INTERNATIONAL JOURNAL OF ENERGY RESEARCH
Int. J. Energy Res. 2012; 36:545 552
Published online 26 August 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1774
SHORT COMMUNICATION
Spatial estimation of wind speed
Mohamed A. Mohandes1, ,y, Shafiqur Rehman2 and Syed Masiur Rahman3
1
Electrical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran-31261, Saudi Arabia
2
Center for Engineering Research, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran-31261, Saudi Arabia
3
Civil Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran-31261, Saudi Arabia
SUMMARY
This study utilizes Abductory Induction Mechanism to estimate the mean monthly wind speed at some locations in
Saudi Arabia based on wind data at other available recording stations in addition to some historical wind speed
data at the target site. Wind speed data from 20 meteorological stations over a period of 16 years between 1990 and
2005 was used to accomplish the set objective. To validate the model, data from 19 stations was used to estimate
the wind speed at the 20th location. Evaluation was performed for every one of the 20 available locations. Results
show good agreement between estimated and measured monthly mean wind speed values. Copyright r 2010 John
Wiley & Sons, Ltd.
KEY WORDS
abductory induction mechanism (AIM); group method of data handling (GMDH); wind speed estimation; meteorology; renewable
energy
Correspondence
*Mohamed A. Mohandes, KFUPM BOX ] 1885, Dhahran-31261, Saudi Arabia.
y
E-mail: [e-mail]
Received 5 July 2010; Accepted 6 July 2010
1. INTRODUCTION Therefore, only 30 measurement locations are not
sufficient to get an overview about wind potential over
One of the major hurdles in the usage and development Saudi Arabia. Accordingly, this study concentrates on
of wind power resources is the intermittent nature of the estimation of wind speed at sites where only
the availability of wind during 24 h a day and 7 days a historical measurements are available using group
week. Hence, to assure a certain level of wind power method of data handling (GMDH) approach. A sin-
penetration level into an existing conventional energy cere and comprehensive effort on realistic prediction of
grid system one has to determine the instant potential wind speed is being put around the globe by experts as
of the regions. Therefore, for accurate wind power can be seen from the currently on going literature given
assessment, control, scheduling, maintenance, and below.
resource planning of wind energy conversion systems, Damousis et al. [1] developed a fuzzy model to
wind speed values should be available at the site of perform forecasting of wind speed and electrical
wind farm development. Various critical applications, power up to 2 h ahead. Their model was trained with
such as aviation, shipping, agriculture, and environ- measured wind data from neighboring meteorological
ment, require accurate wind speed values ahead of stations at a radius of up to 30 km. Their method
time. The wind speed measurement network is still very provided significant improvement over the persistent
sparse even in developed countries. In Saudi Arabia, method for a flat terrain. A recent paper of Alexiadis
there are around 30 meteorological stations, mostly at et al. [2] examined the contribution of data from local
national and international airports, maintained by and remote sites to forecasting using neural network
Presidency of Meteorology and Environment (PME), a models, and suggested a possible way to improve
government organization. prediction accuracy.
¨
Wind speed is the most difficult parameter to Oztopal [3] used daily wind velocity measurements
model and predict both in time and spatial domains. in the Marmara region from 1993 to 1997 and found
Copyright r 2010 John Wiley & Sons, Ltd.
545
M. A. Mohandes, S. Rehman and S. M. Rahman Spatial estimation of wind speed
that the ANN model is more appropriate for winter
Table I. Site coordinates of stations used in this study.
period daily wind velocities prediction. Bilgili et al. [4]
S. No. Station Lat Lon Alt (m) SH (m)
applied ANNs to predict the mean monthly wind speed
of any target station using the mean monthly wind
1 Dhahran 26106 50110 22 10
speeds of neighboring stations. The maximum mean
2 Gizan 16152 42135 5 8
absolute percentage error was found to be 14.13% for
3 Guriat 31125 37116 540 10
the Antakya meteorological station and the best result
4 Jeddah 21130 39112 17 10
was found to be 4.49% for the Mersin meteorological 5 Turaif 31141 38140 827 8
station. Song [5] developed an ANN-based model to 6 Riyadh 24142 46144 624 10
7 Yanbo 24107 38103 6 10
perform one-step ahead prediction, which is found to
8 Abha 18113 42131 2200 12
be good when the wind data does not change rapidly.
9 Hail 27131 41144 992 9
Alexiadis et al. [6] found that ANN predictor is about
10 Al-Jouf 29156 40112 562 7
10% better than persistence model for one-step ahead
11 Al-Wejh 26114 36126 22 10
prediction. Bechrakis and Sparis [7] applied the ANN
12 Arar 30154 41108 542 6
method for the prediction of wind speed at a given
13 Bisha 19158 42140 1167 5
site utilizing past values of wind speed as input.
14 Gassim 26118 43158 648 7
This method demonstrated optimum results for 3-day
15 Khamis-Mushait 18118 42148 2060 9
period predictions. Lopez et al. [8] used few measure-
16 Nejran 17134 44114 1275 8
ments at the selected site and data collected at nearby
17 Qaisumah 28120 46107 359 8
fixed stations to predict annual average wind speed
18 Rafha 29138 43129 443 12
with errors below 2%.
19 Tabouk 28122 36135 771 9
This study is the first attempt to utilize abductory
20 Taif 21129 40132 1471 8
induction mechanism (AIM) network to predict
monthly mean wind speed data at locations where only
historical measurements are available, based on wind
data from existing meteorological stations. Results speeds. Therefore, this study uses monthly mean values
show good performance of this method for predicting of wind speed.
monthly mean wind speed values in several locations in The wind speed data, used in this study, covers a
Saudi Arabia. The developed system would provide an period of about 16 years between 1990 and 2005. The
estimate of the wind speed data for any station that latitude (Lat), longitude (Lon), altitude (Alt) above
might be intermittently or permanently closed due to mean sea level (AMSL), and wind speed sensor height
any reason. (SH) above ground level (AGL) are summarized in
Table I. The location map is shown in Figure 1. The
figure shows that the measurement stations are
2. DATA AND SITE DESCRIPTION concentrated around the eastern and western regions
while no coverage for the central region. The site
Almost all Saudi Arabian land consists of desert and altitude varies between a minimum of 5 m at Gizan and
semi-desert with oases, where half of the total surface a maximum of 2200 m above mean sea level at Abha,
is uninhabitable desert. The major part of the western as seen from Table I.
area of Saudi Arabia is plateau while the East is
lowland with very hot climate. The southwest region
has mountains as high as 3000 m. Saudi Arabia, 3. GROUP METHOD OF DATA
one of the driest and hottest countries in the world, HANDLING (GMDH)
is roughly located between North latitudes of 17
and 31 and East longitudes of 37 and 56 as explained The GMDH algorithm was introduced to provide an
by Alkolibi [9]. Maximum summer temperatures objective model of high-order polynomial in the input
often exceed 451C, relative humidity is very low and variables to solve prediction, identification, control
skies are clear most of the time. Very little preci- synthesis, and other system problems [10]. This
pitation is observed in the central region of Saudi algorithm starts with regression equations of two or
Arabia. three orders for each pair of input variables to produce
In Saudi Arabia, there are around 30 meteorological the output. Thus for n input variables there will be
stations, mostly at national and international airports, n(n 1)/2 higher-order variables which will be used for
maintained by PME. The meteorological sensors predicting the output in lieu of the original n input
at these stations are calibrated and maintained variables. The algorithm selects the relationships that
according to the World Meteorological Organization have good predicting capabilities within each phase
standards. The data are recorded in hourly bases. and prevents exponential growth of the developed
However, wind farm potential assessment and devel- system and limits the model complexity. After finding
opment requires long-term seasonal and annual wind out the optimum generation, the best polynomial in that
546 Int. J. Energy Res. 2012; 36:545 552 © 2010 John Wiley & Sons, Ltd.
DOI: 10.1002/er
Spatial estimation of wind speed M. A. Mohandes, S. Rehman and S. M. Rahman
Figure 1. Location map of meteorological stations.
generation is selected. The Ivakhnenko polynomial Peirce [15] introduced the term abductory induction, a
shown below is the final result of this algorithm [11]. unique class of induction, which derives abductive
principles from facts under uncertainty using numeric
n n n
X XX
functions and measures. If there exists a relationship
outputźw0þ wixiþ wijxixj
among data, the AIM network provides a modeling
iź1 iź1 jź1
solution by subdividing the input variables into groups,
n n n
XXX
þ wijkxixjxkþ ð1Þ directing them to individual nodes of a network,
iź1 jź1 kź1
summarizing the relationships among each group, and
feeding these results to the next layer of the network [14].
The attractive features of GMDH include: (i) determina-
The AIM is a GMDH algorithm, which auto-
tion of the structure of non-linear systems, (ii) solution
matically synthesizes abductive networks from a data-
of the problem of overfitting, and (iii) capability of
base of inputs and outputs having complex and
consideration of multi-criteria objective function for
non-linear relationships [16]. The AIM provides an
validation [12]. The extensive number of GMDH
environment to synthesize, analyze, and encode ab-
applications and their ability to model ill-defined
ductive networks for complex decision, prediction,
problems with reasonable accuracy have proved and
control, and classification problems. The AIM uses
strengthened its position as an appropriate non-linear
mathematical models to represent complex and un-
method for structural identification and prediction
certain relationships along with polynomial networks
tasks [13].
to represent the underlying process [17]. The nodes of a
typical feed-forward the AIM network can be Singles,
3.1. AIM networks
Doubles, and Triples, which are third-order poly-
Montgomery and Drake [14] defined induction as the act nomials with one, two, or three inputs, respectively.
or process of reasoning from facts to general principles. A Double and Triple are defined as the following
Int. J. Energy Res. 2012; 36:545 552 © 2010 John Wiley & Sons, Ltd. 547
DOI: 10.1002/er
M. A. Mohandes, S. Rehman and S. M. Rahman Spatial estimation of wind speed
equations: Arabia. These data were divided into 180 for model
training and the remaining 17 is used for model
Double0s outputźw0þw1x1þw2x2þw3x2þw4x2
1 2
evaluation.
þw5x1x2þw6x2x2þw7x1x2
The AIM algorithm automatically determines the
1 2
network size, element types, connectivity, and coeffi-
þw8x3þw9x3 ð2Þ
1 2
cients for the optimum model using well-proven opti-
Triple0s outputźw0þw1x1þw2x2þw3x3þw4x2 mization criteria. However, it provides the flexibility to
1
optionally change a few important parameters. The
þw5x2þw6x2þw7x1x2þw8x1x3 AIM model starts building the network layer by layer
2 3
þw9x2x3þw10x2x2þw11x1x2 as long as the performance continues to improve but it
1 2
þw12x2x3þw13x2x2þw14x2x3 does not exceed a predefined limiting number of layers.
2 3 1
After several investigations it was found that networks
þw15x1x2þw16x3þw17x3
3 1 2
with six layers perform reasonably well for all the
þw18x3þw19x1x2x3 ð3Þ models. The number of inputs to the first layer is 19.
3
Each of these inputs is the mean monthly wind speed at
where x1 and x2 are input variables and wn are
one of the 19 available measurement stations. At each
obtained weights after training.
The AIM uses  Normalizers that normalized the
input variables to become zero mean and unit variance.
It also uses  Unitizers that change the range of net-
work outputs to a range with the mean and variance of
the output values of training data. The AIM auto-
matically determines the optimum model characterized
by network size, element types, connectivity, and
coefficients [17]. The selection criteria of the model lead
to a network model without overfitting the training
data. It is accomplished by performing a tradeoff be-
tween model complexity and accuracy [14]. Barron [18]
derived the modeling criterion of the AIM network,
which is known as predicted squared error (PSE). The
PSE can be obtained by:
PSEźFSEþCPM 2K s2=N ð4Þ Figure 2. The effect of CPM parameter on MAE corresponding
r
to the monthly wind speed of Dhahran.
FSE is the fitting squared error of the model based
on the training data, K is the total number of coeffi-
cients used in the model, N is the number of training
Table II. Performance of the AIM networks for the 20 stations.
data, S2 represents the estimated true unknown model
r
Station MAE (m s 1)
error variance, and complexity penalty multiplier
(CPM) is a user-defined penalty multiplier. The value
Dhahran 0.45
of the second term in Equation (4) increases linearly
Gizan 0.27
and the first term decreases when the model becomes
Jeddah 0.38
more complex compared with the size of the training
Guraiat 0.51
set. For an optimum model size, PSE passes through a
Turaif 0.50
minimum that ensures a balance between accuracy and
Riyadh 0.35
simplicity [19]. The user-defined value of CPM para-
Yanbou 0.75
meter can affect this tradeoff. Generally, larger values
Abha 0.65
of CPM compared with the default 1 lead to simpler
Hail 0.44
models with less accuracy and on the other hand, lower
Al Jouf 0.28
values over fit the training data with degraded actual Al Wejh 0.39
prediction performance [20]. Arar 0.38
Bisha 0.35
Gassim 0.50
Kamis Mushait 0.41
4. RESULTS AND DISCUSSION
Nejran 0.46
Qaisumah 0.45
In this study, the abductive network was synthesized
Rafha 0.60
based on the monthly mean wind speed. The available
Tabouk 0.41
data consists of 197 mean monthly wind speed of
Taif 0.45
20 recording stations across the Kingdom of Saudi
548 Int. J. Energy Res. 2012; 36:545 552 © 2010 John Wiley & Sons, Ltd.
DOI: 10.1002/er
Spatial estimation of wind speed M. A. Mohandes, S. Rehman and S. M. Rahman
succeeding layer, the AIM model considers a list of at the targeted station at the same time of the
candidate sub-networks for inclusion and the list 19 measurement stations.
decreases in size at each subsequent layer. The output PSE compromises between the accuracy of fitting the
of the AIM network is the mean monthly wind speed training data and the complexity of the network. The
CPM is a parameter pre-selected by the user to control
the generalization capability of the model. Different
values of CPM ranges from 0.01 to 5 were investigated
for Dhahran station as shown in Figure 2. Figure 2
shows that the CPM value of 0.4 leads to the minimum
mean absolute errors in prediction of the mean
monthly wind speed value at Dhahran station. In-
vestigations on data from all the stations under
consideration show that the CPM value of 1 and 0.4
alternately lead to better overall performing networks.
Table II shows the MAE from the best performing
Figure 3. AIM network layout for Riyadh. AIM network for each case.
Figure 4. Comparison between measured and predicted monthly mean wind speed for some selected stations: (a) Al-Wejh;
(b) Guriat; (c) Gizan; (d) Jeddah; (e) Al-Jouf; (f) Riyadh; (g) Taif; and (h) Tabouk.
Int. J. Energy Res. 2012; 36:545 552 © 2010 John Wiley & Sons, Ltd. 549
DOI: 10.1002/er
M. A. Mohandes, S. Rehman and S. M. Rahman Spatial estimation of wind speed
Owing to the limited number of available stations, Al-Wejh, Guriat, Gizan, Jeddah, Al-Jouf, Riyadh, Taif
we use the leave-one-out method, where data from and Tabouk, in order. At Al-Wejh, as seen from
19 stations are used to predict the wind speed at the Figure 4(a), the maximum deviation of predicted value
20th location. This process is repeated one-by-one of the mean monthly wind speed from the measured
throughout the available stations. Therefore, 20 mod- one is about 1 m s 1 in month 2. In most of the cases,
els were developed to predict the monthly mean wind the deviation is very minimal, and the maximum de-
speed at the available stations. The MAE of the se- viation between the measured and predicted mean
lected models varies between 0.26 and 0.76 m s 1. The monthly wind speed values is 1.2 m s 1 for Riyadh in
AIM is self-organizing in the sense that it auto- month 1, as can be seen from Figure 4. Figure 5 shows
matically finds the type and the number of layers the scatter plots with R2 value of the prediction models
needed to model the input/output data optimally. for the stations as shown in Figure 4. It is evident from
Figure 3 shows a typical sample of the developed AIM these plots that the predicted values are in close
network for predicting wind speed in Riyadh. The agreement with the measured monthly mean wind
predicting the AIM networks for the monthly mean speed with coefficient of determination more than
wind speed at the other 19 stations have layout similar 97%. The performance of the other 12 AIM networks
to the one shown in Figure 3. for the stations not shown in Figures 4 and 5 are si-
Figure 4(a h) shows the performance of some milar with coefficient of determination more than 95%
typical developed AIM networks corresponding to for all cases.
Figure 5. Scatter diagrams of estimated versus measured monthly mean wind speeds for some selected stations: (a) Al-Wejh;
(b) Guriat; (c) Gizan; (d) Jeddah; (e) Al-Jouf; (f) Riyadh; (g) Taif; and (h) Tabouk.
550 Int. J. Energy Res. 2012; 36:545 552 © 2010 John Wiley & Sons, Ltd.
DOI: 10.1002/er
Spatial estimation of wind speed M. A. Mohandes, S. Rehman and S. M. Rahman
5. CONCLUSIONS ACKNOWLEDGEMENTS
The authors acknowledge the support provided by
This study developed abductive networks to predict the
King Fahd University of Petroleum and Minerals for
mean monthly wind speed at a location depending on a
this research.
few other geographically dispersed stations. Owing to
the inherent difficulties in modeling and forecasting
wind speed the attempt to develop spatial model is also
difficult. This study utilized the proven optimization
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