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ORIGINAL ARTICLE
The prediction of meteorological variables using artificial neuralnetwork
Ahmet Erdil • Erol Arcaklioglu
Received: 29 April 2011 / Accepted: 25 September 2012 / Published online: 6 October 2012
� Springer-Verlag London 2012
Abstract Artificial neural network model had been
implemented in different areas such as industrial processes,
sciences, and business. In these days, climatic changes
have occurred. In this study, meteorological variables are
predicted using ANN model. The experimental values are
obtained from the Turkish Meteorological Center for dif-
ferent measurement stations. The prediction of the meteo-
rological values are realized, when the neural network
model have been trained and tested. Obtained results show
that the difference between estimated and measured values
is very low. The neural network models for prediction are
successfully applied to the meteorological variables.
Keywords Artificial neural networks � Meteorological
variables � Solar radiation
1 Introduction
Real-world problems are effectively modeled and solved
using artificial neural network (ANN) by easy implementa-
tion. ANN method is effectively applied to different fields
such as industrial processes, sciences, and business. One of
the most interesting applications of this method is the esti-
mation of the meteorological variable(s). Climatic condi-
tions are changed with different influence in these days. For
example, air pollution is increased, so climate change occurs
and threats the planet. The temperatures of the global aver-
age air and ocean are increased, the snow and ice are com-
monly melted, and global mean sea level has increased. The
average surface temperature of the earth has increased by
0.76 �C since 1850. Most of the warming has happened for
the last 50 years because of the human activities. According
to the study of the climate changes, if the greenhouse gas
emissions decrease, the global average temperature will rise
between 1.8 and 4.0 �C in this century, or in the worst case
scenario this value could be 6.4 �C [1]. Therefore, meteo-
rological studies will be important from this point of view.
Some of the studies about this subject are explained in
the following: Elminir et al. [2] predicted insolation data in
different spectral bands for Helwan (Egypt) monitoring
station using Levenberg optimization function. They
compared the predicted values with actual values in terms
of usual statistics. The results show that the ANN model
predicted infrared, ultraviolet, and global insulation with a
good accuracy. Mubiru and Banda [3] investigated the
possibility of developing a prediction model using artificial
neural networks (ANN). Monthly average daily global
solar irradiation on a horizontal surface for locations is
estimated in Uganda by means of weather station data
(such as sunshine duration, maximum temperature, cloud
cover) and location parameters (such as latitude, longitude
and altitude) using ANN method. They found that the
results have shown good agreement between the estimated
and measured values of global solar irradiation.
Sozen and Arcaklioglu [4] investigated the effect of
relative humidity on solar potential using artificial neural
networks. They found that the humidity has only a negli-
gible effect upon the prediction of solar potential using
artificial neural networks. Białobrzewski [5] studied the
prediction of relative air humidity using artificial neural
network with MATLAB and STATISTICA. Cadenas and
A. Erdil (&)
Engineering Faculty, Kocaeli University,
Umuttepe Campus, 41380 Kocaeli, Turkey
e-mail: [email protected]
E. Arcaklioglu
Engineering Faculty, Karabuk University,
78050 Karabuk, Turkey
123
Neural Comput & Applic (2013) 22:1677–1683
DOI 10.1007/s00521-012-1210-0
Rivera [6] studied short-term wind speed forecasting
applying the technique of artificial neural network to the
hourly time series. The developed model for short-term
wind speed forecasting demonstrated a very good accuracy
to be used by the Electric Utility Control Centre in Oaxaca
for the energy supply. Huang et al. [7] used the ANN
approach to model and predict the occurrence of dust storms
in Northwest China, by using a combination of daily mean
meteorological measurements and dust storm occurrence.
Rehman and Mohandes [8] studied the estimation of global
solar radiation in the future time domain using artificial
neural network model. Santhanam and Subhajini [9]
investigated an efficient weather forecasting system using
radial basis function neural network. They found that the
results show that proposed radial basis function neural
network is better than back-propagation neural network.
In this study, we trained two networks. Firstly, we obtained
the maximum and minimum pressures (atmospheric pressure)
and secondly solar radiation. The atmospheric pressure is
predicted using different input variables. Because the atmo-
spheric pressure and wind are both significant controlling
factors of Earth’s weather and climate, the atmospheric pres-
sure which is strongly dependent on the wind is predicted.
Pressure differences in the horizontal and vertical axis are
caused to the wind velocity. Another word, the pressure data
may give the air pollution, because the density of air will
increase with the more polluted air. Input layer selected for the
prediction of pressure consists of the following variables: lat-
itude, longitude, altitude, months, temperature, relative
humidity, and sunshine duration. The latitude affects the
temperature. Longitude determines the time. Altitude relates to
the pressure value. The months of the year relate to the evap-
oration. The pressure decreases with increasing temperature.
The relative humidity affects the temperature and temperature
affects the pressure. Finally, the density of air decrease with
increasing sunbath time and from here, the pressure decreases
with the decreasing density.
Input layer in the second network also has the following
variables: latitude, longitude, altitude, months, tempera-
tures, relative humidities, maximum, and minimum pres-
sures, which are obtained from the first network. Solar
radiation (I) value was used at the output of second ANN.
In Sect. 2, we lay out the basics of meteorology while
Sect. 3 is on the methodology of ANN application and
modeling data with network. Section 4 gives results, dis-
cussion, and conclusion.
2 Basics of the meteorology
Meteorological processes are related with the observable
weather events and can be defined as the meteorology
science. Observable weather events are influenced by the
physical variables that exist in Earth’s atmosphere. These
variables are air pressure, temperature, humidity, the gra-
dients, and interactions of each variable. The greater part of
Earth’s observed weather is found in the troposphere.
Meteorology (prediction of weather conditions) is
important for the different areas such as agriculture, air
traffic, marine, forestry, and electricity and gas companies.
In the agriculture, the farmers want to know the weather
forecast in order to do some works. The farmers also want
to dry the agricultural products in dry weather conditions.
Relative humidity in air is important for this process. Long
drying periods will damage the agricultural products. In the
air traffic, the aviation industry is strongly dependent on
the weather conditions. Many aircraft from landing and
taking off is affected by fog or low clouds. Turbulence and
atmospheric icing are also important in-flight hazards. In
the marine, wind direction and speed, wave periodicity and
heights, tides, and rainfall affect commercial and leisure
use of waterways. In the forestry, wind velocity, rainfall,
and relative humidity are important to control wildfires. In
the electricity and gas companies, the both consumption of
electricity and gas is related to the weather forecast. In
winter, the gas consumption increases with decreased air
temperature. In summer, the electricity utilization increases
with increased air temperature.
Today, many countries have the national meteorological
stations. Particularly in Turkey, many meteorological sta-
tions have been built for the weather conditions. All of the
stations are related to the Turkish State Meteorological
Service, TSMS in Turkey.
Turkey is divided into seven geographical regions.
These are the Aegean, the Black Sea, the Marmara, the
Mediterranean, Central Anatolia, Eastern, and Southeastern
Anatolia Regions. Wind energy would be effective in
Turkey because of the Turkey’s geographic location.
Humidity and warm climatic air cause the changes of
weather conditions of Turkey and most of the European
countries. In the large portion of coastal areas, climate
conditions have the typical Mediterranean, since Turkey is
surrounded by seas at three sides: Mediterranean Sea at the
south, Aegean Sea at the west, the Black sea at the north.
The prediction of atmospheric pressure is realized in this
study. Atmospheric pressure is explained as the force per
unit area exerted against a surface by the weight of air
above that surface at any given point in the Earth’s atmo-
sphere. High atmospheric pressure prevents to disperse the
emission gases to the surrounding air (CO, CO2, NOX, etc.)
in the winter months. On weather maps, high- and low-
pressure systems are valid. If the air becomes less dense as
a result of heating, the low-pressure systems are usually
produced. However, when the air cools and sinks back
down to the ground, a high-pressure system is produced.
High-pressure systems are related with clear, cool weather.
1678 Neural Comput & Applic (2013) 22:1677–1683
123
Low-pressure areas have less atmospheric mass above
their location, whereas high-pressure areas have more
atmospheric mass above their location. Similarly, as ele-
vation increases there is less overlying atmospheric mass,
so that pressure decreases with increasing elevation.
Atmospheric pressure is effective on the weather condi-
tions and climate.
3 Methodology of ANN application and modeling data
with network
ANNs have been employed successfully to solve the
complex problems in various engineering fields as a com-
putational tool. ANN can simulate operational features of
the human brain. The ANN architecture is composed of one
input layer, one output layer, and one or more hidden
layers. In the NN architecture, the layers are composed of
neurons and the neurons are the fundamental processing
element of ANN. Each input is multiplied by a connection
weight; products and biases are simply summed, then
transformed through a transfer function to generate a result,
and finally obtained output [10, 11].
The back-propagation (BP) algorithm is quite widely used
training algorithm for multi-layered feed-forward networks.
The BP algorithm basically consists of two phases. The first
one is the forward phase where the activations are propa-
gated from the input to the output layer. In the first phase,
forward phase, the activations are propagated from the input
to the output layer. In the next phase, backward phase, the
error between the observed actual value and the desired
nominal value in the output layer is propagated backwards in
order to modify the weights and bias values.
An important stage is the training step, in which an input
is introduced to the network together with the desired
outputs, the weights and bias values are initially chosen
randomly and the weights are adjusted so that the network
attempts to produce the desired output. The weights, after
training, contain meaningful information, whereas before
training, they are random and have no meaning. When a
satisfactory level of performance is reached, the training
stops, and the network use these weights to make decisions.
The goal of any training algorithm is to minimize the
global error level, such as the mean % error, root mean
square (RMS), and absolute fraction of variance (R2) [12].
An important characteristic of this function is differentiable
throughout its domain. The errors for hidden layers are
determined by propagating back the error determined for
the output layer.
For ANNs, two data sets are needed: one for training the
network and the second for testing it. The usual approach is
to prepare a single data set and differentiate it by a random
selection.
In order to train the network, different weather variables
are obtained from the Turkish Meteorology Center. Some
of the variables are directly measured. But the others are
calculated from the measured variables. Measured vari-
ables are daily maximum and minimum atmospheric
pressures, daily maximum and minimum temperatures,
daily sunshine duration, daily evaporation, daily relative
humidity, and daily rain quantity. Atmospheric pressure is
measured by means of equilibrium of liquid head. In this
method, mercury with low vapor pressure is used for the
pressure measurement. Daily maximum temperature is
measured using the expanded mercury’s volume with
temperature in a capillary tube. Like this, daily minimum
temperature is measured using the decreased alcohol’s
volume with temperature. In this condition, low tempera-
ture values can be measured by using the alcohol fluid.
Relative humidity is the ratio of the amount of water vapor
in the air to the amount the air can hold at that temperature.
Daily relative humidity is measured using hygrometer. In
order to measure the relative humidity, hair bundle is
extended/shortened with the increased/decreased relative
humidity in air. Daily sunshine duration is measured using
heliograph. In this method, the radiation from the sun is
recorded to the diagram. Radiation measurements are car-
ried out by the actinograph device. The device records total
radiation intensity in a horizontal surface.
For ANNs, two data sets are needed: one for training the
network and a second one for testing it. The usual approach
is to prepare a single data set and differentiate it by a
random selection. As mentioned above, we have studied
two networks. In the first network, we have used latitude
(L), longitude (Lg), altitude (A), month (M), daily mini-
mum humidity (Hmin), daily maximum humidity (Hmax),
mean sunshine duration (S), daily minimum temperature
(Tmin), and daily maximum temperature (Tmax) at the input
layer while maximum and minimum pressure (Pmin and
Pmax) values were used at the output of ANN. In the second
network, we have used L, Lg, A, M, Hmin, Hmax, S, Tmin,
Tmax, Pmin, and Pmax at the input layer while solar radiation
(I) value was used at the output of ANN. So output values
of the first network were used as input values of the second
network. Since pressure measurement is difficult than
others, we predicted the pressure with first network, then
we used the pressure as one of the inputs for second net-
work. The selected ANN structures are similar as [3].
In this study, the learning algorithm that called back
propagation was applied for single hidden layer. Scaled
conjugate gradient (SCG) and Levenberg–Marquardt (LM)
have been used for the variants of the algorithm. Normal-
ized both for inputs and outputs are realized between the
values of 0 and 1. Neurons in the input layer have no
transfer function. Logistic sigmoid (logsig) transfer func-
tion has been used.
Neural Comput & Applic (2013) 22:1677–1683 1679
123
ANN was trained and tested by means of the MATLAB
software on a usual PC. Ten percent of the data are used to
test the network. The selected test data contain the mea-
surements of all of the meteorological stations in order to
represent all of the data. Training data are not used as a test
data, and test data are not used as a training data. In order to
identify the output precisely for training stage, increased
number of neurons (7–9) in hidden layer was tried. Firstly,
the network was trained successfully, and then the test data
were used to test the network. By means of the results
deduced by the network, a comparison was carried out using
statistical methods. Errors occured at the learning and testing
stages are described the RMS and R2, maximum and mean
error percentage values, defined as follows, respectively:
RMS ¼ 1=nð ÞXn
i¼1
ti � oij j2 !1=2
ð1Þ
R2 ¼ 1�Pn
i¼1 ti � oið Þ2Pn
i¼1 oið Þ2
!ð2Þ
Mean%Error ¼ 1
n
Xn
i¼1
ti � oi
ti� 100
� �ð3Þ
where t is the target value, o is the output value, and n is the
pattern [9].
4 Results and discussion
As said before, increased number of neurons (7–9) in
hidden layer has been studied for the SCG and LM algo-
rithms. The best algorithms for the first and the second
networks were generally the LM with seven neurons and
the LM with eight neurons, respectively. Therefore, the
results provided in the following sections are based on
these configurations.
In Tables 1 and 2, the statistical values of the outputs for
two networks have been shown for both the training and
testing data, respectively. Each of the error values of the
outputs is given in the tables.
For the first network, the formulations of the outputs are
given by Eqs. 4–5. Using these formulae, similarly, mini-
mum and maximum pressure values may be calculated
within the error ranges given in the tables.
where Fi (i = 1,2,…) can be calculated using Eq. 6.
Fi ¼1
1þ e�Eið6Þ
When using these equations in Table 3, L, Lg, Hmin, and
Hmax values are normalized by dividing them by 5,000,
5,000, 100, and 100, respectively. A, M, S, Tmin, and Tmax
values are normalized according to Eq. 7. The Xmin and
Table 1 Statistical values of predictions-based hidden layer for first network, LM7
Outputs RMS training R2 training Mean % error
training
RMS test R2 test Mean % test
Pmin 0.001657 0.999996 0.161572 0.001873 0.999994 0.17738
Pmax 0.001735 0.999995 0.169452 0.001985 0.999994 0.193151
PMin ¼1
1þ e�ð�0:2429 F1þ1:569 F2þ3:386 F3�1:4456 F4�3:0013 F5þ2:5181 F6þ2:8344 F7�1:3122Þ ð4Þ
PMax ¼1
1þ e�ð�0:2418 F1þ1:563 F2�1:1412 F3�1:4307 F4�3:173 F5�0:5493 F6þ2:8415 F7þ3:1972Þ ð5Þ
1680 Neural Comput & Applic (2013) 22:1677–1683
123
Xmax values in this equation for basic indicators are given
in Table 4. For outputs, Pmin and Pmax values need to be
dividing by 1,200 both. The obtained results show that the
error levels for the first network are lower than the error
levels in [3].
X ¼ 0:8� XActual � XMin
XMax � XMin
� �þ 0:1 ð7Þ
For the second network, the formulation of the output is
given by Eq. 8. Using these formulae, similarly, solar
radiation value may be calculated within the error ranges
given in the tables.
where Fi (i = 1,2,…) can also be calculated using Eq. 6.
When using the equations in Table 5, L, Lg, Hmin, Hmax,
Pmin, and Pmax values are normalized by dividing them by
5,000, 5,000, 100, 100, 1,200, and 1,200, respectively. A,
M, S, Tmin, and Tmax values are normalized according to
Eq. 7. The Xmin and Xmax values in this equation for basic
indicators are given in Table 4. For output, solar radiation
value needs to be dividing by 750. The obtained results
show that the error levels for the second network are
slightly higher than the error levels in reference 3.
In Figs. 1 and 2, measured and predicted daily maxi-
mum and minimum pressure values of the test data corre-
sponding to the network 1 are compared, respectively. In
Figs. 1 and 2, the results corresponding to test data show
that the estimated and measured pressure values are very
close to each other.
Similarly, in Fig. 3, measured and predicted solar radi-
ation values of the test data corresponding to the network 2
are also compared, and the estimated and measured solar
radiation values are also very close to each other.
5 Conclusion
Daily maximum and minimum pressures are successfully
predicted using ANN method. In this prediction, the error
ranges of the minimum and maximum pressures are
0.17738 and 0.193151 %. As a result, some of the mete-
orological variables are computed using the obtained for-
mulae as if experiments were done. When meteorological
Table 2 Statistical values of predictions-based hidden layer for second network, LM8
Outputs RMS training R2 training Mean % error training RMS test R2 test Mean % test
I 0.022517 0.998017 4.400726 0.026329 0.997189 5.77565
Table 3 The weights between input layer and hidden layer for LM7 for first network
i Ei = C1*L ? C2*Lg ? C3*A ? C4*M ? C5*Hmin ? C6* Hmax ? C7*S ? C8* Tmin ? C9* Tmax ? C10
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
1 5.3757 0.7609 1.9463 5.5758 0.9899 3.1919 1.5247 2.5186 4.4100 -11.295
2 -2.9765 4.5817 -4.1942 -0.0118 0.0167 -0.3376 -0.3245 0.3956 -0.9578 0.4108
3 3.7722 -1.8197 2.5462 1.7783 -1.2608 -0.2619 1.0884 2.6604 3.6761 3.5807
4 -3.8049 4.7497 0.7894 -0.1770 0.0983 -0.2049 -0.2631 0.9758 -0.6295 0.2274
5 -2.5861 1.7313 -1.6332 -0.5570 -0.5489 -1.2172 -2.1980 -0.7356 -3.0920 1.4777
6 -4.9504 -0.6351 0.1505 0.4413 -1.6012 -0.0796 -2.2445 3.1808 -3.7177 -1.9028
7 -2.4516 -1.8819 5.3541 0.1139 0.8293 -1.3338 -1.7574 1.1357 0.4301 -4.2644
Table 4 Values for normalization
Xmin Xmax
A 0 2000
M 1 12
S 0 15
Tmin -25 30
Tmax -10 45
I ¼ 1
1þ e�ð108:6559 F1�77:0753 F2þ33:8709 F3þ250:1862 F4�2:3223 F5�84:8213 F6þ63:1685 F7�78:5069F8�206:6237Þ ð8Þ
Neural Comput & Applic (2013) 22:1677–1683 1681
123
Ta
ble
5T
he
wei
gh
tsb
etw
een
inp
ut
lay
eran
dh
idd
enla
yer
for
LM
8fo
rse
con
dn
etw
ork
iE
i=
C1*
L?
C2*
Lg
?C
3*
A?
C4*M
?C
5*H
min
?C
6*
Hm
ax
?C
7*
S?
C8*
Tm
in?
C9*
Tm
ax
?C
10*
Pm
in?
C11*
Pm
ax
?C
12
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
1-
0.3
79
7-
0.0
77
5-
7.3
85
94
.92
71
0.5
41
2-
0.7
04
80
.16
57
0.9
76
2-
0.0
91
5-
13
.24
59
-2
1.4
14
62
9.7
45
0
2-
20
8.5
46
54
.97
20
-4
6.2
04
11
.69
36
-1
.26
90
2.6
68
4-
1.1
25
8-
6.4
05
9-
1.6
62
4-
51
.27
14
-5
2.3
69
82
37
.35
07
31
.92
62
0.2
59
24
.40
25
-2
.49
85
0.0
80
30
.17
58
0.6
31
1-
0.1
73
20
.44
02
0.5
36
82
0.2
29
2-
19
.85
93
4-
14
8.0
23
39
.77
49
-3
7.2
29
21
.53
67
-1
.32
90
2.1
66
3-
1.1
32
0-
5.3
78
8-
1.8
20
1-
31
.85
44
-6
2.5
20
11
88
.86
57
51
8.3
83
62
.39
68
22
.90
31
-1
.39
71
0.7
58
22
.16
58
1.0
51
92
.30
99
0.3
42
3-
15
3.9
57
32
65
.07
09
-1
14
.01
79
6-
14
.95
83
18
.69
87
5.0
08
3-
1.4
41
01
.94
70
-0
.79
98
1.7
82
7-
2.8
06
06
.11
34
31
5.7
49
1-
28
4.3
99
4-
38
.06
99
7-
13
.06
02
-9
3.1
99
11
3.6
74
4-
4.5
37
4-
18
.90
95
28
.06
08
-8
.47
91
32
.00
90
-1
6.4
34
51
65
.01
98
-1
8.0
21
9-
89
.85
12
80
.07
87
-0
.10
08
-8
.88
89
5.3
88
20
.75
18
-0
.92
01
0.3
47
41
.28
42
0.0
23
7-
14
.72
84
-2
6.9
91
33
5.2
02
20.6
0.7
0.8
0.9
0.6 0.7 0.8 0.9
Measured values
Est
imat
ed v
alue
s
Fig. 1 Comparison of measured and predicted daily maximum
pressure of test data corresponding to the first network
0.6
0.7
0.8
0.9
0.6 0.7 0.8 0.9
Measured values
Est
imat
ed v
alue
s
Fig. 2 Comparison of measured and predicted daily minimum
pressure of test data corresponding to the first network
0.1
0.3
0.5
0.7
0.9
0.1 0.3 0.5 0.7 0.9
Measured values
Est
imat
ed v
alue
s
Fig. 3 Comparison of measured and predicted solar radiation of test
data corresponding to the second network
1682 Neural Comput & Applic (2013) 22:1677–1683
123
variables are predicted with these formulae, the experi-
mental measurements are not required from different
meteorological stations.
Advantages of the ANNs are speed of calculation,
capability of learning from examples and simplicity. All of
these advantages have also been observed in our applica-
tion. These features enable us to use the ANNs in the
prediction of meteorological variables and will help the
people studying in this field. So, experimental studies can
be reduced to minimum at the places where the use of
ANNs is appropriate.
Acknowledgments We are thankful to directorship of Kocaeli
Meteorology in Turkey, for the support in the accomplishment of the
present study, directorship manager for his valuable help.
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