Comparison of ann and mlr models for

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Comparison of ANN and MLR models for estimating solar radiation
in Turkey using NOAA/AVHRR data
Mehmet Sßahin a,⇑
, Yılmaz Kaya b
, Murat Uyar a
a
Department of Electrical and Electronics Engineering, Siirt University, 56100 Siirt, Turkey
b
Department of Computer Engineering, Siirt University, 56100 Siirt, Turkey
Received 15 September 2012; received in revised form 12 October 2012; accepted 13 October 2012
Available online 22 October 2012
Abstract
In this paper, the estimation capacities of MLR and ANN are investigated to estimate monthly-average daily SR over Turkey. The
satellite data are used for 73 different locations over Turkey. Land surface temperature, altitude, latitude, longitude and month are
offered as the input variables for modeling ANN and MLR to get SR. Estimations of SR are evaluated with the meteorological values
by using the statistical bases. The obtained results indicated that the ANN model could achieve a satisfactory performance when com-
pared to the MLR model. Moreover, it is understood that more accurate results in estimation of SR are obtained in the use of satellite
data, rather than the use of meteorological station data. Finally, the built ANN model is used to estimate the yearly average of daily SR
over Turkey. As a result, satellite-based SR map for Turkey is generated.
Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Solar radiation; Mapping; Land surface temperature; Artificial neural network; Multiple linear regression; NOAA/AVHRR
1. Introduction
Solar energy is one of the oldest, cleanest and the most
reliable renewable energy sources in the world. It is sup-
plied from the sun in the form of solar radiation (SR).
The knowledge of SR distribution at a specific geographic
region is of great importance in diverse fields such as engi-
neering, agriculture, environment, hydrology, ecology, etc.
(Ranzi and Rosso, 1995; Lindsey and Farnsworth, 1997;
Roebeling et al., 2004; Walton et al., 2005; Benghanem
and Mellit, 2010). In particular, estimation of SR is crucial
for designing solar furnaces, interior illumination of build-
ings, modeling climate change, concentrating solar collec-
tors, sizing photovoltaic systems and site selection of
solar power plants (Samanta and Al-Balushi, 1998;
Ferriere and Rivoire, 2002; Kumar and Umanand, 2005;
Escobedo et al., 2009; Faghih and Bahadori, 2009; Martıń
et al., 2010). Although SR data are known to be very
important, providing them is not so easy because the equip-
ment needed to obtain the knowledge of SR is too expen-
sive. Unfortunately, there are not always adequate
facilities to mount viable monitoring programs for this
equipment. On the other hand, the number of such meteo-
rological stations is usually not sufficient to provide SR
data for the desired areas, especially in developing coun-
tries. This is mainly due to the cost and the difficulty of
equipment installation, maintenance and calibration
(Sozen et al., 2004; Mellit et al., 2006; Bulet and Buyukal-
aca, 2007; Senkal and Kuleli, 2009). Moreover, previous
studies have reported that sometimes the measurement
error may rise up to 25% due to calibration uncertainties,
especially when using of measurement equipment such as
pyranometers (Justus et al., 1986; Kandırmaz et al., 2004).
Although there have been several attempts to estimate
SR by using meteorological and physical parameters, the
lack of the measured atmospheric variables limits the use
0273-1177/$36.00 Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.asr.2012.10.010
⇑ Corresponding author. Tel.: +90 484 223 12 24; fax: +90 484 223 66
31.
E-mail addresses: sahanmehmet2000@yahoo.com, msahin@siirt.edu.tr
(M. Sßahin), ykaya72@hotmail.com (Y. Kaya), muratuyar1@gmail.com
(M. Uyar).
www.elsevier.com/locate/asr
Available online at www.sciencedirect.com
Advances in Space Research 51 (2013) 891–904

of many analytical procedures. These limitations force sci-
entists and researchers to use different methods in order to
provide SR data (Bocco et al., 2010). Recently, satellite
based remote sensing (RS) is a method used increasingly
by scientists for obtaining SR data. This is mainly because
it is quick and reliable in data processing, practical to
obtain data from inaccessible or remote regions (mountain-
ous and rural), easy to handle with the computer, etc.
(Cano et al., 1986; Kant and Badarinath, 2000). In addi-
tion, the previous studies have clearly indicated that at
ground level SR can be estimated within the acceptable
error limits that are better than 10%, by using satellite data
(Cano et al., 1986; Diabate´ et al., 1989; Kandırmaz et al.,
2004).
In the recent years, the soft computing approaches such
as artificial neural networks (ANNs) have been used as an
alternative to previous methods such as statistical, analytic
and empirical methods for estimating SR. ANN provides a
computationally efficient way of determining an empirical,
possibly nonlinear relationship between a number of inputs
and one or more outputs. It has been applied for modeling,
identification, optimization, prediction and control of com-
plex systems (Li and Jiang, 2010). ANNs have been used in
SR estimation studies for locations with different latitudes
and climates such as Saudi Arabia (Mohandes et al., 1998),
Spain (Lopez et al., 2005), Uganda (Mubiru and Banda,
2007), China (Jiang, 2008) and Turkey (Koca et al.,
2011). They modeled SR by using various internal topolo-
gies, different input variables (geographical and climatolog-
ical) and several time scales (monthly, daily and hourly). In
these studies, the measurement of basic ground variables is
typically used for estimating SR. Although the methods
used for obtaining the ground data have good performance
for estimating SR, they are incapable for mountainous or
deserts where the input variables do not exist.
Also, there are several studies using satellite data for
estimating SR. These can be briefly summarized in the fol-
lowing discussions. Sßenkal and Kuleli estimated SR by
using ANN for analyzing satellite data. They showed that
root mean square error (RMSE) between the estimated and
ground values for monthly average daily sum analyzed by
ANN and physical method values have been found to be
3.94 MJ/m2
and 5.37 MJ/m2
for testing data, respectively
(Sßenkal and Kuleli, 2009). In another study, Sßenkal esti-
mated SR using a different architecture of ANN with the
RMSE of 6.59% (Sßenkal, 2010). Rahimikhoob tested
ANN for estimating SR as a function of air temperature
data in a semi-arid environment. The study demonstrated
that modeling of daily SR through the use of the ANN
technique gave better estimations than the empirical tech-
niques. For the comparison between observed and esti-
mated SR, RMSE and R2
for the tested data using the
proposed ANN model were 2.534 MJ/m2
and 0.889,
respectively (Rahimikhoob, 2010). Lu et al. (2011) used a
simple algorithm with ANN modeling and proposed to
explore the non-linear physical relationship between daily
ground SR measurements and Multi-Functional Transport
Satellite (MTSAT) on all-channel observations in an effort
to fully exploit information contained in both data sets.
The daily and monthly-average SR obtained from the
ANN model had an average bias of À0.33 MJ/m2
(À2.4%) and À0.41 MJ/m2
(À2.9%), an average RMSE
of 2.85 MJ/m2
(20.4%) and 1.63 MJ/m2
(11.4%) and an
average coefficient of determination of 0.85 and 0.92,
respectively. Qin et al. (2011) utilized the ANN to build
the mathematical relationship between measured
monthly-average daily SR and several remote sensing
products available for the public, including Moderate Res-
olution Imaging Spectroradiometer (MODIS) monthly
averaged land surface temperature (LST), the number of
days in which the LST retrieval was performed in one
month, MODIS enhanced vegetation index, Tropical Rain-
fall Measuring Mission (TRMM) satellite monthly precip-
itation. After training, validation results indicated that the
ANN-based method presented in the study could estimate
monthly-average daily SR at a spatial resolution of about
5 km with high accuracy.
As stated previously, it is very important to estimate
accurate SR data which is used for many purposes. In lit-
erature, some studies that used satellite data were studied
with a limited amount of data from only certain locations
of the relevant region. Accordingly, solar energy potentials
of the relevant locations have been reported. Furthermore,
the performances of the method proposed in these studies
were tested with these limited data. It may reduce validity
and reliability of estimation results of the relevant region
of which solar energy potential was estimated. In addition,
previous studies indicate that there is a limited amount of
satellite based studies for estimating SR and there is still
a need for this kind of studies, especially in countries with
high SR level such as Turkey.
In this paper, SR estimation is obtained for Turkey,
which is located in hot climate band and which is highly
affected from SR. Furthermore, the performance of ANN
and multiple linear regression (MLR) methods, which have
been used widespread in the recent years, are evaluated
comparatively for estimating SR as a function of LST. In
the study, National Oceanic and Atmospheric Administra-
tion/Advanced Very High Resolution Radiometer
(NOAA/AVHRR) satellite data and meteorological data
from 2000 to 2002 at 73 locations covering approximately
the entire areas of Turkey are used for modeling and test-
ing ANN and MLR. Here, the meteorological data are
used only to assess the performance of the study. Whereas,
in both approaches five parameters such as satellite-esti-
mated LST, altitude, latitude, longitude and months of
year are selected as input parameters, SR is determined
as output parameter. While MLR and ANN models are
formed, the dataset is divided into three parts (%60–
%20–%20): 43 locations for training, 15 locations for vali-
dation and the remaining 15 locations for testing. The per-
formance of MLR and ANN models for both data sets are
evaluated statistically in order to show the accuracy of SR
estimation in these testing locations after the training. The
892 M. Sßahin et al. / Advances in Space Research 51 (2013) 891–904

obtained results indicate that this study has a potential to
provide important information about solar energy poten-
tial of Turkey.
2. Study area and data sources
When a study concerning the estimation of SR potential
of a location will be carried out, using the parameters of a
larger scale of the studied area is rather important in get-
ting accurate estimations. In this study, the 73 locations
over Turkey are chosen as study area. Their geographic
information such as altitude, latitude and longitude are
presented in Table 1.
This study is realized by using two separate datasets.
They are NOAA/AVHRR satellite data and meteorologi-
cal data. The meteorological data are used only to assess
the performance of the study. Meteorological data, a total
of 3-years (2000–2002), are obtained from Turkish State
Meteorological Service (TSMS) while satellite data are
obtained from Scientific and Technological Research
Council of Turkey-Bilten, simultaneously.
To build an effective estimation model, the common
practice is to evaluate the data in three parts: the training,
validation, and test dataset (Yao and Liu, 1997). Training
set is used to find the relationship between a set of depen-
dent and independent variables whereas the validation set
is often used to find the optimal number of hidden units
or determine a stopping point for ANN. In test dataset,
the performance of a fully-trained model is evaluated on
a set of samples which not used in training and validation
stage.
In Fig. 1, the geographical locations of training, valida-
tion and testing sites used in this study are illustrated. As
shown in Fig. 1, these locations, covering approximately
the whole of Turkey are distributed to the seven geograph-
ical regions. Moreover, in order to check the generalization
capability of the constructed models, the testing locations
contain the different land cover types such as seaside,
semi-desert, mountainous and forests (see Fig. 1).
To construct a better functional relationship by ANN or
MLR between input variables and target variable, the effec-
tive input variables must be determined. As aforemen-
tioned, RS product is used in input vector to train the
ANN and the MLR for building their mathematical rela-
Table 1
Geographic information from 73 locations over Turkey.
City Altitude (m) Latitude (°N) Longitude (°E)
Adana 27 37.03 35.21
Adıyaman 672 37.45 38.17
Ag˘rı 1632 39.43 43.03
Aksaray 961 38.23 34.03
Aksßehir 1002 38.21 31.25
Amasya 411 40.39 35.51
Ankara 891 39.57 32.53
Antakya 100 36.12 36.10
Antalya 64 36.42 30.44
Artvin 628 41.11 41.49
Aydın 56 37.51 27.51
Balıkesir-Go¨nen 37 40.06 27.39
Batman 310 37.35 41.07
Bilecik 539 40.09 29.59
Bingo¨l 1177 38.52 40.30
Birecik 345 37.01 35.57
Bitlis 1573 38.22 42.06
Burdur 957 37.43 30.18
Bursa 100 40.13 29.00
Ç anakkale 6 40.08 26.24
Ç orum 776 40.33 34.58
Diyarbakır 674 37.54 40.12
Denizli 425.29 37.47 29.05
Develi 1180 38.23 35.30
Dinar 864 38.04 30.10
Do¨rtyol 28 36.51 36.13
Du¨zce 145.67 40.50 31.10
Edirne 49 41.41 26.33
Elazıg˘ 989.75 38.39 39.15
Ergani 1000 38.17 39.46
Erzincan 1218.22 39.45 39.30
Erzurum 1758.18 39.57 41.40
Gaziantep 854 37.03 37.21
Gu¨mu¨sßhane 1219 40.28 39.28
Hakkaˆri 1727.74 37.34 43.44
Ig˘dır 858 39.55 44.03
Isparta 996.88 37.45 30.33
_Iskenderun 3.59 36.35 36.10
_Istanbul-Go¨ztepe 32.98 40.58 29.05
_Izmir 28.55 38.23 27.04
Kahramanmarasß 572.13 37.36 36.56
Karaman 1023.05 37.12 33.13
Karatasß 22 36.34 36.23
Kars 1775 40.37 43.06
Kastamonu 800 41.22 33.47
Kayseri 1092 38.43 35.29
Kırsßehir 1007.17 39.09 34.10
Kilis 650 36.42 37.06
Kocaeli-_Izmit 76 40.46 29.56
Konya 1030 37.52 32.28
Ku¨tahya 969.25 39.25 29.58
Ku¨tahya-Tavsßanlı 833 39.33 29.30
Malatya 947.87 38.21 38.13
Marmaris 16.19 36.51 28.15
Mersin 3.4 36.48 34.38
Mug˘la 646 37.13 28.22
Musß 1322.76 38.41 41.29
Nig˘de 1210.5 37.58 34.41
Ordu 4.1 40.59 37.54
Rize 8 41.02 40.30
Samsun 4 41.21 36.15
Siirt 895.54 37.55 41.57
Silifke 15.01 36.23 33.56
Sinop 32 42.02 35.50
Sivas 1285 39.45 37.01
Sßanlıurfa 547.18 37.09 38.47
Tokat 607.9 40.18 36.34
Trabzon 30 40.59 39.45
Tunceli 980 39.07 39.33
Van 1670.58 38.28 43.21
Yalova 3.81 40.40 29.17
Yozgat 1298.33 39.49 34.48
Zonguldak 135.35 41.27 31.38
M. Sßahin et al. / Advances in Space Research 51 (2013) 891–904 893

tionship with measured SR. However, these RS products
must include information that may influence SR. LST is
one of the key parameter in determining the exchange
energy and the matter between the Earth’s surface and
atmosphere. At the same time, it is an important measure-
ment in energy-balance applications and thus has a quite
large influence on SR at the earth’s surface (Qin et al.,
2011). In addition, it was often used as input parameter
in previous studies (Sßenkal, 2010; Qin et al., 2011). Thus,
NOAA’s monthly averaged LSTs are selected as one part
of inputs to train ANN and MLR. The entire input vector
to ANN is represented as X = [LST, Al, Lt, Ln, M]T
in
which Al (m), Lt (°), Ln (°) and M (months) denotes alti-
tude, latitude, longitude and the number of months, respec-
tively. The output vector Y includes monthly-average daily
SR (MJ/m2
).
3. Methodology
3.1. Estimation land surface temperature by using NOAA/
AVHRR
The channels 4 and 5 of Advanced Very High Resolu-
tion Radiometer (AVHRR) are used widely for deriving
surface temperature (Kant and Badarinath, 2000).
AVHRR is a space-borne sensor embarked on the
National Oceanic and Atmospheric Administration
(NOAA) family of polar orbiting platforms. AVHRR
instruments measure the reflectance of the Earth in five rel-
atively wide spectral bands. The first two are centered on
the red (0.580–0.680 lm) and near-infrared (0.725–
1.100 lm) regions, the third one is located around 3.55–
3.93 lm, and the last two sample the thermal radiation
emitted by the planet, around 10.30–11.30 lm (channel 4)
and 11.50–12.50 lm (channel 5), respectively (Key and
Intrieri, 2000).
In order to obtain the LST value, images of the channels
4 and 5 of AVHRR need to be transformed. An approach
based on the differential absorption in two adjacent infra-
red channels, called the “Split-Window” technique, is used
for determining LST (Price, 1984). Lots of algorithms have
been propounded by researchers (Price, 1984; Becker and
Li, 1990; Vidal, 1991; Sobrino et al., 1994; Coll et al.,
1994; Katsiabani et al., 2009; Sßahin and Kandırmaz,
2010; Zaksˇek and Osˇtir, 2012). These studies indicated that
it is possible to retrieve LST at a reasonable accuracy
(RMSE of 1–3 K) from current operational and research
satellite-borne visible/infrared radiometers.
In this study, split-window technique proposed by Price
is used to get LST (Price, 1984). The technique assumes
that atmospheric attenuation (due to mostly atmospheric
water vapor) is greater in channel 5 than in channel 4
and that the difference in measured radiance between the
two channels increases with increasing water vapor (Price,
1984). Firstly, raw data of NOAA 12-14-15/AVHRR
which had no cloud, are translated into Level-1B format
by using Quorum Software and in second step, brightness
temperature of channel-4 and channel-5 (range 10.3–
11.3 lm and range 11.5–12.5 lm, respectively) are obtained
from Level-1B data by using Envi 4.3 image-processing
programmer. Then, radiometric and geometric calibrations
are applied to the images to correct the deficiencies and
flaws in the imaging sensors of the satellite.
As it is known, basic split-window technique is written
as given in Eq. (1):
Ts ¼ ½T4 þ aðT4 À T5Þ þ bŠ ð1Þ
where coefficient a and b account for atmospheric condi-
tions (related to spectral radiance and transmission) and
Fig. 1. Distribution of stations used for training, validation and testing.

surface emissivity respectively. However, linear empirical
formulations do not always hold. Hence, water vapor
dependence is subsequently incorporated in a nonlinear
quadratic equation (Coll et al., 1994; Francßois and Ottle,
1996; Katsiabani et al., 2009; Sßahin and Kandırmaz,
2010; Zaksˇek and Osˇtir, 2012). Coefficient a in Eq. (1) is gi-
ven as follows:
a ¼
a5
a4

À 1
À1
ð2Þ
where a5/a4 is determined from DT5 (DT4)À1
(spatial varia-
tions of brightness temperature in channels 5 and 4 of
AVHRR) for small area under study. The value of a5/a4
is calculated to be 1.30, a = 3.33 and b is linked to differ-
ence of emissivity De ¼ e4 À e5, and e depends on e4 and
e5 as in the formulation e ¼ e4þe5
2
, where e4 and e5 are emis-
sivities of channel 4 and channel 5; T4 and T5 are brightness
temperatures of channel 4 and channel 5 of NOAA/
AVHRR, respectively (Dash et al., 2002). e4 and e5 are
the surface emission coefficients which are estimated from
atmospherically corrected and normalized difference vege-
tation index (NDVI) using the equations given by Valor
and Casselles for channel 4 and channel 5, respectively (Va-
lor and Casselles, 1996).
e4 ¼ 0:9897 þ 0:029 lnðNDVIÞ ð3Þ
e4 À e5 ¼ 0:01019 þ 0:01344 lnðNDVIÞ ð4Þ
where NDVI is a simple graphical indicator that can be
used to analyze RS measurements and assess whether the
target being observed contains live green vegetation or
not. Live green plants absorb SR in the photo-synthetically
active radiation spectral region, on which they use as a
source of energy in the process of photosynthesis. Leaf cells
have also evolved to scatter (i.e., reflect and transmit) SR in
the near-infrared spectral region (which carries approxi-
mately half of the total incoming solar energy) because
the energy level per photon in that domain (wavelengths
longer than about 700 nm) is not sufficient to be useful to
synthesize organic molecules. A strong absorption at these
wavelengths would only result in over-heating the plant
and possibly damage the tissues. Hence, live green plants
appear relatively dark in the photo-synthetically active
radiation and relatively bright in the near-infrared (Gates,
1980). In contrast, clouds and snow tend to be rather bright
in the red (as well as other visible wavelengths) and quite
dark in the near-infrared. The pigment in plant leaves,
chlorophyll, strongly absorbs visible light (from 0.4 lm to
0.7 lm) for use in photosynthesis. The cell structure of
the leaves, on the other hand, strongly reflects near-infra-
red light (from 0.7 lm to 1.1 lm). The more leaves a plant
has, the more these wavelengths of light are affected. Since
early instruments of earth observation, such as NOAA’s
AVHRR, acquired data in visible and near-infrared, it is
natural to exploit the strong differences in plant reflectance
to determine their spatial distribution in this satellite
images. The NDVI is calculated from these individual mea-
surements as follows:
NDVI ¼
NIR À VIS
NIR þ VIS
ð5Þ
where VIS and NIR stand for the spectral reflectance mea-
surements acquired in the visible (red) and near-infrared re-
gions, respectively (Goward et al., 1991; Santos and Negri,
1997). The last form of equation is as follows:
Ts ¼ ½T4 þ 3:33ðT4 À T5ÞŠ
5:5 À e4
4:5

À 0:75T 5De ð6Þ
3.2. Artificial neural network
Artificial neural network (ANN) is a mathematical
model that tries to simulate the structure and/or functional
aspects of biological neural networks. It consists of an
interconnected group of artificial neurons and it processes
information using a connection to approach the computa-
tion. In most cases an ANN is an adaptive system that
changes its structure based on external or internal informa-
tion that flows through the network during the learning
phase. They can be used for modeling complex relation-
ships between inputs and outputs or finding patterns in
data. Basically, the advantages of ANNs are that they
are able to represent both linear and nonlinear relation-
ships and learn these relationships directly from data
(Haykin, 1999). ANNs have been trained to overcome
the limitations of the conventional approaches to solve
complex problems (Kalogirou, 2000).
The use of the ANNs for modeling and prediction pur-
poses has been increasingly becoming popular in the last
decades. Researchers have been applying the ANN method
successfully in various fields of mathematics, engineering,
medicine, economics, meteorology, psychology, neurology,
in electrical and thermal load predictions, in adaptive and
robotic control and so on (Ç am et al., 2005; Sßahin, 2012;
Sßahin et al., 2012). An ANN modeling is composed of an
input layer, one or more hidden layer, and an output layer.
Fig. 2. The typical ANN architecture.

Generally, the number of neuron in the input layer is equa-
ted to the input number in the problem while the number of
neuron in the output layer is equated to the desired output
number. The number of hidden layer and the neuron num-
ber in the hidden layer are determined by trials. The cells in
the input layer are sent to the next layer without making
any changes on the input. In the hidden layer, inputs and
relevant weights are multiplied, and then the results are
transmitted to transfer function (Yongjae and Sehun,
2005). The typical ANN architecture can be seen in Fig. 2.
Neurons in each of the layer and weights that connect
these to one another are shown in Fig. 2. The items shaped
like spheres represent neurons while lines that bind neurons
to one another represent for weights. One of most impor-
tant issue in an ANN is the bindings that provide data
transmit between neurons. A binding that transmits data
from a neuron to another one has also a weight value.
G(x) is a summation function, and calculates the exact
input that comes to a neuron. The input, by multiplying
with variables and weight coefficients builds up input for
G(x) summation function. The basic structure of an artifi-
cial neuron is shown in Fig. 3.
Mathematical statement of an artificial neuron can be
written as;
yi ¼F ðGðxÞÞ¼F
Xn
i¼1
wijxj ÀQi
!
; xi ¼ðx1;x2;...xnÞ ð7Þ
where x = {x1,x2,x3 . . .xn} is an input variable to be pro-
cessed. On the other hand, w = {w00,w01,. . .wij} is weight,
and it shows the importance of a data incoming to neuron
and the impact on the neuron (Karem et al., 2008). The val-
ues of the weights can change at the process of training. Qi,
represents for threshold value whereas F(.) is activation
function. An activation function takes the neuron input va-
lue and produces a value which becomes the output value
of the neuron. A neuron is connected to other neurons
via its input and output links. Each incoming neuron has
an activation value and each connection has a weight asso-
ciated with it. The neuron sums the incoming weighted val-
ues and this value is input to an activation function. The
output of the activation function is the output from the
neuron. There are different activation functions such as sig-
moid, tangent sigmoid, sin, and radial basis. In ANN, all of
the neurons may have the same or different activation func-
tions. Especially, many ANN models, to be able to make
the calculations easier, require activation functions of
which derivatives can be taken. Type of activation function
is decided in consequence of the user trials.
There are many types of ANN architectures for various
applications in the literature. Radial basis function net-
works and multi-layer perceptron are the examples of
feed-forward networks. However, MLP is the simplest
and the most commonly used ANN architecture for predic-
tion (Sozen and Akcayol, 2004). ANN architecture used in
this study is a multilayer feed-forward network with a sin-
gle hidden layer, as shown in Fig. 4. The model composes
of input layer, hidden layer and one output layer.
As aforementioned, there is no mathematical formula to
determine type of the activation function and the number of
optimum neuron in the hidden layer of ANN. Thus, type of
activation function and the number of neuron in the hidden
layer must be usually decided after training of network. In
this study, to be able to obtain the relatively optimum net-
work model, the number of neuron in the hidden layer is
changed between 2 and 50 in step of 2 and the different con-
figurations according to type of activation functions are
tested. At the end of the 25 training runs, the best perfor-
mance which is measured according to RMSE is obtained
from ANN configuration in Table 2. As can be seen, the
learning algorithm is the Levenberg–Marquardt. The acti-
vation function of the model in the hidden layer is tansig,
while the activation function in the output layer is linear.
Furthermore, there are 5 neurons in the input layer of
ANN, 26 in the hidden layer, and 1 in the output layer.
3.3. Multiple linear regression
The analysis of multiple linear regression (MLR) is a
statistical method that examine cause-effect relationships
between dependent and independent variables. In MLR,
the relationship between input variable more than one (x1
,x2,. . .xn) and a dependent variable (y) is examined. The
regression function that will be used here is defined as
follow:
x1
x2
xn
xn-1
∑
w1
w2
wn-1
wn
Synaptic weightsInputs
∑ −= F(G(x)) y
y=1/[1+exp(-G(x))]
Activation function
Q
Processing element
Output
Fig. 3. The basic model of an artificial neuron.

y ¼ b0 þ b1x1 þ b2x2 þ Á Á Á þ bnxn ð8Þ
where it is accepted that each independent variable has a
linear relationship with a dependent variable (Civelekoglu
et al., 2008).
The functional connection between dependent and inde-
pendent variable can be stated with matrix form as below.
Y ¼ Xb þ e ð9Þ
where Y is an output variable vector of size n Â 1; X is an
input variable matrix of size n Â (p + 1); b is a coefficient
vector of size (p + 1) Â 1 and e is an error vector of size
n Â 1. According to Eq. (9), a variable multi-linear of p
regression can be written as below;
Y 1
Y 2
Á
Y n
2
6
6
6
4
3
7
7
7
5
¼
1 X11 Á X1p
1 X21 Á X2p
Á Á Á Á
1 Xn1 Á Xnp
2
6
6
6
4
3
7
7
7
5
b1
b2
Á
bn
2
6
6
6
4
3
7
7
7
5
þ
e1
e2
Á
en
2
6
6
6
4
3
7
7
7
5
ð10Þ
b regression parameter coefficients in matrix can be
showed as below;
b ¼ ðX0
XÞÀ1
X0
Y ð11Þ
where b regression coefficients are obtained through least
square method (Apaydın et al., 1994; O¨ zdamar, 2004).
3.4. Performance criteria
In this study, the estimation performances of the both
models (ANN and MLR) are tested using the following
statistical error criteria: root mean square error (RMSE),
mean bias error (MBE), and coefficient of determination
(R2
). The two models are compared on the basis of statis-
tical error criteria. The accuracy and the consistency of
SR estimation for the two methods are determined by using
these criteria. They are defined by the following equations
(Ma and Iqbal, 1983; Akinoglu and Ecevit, 1990; Bakirci,
2009):
RMSE ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
n
Xn
i¼1
ð^Y i À Y iÞ2
s
ð12Þ
MBE ¼
1
n
Xn
i¼1
½^Y i À Y iŠ ð13Þ
R2
¼
Pn
i¼1ðY i À Y iÞ
2
À
Pn
i¼1ðY i À ^Y iÞ
2
Pn
i¼1ðY i À Y iÞ2
ð14Þ
where, Y is the actual SR value; Y is the mean of actual SR
value; ^Y is the estimated SR value and n is the total number
of observations. The MBE provides information on the
long-term performance of a model. A positive MBE repre-
sents an overestimation while a negative MBE shows an
underestimation. The RMSE provides information on the
short-term performance of a model. The value of RMSE
is always positive, representing zero in the ideal case (Ma
and Iqbal, 1983). The R2
can be used to determine the lin-
ear relationship between the measured and estimated val-
ues (Bakirci, 2009). For ideal data modeling, RMSE and
MBE should be closer to zero, but value of R2
should ap-
proach to 1 as closely as possible.
4. Results and discussion
4.1. Estimation of land surface temperature
As aforementioned, LST considered as an important
input parameter should be estimated to get SR. In this
way, the data of NOAA 12-14-15/AVHRR are initially
converted into Level-1B format that can be recognized by
Image Processing Programs via Quorum software. Then,
radiometric and geometric editing of the images in the for-
mat of Level-1B is done by employing Envi 4.3 and Idrisi
image processing programs. The prime factor in determin-
ing LST is the value of brightness temperature. The bright-
ness temperatures of the 4th and 5th channels of the images
are acquired once again through Envi 4.3 and Idrisi Andes
image processing programs. Another factor that is neces-
sary to calculate LST is the value of NDVI. In Eq. (5),
1st and 2nd channels of NOAA 12-14-15/AVHRR are
employed to get the stated values, and NDVI images are
obtained. Then, the value of emissivity for the 4th and
5th channels of the satellite is achieved by using NDVI
image in Eqs. (3) and (4). By adding e4 and e5 values, which
were calculated before, to De = e4 À e5 and e ¼ e4þe5
2
for-
mula, the emissivity difference and mean of emissivity of
the 4th and 5th channels are acquired, respectively. Subse-
quently, the maps of LST are obtained according to Eq.
(6). LST obtained at 03.41 pm with local time on 11 August
2002 through split window algorithm is shown in Fig. 5.
As can be seen in Fig. 5, most of the LST over Turkey
has values between 302 K and 314 K. It is understood from
the map that Central Anatolia and South Eastern Anatolia
has a very high temperature at the stated hour. Moreover,
the temperature in East Black Sea region has a temperature
between 281 K and 296 K. Similarly, 47 monthly average
Altitude
Latitude
Longitude
Months
LST
Solar radiation
1
n
Fig. 4. ANN architecture used in this study.

LST satellite images are totally acquired providing that
least one satellite image per month that based on split win-
dow algorithm for every year from 2000 through 2002.
Over the relevant images, LST values are obtained by
using the coordinates of 73 locations stated in Table 1.
By using Eqs. (12)–(14), 2628 LST values obtained via
satellite are compared to those taken from Turkish State
Meteorological Service. As a result of the comparison,
R2
, MBE and RMSE values are found to be 0.940,
0.339 K and 2.730 K, respectively. And also, all of them
are shown in Fig. 6.
In the previous studies, LST was estimated for various
regions of the world using satellite data. It is emerged that
RMSE range is between 1 K and 3 K (Price, 1984; Becker
and Li, 1990; Vidal, 1991; Sobrino et al., 1994; Coll
et al., 1994; Katsiabani et al., 2009; Sßahin and Kandırmaz,
2010; Zaksˇek and Osˇtir, 2012). As a result, it is shown that
the results of this study are in good agreement with the lit-
erature because the value of RMSE is found to be 2.73 K.
4.2. Estimation of solar radiation
As mentioned in Section 2, this study is realized with
two diﬀerent datasets, called DS1 and DS2. Whereas
LST, which used as input in DS1, is obtained through
NOAA/AVHRR satellite, LST values of the other one
(DS2) are obtained through meteorological (ground) mea-
surements, which are used for evaluating overall perfor-
mance of the study. The rest of input variables such as
altitude, latitude, longitude and month are common vari-
ables in two data sets. In other word, while LST, altitude,
latitude, longitude and month are used as input, SR is
Table 2
ANN architecture and training parameters.
Architecture The number of layers 3
The number of neuron on
the layers
Input: 5, Hidden: 26,
Output: 1
The initial weights and
biases
Random
Activation functions Hidden: tansig, Output:
linear
Training
parameters
Performance function RMSE
Maximum validation
failure
5
Learning rule Levenberg–Marquardt
back-propagation
Learning rate 0.5
Moment constant 0.99
Performance goal 1EÀ08
Fig. 5. LST map depending on split window algorithm.
250 260 270 280 290 300 310 320 330
250
260
270
280
290
300
310
320
330
Satellitevalues(K)
Fig. 6. The comparison of LST values obtained through split window
algorithm with meteorological values.

obtained from the output. Firstly, DS1 dataset from 2000
to 2002 at 73 locations is used for modeling and testing
ANN. This dataset is split into three parts (60%–20%–
20%): 43 locations for training, 15 locations for validation,
and the remaining 15 locations for testing. The first and
second parts (1548 input/output pairs for training) and
540 input/output pairs for validation) are used to select
the best model whereas remaining part (540 input/output
pairs for testing) is reserved to test the estimation accuracy
of methods in these unseen locations after the training.
Here, the main purpose of a validation dataset is to prevent
overfitting by measuring the error with respect to this inde-
pendent data which is not used in training. Accordingly,
when the chosen error of the validation dataset is lower
than its value in the previous iteration, the training of the
network is maintained; otherwise, the training is ended.
In this way, the best ANN configuration for DS1 is
obtained (see Table 2). After training process, a compari-
son is performed between the estimated SR and the mea-
surement ones at 15 test locations, which is considered as
unseen locations. Similarly, same data set (DS1) which is
used for modeling ANN is also used to build MLR model.
Figs. 7 and 8 show the estimation results of the DS1 for
ANN and MLR. As seen in Fig. 7(c), for overall of 15 loca-
tions, ANN model gives good prediction performance with
the lowest RMSE of 2.018 MJ/m2
, MBE of À0.213 MJ/m2
,
and highest R2
of 0.913, which is better than MLR model.
In addition, a comparison is performed between the
estimated SR and the measured ones at the training and
validation datasets in order to examine the training perfor-
mance. Their results are also illustrated in Figs. 7(a) and (b)
and 8(a) and (b). As seen, the error rates of training and
0 5 10 15 20 25 30
0
5
10
15
20
25
30
R2= 0.913
MBE = -0.213
RMSE = 2.018
0 5 10 15 20 25 30
0
5
10
15
20
25
30
R2 = 0.901
MBE = 0.282
RMSE = 2.234
0 5 10 15 20 25 30 35
0
5
10
15
20
25
30
35
R2 = 0.946
MBE = -0.167
RMSE = 1.554
Estimation(MJm-2)
N = 540 N = 540N = 1548
a b c
Fig. 7. Comparison between ANN model estimation and (a) measurements at 43 training locations, (b) measurements at 15 validation locations and (c)
measurements at the rest 15 training locations.
5 10 15 20 25 30
5
10
15
20
25
30 R2 = 0.798
MBE= -0.509
RMSE= 3.069
Estimation(MJm-2)
0 5 10 15 20 25 30
0
5
10
15
20
25
30 R2= 0.769
MBE = 0.547
RMSE= 3.334
0 5 10 15 20 25 30
0
5
10
15
20
25
30
R2= 0.760
MBE= 0.581
RMSE= 3.259
N = 540 N = 540N = 1548
a b c
Fig. 8. Comparison between MLR model estimation and (a) measurements at 43 training locations, (b) measurements at 15 validation locations and (c)
measurements at the rest 15 testing locations.

validation dataset are very close to those from test set. It
proves that validation dataset used for early stopping can
reduce the overfitting effect.
The above analysis may not guarantee that the built
models can be used to estimate SR on the desired area.
Thus, the functional relationship between input parameters
0 5 10 15 20 25 30
0
5
10
15
20
25
30
R2 = 0.656
MBE = 0.698
RMSE = 4.031
N = 540
0 5 10 15 20 25 30
0
5
10
15
20
25
30
R2 = 0.906
MBE = 0.262
RMSE = 2.129
N = 540
Estimation(MJm-2)
a b
Fig. 9. The results at 15 testing locations for DS2 (a) Comparison between ANN model estimation and measurements, (b) Comparison between MLR
model estimation and measurements.
0 5 10 15 20 25 30 35
0
10
20
30
40
50
SR(MJm-2)
ANN
MLR
Measurement
0 5 10 15 20 25 30 35
0
10
20
30
40
50
ANN
MLR
Measurement
0 5 10 15 20 25 30 35
0
10
20
30
40
50
ANN
MLR
Measurement
0 5 10 15 20 25 30 35
0
10
20
30
40
SR(MJm-2)
0 5 10 15 20 25 30 35
0
10
20
30
40
0 5 10 15 20 25 30 35
0
10
20
30
40
0 5 10 15 20 25 30 35
0
10
20
30
40
SR(MJm-2)
0 5 10 15 20 25 30 35
0
10
20
30
40
0 5 10 15 20 25 30 35
0
10
20
30
40
0 5 10 15 20 25 30 35
0
10
20
30
40
SR(MJm-2)
0 5 10 15 20 25 30 35
0
10
20
30
40
0 5 10 15 20 25 30 35
0
10
20
30
40
0 5 10 15 20 25 30 35
0
10
20
30
40
SR(MJm-2)
0 5 10 15 20 25 30 35
0
10
20
30
40
0 5 10 15 20 25 30 35
0
10
20
30
40
a b c
Time period from 2000 to 2002 Time period from 2000 to 2002 Time period from 2000 to 2002
d e f
g h i
j k l
m n o
Fig. 10. Individual results at each testing locations. They are Adana, Ankara, Antalya, Balıkesir, Bitlis, Ç orum, Du¨zce, Erzincan, _Izmir, Kayseri,
Malatya, Mug˘la, Sßanlıurfa, Yalova, Rize from (a) to (o), respectively.

of DS1 and SR must be verified by comparison with those
obtained from DS2. For this purpose, the SR estimation
results from DS1 are also compared with those obtained
from DS2. The estimation performances of the both mod-
els (ANN and MLR) are presented in Fig. 9. As shown in
Fig. 9(a), RMSE, MBE and R2
values obtained from ANN
model for DS2 are 2.129 MJ/m2
, 0.262 MJ/m2
and 0.906,
respectively. However, they are 4.031 MJ/m2
, 0.698 MJ/
m2
and 0.656 for MLR. As a result, SR estimations based
on DS1 (satellite observations) are in good agreement with
SR estimations based on DS2 (ground measurements)
though the results obtained from DS1 have an appreciable
improvement than those obtained from DS2. In addition,
the comparison results showed that ANN model gave bet-
ter results than MLR model for DS2.
Moreover, the results of this study are compared with
those of the previous SR estimation studies in the literature
so that the validity of the results and effectiveness of the
study could be assessed. The papers of Lefevre et al.
(2007), Yeom et al. (2008), Sßenkal and Kuleli (2009) and
Lu et al. (2011) are selected for the comparison because
of including satellite records of monthly-average SR using
ANN. In the previous studies, it is seen that the values of
RMSE which is one of the performance assessment criteria
are in the range of 1.63–3.94 MJ/m2
. In this study, the
value of RMSE is found to be 2.018 MJ/m2
when DS1 is
applied as input to ANN; whereas the same value is
3.334 MJ/m2
by MLR. As can be understood from the
error statistics, this study is in good agreement with other
studies in the literature although the built ANN model
through DS1 provides better results than those of Lefevre
et al. (2007), Yeom et al. (2008) and Senkal and Kuleli
(2009) studies, which their RMSE values are 2.16 MJ/m2
,
2.89 MJ/m2
and 3.94 MJ/m2
, respectively.
In the above types of case studies, distribution of SR
over Turkey was performed through all of test locations.
In other case, the estimation accuracy of SR time series
for each test location is separately evaluated on basis of
statistical error criteria by using only DS1. The acquired
results are presented in Fig. 10 and the error statistics are
also comparatively given in Table 3. As seen in Fig. 10
and Table 3, ANN method exhibits overall stronger retrie-
val ability than MLR method at each testing locations. At
nine locations (Ankara, Balıkesir-Go¨nen, Ç orum, Du¨zce,
Table 3
Estimation performance of two methods at each testing locations for DS1.
Site ANN MLR
RMSE (MJ/m2
) MBE (MJ/m2
) R2
RMSE (MJ/m2
) MBE (MJ/m2
) R2
Adana 2.089 1.462 0.942 3.093 1.929 0.850
Ankara 1.361 À0.544 0.966 2.482 À1.351 0.905
Antalya 2.214 1.318 0.946 4.013 1.980 0.773
Balıkesir-Go¨nen 1.459 À0.426 0.951 2.655 0.064 0.845
Bitlis 2.934 À2.369 0.936 3.456 À2.533 0.885
Ç orum 1.299 0.456 0.966 2.169 À0.037 0.884
Du¨zce 1.633 À0.775 0.941 3.655 0.259 0.756
Erzincan 1.197 0.356 0.976 2.703 À0.021 0.878
_Izmir 3.155 2.579 0.982 5.511 3.852 0.763
Kayseri 1.416 0.056 0.955 2.032 À0.577 0.915
Malatya 1.201 0.517 0.975 2.028 0.205 0.913
Mug˘la 1.650 À1.338 0.976 2.529 À0.809 0.847
Sßanlıurfa 2.261 1.304 0.964 4.096 2.541 0.818
Yalova 1.749 0.204 0.971 2.544 0.062 0.876
Rize 3.026 À2.327 0.911 4.726 À2.216 0.606
23
12
8
16
4
0
Fig. 11. Yearly average SR map estimated by ANN model.

Erzincan, Kayseri, Malatya, Mug˘la, Yalova), SR estima-
tions are more accurate than the results obtained through
overall of 15 test locations, where RMSE was found to
be 2.018 MJ/m2
. However, it is found that the obtained
errors are slightly large at remaining locations (Adana,
Antalya, Bitlis, _Izmir, Sßanlıurfa, Rize) and biggest RMSE
value reach 3.14 MJ/m2
at _Izmir: that is, it is still an accept-
able RMSE level. It proves that ANN model can be used to
estimate SR for any location within the study region.
As shown in above case study, SR may estimate by using
meteorological station-based data with high accuracy.
However, it is impossible to estimate SR on the desired
area, where records of input variables are unavailable.
The ANN model constructed by using satellite-based data
(DS1) can be applied to estimate SR over the Turkey and
its surroundings because the input variables can be easily
provided by using satellite-based observations on the
desired area. In Fig. 11, the results are illustrated as maps
showing the yearly average of daily SR over the Turkey
and its surroundings. It is observed that high SR areas pro-
gressively expand from the southern coastal areas to the
southeastern part of the country with irregular pattern.
In the southern coastal areas of the country, most areas
receive SR in the range of 16–18 MJ/m2
whereas in the
southern inner part, SR is in the range of 12–15 MJ/m2
.
Moreover, in some locations of this area, SR is observed
slightly in the range of 18–20 MJ/m2
. In the southeast,
most areas receive radiation in the range of 16–21 MJ/m2
whereas in the southeastern inner part, SR is in the range
of 12–16 MJ/m2
. The low SR areas are in the northeastern
part of the country, where it is in the range of 6–12 MJ/m2
.
Finally, the yearly average of daily SR over country is
found to be 16.1 MJ/m2
.
5. Conclusion
In this paper, the estimation capabilities of two different
approaches are comparatively presented for estimating SR
as a function of LST over Turkey. They are ANN and
MLR models, which are also used commonly in different
areas. To test the effectiveness of the study, a number of
case studies on 73 locations covering approximately the
whole of Turkey are carried out. Two different data sets
(DS1, DS2) are used in the study. Whereas LST, which is
used as input in the first data set (DS1), is provided
through records of NOAA/AVHRR satellite, in the second
data set (DS2), LST is obtained through records of meteo-
rological station. Five independent variables such as satel-
lite-estimated LST, altitude, latitude, longitude and month
are applied as the input to ANN and MLR models, sepa-
rately. The performance of models is evaluated using
RMSE, MBE and R2
. With the use of ANN for DS1, the
values with R2
of 0.913, RMSE of 2.018 MJ/m2
and
MBE of À0.213 MJ/m2
are found. With the use of MLR,
the values with R2
of 0.769, RMSE of 3.334 MJ/m2
and
MBE of 0.547 MJ/m2
are acquired. Similarly, for DS2 data
set, R2
value of 0.906 is found on the use of ANN. In addi-
tion, RMSE and MBE values are determined as 2.129 MJ/
m2
and 0.262 MJ/m2
, respectively. For MLR, the error sta-
tistic values are R2
of 0.656, RMSE of 4.031 MJ/m2
and
MBE of 0.698 MJ/m2
. For both data sets, R2
acquired with
ANN is found higher than the result obtained through
MLR, and RMSE and MBE values are achieved lower.
In this case, it is seen that the ANN model is more success-
ful than MLR for estimating SR. Moreover, the ANN
model is applied in order to map the SR distribution over
the Turkey. The obtained map illustrates that yearly aver-
age daily SR is found to be 16.1 MJ/m2
for all areas of
Turkey.
Finally, this study has showed that the usage of satellite
based data instead of meteorological data for estimating
SR, gives more accurate results. This result is very impor-
tant because the installation of meteorological stations all
across the country and achieving consistent measurements
are hard and economically burdensome. Even if they are
founded, the distribution of the stations may not be in
the desired level because of geographical conditions.
Instead of meteorological stations, the meteorological sat-
ellites which are capable of scanning a whole district will
be more reasonable. In addition, the usage of satellite data
and ANN can help researchers develop SR distribution
maps for cities and countries. It is expected to be a poten-
tial tool for analysis and design of solar energy systems.
Acknowledgments
We would like to express our gratitude to Republic of
Turkey Ministry of Forestry and Water Affairs (Turkish
State Meteorological Service) personnel, providing us every
kind of facilities on getting the meteorological data and to
Scientific and Technological Research Council of Turkey-
Bilten personnel, providing every kind of facilities on get-
ting the satellite data.
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