by ELM. As canbe understood from the statistics, ELM is clearly more successful than ANN in SRestimation.

1. Introduction

Solar radiation (SR) is a general expression of electromagnetic radiation emitted by theSun. Energy can be captured and converted into a useful form of energy, especially heatand electrical energy. In recent years, many studies for various purposes in the field of solarradiation have been used. These can be listed under agronomy, hydrology and ecology,photovoltaic cells and thermal solar systems, solar furnaces, concentrating collectors, andinterior illumination of buildings, etc. (Benghanem, Mellit, and Alamri 2009; Ulgen andHepbasli 2009).

Although solar radiation is very important, values of SR cannot be easily obtained likeother meteorological parameters such as air temperature, land-surface temperature (LST),and relative humidity. SR measurement is limited for various practical reasons such as thepurchase of vehicles engaged in measuring, maintenance and repair costs, and calibrationof instruments (Bakirci 2009). In fact, even in developed countries, SR measurement instru-ments are not found in all meteorological stations. However, SR values from all stations areneeded to enable the validity of research. In order to overcome this problem, researchershave tried to acquire SR values by using artificial neural network (ANN) methods thatmay be applied to parameters such as latitude, longitude, altitude, sunshine duration, LST,

*Email: [email protected]

© 2013 Taylor & Francis

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International Journal of Remote Sensing 7509

air temperature, relative humidity, pressure, and rainfall, which are easily obtained bymeteorological stations unable to measure SR.

The efficiency of ANN models in SR estimation is proved through the comparison ofobtained values with real values, and researchers agree that ANN models are suitable forand applicable to SR estimation (Bechrakis and Sparis 2004). In developing this process,some researchers have attempted to obtain SR values for measured locations (Koca et al.2011; Ozgoren, Bilgili, and Sahin 2012). Then, researchers have trained ANN benefitingfrom the points of the measurement of SR and applying to the same or different locationsin used ANN models. Although ANN methods are accepted to be successful, especially inestimation of SR in the early days, lack of the ANN methods has been understood with timeat locations that have not got meteorological stations. So it is clear that there is no facilityto get basic meteorological parameters such as LST, air temperature, relative humidity,pressure, and rainfall to estimate SR on these places. To overcome this problem, researchershave begun to use remote-sensing methods to estimate the SR (Cracknell and Varotsos2007). The satellites are used as effective instruments in remote-sensing methods, and thedata obtained from satellite channels are converted to a suitable form so that SR can beestimated without the use of ANN models by using various algorithms (Janjai et al. 2011;Polo et al. 2011). However, ANN methods dependent on satellite data are now being usedto estimate SR (Qin et al. 2011; Lu et al. 2011; Rahimikhoob, Behbahani, and Banihabib2013).

Nowadays, researchers have developed ANN and various intelligent methods to pre-dict target properties, one of these being extreme learning machines (ELMs). The classicallearning algorithm in neural networks such as ANN requires the setting of several user-defined parameters. However, ELM only requires the setting of the number of hiddenneurons and the activation function. It does not require adjustment of input weights andhidden layer biases during implementation of the algorithm, and it produces only one opti-mal solution (Cheng, Cai, and Pan 2009). Therefore, it has been determined by variousstudies that the training of large data sets and developed network of testing time by theELM method requires only a short time according to ANN methods (Huang, Zhu, andSiew 2006; Yeu et al. 2006; Feng et al. 2009; Huang, Wang, and Lan 2011). This is a dif-ferent innovation that ELM has contributed to the literature. ELM is used in various fieldsdepending on these features. Fields that can be expressed include remote sensing (Pal 2009;Chang et al. 2010), health (Kwak and Kwon 2008; Bharathi and Natarajan 2011; Qu et al.2011), recognition of handwriting characters (Chacko et al. 2012), image deblurring (Wanget al. 2011), the effects of the electrical storm transmission (Yang et al. 2011), electricityprice forecasting (Chen et al. 2012), reservoir permeability prediction (Cheng, Cai, and Pan2009), classification of electronic nose data (Prakash and Rajesh 2011), sales forecasting(Sun et al. 2008), metagenomic taxonomic classification (Rasheed and Rangwala 2012),particle swarm optimization (Han, Yao, and Ling 2012), abnormal paediatric gait classifi-cation (Rani and Arumugam 2010), etc. However, no study has been reported on estimationof SR by ELM, either with satellite or meteorological data, and this study is the first to useELM for SR estimation.

In this study, SR prediction was achieved by using both ANN and ELM for satellite datapertaining to the same training and testing locations, with the aim of acquiring missing SRdata. A further aim was to determine the success of the ELM method in comparison withANN, which is commonly utilized in modelling SR over Turkey. Because the data from2002 and 2003 are employed to train the network, those for 2004 were used to test the

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accuracy of both methods in 61 locations. Month, altitude, latitude, longitude, and LSTwere considered as input data during the training of the network. The 603 LST maps wereobtained using the normalized difference vegetation index (NDVI) and emissivity maps for2002–2004. Then, 42 monthly mean LST maps were created from related 603 LST maps.LST values were created using data obtained from the National Oceanic and AtmosphericAdministration Advanced Very High Resolution Radiometer (NOAA-AVHRR) sensor inthe Becker–Li (1990) algorithm.

2. Study area and data sources

Turkey is divided into seven geographical regions depending on the climatic conditions.These are the Mediterranean Region, Aegean Region, Marmara Region, Black Sea Region,Central Anatolia Region, Eastern Anatolian Region, and Southeastern Anatolia Region,each region having its own unique climate characteristics. The sixty-one locations whichare selected as the control points in the study are provided based on the distribution ofproperty over seven geographical regions (see Figure 1).

The altitudes, latitudes, and longitudes used as input parameters in ANN and ELM toestimate SR and geographical regions are shown in Table 1. The satellite data used forthe purpose of both training and testing for the period 2002–2004 were provided by theScientific and Technological Research Council of Turkey-Bilten. The meteorological valuesfor related time periods were obtained from the Republic of Turkey Ministry of Forestryand Water Affairs (Turkish State Meteorological Service).

3. Methodology

3.1. Estimation of NDVI

NDVI is a simple graphical indicator that can be used to analyse remote-sensing mea-surements and assess whether the target being observed contains live green vegetationor not. Data from the red and near-infrared channels are taken from satellite sensors inremote-sensing studies. When received data are analysed, marked differences in reflectionsof the red and near-infrared channels of plants are observed depending on spatial resolution.Accordingly, the value of NDVI in NOAA-AVHRR is formulated as follows:

NDVI = NIR − RED

NIR + RED, (1)

where RED and NIR are spectral reflection in near-infrared and visible regions, respec-tively. If Equation (1) is rewritten relative to NOAA-AVHRR, Equation (2) can beobtained:

NDVI = CH2 − CH1

CH2 + CH1, (2)

where CH1 and CH2 are the reflectance values of the first and second channels on board theNOAA-AVHRR, respectively. According to Equation (2), NDVI can take values between−1 and +1, directly dependent on the energy absorption and photosynthetic capacity of thevegetation (Sellers 1985; Myneni et al. 1995).

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Table 1. Locations used in the study.

Location Altitude (m) Latitude (◦N) Longitude (◦E) Geographical region*

Adana 27 37.03 35.21 1Adıyaman 672 37.45 38.17 2Agrı 1632 39.43 43.03 3Aksaray 960.77 38.23 34.03 4Amasya 411.19 40.39 35.51 5Ankara 890.52 39.57 32.53 4Antakya 100 36.12 36.10 1Antalya 63.57 36.42 30.44 1Artvin 628.30 41.11 41.49 5Aydın 56.30 37.51 27.51 6Balıkesir-Gönen 37 40.06 27.39 7Batman 310 37.35 41.07 2Bilecik 539.19 40.09 29.59 7Bingöl 1177 38.52 40.30 3Bitlis 1573 38.22 42.06 3Burdur 957 37.43 30.18 1Bursa 100.32 40.13 29 7Çanakkale 5.5 40.08 26.24 7Çorum 775.91 40.33 34.58 5Diyarbakır 674 37.54 40.12 2Denizli 425.29 37.47 29.05 6Edirne 85 41.41 26.33 7Elâzıg 989.75 38.39 39.15 3Erzincan 1218.22 39.45 39.30 3Erzurum 1758.18 39.57 41.40 3Gaziantep 854 37.03 37.21 2Gümüshane 1219 40.28 39.28 5Hakkâri 1727.74 37.34 43.44 3Igdır 858 39.55 44.03 3Isparta 996.88 37.45 30.33 1Istanbul-Göztepe 32.98 40.58 29.05 7Izmir 28.55 38.23 27.04 6Kahramanmaras 572.13 37.36 36.56 1Karaman 1023.05 37.12 33.13 4Kars 1775 40.37 43.06 3Kastamonu 800 41.22 33.47 5Kayseri 1092 38.43 35.29 4Kırsehir 1007.17 39.09 34.10 4Kilis 650 36.42 37.06 1Kocaeli-Izmit 76 40.46 29.56 7Konya 1030 37.52 32.28 4Kütahya 969.25 39.25 29.58 6Malatya 947.87 38.21 38.13 3Mersin 3.40 36.48 34.38 1Mugla 646 37.13 28.22 6Mus 1322.76 38.41 41.29 3Nigde 1210.50 37.58 34.41 4Ordu 4.10 40.59 37.54 5Rize 8 41.02 40.30 5Samsun 4 41.21 36.15 5Siirt 895.54 37.55 41.57 2Sinop 32 42.02 35.50 5Sivas 1285 39.45 37.01 4

(Continued)

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Table 1. (Continued).

Location Altitude (m) Latitude (◦N) Longitude (◦E) Geographical region*

Sanlıurfa 547.18 37.09 38.47 2Tokat 607.90 40.18 36.34 5Trabzon 30 40.59 39.45 5Tunceli 980 39.07 39.33 3Van 1670.58 38.28 43.21 3Yalova 3.81 40.40 29.17 7Yozgat 1298.33 39.49 34.48 4Zonguldak 135.35 41.27 31.38 5

Note: *Mediterranean Region (1), Southeastern Anatolia Region (2), Eastern Anatolian Region (3), CentralAnatolia Region (4), Black Sea Region (5), Aegean Region (6), and Marmara Region (7).

3.2. Estimation of surface emissivity

Surface emissivity is defined as the ability of the heat energy of land surfaces to be trans-formed into light energy as black body modelling. According to this principle, NDVI mapswere used to obtain the following emissivity formulae:

ε4 = 0.9897 + 0.029 ln (NDVI), (3)

ε4 − ε5 = 0.01019 + 0.01344 ln (NDVI), (4)

where ε4 and ε5 are emissivity values related to the fourth and fifth channels of theNOAA-AVHRR sensor, respectively (Cihlar et al. 1997). Also, ε4 and ε5 are used in theEquations (5) and (6) to obtain the formula of difference of emissivity (�ε) and average ofemissivity (ε), respectively:

�ε = ε4 − ε5, (5)

ε = ε4 + ε5

2. (6)

3.3. Estimation of LST by NOAA-AVHRR

Land surface is a key parameter in many applications, such as the Earth’s energy andwater cycles, water–heat balance, energy balance, drought monitoring, agriculture mete-orology, forest fires, disaster monitoring, etc. (Vazquez, Reyes, and Arboledas 1997). LSTis estimated using satellites that can scan land surfaces at different spectral channels. Onesatellite, NOAA-AVHRR, has two thermal channels (4 and 5) operating at 10.5–11.3 µmand 11.5–12.5 µm, respectively, for land-surface monitoring (Prabhakara, Dalu, and Kunde1974; McMillin 1975). Various split-window algorithms have been developed based on thetwo adjacent thermal channels, one of which is that by Becker and Li (1990), who deriveda local split-window for viewing angles of up to 46◦ from nadir, given as follows:

TBecker−Li−1990 = 1.274 + PT4 + T5

2+ M

T4 − T5

2, (7)

P = 1 + 0.156161 − ε

ε− 0.482

�ε

ε2, (8)

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7514 M. Sahin

M = 6.26 + 3.981 − ε

ε+ 38.33

�ε

ε2, (9)

where T4 and T5 are brightness temperatures of channels 4 and 5 of NOAA-AVHRR,respectively. P and M are coefficients dependent on atmospheric effects and regionalsurface emissivity. The coefficients of P and M used in Equation (7) were found byLOWTRAN 6 simulation program (US Air Force Research Laboratory, Wright-PattersonAFB, OH, USA).

3.4. Artificial neural network

ANN creates modelling based on a biological neural system. This method is learned fromgiven examples by constructing input–output mapping in order to perform predictions(Kalogirou 2000). ANN modelling is composed of an input layer, one or more hiddenlayers, and an output layer. Neurons in each of the layers and weights interconnect. Oneof most important issues in ANN is the bindings that provide data transmission betweenneurons. A binding that transmits data from one neuron to another also has a weight value.G(x) is a summation function that calculates the exact input reaching a neuron. The input,by multiplying with variables and weight coefficients, builds up input for G(x) summationfunction. The mathematical expression of an artificial neuron can be written as

yi = F [G (x)] = F

(n∑

i=1

wijxj − Qi

); xi = (x1, x2, . . . , xn), (10)

where x = {x1, x2, x3, . . . xn} is an input variable to be processed. On the other hand,w = {w00, w01, . . . ,wij} is weights and shows the importance of data reaching a neuron andtheir impact on it (Karem et al. 2008). The values of weights can change in the process oftraining. Qi represents threshold value; F (.) is an activation function. G (.), that comes toF(.), is the function that produces the output by processing the inputs.

3.5. Extreme learning machine

ELM is a feed-forward neural network model that has a single hidden layer, and calculatesinput weights randomly and output weights analytically. The nondifferentiable or discon-tinuous activation functions can also be used with activation functions such as sigmodial,sine, Guassian, and hard-limiting in the hidden layer of ELM (Suresh, Saraswathi, andSundararajan 2010).

Traditional feed-forward neural networks depend on parameters such as momentumand learning rate. In this type of network, parameters such as weights and threshold valuesshould be updated with gradient-based learning algorithms. However, the learning processtakes time and is affected by local point errors to ensure optimum performance. Changingthe momentum value may prevent point of the error locally, but will not affect the long-term impact of the learning process. ELM also generates input weights and threshold valuesrandomly, but output weights are calculated mathematically (Huang, Zhu, and Siew 2006).The ELM network is the customized state of an ANN model comprising a single hiddenlayer and feed-forward.

If X = (X1, X2, X3, . . . , XN ) and Y determine input and output features, respectively, themathematical expression of the network with M neurons in the hidden layer is indicated asfollows (Suresh, Saraswathi, and Sundararajan 2010):

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M∑i=1

βig(WiXk + bi) = Ok , k = 1, 2, . . . . . . . . . N , (11)

where Wi = (Wi1, Wi2 . . . . . . . . . Win) and βi = (βi1, βi2 . . . . . . . . . βim) express weightsin the input and output layers, respectively. While bi determines threshold values in thehidden layer, Ok represents output values. g(.) is the activation function (Rong et al. 2008).

The purpose of N input features in a network is achieving the error asN∑

k=1(Ok − Yk) = 0

or min

∣∣∣∣ N∑k=1

(Ok − Yk)2

∣∣∣∣. Therefore, Equation (11) can be rewritten as follows (Huang, Zhu,

and Siew 2006):

M∑i=1

βig(WiXk + bi) = Yk , k = 1, 2, . . . . . . . . . , N . (12)

In addition, the Hβ = Y equation can be used in Equation (12) (Huang, Zhu, and Siew2006). H , β, and Y are indicated as follows (Suresh, Saraswathi, and Sundararajan2010):

H =⎡⎣ g(W1X1 + b1) · · · g(WM X1 + b1)

.... . .

...g(W1XN + b1) · · · g(WM XN + bM )

⎤⎦

N×M

, (13)

β =⎡⎢⎣

βT1..

βTM

⎤⎥⎦

Mxm

and Y =⎡⎢⎣

Y T1..

Y TM

⎤⎥⎦

Nxm

, (14)

where H is the input matrix in the hidden layer. Training of the network in a feed-forwardANN corresponds to searching for the solution of linear least squares in the equation Hβ =Y by the ELM method. The ELM algorithm can be summarized in three steps, as follows(Huang, Zhu, and Siew 2004; Liang et al. 2006):

(1) Wi = (Wi1, Wi2 . . . . . . . . . , Win) input weights and threshold values of bi of thehidden layer are generated randomly;

(2) H hidden layer output is calculated;(3) β output weights are calculated according to β = H†Y . Y is the target feature.

3.6. Performance criteria

In statistics, the coefficient of determination (R2) is used in the context of statistical modelswhose main purpose is the prediction of future outcomes on the basis of other related infor-mation. It is the proportion of variability in a data set that is accounted for by the statisticalmodel. This provides a measure of how well future outcomes are likely to be predicted bythe model (Steel and Torrie 1960). Mean bias error (MBE) testing provides informationon the long-term performance, with a low MBE being desirable. Ideally, a zero value forMBE should be obtained. A positive value gives the average amount of overestimation, anda negative value underestimation. The root mean square error (RMSE) is always positive

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and a zero value is ideal. This test provides information on the short-term performance ofthe models by allowing a term-by-term comparison of actual deviation between the cal-culated and measured values (Katiyar et al. 2010). Recently, Willmott’s index (WI) hasbeen widely used to analyse comparison studies, and is intended as a descriptive measure.It is both a relative and bounded measure that may be applied in many different fieldsin order to make cross-comparisons between models (Willmott 1982). WI takes values of0 ≤ WI ≤ 1.

In this study, R2, MBE, RMSE, and WI are used statistically to establish criteria forthe estimation of LST and SR, and also for comparison of ANN with ELM. These criteriaindicate how input features explain SR, and the criteria are calculated using the followingformulae:

R2 =

n∑i=1

(Yi − Y i)2−n∑

i=1(Yi − Yi)2

n∑i=1

(Yi − Y i)2

, (15)

MBE = 1

n

n∑i=1

[Yi − Yi

], (16)

RMSE =√√√√1

n

n∑i=1

(Yi − Yi

)2, (17)

WI = 1 −[

n∑i=1

(Yi − Yi

)2/

n∑i=1

(∣∣∣Y ′i

∣∣∣+ ∣∣Y ′i

∣∣)2]

, (18)

where n is total sample size, Y is actual SR values, and Y and Y define average actual SRvalues and estimated SR values, respectively (Erdinç 2005; Sousa et al. 2007). Additionally,Y ′ and Y ′ can be expressed as Y ′ = Y − Y and Y ′ = Y − Y , respectively.

4. Results and discussion

4.1. Land-surface temperature

First, images of NOAA 12-14-15-16/AVHRR were converted to the format of Level-1B,which can recognize the format by image processing programs, through Quorum software.Then, Envi 4.3 (ITT Exelis Company, Colorado Springs, CO, USA) and Idrisi Andes (ClarkLabs Company, Jamestown, NY, USA) image processing programs were used to makeradiometric and geometric corrections of the images. The channels of the first and sec-ond obtained images were used in Equation (2) to create NDVI images. One of the images,shown in Figure 2(a), was generated on 20 May 2002, at 06:44 local time. When the NDVIimage is examined, it is clear that the image takes values varying between −0.68 and+0.75 (see Figure 2(a)). This form of NDVI image is not appropriate to use statistically inEquations (3)–(4) because the ln(NDVI) function is undefined in the range −1 ≤ NDVI ≤ 0.Therefore, the values between −1 ≤ NDVI ≤ 0 are removed from the NDVI images (seeFigure 2(b)). When the figure is examined, it will be seen that NDVI values in westernTurkey are between 0.14 and 0.38. While the effective NDVI range in the northwest of thecountry is between 0.24 and 0.42, it is occasionally possible to find NDVI values between0.52 and 0.57 in individual locations, and in northern Turkey the range is 0.28–0.71 where

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(a)

(b)

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high rainfall leads to marked plant diversity. NDVI values are in the range 0.28–0.47 in theeastern part of the country, but may reach 0.61 in individual locations; these values wererecorded for plateaux on high mountains, and the region is rich in vegetation. The southernpart of the country has an NDVI range of 0.14–0.57, while in regions with irrigated farm-ing the range is 0.61–0.71. NDVI values in some interior regions are between 0.9 and 0.42.It will be seen from the NDVI map that Turkey’s neighbour, Syria, has poor plant cover.

The emissivity maps of the fourth and fifth channels of the NOAA-AVHRR sensor wereobtained by using the final form of the NDVI image in Equations (3) and (4), respectively(see Figures 2(c) and (d)). When Figures 2(c) and (d) are examined, it will be seen that ε4 isbetween 0.83 and 0.97 while ε5 is between 0.93 and 0.97. The emissivity values in thermalchannels of the same image from different wavelengths have different values. It will beseen that the channel 5 emissivity value of AVHRR is higher than that of channel 4.

The emissivity images for the fourth and fifth channels of NOAA-AVHRR were usedin Equations (5) and (6) to obtain emissivity difference (�ε) and average of emissivity (ε)(see Figures 2(e) and (f )). When Figures 2(e) and (f ) are examined, it will be understoodthat �ε is mostly between −0.17 and −0.04 while ε is between 0.86 and 0.97.

In addition, brightness temperatures of the fourth and fifth channels were created byIdrisi Andes and Envi 4.3 image processing software. Thereafter, brightness temperature,�ε, and ε images were employed in Equations (7)–(9) to get LST maps according to theBecker–Li (1990) algorithm (see Figure 3).

When the map of Turkey is examined, it will be understood that the vast majority of LSTvalues vary between 289 K and 296 K. LST values in the northern part are between 286 Kand 296 K; in the eastern and northeastern parts are between 282 K and 287 K; and in thewestern part are between 291 K and 296 K. Although effective LST values vary between291 K and 298 K in the southern part, it will be observed that some values are between282 K and 287 K. The air temperature change range is 298–305 K in neighbouring Iraqand Syria.

LST is not achieved in points where there are seas, lakes, and rivers because these pointshave water. This is an expected result because the emissivity values used in the algorithmare obtained from NDVI values. It is understood that there are not any plants sufficiently inthe points, especially in seas, lakes, and rivers. This problem may seem like a lack in themethod; as operating points are based on pixels that are not selected over lakes, rivers, andseas, it does not constitute an obstacle.

<273.41–275.68275.69–277.96277.97–280.23

289.36–291.63

300.75–303.02

307.59–309.86305.31–307.58303.03–305.30

298.47–300.74296.19–298.46293.92–296.18291.64–293.91

287.08–289.35284.8–287.07282.52–284.79280.24–282.51

Figure 3. Land-surface temperature map (in kelvin) for 20 May 2002, at 06:44 local time.

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A total of 603 LST images were employed in the study (see Table 2), and the images arereal-time data. Making use of these images, 42 monthly mean LST images were exposedin 2002–2004 using the same method of calculation. Furthermore, the 2196 LST valuesfrom 61 locations were achieved via satellite data over a period of three years. These valueswere compared statistically with meteorological values, using Equations (15)–(18); withthe R2 having a value of 0.970, RMSE, MBE, and WI were 1.790 K, 0.08 K, and 0.991,respectively (see Figure 4). Recent studies have employed detrended fluctuation analysis(DFA) in statistical comparisons. One of these studies is ‘new features of land and seasurface temperature anomalies’, in which Efstathiou et al. (2011) statistically analysedglobal mean land and sea surface temperature (LSST) anomalies with DFA, for the periodJanuary 1850 to August 2008, for both hemispheres. These workers carried out a correla-tion between LSST statistics, proposing that the results of DFA in LSST time series canenhance the reliability of climate dynamics modelling. In addition, scientists have esti-mated LST with satellite data derived from various regions of the world. The RMSE valuesof all studies researched appear to vary within an error range of 1–3 K (Vidal 1991; Coll,Sobrino, and Valor 1994; Ouaidrari et al. 2002; Katsiabani, Adaktilou, and Cartalis 2009;Sahin and Kandirmaz 2010). The results of the present study are in accord with the above,in that RMSE was found to be 1.790 K.

The R2, RMSE, MBE, and WI values were calculated for selected locations as controlpoints (see Table 3).

When Table 3 is analysed, the lowest RMSE value is found for the province of Agrı(1.356 K) and the maximum for Çanakkale (2.187 K). RMSE in other locations rangesfrom 1.356 K to 2.187 K. The highest R2 was obtained for Balıkesir-Gönen (0.989), withKaraman the lowest (0.942). It is irrelevant whether MBE is positive or negative, providingit is close to zero. According to this rule, the best and worst MBE values were found to be−0.014 K and −1.156 K for the provinces of Burdur and Balıkesir-Gönen, respectively. Thelowest WI was recorded for Çanakkale and Karaman (0.983) and the highest for Antalya(0.996).

4.2. Solar radiation

Although month, latitude, longitude, and LST are very important as input parameters inacquiring SR values, altitude is also very important. Furthermore, it has been verified usingANN methods that the altitude of any point in the sky has an influence on SR values.Alexandris et al. (1999) studied measurements of solar biological effective ultraviolet (UV)radiation over the period 7–14 June 1997 using an aircraft-based radiometer, at severaldifferent altitudes from sea level up to 13 km. The results showed that an increase in bio-logical effective UV radiation of about 7% per kilometre occurs throughout the troposphere.This increase has been compared with the burden ozone content at each height level as itis derived from concurrent ozone measurements obtained from ozonesonde ascents. Thiscomparison showed a strong anti-correlation between biological effective UV radiation andtotal ozone content above the UV measurement height level. Moreover, it was reported thatglobal total ozone dynamic’s surface solar ultraviolet radiation has an impact on variabil-ity and ecosystems. Kondratyev and Varotsos (1996) studied global total ozone changesand biologically active surface solar ultraviolet radiation variation on the basis of satel-lite and conventional surface observations. In that study, relevant impacts on terrestrialand aquatic ecosystems, and biochemical cycles, were discussed. There is a possibility ofremote-sensing techniques being used to obtain atmospheric concentrations of various tracegases.

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7520 M. Sahin

Table 2. Dates of images used in the study.

2002

2 January 2002 21 March 2002 12 June 2002 15 September 2002 15 December 20024 January 2002 24 March 2002 14 June 2002 17 September 2002 17 December 20025 January 2002 25 March 2002 16 June 2002 20 September 2002 18 December 20027 January 2002 27 March 2002 18 June 2002 21 September 2002 20 December 20028 January 2002 30 March 2002 19 June 2002 23 September 2002 21 December 200211 January 2002 1 April 2002 22 June 2002 25 September 2002 23 December 200214 January 2002 2 April 2002 23 June 2002 27 September 2002 26 December 200216 January 2002 3 April 2002 25 June 2002 29 September 2002 27 December 200219 January 2002 4 April 2002 27 June 2002 30 September 2002 31 December 200224 January 2002 5 April 2002 28 June 2002 1 October 200225 January 2002 7 April 2002 30 June 2002 2 October 200226 January 2002 8 April 2002 1 July 2002 3 October 200227 January 2002 11 April 2002 2 July 2002 4 October 200229 January 2002 12 April 2002 5 July 2002 6 October 200230 January 2002 13 April 2002 7 July 2002 8 October 20021 February 2002 15 April 2002 9 July 2002 10 October 20022 February 2002 16 April 2002 11 July 2002 12 October 20024 February 2002 17 April 2002 13 July 2002 14 October 20025 February 2002 18 April 2002 15 July 2002 16 October 20026 February 2002 20 April 2002 16 July 2002 18 October 20027 February 2002 22 April 2002 19 July 2002 20 October 20028 February 2002 23 April 2002 20 July 2002 24 October 20029 February 2002 26 April 2002 22 July 2002 26 October 200210 February 2002 27 April 2002 23 July 2002 28 October 200211 February 2002 29 April 2002 24 July 2002 30 October 200212 February 2002 1 May 2002 28 July 2002 31 October 200214 February 2002 2 May 2002 29 July 2002 2 November 200215 February 2002 5 May 2002 2 August 2002 3 November 200216 February 2002 6 May 2002 4 August 2002 6 November 200217 February 2002 7 May 2002 6 August 2002 7 November 200220 February 2002 9 May 2002 8 August 2002 9 November 200221 February 2002 10 May 2002 9 August 2002 11 November 200222 February 2002 12 May 2002 12 August 2002 13 November 200223 February 2002 13 May 2002 14 August 2002 15 November 200225 February 2002 15 May 2002 16 August 2002 17 November 200226 February 2002 16 May 2002 18 August 2002 20 November 200227 February 2002 18 May 2002 20 August 2002 22 November 20021 March 2002 20 May 2002 22 August 2002 24 November 20024 March 2002 22 May 2002 24 August 2002 26 November 20025 March 2002 23 May 2002 26 August 2002 28 November 20026 March 2002 26 May 2002 27 August 2002 30 November 20027 March 2002 28 May 2002 1 September 2002 2 December 20028 March 2002 30 May 2002 2 September 2002 3 December 200210 March 2002 3 June 2002 3 September 2002 6 December 200211 March 2002 4 June 2002 5 September 2002 7 December 200214 March 2002 5 June 2002 7 September 2002 9 December 200216 March 2002 8 June 2002 9 September 2002 11 December 200218 March 2002 9 June 2002 12 September 2002 12 December 200220 March 2002 11 June 2002 13 September 2002 14 December 2002

2003

1 January 2003 7 April 2003 1 July 2003 24 September 2003 28 December 20034 January 2003 9 April 2003 3 July 2003 26 September 2003 31 December 20035 January 2003 10 April 2003 4 July 2003 27 September 20036 January 2003 12 April 2003 7 July 2003 1 October 2003

(Continued)

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7 January 2003 13 April 2003 8 July 2003 2 October 200310 January 2003 16 April 2003 9 July 2003 3 October 200312 January 2003 17 April 2003 10 July 2003 4 October 200315 January 2003 18 April 2003 12 July 2003 5 October 200316 January 2003 20 April 2003 13 July 2003 7 October 200318 January 2003 22 April 2003 15 July 2003 8 October 200320 January 2003 23 April 2003 19 July 2003 11 October 200322 January 2003 26 April 2003 20 July 2003 13 October 200324 January 2003 27 April 2003 22 July 2003 14 October 200326 January 2003 28 April 2003 23 July 2003 17 October 200328 January 2003 30 April 2003 25 July 2003 18 October 200330 January 2003 2 May 2003 27 July 2003 19 October 20032 February 2003 3 May 2003 28 July 2003 21 October 20034 February 2003 7 May 2003 1 August 2003 22 October 20036 February 2003 8 May 2003 2 August 2003 23 October 20037 February 2003 11 May 2003 4 August 2003 26 October 200310 February 2003 13 May 2003 5 August 2003 27 October 200311 February 2003 14 May 2003 7 August 2003 29 October 200313 February 2003 16 May 2003 8 August 2003 4 November 200315 February 2003 17 May 2003 10 August 2003 6 November 200317 February 2003 19 May 2003 11 August 2003 9 November 200320 February 2003 21 May 2003 12 August 2003 11 November 200322 February 2003 22 May 2003 15 August 2003 14 November 200324 February 2003 24 May 2003 16 August 2003 15 November 200326 February 2003 25 May 2003 17 August 2003 16 November 200328 February 2003 27 May 2003 18 August 2003 19 November 20032 March 2003 29 May 2003 20 August 2003 20 November 20033 March 2003 3 June 2003 21 August 2003 24 November 20035 March 2003 4 June 2003 24 August 2003 26 November 20038 March 2003 5 June 2003 25 August 2003 27 November 20039 March 2003 7 June 2003 26 August 2003 29 November 200311 March 2003 8 June 2003 29 August 2003 3 December 200314 March 2003 10 June 2003 2 September 2003 5 December 200315 March 2003 13 June 2003 5 September 2003 6 December 200317 March 2003 14 June 2003 6 September 2003 9 December 200319 March 2003 15 June 2003 7 September 2003 11 December 200321 March 2003 17 June 2003 9 September 2003 13 December 200323 March 2003 18 June 2003 10 September 2003 14 December 200325 March 2003 21 June 2003 13 September 2003 17 December 200327 March 2003 22 June 2003 15 September 2003 18 December 200329 March 2003 24 June 2003 17 September 2003 21 December 200331 March 2003 25 June 2003 18 September 2003 22 December 20031 April 2003 27 June 2003 20 September 2003 23 December 20033 April 2003 28 June 2003 21 September 2003 26 December 20036 April 2003 30 June 2003 23 September 2003 27 December 2003

2004

2 January 2004 24 March 2004 27 June 2004 23 September 2004 25 December 20043 January 2004 25 March 2004 29 June 2004 26 September 2004 26 December 20044 January 2004 26 March 2004 30 June 2004 27 September 2004 28 December 20047 January 2004 27 March 2004 2 July 2004 29 September 2004 30 December 20048 January 2004 28 March 2004 3 July 2004 30 September 20049 January 2004 30 March 2004 5 July 2004 3 October 200411 January 2004 1 April 2004 6 July 2004 5 October 200412 January 2004 2 April 2004 8 July 2004 6 October 200414 January 2004 4 April 2004 9 July 2004 10 October 2004

(Continued)

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7522 M. Sahin


15 January 2004 5 April 2004 11 July 2004 12 October 200417 January 2004 7 April 2004 12 July 2004 13 October 200418 January 2004 8 April 2004 14 July 2004 15 October 200421 January 2004 12 April 2004 17 July 2004 16 October 200422 January 2004 14 April 2004 20 July 2004 19 October 200423 January 2004 17 April 2004 21 July 2004 21 October 200425 January 2004 19 April 2004 25 July 2004 22 October 200426 January 2004 22 April 2004 27 July 2004 24 October 20041 February 2004 23 April 2004 29 July 2004 26 October 20042 February 2004 25 April 2004 30 July 2004 28 October 20045 February 2004 26 April 2004 1 August 2004 30 October 20046 February 2004 29 April 2004 4 August 2004 3 November 20047 February 2004 30 April 2004 5 August 2004 5 November 200411 February 2004 2 May 2004 8 August 2004 7 November 200412 February 2004 3 May 2004 9 August 2004 8 November 200413 February 2004 6 May 2004 11 August 2004 10 November 200414 February 2004 8 May 2004 12 August 2004 11 November 200415 February 2004 10 May 2004 14 August 2004 14 November 200417 February 2004 11 May 2004 15 August 2004 15 November 200418 February 2004 13 May 2004 17 August 2004 16 November 200420 February 2004 15 May 2004 18 August 2004 18 November 200421 February 2004 17 May 2004 20 August 2004 20 November 200424 February 2004 20 May 2004 23 August 2004 25 November 200425 February 2004 21 May 2004 25 August 2004 27 November 200427 February 2004 23 May 2004 26 August 2004 28 November 200428 February 2004 25 May 2004 28 August 2004 29 November 20041 March 2004 28 May 2004 29 August 2004 1 December 20042 March 2004 29 May 2004 2 September 2004 6 December 20044 March 2004 4 June 2004 5 September 2004 7 December 20045 March 2004 6 June 2004 6 September 2004 8 December 20047 March 2004 8 June 2004 8 September 2004 10 December 20048 March 2004 9 June 2004 9 September 2004 11 December 200410 March 2004 11 June 2004 11 September 2004 13 December 200411 March 2004 14 June 2004 14 September 2004 14 December 200413 March 2004 16 June 2004 15 September 2004 16 December 200414 March 2004 18 June 2004 16 September 2004 18 December 200416 March 2004 20 June 2004 18 September 2004 19 December 200417 March 2004 21 June 2004 19 September 2004 20 December 200419 March 2004 24 June 2004 20 September 2004 23 December 200420 March 2004 25 June 2004 22 September 2004 24 December 2004

Katsambas et al. (1997) showed that daily total ozone observations made by satellitebetween 1985 and 1993 have been used to investigate fluctuations in daily broadband andspectral solar ultraviolet radiation reaching the ground. That study, carried out in summerover Athens (Greece), showed increases in ultraviolet irradiance reaching the ground of0.54%, 0.98%, 2.60%, and 0.79% per decade for the month of July at 300 nm, 312 nm,320 nm, and UVB (280–320 nm), respectively. Similar results were also obtained by Feretiset al. (2002).

In the present study, ANN and ELM were used to acquire solar radiation values. Forthis purpose, the data belonging to 61 centres of localization are chosen as control pointsin the period 2002–2004 in Turkey. While the data for the years 2002 and 2003 are usedfor training ANN and ELM models, the constructed models have been tested for accuracywith the data of 2004. The ANN model used in this study consists of the input layer, hiddenlayer, and output layer. While month, altitude, latitude, longitude, and LST derived fromsatellite data are used as input layer, solar radiation values are obtained from the outputlayer (see Figure 5).

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270

260

250250 260

R2 = 0.970

y = 0.9998x

270 280 290 300 310 320 330

Meteorological values (K)

Sat

ellit

e va

lues

(K

)

280

290

300

310

320

330

Figure 4. Comparison of satellite and meteorological LST values for coefficient of determination(R2 = 0.970).

There is no mathematical formula to determine optimum nerve cell (neuron) numberin the hidden layer of the ANN model, the number being decided during training of thenetwork. Neuron numbers increased from 2 to 50 according to the rule of two-by-two inthe hidden layer to achieve the most appropriate ANN model.

However, the creation of ANN initial weights was random and the appropriate ANNmodel was determined as a result of trial and error. In addition, different training algorithmswere tested during the training of the network. The best models developed according totraining algorithms and transfer functions, and number of the neurons in the hidden layerare shown in Table 4.

According to Table 4, the lowest and highest values of R2 will be seen to be 0.846 and0.943, respectively. The ANN model with the highest value of R2 was that with the train-ing algorithm trainlm. Its transfer functions in the hidden and output layers were recordedas logsig and linear, respectively. This network is being developed using the 20 neuronsin the hidden layer. This model has the lowest R2, showing that the training algorithm,transfer function in the hidden layer, and transfer function in the output layer are trainscg,logsig, and linear, respectively. There are 48 neurons in the hidden layer of the network,and the highest and lowest values for RMSE were found to be 2.458 and 1.604 MJ m−2,respectively. The model which is effective to try development of R2 is identical to RMSEstatistics. MBE values were also calculated in the developed models. The best and worstMBE values were calculated as 0.013 and −0.310 MJ m−2. The model with the best MBEhad a training algorithm and transfer functions in the hidden and ouput layers as trainoss,logsig, and linear, respectively. There are 16 neurons in the hidden layer. The training algo-rithm with the worst MBE was trainlm. The transfer function in the hidden layer is logsig,while the transfer function in the output layer is linear. There are 36 neurons in the hiddenlayer, with the highest WI 0.985 and the lowest 0.961. The ANN model that achieved thehighest WI had the training algorithm and hidden and output functions as trainlm, logsig,

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Tabl

e3.

MB

E,R

MS

E,R

2,a

ndW

Iva

lues

byst

udy

loca

tion

.

Pro

vinc

eM

BE

(K)

RM

SE

(K)

R2

WI

Pro

vinc

eM

BE

(K)

RM

SE

(K)

R2

WI

Ada

na0.

023

1.54

80.

973

0.99

3Iz

mir

−0.4

381.

458

0.97

80.

994

Adı

yam

an0.

789

1.87

80.

974

0.99

2K

ahra

man

mar

as0.

031

1.99

10.

959

0.98

9A

grı

0.05

01.

356

0.97

60.

994

Kar

aman

0.38

52.

062

0.94

20.

983

Aks

aray

0.05

41.

493

0.97

10.

992

Kar

s0.

331

1.72

00.

969

0.99

2A

mas

ya0.

164

1.49

80.

973

0.99

3K

asta

mon

u0.

323

1.65

30.

962

0.98

9A

nkar

a−0

.841

1.57

80.

988

0.99

6K

ayse

ri−0

.094

1.79

90.

973

0.99

3A

ntak

ya−0

.267

1.90

20.

964

0.99

0K

ırse

hir

−0.4

291.

979

0.95

10.

986

Ant

alya

0.37

11.

658

0.98

50.

996

Kil

is0.

856

1.91

20.

963

0.98

8A

rtvi

n0.

142

1.55

10.

968

0.99

1K

ocae

li-I

zmit

−0.8

231.

904

0.95

70.

985

Ayd

ın0.

106

1.51

70.

971

0.99

5K

onya

−0.0

161.

481

0.97

60.

994

Bal

ıkes

ir-G

önen

−1.1

561.

631

0.98

90.

995

Küt

ahya

0.19

41.

827

0.94

30.

985

Bat

man

0.18

61.

759

0.96

50.

990

Mal

atya

−0.4

891.

730

0.97

10.

992

Bil

ecik

−0.7

871.

875

0.95

90.

987

Mer

sin

0.93

62.

095

0.96

20.

987

Bin

göl

1.12

82.

066

0.97

30.

990

Mug

la0.

564

2.01

00.

957

0.98

7B

itli

s−0

.466

2.01

80.

957

0.98

8M

us−0

.444

1.74

40.

975

0.99

3B

urdu

r−0

.014

1.77

10.

952

0.98

7N

igde

0.02

21.

820

0.96

70.

991

Bur

sa0.

800

1.97

90.

958

0.98

7O

rdu

−0.4

641.

817

0.96

70.

990

Çan

akka

le0.

147

2.18

70.

944

0.98

3R

ize

−0.4

861.

712

0.94

90.

986

Çor

um1.

136

1.76

40.

969

0.98

7S

amsu

n−0

.241

1.62

60.

968

0.99

1D

iyar

bakı

r0.

090

2.09

70.

958

0.98

9S

iirt

0.62

11.

821

0.97

40.

992

Den

izli

0.09

61.

941

0.96

70.

991

Sin

op0.

268

1.59

40.

966

0.99

1E

dirn

e0.

300

1.83

30.

967

0.99

1S

ivas

0.38

91.

434

0.97

60.

993

Elâ

zıg

−0.5

671.

982

0.95

70.

988

San

lıur

fa−0

.123

1.44

10.

982

0.99

5E

rzin

can

−0.0

781.

855

0.96

20.

989

Toka

t0.

192

1.65

80.

972

0.99

2E

rzur

um0.

691

1.79

90.

974

0.99

2T

rabz

on−0

.383

1.72

60.

957

0.98

8G

azia

ntep

0.43

42.

037

0.96

50.

990

Tunc

eli

0.46

11.

860

0.96

40.

990

Güm

üsha

ne0.

509

1.87

90.

962

0.98

9V

an−0

.448

1.56

50.

981

0.99

5H

akkâ

ri0.

242

2.06

30.

965

0.99

1Y

alov

a0.

208

1.52

60.

970

0.99

2Ig

dır

0.65

31.

907

0.97

20.

992

Yoz

gat

−0.0

791.

957

0.95

00.

985

Ispa

rta

−0.1

971.

856

0.96

20.

989

Zon

guld

ak0.

136

1.51

90.

966

0.99

1Is

tanb

ul-G

özte

pe0.

175

1.95

30.

960

0.98

8

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Altitude

Latitude

Longitude

Month

LST

Solar radiation

Figure 5. ANN and ELM architecture used in this study.

and linear, respectively. The hidden layer had 20 neurons. The training algorithm of ANNwith the lowest WI value is trainscg, while the transfer function of the hidden and outputlayers is logsig and linear, respectively. Moreover, it will be seen from Table 4 that there are48 neurons in the hidden layer of the model.

In this study, although the ANN network was trained with the data for 2002 and 2003,the success of the network was tested with the data for 2004. The success of a one-yearstudy is assessed according to RMSE values. The lowest RMSE value, as mentioned previ-ously, was 1.604 MJ m−2 and this was developed as the most successful model (Table 4).The result of the tests was that the ANN (5:20:1) structure model gave the most accuratevalues in ANN models. The model recorded five neurons (month, altitude, latitude, lon-gitude, LST) in the input layer, 20 in the hidden layer, and one in the output layer (solarradiation). The network training algorithm and transfer function in the hidden layer aretrainlm and logsig, respectively. The linear function is used as transfer function in the out-put layer. The values of MBE, RMSE, R2, and WI were calculated depending on location,and are shown in Table 5.

In this study, whereas the highest RMSE was 3.005 MJ m−2 (the province of Batman),the lowest was 0.879 MJ m−2 (the province of Kahramanmaras).

Moreover, the lowest R2 is found as 0.892, which belonged to province of Isparta.Malatya has the highest value of R2 as 0.984. And also, the best and worst MBE valuesare obtained in order to take 0.009 MJ m−2 and 2.468 MJ m−2 for provinces of Artvinand Batman, respectively. Other locations take the R2 values between 0.892 and 0.984, andRMSE values between 0.879 MJ m−2 and 3.005 MJ m−2. The approach to zero of MBEvalues vary between 0.009–2.468 MJ m−2. In addition, the lowest WI value is obtained forBatman province as 0938. The highest value of WI is 0.996. This value is calculated for theprovince of Kahramanmaras.

It is clear from the statistical results of this study that SR as estimated by the ANNmethod gave the optimum value for the province of Kahramanmaras and the worst forBatman. The estimated and the actual SR data for these two provinces are given as totaldaily SR per month (see Figures 6(a)–(b)).

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Table 4. ANN models developed.

Trainingalgorithm

Hiddentransferfunction

Outputtransferfunction

Number ofneurons in

hidden layerMBE

(MJ m−2)RMSE

(MJ m−2) R2 WI

trainlm tansig linear 30 −0.241 1.765 0.929 0.981trainlm tansig linear 16 −0.194 1.665 0.939 0.984trainlm tansig linear 22 −0.159 1.664 0.938 0.983trainlm tansig linear 36 −0.138 1.697 0.935 0.983trainlm logsig linear 16 −0.197 1.690 0.936 0.983trainlm logsig linear 20 −0.148 1.604 0.943 0.985trainlm logsig linear 36 −0.310 1.726 0.935 0.982trainlm logsig linear 48 −0.127 1.741 0.933 0.982trainlm logsig tansig 14 −0.263 1.634 0.942 0.984trainlm logsig tansig 50 −0.257 1.744 0.935 0.982trainlm tansig tansig 26 −0.126 1.761 0.927 0.981trainlm tansig logsig 18 −0.173 1.609 0.941 0.984trainlm tansig logsig 44 −0.212 1.624 0.942 0.984trainlm logsig logsig 20 −0.236 1.769 0.931 0.981trainscg logsig linear 44 −0.224 2.149 0.873 0.969trainscg logsig linear 48 −0.099 2.458 0.846 0.961trainscg tansig linear 28 −0.127 1.988 0.904 0.975trainscg tansig linear 24 −0.141 2.000 0.903 0.975trainscg tansig tansig 4 −0.202 2.063 0.898 0.974trainscg tansig tansig 25 −0.078 1.975 0.905 0.976trainscg tansig tansig 48 −0.130 1.989 0.903 0.975trainscg tansig logsig 26 −0.187 1.930 0.910 0.977trainscg tansig logsig 28 −0.123 1.962 0.908 0.976trainscg tansig logsig 38 −0.139 1.922 0.912 0.977trainscg tansig logsig 48 −0.065 1.847 0.916 0.977trainscg logsig tansig 25 −0.147 2.043 0.897 0.974trainoss logsig linear 16 0.013 2.172 0.883 0.970trainoss tansig tansig 16 −0.179 2.108 0.892 0.972trainoss logsig logsig 46 −0.138 2.021 0.902 0.975trainbfg logsig linear 26 −0.176 1.959 0.908 0.976trainbfg logsig linear 44 −0.240 1.935 0.912 0.977trainbfg tansig linear 32 −0.229 1.978 0.909 0.976trainbfg tansig linear 38 −0.176 1.872 0.916 0.978trainbfg tansig linear 50 −0.227 1.797 0.925 0.980trainbfg tansig tansig 16 −0.092 1.956 0.906 0.976trainbfg tansig tansig 46 −0.054 1.925 0.910 0.977trainbfg tansig logsig 36 −0.071 1.972 0.902 0.975trainbfg logsig logsig 42 −0.227 1.962 0.907 0.976trainbfg logsig tansig 36 −0.039 1.974 0.903 0.975

Differences between estimated and actual values according to the ANN methodranged between 0.010 and 1.525 MJ m−2 and between 0.012 and 5.490 MJ m−2 forKahramanmaras and Batman, respectively. The ELM method was applied to the same dataset to evaluate SR.

Month, altitude, latitude, longitude, and LST derived from satellite data were used asinput in the input layer by the ELM method, and SR was obtained as output from the outputlayer (see Figure 5). There are five neurons in the input layer and one in the output layer.The best model was generated to establish the most appropriate model by increasing theneurons five by five from 10 to 150 in the hidden layer. The tansig, sinus, sigmoid, radialbasis, and probate transfer functions were used in the hidden layer, while the linear transferfunction was selected in the output layer (see Table 6).

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Table 5. MBE, RMSE, R2, and WI values by province.

Province MBE (MJ m−2) RMSE (MJ m−2) R2 WI

Adana −1.133 1.591 0.972 0.981Adıyaman −0.513 1.541 0.966 0.982Agrı −0.439 1.472 0.949 0.983Aksaray 0.328 1.294 0.961 0.989Amasya 0.174 1.438 0.952 0.987Ankara −0.607 1.229 0.965 0.990Antakya 0.337 1.037 0.969 0.991Antalya −1.731 2.512 0.953 0.966Artvin 0.009 1.561 0.939 0.983Aydın −2.189 2.683 0.964 0.962Balıkesir-Gönen −0.340 1.765 0.936 0.979Batman 2.468 3.005 0.945 0.938Bilecik −0.715 1.636 0.953 0.979Bingöl 1.655 2.335 0.946 0.971Bitlis −1.579 1.858 0.974 0.980Burdur 0.919 1.710 0.952 0.982Bursa 0.101 2.008 0.923 0.975Çanakkale −0.967 1.578 0.957 0.985Çorum −0.103 1.175 0.961 0.990Diyarbakır −0.347 1.224 0.964 0.991Denizli −0.478 1.271 0.948 0.986Edirne −1.447 1.939 0.967 0.977Elâzıg −0.523 1.048 0.981 0.994Erzincan 0.277 1.248 0.962 0.989Erzurum −1.577 1.948 0.959 0.967Gaziantep −0.146 1.221 0.963 0.989Gümüshane −1.399 1.928 0.931 0.980Hakkâri 0.293 1.042 0.969 0.991Igdır −0.421 1.320 0.959 0.988Isparta 0.873 2.226 0.892 0.966Istanbul-Göztepe 1.172 1.711 0.959 0.982Izmir −0.689 1.473 0.963 0.990Kahramanmaras 0.198 0.879 0.981 0.996Karaman −0.211 1.055 0.974 0.994Kars −0.238 1.347 0.954 0.983Kastamonu −0.097 1.810 0.908 0.969Kayseri −0.343 1.104 0.977 0.992Kırsehir 0.773 1.519 0.953 0.984Kilis 0.443 1.185 0.970 0.991Kocaeli-Izmit −0.875 1.767 0.955 0.976Konya 0.094 1.391 0.957 0.988Kütahya −0.523 1.588 0.945 0.985Malatya 0.600 0.994 0.984 0.994Mersin −0.054 0.991 0.978 0.994Mugla −0.383 1.370 0.955 0.986Mus −0.812 1.567 0.957 0.987Nigde −0.765 1.206 0.981 0.992Ordu −0.024 1.363 0.939 0.985Rize −0.149 1.358 0.913 0.977Samsun 0.587 1.804 0.928 0.979Siirt −1.261 2.301 0.951 0.968Sinop 2.196 2.567 0.960 0.966Sivas −0.289 1.225 0.971 0.990

(Continued)

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7528 M. Sahin


Province MBE (MJ m−2) RMSE (MJ m−2) R2 WI

Sanlıurfa 0.541 1.090 0.979 0.993Tokat −0.288 1.613 0.946 0.984Trabzon −0.132 1.263 0.921 0.981Tunceli 0.045 1.298 0.967 0.991Van 0.159 1.183 0.971 0.993Yalova −0.416 1.193 0.968 0.992Yozgat 0.298 1.541 0.943 0.984Zonguldak 0.620 1.351 0.971 0.989

The most successful ELM model had the structure (5:150:1), with 150 neurons inthe hidden layer. The transfer function model is tansig in the hidden layer, and thetransfer function in the output layer is linear. If the results are evaluated statisticallyaccording to the criteria, R2, RMSE, MBE, and WI values are calculated as 0.961 and0.672 MJ m−2, 0.045 MJ m−2, and 0.997, respectively. At the same time, these values wereobtained depending on location by taking into consideration the ELM (5:150:1) model(see Table 7).

It is clear from Table 7 that the lowest R2 was recorded for Aksaray (0.940), with thehighest 0.993 for the province of Isparta. Tunceli recorded the lowest MBE and RMSE(0.012 and 0.347 MJ m−2, respectively), while the highest (0.158 and 1.257 MJ m−2,

(c)(d)

(b)(a)

30

25

20

15

Month

MonthMonth

Month

Sol

ar r

adia

tion

(MJ

m–2

day

–1)

Sol

ar r

adia

tion

(MJ

m–2

day

–1)

Sol

ar r

adia

tion

(MJ

m–2

day

–1)

Sol

ar r

adia

tion

(MJ

m–2

day

–1)

10

5

0

Janu

ary

Febr

uary

March

April

MayJu

ne July

Augus

t

Septem

ber

Octobe

r

Novem

ber

Decem

ber

Janu

ary

Febr

uary

March

April

MayJu

ne July

Augus

t

Septem

ber

Octobe

r

Novem

ber

Decem

ber

Janu

ary

Febr

uary

March

April

MayJu

ne July

Augus

t

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ber

Octobe

r

Novem

ber

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ber

Janu

ary

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ber

30

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0

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15

10

5

0

30 Actual valueANN value

Actual valueANN value

Actual valueELM value Actual value

ELM value

25

20

15

10

5

0

Figure 6. Estimated and actual SR values for Kahramanmaras (a), Batman (b), Tunceli (c), andAksaray (d).

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Table 6. ELM training and testing parameters.

Number of layers 3

Number of neurons in layers Input: 5Hidden: 10 . . . 150Output: 1

Activation functions Tangent sigmoid; sinus; sigmoid; radial basis; probit; purelinLearning rule The ELM for SLFNsSum-squared error 0.0001

Note: ELM, extreme learning machine; SLFN, single-hidden layer feedforward neural network.

respectively) were recorded at Aksaray. R2 varied between 0.940 and 0.993 for mostlocations, with MBE between 0.012 and 0.158 MJ m−2. RMSE was in the range0.347–1.257 MJ m−2. The lowest WI was for Gaziantep (0.989) and the highest (formore than one city) was 0.999 (Table 7). The names of these provinces were Bingöl,Çanakkale, Diyarbakır, Istanbul-Göztepe, Izmir, Karaman, Kilis, Koceli-Izmit Kütahya,Malatya, Nigde, Samsun, Tokat, and Tunceli. The best estimation was for Tunceli, andthe worst for Aksaray. Using the ELM method, actual and estimated daily total SR monthlydata for these two locations are shown in Figures 6(c)–(d).

The actual and estimated data obtained by the ELM method are compatible witheach other for Tunceli, but not for Aksaray. According to monthly data, while differencesbetween actual and estimated data ranged between 0.046 and 0.831 MJ m−2 in Tunceli, inAksaray these ranged from 0.102 to 1.608 MJ m−2.

5. Conclusion

In this study, SR was estimated using both ELM and ANN in 61 locations with varyingclimatic conditions. Both methods were trained with data from 2002 and 2003, whilemodel accuracy was tested with data from 2004. Solar radiation values obtained fromthe use of ANN and ELM models were compared statistically with the values of SR asmeasured by meteorological stations. The (5:20:1) model proved to be the most success-ful ANN model, calculating SR with statistical values of R2, MBE, RMSE, and WI as0.943, −0.148 MJ m−2, 1.604 MJ m−2, and 0.996, respectively. In addition, this modelhas a training algorithm that is trainlm, with transfer functions in the hidden and outputlayers being logsig and linear, respectively. There were 20 neurons in the hidden layer.The (5:150:1) model proved to be the best ELM model, with 150 neurons in the hid-den layer. The transfer functions of the ELM (5:150:1) model in the hidden and outputlayers are tansig and linear, respectively. R2, MBE, RMSE, and WI were calculated as0.961, 0.045 MJ m−2, 0.672 MJ m−2, and 0.997, respectively. Use of RMSE is a generalprecept rather than that of MBE, especially in short-term (e.g. 1 year) comparison. Sincethe RMSE of the ELM method (0.672 MJ m−2) was lower than that of the ANN method(1.604 MJ m−2), these results show that ELM was more successful than ANN. The EMLmethod to obtain result significant statistically in SR calculation is more successful thanANN method, is an innovation in terms of literature.

Estimation of SR cannot be achieved with only a very small error using the ELMmethod and depending on satellite data. Construction of a suitable network of meteoro-logical stations throughout any country and the recording of permanent measurements arevery difficult and burdensome economically. Moreover, even if these were to be established,

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7530 M. SahinTa

ble

7.E

rror

valu

esby

loca

tion

.

Pro

vinc

eM

BE

(MJ

m−2

)R

MS

E(M

Jm

−2)

R2

WI

Pro

vinc

eM

BE

(MJ

m−2

)R

MS

E(M

Jm

−2)

R2

WI

Ada

na−0

.025

0.49

70.

971

0.99

8Iz

mir

−0.0

180.

426

0.98

50.

999

Adı

yam

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.061

0.78

30.

989

0.99

4K

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man

mar

as0.

039

0.62

10.

964

0.99

8A

grı

−0.0

360.

603

0.96

70.

997

Kar

aman

−0.0

340.

584

0.97

50.

999

Aks

aray

0.15

81.

257

0.94

00.

994

Kar

s−0

.035

0.58

80.

980

0.99

6A

mas

ya−0

.028

0.52

90.

982

0.99

8K

asta

mon

u−0

.046

0.68

10.

953

0.99

5A

nkar

a−0

.095

0.97

70.

967

0.99

4K

ayse

ri−0

.031

0.56

00.

984

0.99

8A

ntak

ya−0

.045

0.66

80.

965

0.99

6K

ırse

hir

0.12

21.

103

0.96

00.

994

Ant

alya

−0.1

191.

092

0.95

20.

994

Kil

is0.

014

0.37

70.

982

0.99

9A

rtvi

n−0

.025

0.50

00.

971

0.99

8K

ocae

li-I

zmit

−0.0

170.

410

0.99

00.

999

Ayd

ın−0

.029

0.54

10.

979

0.99

8K

onya

0.05

00.

710

0.98

60.

998

Bal

ıkes

ir-G

önen

−0.0

610.

783

0.96

50.

996

Küt

ahya

−0.0

260.

507

0.98

00.

999

Bat

man

0.03

00.

548

0.96

40.

998

Mal

atya

0.02

00.

453

0.98

60.

999

Bil

ecik

−0.0

560.

750

0.96

40.

995

Mer

sin

−0.0

350.

588

0.98

20.

998

Bin

göl

0.02

40.

486

0.97

60.

999

Mug

la−0

.065

0.80

60.

947

0.99

5B

itli

s−0

.031

0.56

00.

969

0.99

8M

us−0

.076

0.87

20.

969

0.99

6B

urdu

r0.

035

0.59

40.

985

0.99

8N

igde

−0.0

200.

452

0.98

80.

999

Bur

sa0.

045

0.67

20.

974

0.99

7O

rdu

−0.0

310.

553

0.96

70.

998

Çan

akka

le−0

.023

0.48

10.

979

0.99

9R

ize

−0.0

420.

648

0.96

40.

996

Çor

um−0

.034

0.58

40.

987

0.99

8S

amsu

n0.

020

0.44

70.

980

0.99

9D

iyar

bakı

r−0

.018

0.42

50.

992

0.99

9S

iirt

−0.0

350.

595

0.97

70.

997

Den

izli

−0.0

550.

738

0.96

20.

996

Sin

op0.

083

0.91

10.

962

0.99

6E

dirn

e−0

.039

0.62

20.

973

0.99

8S

ivas

−0.0

660.

810

0.97

60.

996

Elâ

zıg

0.05

30.

727

0.96

50.

997

San

lıur

fa0.

039

0.62

70.

982

0.99

8E

rzin

can

0.02

60.

510

0.95

40.

998

Toka

t−0

.017

0.40

90.

981

0.99

9E

rzur

um−0

.037

0.61

00.

968

0.99

6T

rabz

on0.

050

0.70

90.

966

0.99

5G

azia

ntep

−0.1

481.

216

0.95

10.

989

Tunc

eli

0.01

20.

347

0.98

80.

999

Güm

üsha

ne−0

.063

0.79

10.

974

0.99

7V

an−0

.055

0.73

90.

960

0.99

8H

akkâ

ri0.

047

0.68

40.

980

0.99

7Y

alov

a−0

.035

0.58

80.

961

0.99

8Ig

dır

−0.0

350.

594

0.97

40.

997

Yoz

gat

−0.0

370.

611

0.97

20.

998

Ispa

rta

−0.0

440.

665

0.99

30.

998

Zon

guld

ak0.

051

0.71

70.

987

0.99

7Is

tanb

ul-

Göz

tepe

0.01

50.

393

0.98

10.

999

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the distribution of the stations might not adequate. Rather, it would be more appropriate toutilize meteorological satellites which are capable of scanning all regions. For this reason,SR obtained from satellite data using the ELM method is recommended for researchersstudying SR.

AcknowledgementsI would like to express my gratitude to the Republic of Turkey’s Ministry of Forestry and WaterAffairs (Turkish State Meteorological Service) personnel, who provided a wide range of facilities foracquiring meteorological data; and to the Scientific and Technological Research Council of Turkey-Bilten personnel, who provided a wide range of facilities for acquiring satellite data.

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