Application of extreme learning machine for estimating solar radiation from satellite data

1. Application of extreme learning machine for estimating
solar radiation from satellite data
Mehmet Şahin1,
*,†
, Yılmaz Kaya2
, Murat Uyar1
and Selçuk Yıldırım1
1
Department of Electrical and Electronics Engineering, Siirt University, 56100 Siirt, Turkey
2
Department of Computer Engineering, Siirt University, 56100 Siirt, Turkey
SUMMARY
In this paper, a simple and fast method based on extreme learning machine (ELM) for the estimation of solar radiation in
Turkey was presented. To design the ELM model, satellite data of the National Oceanic and Atmospheric Administration
advanced very high-resolution radiometer from 20 locations spread over Turkey were used. The satellite-based land surface
temperature, altitude, latitude, longitude, month, and city were applied as input to the ELM, and the output variable is the
solar radiation. To show the applicability of the ELM model, a performance comparison in terms of the estimation capabil-
ity and the learning speed was made between the ELM model and conventional artificial neural network (ANN) model with
backpropagation. The comparison results showed that the ELM model gave better estimation than the ANN model for the
overall test locations. Moreover, the ELM model was about 23.5 times faster than the ANN model. The method could be
used by researchers or scientists to design high-efficiency solar devices such as solar power plant and photovoltaic cell.
Copyright © 2013 John Wiley & Sons, Ltd.
KEY WORDS
solar radiation; extreme learning machine; remote sensing; satellite data; NOAA
Correspondence
*Mehmet Şahin, Department of Electrical and Electronics Engineering, Siirt University, 56100 Siirt, Turkey.
†
E-mail: sahanmehmet2000@yahoo.com, msahin@siirt.edu.tr
Received 28 March 2012; Revised 23 January 2013; Accepted 24 January 2013
1. INTRODUCTION
If long-term solar radiation (SR) estimations are performed
in a geographical region, operating conditions of many
solar energy systems, which are in design and development
stage, can be simulated in the related region [1]. More
specifically, long-term SR estimations are an indispensable
parameter for engineering applications such as modeling
solar power plants, modeling photovoltaic cells, and mod-
eling solar heating systems [2]. Therefore, it is necessary to
correctly estimate SR, which is an extremely valuable
information.
In the previous years, SR estimation models have been
developed in accordance with parameters such as air
temperature, humidity, sunshine duration, and cloud cover-
age, which were measured from conventional meteorolog-
ical stations and which were evaluated indirectly as a
function of SR [3]. These models can be classified into
two groups, namely parametric methods such as Ångström
[4] and nonparametric methods that are based on artificial
intelligence [5,6]. In the literature, it has been observed
that SR information in a specific location can be estimated
using these models. However, it may not be possible to
obtain accurate and continuous data from every station
because maintenance and calibration of measuring devices,
which are installed in meteorological stations for SR
measurement, are difficult and installation costs are high
[7]. Furthermore, the fact that the number of meteorologi-
cal stations are limited especially in developing countries
and inefficient recording of data due to device malfunc-
tions constitute another limitation in obtaining SR data
[8]. Thus, these limitations forced researchers toward a
tendency to develop alternative estimation methods and find
more reliable data sources for the regions where SR data
cannot be directly measured or stations are insufficient.
In recent years, satellite-based remote sensing (RS)
techniques are widely used as an alternative method and
as a data source for SR estimations [7,9]. One of the most
important advantages of RS is that it is a reliable and fast
method for obtaining up-to-date and continuous informa-
tion about large geographical areas. In addition to this,
satellite-based RS provides opportunity to perform SR esti-
mations in rural, mountainous, and remote places where
meteorological stations are insufficient.
In the literature, some models have been recommended
to estimate SR at ground levels by using satellite data.
INTERNATIONAL JOURNAL OF ENERGY RESEARCH
Int. J. Energy Res. 2014; 38:205–212
Published online 12 March 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3030
Copyright © 2013 John Wiley & Sons, Ltd. 205

2. These can be classified in three main categories: statistical,
physical, and artificial intelligence techniques [9,10].
However, it has been observed that efficient results have
been obtained in satellite data-based SR estimation when
artificial intelligence techniques such as artificial neural
network (ANN) have been used [7,10–12]. Although
ANN-based approaches show better performance
compared with the aforementioned techniques, its most
important disadvantage is the fact that learning speed is
highly low in training stage especially when working with
large data sets as in this study. Thus, it is urgently required
to develop more accurate and fast methods to estimate SR.
Previous studies have proven that extreme learning
machine (ELM) has the potential to estimate unmeasured
parameters [13]. However, application of ELM in estimat-
ing SR using satellite data has not been reported in the
literature before.
The aim of this study was to investigate the efficiency
and applicability of ELM for estimating SR. For this
purpose, its performance was tested with case studies that
were conducted in 20 locations that represent different
climatic conditions of Turkey. We believe that the
proposed method can be an ideal tool that will increase
the performance of SR estimation studies.
2. EXTREME LEARNING MACHINE
Extreme learning machine, which was developed by
Huang et al. [13], is a novel learning algorithm for single
hidden layer feedforward networks (SLFNs). It has been
widely used for the solution of estimation problems in
many different fields [14,15]. There are some advantages
of the ELM algorithm. (i) It is easy to use, and no
parameters need to be tuned except predefined network
architecture and thus avoid many difficulties faced by gra-
dient-based algorithms such as learning rate, learning
epochs, and local minima. (ii) It is proven to be a faster
learning algorithm compared with other conventional
learning algorithms such as backpropagation (BP) algo-
rithm. Most training can be accomplished in seconds and
minutes (for large-scale complex applications), which
might not be easily obtained using other traditional learn-
ing methods. (iii) It possesses similar high generalization
performance as BP [16].
For N arbitrary distinct samples (xk,yk) 2 Rn
 Rm
,
the standard SLFNs with M hidden nodes and an activation
g(Á) function are mathematically described as
XM
i¼1
big xk; ; ci; ; aið Þ ¼ yk; k ¼ 1; 2; . . . ; N (1)
where ci 2 R is the randomly assigned bias of the ith hidden
node and wi 2 R is the randomly assigned input weight vec-
tor connecting the ith hidden node and the input nodes. bi
is the weight vector connecting the ith hidden node to the
output node. g(xk;ci,wi) is the output of the ith hidden node
with respect to the input sample xk. Then, Eq. (1) can be
written as
Hb ¼ Y (2)
where
H ¼
g x1; ; c1; ; w1ð Þ . . . g x1; ; cM; ; wMð Þ
⋮ ⋱ ⋮
g xN; ; c1; ; w1ð Þ ⋯ g xN; ; cM; ; wMð Þ
2
4
3
5
NÂM
(3)
b ¼ bT
1 bT
2 ; . . . ; bT
L
À ÁT
mÂM
(4)
and target output (Y)
Y ¼ tT
1 tT
2 ; . . . ; tT
L
À ÁT
mÂM
(5)
The output weights can be derived by finding the least-
square solutions to the aforementioned linear system,
which is given as
b ¼ H†
Y (6)
where H†
is the Moore–Penrose generalized inverse of the
hidden layer output matrix H. The topological structure of
an ELM network is shown in Figure 1.
3. STUDY AREA AND DATA
DESCRIPTION
The 20 locations that represented different climatic condi-
tions over Turkey were chosen as the study area. Their
Figure 1. The topological structure of an extreme learning ma-
chine network.
Modeling of solar radiationM. ŞAHIN ET AL.
206 Int. J. Energy Res. 2014; 38:205–212 © 2013 John Wiley & Sons, Ltd.
DOI: 10.1002/er

3. geographic information such as altitude, latitude, and
longitude were presented in Table I. Also, the geographical
locations of these stations were illustrated in Figure 2.
In this study, satellite-based land surface temperature
(LST) obtained from the National Oceanic and
Atmospheric Administration advanced very high-resolution
radiometer (NOAA-AVHRR) was considered as a function
of SR and used as a part of the inputs for training ELM.
Because it has an extremely large influence upon SR, it
has been frequently preferred as an independent variable
in many previous studies to estimate SR [10,17]. How-
ever, to obtain the LST value, images of NOAA-AVHRR
channels must be transformed by being subjected to the
following three basic processes: estimation of normalized
difference vegetation index (NDVI), calculation of surface
emissivity, and application of LST algorithm-based split-
window technique.
The NDVI value has been formalized as follows:
NDVI ¼
NIR À RED
NIR þ RED
(7)
where NIR and RED represent the spectral reflectance
measurements in near infrared and visible regions, respec-
tively. If Eq. (7) is rewritten according to channel measure-
ment value taken from AVHRR sensors of NOAA
satellites, Eq. (8) is obtained as follows:
NDVI ¼
C2 À C1
C2 þ C1
(8)
where C1 and C2 represent reflectance amount values of
channels 1 and 2 of the AVHRR sensor, respectively.
According to Eq. (8), the NDVI takes values only between
À1 and +1 [18,19].
Surface emissivity is described as the ability of land
surface to transform thermal energy into luminous energy
as in black body modeling. The following emissivity
formulas can be reached using NDVI maps:
e4 ¼ 0:9897 þ 0:029 ln NDVIð Þ (9)
e4 À e5 ¼ 0:01019 þ 0:01344 ln NDVIð Þ (10)
where e4 and e5 represent the emissivity values belonging
to channels 4 and 5 of the NOAA-AVHRR sensor, respec-
tively [20]. Moreover, if e4 and e5 are arranged as seen in
Eqs (11) and (12), emissivity difference (Δe) and emissiv-
ity average (e) formulas are obtained, respectively.
Δe ¼ e4 À e5 (11)
e ¼
e4 þ e5
2
(12)
Split-window technique is one of the widely used tech-
niques in determining LST in accordance with emissivity
parameters. Different surface temperature calculation algo-
rithms have been recommended to develop this technique.
The algorithm recommended by Price [21] is one of the
Table I. The geographical description of the locations in under
study.
City Altitude (m) Latitude (
N) Longitude (
E)
Adana 27 37.03 35.21
Ağrı 1632 39.43 43.03
Ankara 891 39.57 32.53
Antalya 64 36.42 30.44
Artvin 628 41.11 41.49
Balıkesir 37 40.06 27.39
Bursa 100 40.13 29.00
Diyarbakır 674 37.54 40.12
Edirne 85 41.41 59.33
Erzurum 1758 39.57 41.40
İstanbul 33 40.58 29.05
İzmir 29 38.23 27.04
Kayseri 1092 38.43 35.29
Konya 1030 37.52 32.28
Malatya 948 38.21 38.13
Ordu 4 40.59 37.54
Samsun 4 41.21 36.15
Siirt 896 37.55 41.57
Trabzon 30 40.59 39.45
Van 1671 38.28 43.21
Figure 2. Map of Turkey with the locations.
Modeling of solar radiation M. ŞAHIN ET AL.
207Int. J. Energy Res. 2014; 38:205–212 © 2013 John Wiley Sons, Ltd.
DOI: 10.1002/er

4. algorithms that stand out among these algorithms. This
technique is represented as follows.
TPrice-1984 ¼ T4 þ A T4 À T5ð Þ½ Š
5:5 À e4
4:5
À 0:75T5Δe (13)
where T4 and T5 show the brightness temperature values
obtained from thermal channels 4 and 5 of the AVHRR
sensor, respectively. A is a constant with a 3.33 value.
4. RESULT AND DISCUSSION
The main purpose of this study was to estimate SR for 20
locations from the seven regions that represent different
climate conditions of Turkey. For this purpose, LST values
selected as one part of inputs to train ELM must be firstly
obtained. LST map of an image, which was obtained at
06:56 in local time on 10/06/2002 by implementing the
aforementioned conversion steps, was given in Figure 3.
As seen in the figure, it was observed that the large part of
the temperature above Turkey ranged from 296 to 311K. It
was also seen on the map that the highest temperature values
at the stated hour were on Southeastern Anatolia Region.
Temperature values varied between 278 and 296 K in large
parts of East Anatolia and East Black Sea regions. It was
observed on the temperature map that temperature range
was changed between 296 and 305K in large parts of Central
Anatolia, Aegean, and Mediterranean regions.
A total of 43 LST satellite images were formed as at
least one image from each month belonging to years
2000, 2001, and 2002 by following a similar method.
LST values were obtained on the formed images using
the coordinates of 20 locations that were stated in Table I.
A total of 720 LST values, which were obtained with the help
of satellite, were compared with the meteorological values in
the stated years and locations. The correlation between
meteorological and satellite values was seen in Figure 4.
For designing ELM model, six input variables such as
satellite-based LST, altitude, latitude longitude, month,
and city were used, and the one output variable was the
SR. Three layers were employed in the ELM model; those
were input, hidden, and output layers. For optimal ELM
model, the numbers of nodes in hidden layer were gradu-
ally increased between 20 and 50 by an interval of 5. Then,
the nearly optimal node for ELM was selected as 50. As a
result of this, 6-50-1 neurons were used in the layers,
respectively. Besides, the different configurations according
to type of activation functions such as tangent sigmoid, sinus,
sigmoid, and radial basis were tried for hidden and output
layers, and the best performance was obtained as tangent
sigmoid and linear activation functions, respectively. In addi-
tion, to show the potential of the proposed model, a perfor-
mance comparison in terms of the estimation capability and
the learning speed was made between the proposed model
and conventional feedforward ANN model with BP. Because
it is a well-known universal estimator, the results from ANN
can be considered as a rather standard benchmark [22–24].
ANN architecture used in this study was illustrated in
Figure 5. All the simulations for the ELM and conventional
ANN models are carried out in MATLAB environment
running in a Pentium 4, 2.93GHz CPU. Processes similar
to ELM model for optimal model parameters were applied
to ANN. The resultant model was 6-45-1. Similarly, tangent
Figure 4. A comparison between land surface temperature values
obtained through Price algorithm and meteorological values.
Figure 3. Land surface temperature map depending on Price algorithm (K).
Modeling of solar radiationM. ŞAHIN ET AL.
208 Int. J. Energy Res. 2014; 38:205–212 © 2013 John Wiley Sons, Ltd.
DOI: 10.1002/er

5. sigmoid and linear activation functions were used in the
hidden and output layers, respectively. Although there are
many variants of BP algorithm for ANN, a faster BP
algorithm called Levenberg–Marquardt algorithm is used in
models. The two approaches were trained by using satellite
data of 2000 and 2001. Their estimation performances were
tested with the data of 2002. The estimation results of
models were statistically evaluated by using common error
indicators such as root mean square error (RMSE), mean bias
error (MBE), and coefficient of determination (R2
) [25,26].
The results from both approaches were given comparatively
in Table II for each location and overall locations. Moreover,
SR estimation performances of ELM and ANN were also
evaluated in terms of errors in measurement between actual
and estimated SRs. For the overall 20 locations, the obtained
results were shown in Figure 6(a).
As seen in Table II, for the overall 20 locations, the
ELM model gave good prediction performance with the
lowest RMSE of 0.090 MJ/m2
, MBE of 0.008 MJ/m2
,
and the highest R2
of 0.974, which is slightly better than
the ANN model. As seen in Figure 6(a), the ELM model
had error interval of À0.219 errors 0.271 MJ/m2
City
Altitude
Latitude
Longitude
Month
LST
Solar radiation
Figure 5. The architecture of artificial neural network used for the comparison.
Table II. Error values according to satellite-based data.
Locations
ELM ANN
RMSE (MJ/m2
) MBE (MJ/m2
) R2
RMSE (MJ/m2
) MBE (MJ/m2
) R2
Adana 0.060 À0.004 0.980 0.066 0.004 0.957
Ağrı 0.108 0.012 0.922 0.113 0.013 0.925
Ankara 0.096 À0.009 0.985 0.099 À0.010 0.961
Antalya 0.083 À0.007 0.969 0.107 À0.012 0.954
Artvin 0.082 0.007 0.953 0.088 À0.008 0.954
Balıkesir 0.080 0.006 0.966 0.090 0.008 0.932
Bursa 0.066 0.004 0.944 0.120 0.014 0.887
Diyarbakır 0.115 À0.013 0.965 0.092 À0.008 0.946
Edirne 0.072 À0.005 0.965 0.072 0.005 0.931
Erzurum 0.118 À0.014 0.944 0.220 À0.049 0.947
İstanbul 0.063 0.004 0.976 0.087 0.008 0.976
İzmir 0.066 À0.004 0.972 0.116 À0.013 0.961
Kayseri 0.067 À0.004 0.982 0.160 0.026 0.973
Konya 0.066 0.004 0.977 0.138 À0.019 0.975
Malatya 0.056 0.003 0.991 0.125 0.016 0.977
Ordu 0.104 À0.011 0.964 0.107 À0.011 0.952
Samsun 0.084 0.007 0.959 0.102 À0.010 0.959
Siirt 0.097 À0.009 0.931 0.168 À0.028 0.891
Trabzon 0.107 À0.011 0.938 0.129 0.017 0.947
Van 0.146 0.021 0.969 0.145 À0.021 0.903
Overall 0.090 0.0080 0.974 0.121 0.015 0.961
ELM, extreme learning machine; ANN, artificial neural network; RMSE, root mean square error; MBE, mean bias error.
Modeling of solar radiation M. ŞAHIN ET AL.
209Int. J. Energy Res. 2014; 38:205–212 © 2013 John Wiley Sons, Ltd.
DOI: 10.1002/er

6. between actual and estimated SRs, whereas ANN model
had error interval of À0.412 errors 0.197 MJ/m2
. It
was shown that ELM was of smaller error than ANN. Also,
the best values of RMSE, MBE, and R2
were found to be
0.056 MJ/m2
, 0.003 MJ/m2
, and 0.991 for Malatya,
whereas the worst values according to RMSE and MBE
were found to be 0.146 and 0.021 MJ/m2
for Van, respec-
tively. Moreover, a performance comparison in terms of
the learning speed was presented in Table III. As shown
in the table, the ELM model runs about 23.5 times faster
than the ANN model with BP. It could also be seen that
the testing time spent for the ANN is two times longer than
the testing time for ELM. ELM obtained the fastest learn-
ing speed for estimating SR.
Finally, to verify functional relationship between input
parameters (satellite-based RS products) and output parameter
(SR), SR estimation results from records of satellite were also
compared with those obtained from records of the meteorolog-
ical station at the same locations and years. Thus, inputs for
both models were changed as meteorological station-based
LST, altitude, latitude longitude, month, and city; output was
SR. Similarly, the results from the proposed ELM and ANN
models were presented comparatively in Table IV. In terms
of errors in measurement for the overall test locations, the
results were also illustrated in Figure 6(b).
As seen from Table IV, estimation results obtained from
records of the meteorological station were compatible with
those obtained from records of satellite. Even, SR estimation
Figure 6. Errors in measurement for overall test locations. (a) Satellite-based and (b) meteorological station-based extreme learning
machine and artificial neural network models.
Table III. Performance comparison in terms of the learning
speed.
Models
Time (s)
Training Testing
ELM 0.101 0.0312
ANN 2.382 0.0624
ELM, extreme learning machine; ANN, artificial neural network.
Modeling of solar radiationM. ŞAHIN ET AL.
210 Int. J. Energy Res. 2014; 38:205–212 © 2013 John Wiley Sons, Ltd.
DOI: 10.1002/er

7. obtained from satellite-based RS products gave slightly
better results than the other. It was proven that there was a
correlation between input (satellite-based RS products) and
output (SR) parameters. Also in this case, it was shown that
the proposed ELM presented better accurate results than the
ANN, as seen in Table IV and Figure 6(b).
5. CONCLUSION
Solar radiation is crucial for designing solar furnaces,
interior illumination of buildings, concentrating solar col-
lectors, sizing photovoltaic systems, and site selection of
solar power plants. Thus, it is urgently required to develop
a novel and more accurate method to estimate SR when it
is not readily available. The basis of this study was to
investigate the feasibility of using ELM to model the non-
linear relationship between satellite-based input parameters
and SR. For this purpose, the data from 20 locations spread
over Turkey between 2000 and 2001 were used for training
the ELM. The data of 2002 were used to test the perfor-
mance of the ELM model. To show the applicability of
ELM model, a performance comparison in terms of the
estimation capability and the learning speed was also made
between the ELM and conventional ANN models with BP.
The comparison analyses showed that ELM model gave
the lowest RMSE of 0.090 MJ/m2
, MBE of 0.008 MJ/m2
,
and the highest R2
of 0.974 for the overall test locations.
Moreover, the learning speed of ELM was about 23.5
times faster than that of the ANN model. Thus, ELM can
significantly reduce the computational complexity com-
pared with ANN. It was also shown that the ELM model
was feasible for satellite sensor imagery and works without
the need for additional meteorological station data.
Finally, ELM can help improve the deficiency of
conventional ANNs in application of SR analysis, which
typically requires thousands of training data. Also, usage
of satellite-based products and the ELM model seems
promising for evaluating the solar resource potential in
places where there are no monitoring stations in Turkey.
ACKNOWLEDGEMENTS
We would like to express our gratitude to the Republic of
Turkey Ministry of Forestry and Water Affairs (Turkish
State Meteorological Service) personnel, providing us
every kind of facilities on obtaining the meteorological
data, and to the Scientific and Technological Research
Council of Turkey–Bilten personnel, providing every kind
of facilities on obtaining the satellite data.
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Table IV. Error values according to meteorological station-based data.
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ELM ANN
RMSE (MJ/m2
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RMSE (MJ/m2
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Modeling of solar radiation M. ŞAHIN ET AL.
211Int. J. Energy Res. 2014; 38:205–212 © 2013 John Wiley Sons, Ltd.
DOI: 10.1002/er

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DOI: 10.1002/er