Piri et al.: Determinat ion of the best geostatistical method for climatic zoning in Iran [620203]

Piri et al.: Determinat ion of the best geostatistical method for climatic zoning in Iran
– 93 –
APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
http://www.aloki.hu ● ISSN 1589 1623 (Print) ● ISSN 1785 0037 (Online)
DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary DETERMINATION OF THE BEST GEOSTATISTICAL METHOD
FOR CLIMATIC ZONING IN IRAN
PIRI, I.1 ‒KHANAMANI , A.2 ‒ SHOJAEI , S.3 ‒ FATHIZAD , H.4*
1Department of Agriculture, Payame Noor University, Iran
(e-mail: [anonimizat])
2Young Researcher and Elite Cl ub, Jiroft Branch, Islamic Azad University, Iran
(e-mail: [anonimizat] )
3Young Researcher and Elite Club, Zahedan Branch , Islamic Azad University, Iran
(e-mail: [anonimizat])
4Department of Natural Resources and Desert Studies, Yazd Universi ty, Yazd, Iran
(e-mail: [anonimizat] )
*Corresponding author
[anonimizat]
(Received 5th Jul 2016 ; accepted 10th Oct 2016 )
Abstract . Zoning using climatic indices is of significant value in climate studies and climate – related
planning. The aim of this study is to assess De Martonne aridity index and to select the best model to
draw Iran ‘s complete map based on 150 station ‘s temperature and precipitation data over a 25-year period
(1986 -2010). Kolmogorov – Smirn ov test (K –S test) was used to check the normality of the data. In order
to assess De Martonne aridity index, annual temperature and precipitation data were collected from
properly -distributed stations in the study period. Using De Martonne aridity index f ormula, this index was
calculated for all the stations. In the next step, using different geostatistical methods, De Martonne aridity
index map was drawn. Semivariogram was used to show the spatial correlation between aridity index data
in which linear sem ivariograms of 0.84 was the best interpolation model to show the correlation. To
estimate De Martonne aridity index, inverse distance weighting (IDW), global polynomial interpolation
(GPI), radial basis function (RBF), local polynomial interpolation (LPI), as well as Kiriging methods
were used. Root mean square error (RMSE), and mean absolute error (MAE) were used to select the best
interpolation method. Our results showed that simple kriging method shows the highest correlation with
the observed data (R2=0 .77). Moreover , it is shown that Iran's central regions due to locating in low lands
and being far from the northern and western mountain ranges (Alborz and Zagros) has the lowest De
Martonne aridity index (< 5, 5 – 10) and is classified as arid and semi -arid areas while Iran's northern
regions has the highest De Martonne aridity index (> 55) is classified as very humid area showing a wide
climate range of arid to very humid in Iran.
Keywords: GIS, rainfall, interpolation, temperature , semivariogram
Introdu ction
Aridity which is defined as the lack of moisture is a climatic phenomenon that is
based on the average climatic conditions of a consistent region (Tabari et al., 2014).
Increased aridity and subsequent desertification, is one of the environmental pro blems
that affect people's living conditions in the world ‘s arid areas. Paying attention to
different climatic regions and its understanding is quite essential. Understanding
climatic condition is the most essential step in studying different human activit ies such
as agriculture, environment, urban planning, transportation, tourism, etc., (Adnan and
Haider, 2012). Climatic parameters are useful tools to characterize the status of the
climatic system and to perceive its different involving mechanisms (Deniz et al., 2011).

Piri et al.: Determinat ion of the best geostatistical method for climatic zoning in Iran
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APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
http://www.aloki.hu ● ISSN 1589 1623 (Print) ● ISSN 1785 0037 (Online)
DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary Aridity index is a climatic index that can be used to monitor and predict aridity (Nastos
et al, 2013). So far, several climatic indices have been developed and used utilized in
order to s tudy the climatic condition of various regions among which Emberger, Torrent
White (Aliz adeh et al., 2001), De Martonne., etc. can be mentioned (Tabari et al., 2014).
Determination of the most suitable interpolation method in an area and explanation of
its spatial distribution is necessary to estimate the sp atial distribution of the climatic
parameters. There are various methods to assess and estimate such parameters. All these
methods are computationally fast and easy. For example, the classical methods, such as
Thiessen and the arithmetic mean can be mentio ned. There are several methods to
estimate the spatial data among which the most common ones include arithmetic mean,
gradient, and Thiessen (Corwin et al., 1992; Hosseini et al., 1993). But for some
reasons such as not considering the spatial data, and c orrelation between observations ,
such methods are not sufficiently accurate. Of course, there are other methods that due
to consideration of the spatial correlation of data are highly significant. Deficiencies of
the mentioned methods specify the necessity of using geostatistical methods.
Geostatistical methods due to considering the spatial correlation of data are of particular
importance in assessment of the spatial distribution of the geological data, and gives a
better estimate of the underlying paramet er in the areas that are not sampled yet (Karimi
Nazar et al., 2009). One of the currently used alternative methods to the classical
statistical methods (such as regression, weighted inverse square distance, etc.) is the
geostatistical methods. Nowadays, t hese methods are used for interpolation of rainfall
stations an d other spatial variables (Shab ani et al., 2011 ). Many researchers have been
involved in comparison and assessment of various interpolation methods which
represents the importance of this issue to reduce the errors of method selection. To
interpolate the annual rainfall and temperature in an area of five thousand square
kilometers in Portugal, Goovaerts (2000) considered simple kriging method more
appropriate as compared to inverse -square method , linear regression with height,
Thiessen and kriging methods. Tabari et al . (2014) used data from 40 stations in a time
period of 1965 to 2005 to assess De Martonne aridity index. Using the ordinary kriging
climate zoning method, these researchers conclud ed that 88% of Iran involves arid and
hyper -arid areas. Furthermore, De Martonne aridity index was decreased by 18% to 54
% in the western and north -western areas. The aim of this study was climate zoning and
assessment of De Martonne aridity index using a variety of geostatistical methods and
data from 150 rainfall stations in Iran. The aridity index De Martonne modeling was
carried out using Arc GIS 9.3 and GS+ softwares.
Materials and methods
Study area
Iran, with an area of 1648195 square kilometers h as been located between latitude of
25° to 40° N and longitude of 44 ° to 63° E ( Fig.1 ). So in terms of latitude southern parts
are located in tropical areas, and northern parts are located in subtropical regions. Iran
has different climatic conditions due to its geographical position which means fifteen
degrees’ latitude dispute between the most southern and the most northern point, as well
as folds and ups and downs that can be observed on its surface. Apart from these two
factors, the combination of the a ir masses that originate from different regions and
collide on Iran ian plateau, is one of the most important factors to determine Iran ‘s
climatic conditions . Proximity to the Persian Gulf and Oman Sea on one side and the

Piri et al.: Determinat ion of the best geostatistical method for climatic zoning in Iran
– 95 –
APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
http://www.aloki.hu ● ISSN 1589 1623 (Print) ● ISSN 1785 0037 (Online)
DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary
impact of the Mediterranean Sea on the other side, along with the presence of dry
deserts of Arabia and Africa and northeastern great Siberian Plain is effective on type of
the air masses that reach Iran.

Figure 1. The positions of the rainfall stations

Statistical anal ysis
Kolomogra ve – Smirnov test was used to evaluate the normality of the data in the
present study. Rainfall data were used following normalization. The histogram ( Figure 2 )
and the statistical analysis of De Martonne aridity index from 150 stations in the study
area o ver a period of 25 years (1985 -2009) was analyzed in SPSS V.21 software. The
results are presented in Table 1 . Figure 1 shows the positions of the rainfall stations.

Figure 2. Histogram of the normalized De Martonne aridity index

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APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
http://www.aloki.hu ● ISSN 1589 1623 (Print) ● ISSN 1785 0037 (Online)
DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary Table 1. Statistical a nalysis of the data from the study area
parameter mean the mean
standard
error standard
deviation mode variance skewness minimum maximum
value 12.93 0.94 11.60 3.34 134.56 2.42 0.82 71.26

De Martonne aridity index (I)
De Martonne climate classificat ion is one of the conventional methods in climate
classification which is used in most climatology projects, particularly in dam
construction, agriculture, etc. The basis of this method is presented in Equation (1) and
Table 2 (Tabari et al., 2014).

(Eq.1)

Where P is the average annual rainfall in mm, T is the average annual temperature in
Celsius, and I is De Martonne aridity index .

Table 2. De M artonne aridity index climate classification (Tabari et al., 2014)
Climatic condition value IDM
Hyper – arid IDM < 5
arid 5 < I DM < 10
Semi – arid 10 < I DM < 20
Mediterranean 20 < I DM < 24
Sub-humid 24 < I DM < 28
humid 28 < I DM < 35
Very humid 35 < I DM < 55
Extremely humid 55 < I DM

Therefore, annual rain falls and temperature data from 150 rain st ations in a time
period of 1985 to 2009 were extracted. Statistical analysis was carried out in SPSS
V.21. De Martonne aridity index for each station was calculated according to equation I
in Excel 2013. The best geostatistical method for climate zoning wa s selected using Arc
GIS V.9.3 software.

Geostatistical analysis
Geostatistics according to the simplest definition is an interpolation method in which
the interpolation index or estimation is the minimization of estimation variance ( Hohn,
1998). Interpol ation is actually the estimation of continuous unknown variable based on
a known sample in the region ( Lu and Wong, 2008 ). Geostatistical estimation is one of
the most accurate estimation method, since it examines several factors including the
distance bet ween points, anisotropy, and spatial variability. But this method has a high
volume of calculations that increases the calculation time in large operations (Hirsche et
al., 19 98). Geostatistics is the study of phenomena which vary in space and time. It
10TPI

Piri et al.: Determinat ion of the best geostatistical method for climatic zoning in Iran
– 97 –
APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
http://www.aloki.hu ● ISSN 1589 1623 (Print) ● ISSN 1785 0037 (Online)
DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary deals with analysis of samplings with different positions in order to make a continuous
level ( Johnston et al., 2001 ). Geostatistical analysis is looking for a way to characterize
the spatial continuity and to collect statistical tools and to model such chang es. The
basic assumption of this spatial – statistical analysis is that nearby observations as
compared to distant observations show more statistical correlation. It should be
mentioned that the possibility of achieving accurate and efficient results throug h this
type of analysis, is achieved when data are normally distributed and possibly fixed and
their mean and variance do not vary spatially (Bohling, 2005 ).

Variogram
Geostatistics is used to determine the spatial structure of the variables by the avera ge
of probabilistic models. This spatial structure is characterized by variogram (Zamani –
Ahmad Mahmoodi et al., 2014). Actually variogram is the first step to model spatial
structure for Kiriging method. The main aim of semivariogram establishment is to be
able to characterize the structure of variable based on the spatial distance. Variogram is
calculated using the following equation (Webster and Oliver, 2000: 56):

()
2
11[ ( ) ( )]2 ( )nh
i i h
ih z x z xnh


Where, γ (h) is semivariogram for a pair of points that ar e located with h distance from
each other, n is the number of pair of points that are located with distance h from each
other, z (xi) is the observed value for the variable in point X, and z (xi+h) is Observed
value for the variable with distance h from x (Webster and Oliver, 2000: 56 ). In
variogram curve with increasing distance (h), the amount of γ (h) increases, and this
situation will continue until a certain distance from which the value remains constant . In
the present study, De Martonne aridity index was estimated using different interpolation
methods including inverse dist ance weighting (IDW), global polynomial interpolation
(GPI), radial basis function (RBF), local polynomial interpolation (LPI), as well as
Kiriging methods.
Results
Variogram was used to show the spatial correlation between De Martonne aridity
index data. The results are presented in Fig.3 . Then variogram Y (h) was used to fit the
data as it shows the spatial correlation between observed De Martonne aridity index
data better than other variograms. For this matter the ratio between the nugget effect and
sill was used (Co+C) (Li et al., 2015). If the value is <0.25 it indicates high spatial
correlation, if the value is in the range of 0.25 – 0.75 it indicates medium spatial
correlation, and if the value is > 0.75 it shows either low spatial correlation or no spatial
correlation between data (Khodakarami et al., 201 1).

(Eq.2)

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APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
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DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary

Figure 3. Variogram to fit De Martonne aridity index data

Therefore, t his ratio was used to select the best variogram. Based on the obtained
parameters for the variogram Y (h), li near variogram with the ratio of the 0.83 modeled
the best correlation between data and was used as the best interpolation method.
Following linear variogram, Gaussian, spherical, and exponential variograms are placed
with the amount of 0.82, 0.84, and 0.8 3, respectively. Different types of the applied
variograms to fit data are presented in Table 3.

Table 3. The nugget effect and sill obtained for the fitted variograms

The results on different models evaluation is presented in Table 4 . Our results
showed the highest correlation between simpl e- kriging method and the observed data
(R2=0.77).

Table 4. De Martonne aridity index data correlation based on different statistical methods Model type Nugget effect
Co (mm2) Sill (mm2)
Co+C C /Co+C
ratio Distance
Ao (km) R2
Gaussian 118 389 0.69 34 0.81
Linear 107 167 0.35 16 0.84
spherical 106 213 0.50 40 0.84
exponential 105 272 0.61 36 0.83
Method Linear Power Exponential
Emprical 0.54 0.70 0.46
LPI_1 0.53 0.69 0.45
LPI_2 0.54 – –
LPI_3 0.54 – –

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APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
http://www.aloki.hu ● ISSN 1589 1623 (Print) ● ISSN 1785 0037 (Online)
DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary

Q-Q Plot of the original and normalized data in SPSS V.21 is presented in Fig.4 . The
plot representing the observed and predicted De Martonne aridity index data using
simple – kriging method is presented in Fig.5 .

Figure 4. Q-Q Plot of the original (right side) , and normalized (left side) De Martonne aridity
index data.

Fig.6. represents the zoning map of De Martonne aridity index using the simple –
kriging method which shows the highest statistical accuracy than other methods.
Because of the high number of stations in the area and their appropriate distribution, a
complete zoning map of the area can be prepared. Also Figure 6 represents the map of
the difference between the average maximum and minimum temperature (
 ), average
maximum and average minimum temperature. It was statistically predicted that a high
correlation may be observed between
 and De Martonne aridity index, how ever, this
correlation was very low at the level of approximately 10%. Comparison of
 and De
Martonne aridity index maps showed a high correlation between these parameters on
their maps, so that in the central and eastern parts of the country with the lowest De
Martonne aridity index, (
 ) shows the highest value. Furthermore, as we getting GPI_1 0.23 – –
GPI_2 0.22 – –
GPI_3 0.25 – –
IDW_1 0.43 0.63 0.37
IDW_2 0.42 0.66 0.42
IDW_3 0.41 0.66 0.43
RBF 0.50 0.70 0.45
K_O_Ga 0.55 0.73 0.48
K_O_St 0.55 0.73 0.48
K_Si_Ga 0.57 0.69 0.45
K_Si_St 0.57 0.69 0.45
K_Si_Ex 0.72 0.77 0.56
K_Si_ Sp 0.65 0.73 0.50
K_Un_Ga 0.55 0.72 0.47
K_ Un _St 0.55 0.72 0.47

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APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
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DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary closer to the northern strip of the country, De Martonne aridity index is increased, while
(
 ) is decrea sed. Unlike the central and northern strip of the country, a good spatial
correlation is not observed between these two indices in the west and south of the
country. Because of the low rainfall in the southern strip, De Martonne aridity index is
also low, but because of the proximity to the sea as a source of moderating temperatures
and also proximity to the equator, the difference between the minimum and maximum
average temperature is not too much. Also, due to the high rainfall in the west of the
country, De Martonne aridity index is high, and the temperature difference is too much.

Figure 5. Assessment of t he relation between the observed and predicted De Martonne aridity
index data using simple – kriging method.

A B

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DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary

Figure 6. Map of De M artonne Aridity index (A), difference between the average maximum and
minimum temperature (
 ) (B), average maximum temperature (C) and average minimum
temperature (D)

In the present study, 17 interpolation methods including IDW, GPI , RBF, LPI, as
well as Kiriging was used to assess De Martonne aridity index in Iran. Variogram used
in this study clearly showed that semivariograms besides demonstration of the spatial
correlation between De Martonne aridity index data are able to model the changes in the
spatial correlation in various aspects. Our results showed the highest correlation
between Simple -Kriging method and the observed De Martonne aridity index data.
Furthermore, it was shown that linear variogram with the nugget effect /sil l ratio of the
0.83 modeled the best correlation between observed De Martonne aridity index data and
was used as the best interpolation method. Following linear variogram, Gaussian,
spherical, and exponential variograms are placed with the amount of 0.82, 0.84, and
0.83, respectively. Moreover, the relation between the observed and predicted De
Martonne aridity index data ( R2=0.77) was assessed to validate data ( Fig.5 ). The strong
correlation between the observed and e xpected data shows high performance of Simple –
Kriging method as the interpolation method in the present study. Musburger et al .
(2012) used the correlation between the observed and predicted data (R2 = 0.69) to
validate the data series.
Conclusion
Interpolation of data along with GIS is of part icular importance in spatial analysis,
since many of the maps used in GIS operations are provided through interpolation. In
fact, providing continuous models from spatial and temporal distribution of data is
possible through interpolation. De Martonne aridity index is a linear relationship, and as
it has a direct relation with rainfall value, the classification of this index is highly
correlated with rainfall value (R2=0.96) . The lowest De Martonne aridity index belongs
to central, eastern and south -eastern areas which are actually Kavir plain (central Iran)
and Lut plain (Southeast) . Getting away from these areas in all geographical directions,
the aridity is decreased, and as a result De Martonne aridity index is increased. The
highest De Martonne aridity index is observed in northern areas, next to the Caspian
Sea. Astara with the mean annual rainfall of 2000 mm is located in this area (40 times C D

Piri et al.: Determinat ion of the best geostatistical method for climatic zoning in Iran
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APPLIED ECOLOGY AND ENVIRONMENTAL RESE ARCH 15(1): 93-103.
http://www.aloki.hu ● ISSN 1589 1623 (Print) ● ISSN 1785 0037 (Online)
DOI: htt p://dx.doi.org/10 .15666/aeer/ 1501_093103
 2017, ALÖKI Kft., Budapest, Hungary more than the mean annual rainfall of the central areas). Iran‘s climate is highly affected
by the presence of t he Alborz and Zagros Mountains. Alborz Mountains , particularly its
northern slopes devote a high portion of the northern rainfall to itself and prevents the
passage of the northern stream to the central areas. Zagros Mountain which is located in
north -west /south -east direction devotes the Mediterranean rainfall to it and prevents the
rainfall to be passed to the central parts. As a result, a vast part of central areas in Iran
has an arid and semi -arid climate.
Other factors which contribute to the excessiv e dryness of these areas include being
away from the moisture sources and being placed in high pressure mid -latitudes. The
major factors that can affect climate classification within a country are topography and
mountain as other factors such as being away from the moisture sources and being
placed in high pressure mid -latitudes are fixed for a country.
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