INTRODUCTION
The deficiency of major nutrients in arid and semiarid areas is apparent because
of the encasement of nitrogen in the combination of organic materials, slow
mineralization rate of these compounds, weak solubility of phosphorus and stabilization
of potassium by some types of clays. Islam et al.
(2009) studied N, P, K and organic carbon as main plant growth factors.
Their results revealed that plant macro nutrients nitrogen, phosphorous and
potassium were found in significant amount compared to some commonly used organic
manures.
Chemical fertilizers are the most important source for the provision of plant
nutrients and their proper and optimized application is of fundamental role
in the obtainment of the purposed crop yield (Washburn et
al., 2002) and preserve of agroecosystem. If a plant suffers from the
deficiency in one of the major nutrients, NPK; then the increased fertilization
with other nutrients will not lead to the increased yield, unless the limiting
factor is corrected. Soil fertilization management based on particular variations
of each field soil is one of important principles of the reduction of the environmental
pollutions caused by irrationally overuse of chemicals such as chemical fertilizers
(Scharf et al., 2002). With the correct fertilization
management, comprehensive and sufficient information on the rates of soil nutrients
can be applied for better yield of crop plants and to this end, the classification
of the lands from the viewpoint of fertilization recommendations based on the
soil nutrients analysis in laboratory is necessary and in the absence of such
information on soil variation, some soils will receive more fertilizers and
some will get less than the rates they require. Because of the complexity of
local distribution and high variation in soil, the use of geostatistical approaches
for the estimation of soil properties in nonsampled points is necessary (Clark
and Harper, 2000). In such cases, geostatistical approaches including nonparametrical
statistical estimators like weighted moving average and or parametrical landstatistical
approaches such as Kriging and Cokriging methods can be used (Wackernagel,
2003). The difference among these methods lies in the calculation of the
weight factor which is considered for each of the points around a given point.
Nazarizade et al. (2003) applied a geostatistical
approach to analyze local structure and the number of soil samples in order
to study soil characteristics such as the rate of phosphorus and the number
of arbuscular mycorrhizal fungus. They indicated that the variation of these
two factors in irrigated cultivations were of local structures and introduced
Kriging method as an appropriate method for the estimation of local distribution
of phosphorus and arbuscular mycorrhizal fungus spores. Amini
et al. (2003) evaluated the soil pollution of Isfahan region following
Fuzzy login and geo statistics methods and concluded that this integrated approach
made it possible to evaluate multiple element pollutions in the same time and
that the calculated variograms also mainly followed exponential and spherical
models. They prepared regional contaminated area allocation map. Calculating
nutrient buffer index used in fertilizer recommendations. Myers
et al. (2003) indicated that the mentioned index was positive with
phosphorus and potash, reflective of the inadequacy of the fertilizer rate.
Clay et al. (2003) studied and evaluated the efficiency
of various field fertilization management strategies and concluded that the
four hectare netting approach with the lowest error rate was the most appropriate
method for the recommendation of phosphorus and potash. Balasundram
et al. (2006) mentioned Spatial variations in soil fertility can
obscure treatment effects and hence, lead to incorrect fertilizer recommendations.
Their results showed that the effect of treatments on plant growth were not
significant. Growth variables exhibited a significant spatial trend. A corresponding
observation was found for growth residuals. Washburn et
al. (2002) investigated the variability of oneranged soil phosphorus
distribution, but they did not apply geostatistical approaches for fertilizer
recommendations and fertilization management. Kamaruzaman
and Tamaluddin (2001) suggested the preparation of soil variation maps for
the agricultural production with the use of Gs+. Scharf et
al. (2002) have recommended future studies on the determination of the
spatial distribution of nitrogen to find out the variation of nitrogen in the
ranches. Law et al. (2009) quantified the spatial
variability of Soil Organic Carbon (SOC) and estimating SOC concentration in
oil palm. Their Results showed all operational areas exhibited a definable spatial
structure and were described by either spherical or exponential models.
The present research was performed in order to study the spatial variation of soil nutrients including nitrogen, phosphorus and potassium, to compare various geostatistical approaches from the stand point of their efficacy in the estimation of the rates of the nutrients as the major soil fertility determinants and to map their spatial distribution.
MATERIALS AND METHODS
Area identification: This research was conducted in the Southern part
of Uromieh plain of 36690 ha area, in West Azerbaijan Province, Iran, during
years 2008 to 2009. Geographically, located in an area between longitudes 45°
05' 00" E and 45° 20' 00" E and between 37° 15' 00" N and 37° 35"
00" N.

Fig. 1: 
Location of study area and soil profiles 
Figure 1 indicates the location of the region in the country
and province and shows the position of the profiles used in the plain. Based
on the semi detailed pedological studies, the regional soils are classified
as Inceptisols and belong to one of two main subgroups, typical Calcixerepts
and typical Haploxerepts. The distance between the profiles in the studied region
varied between 1300 and 4700 m.
Research framework: Normality of data was tested with ShapiroWilk test
(Shapiro and Wilk, 1965) by SPSS software (Levesque,
2007). To evaluate the spatial distribution of the major soil nutrients
including nitrogen, phosphorus and potassium, the data from 28 profiles were
studied and geo statistical methods including Kriging, Weighed Moving Average
and CoKriging methods (Metternicht and Zinck, 2003)
were used in GIS medium and GS^{+} and ARCVIEW_{8} software
(Goovaerts, 1999) were applied to investigate the spatial
changes and the estimation of soil nutrients. The general equation for these
methods is as Eq. 1.
Where:
Z* (xi) 
= 
The estimated amount 
Z (xi) 
= 
The observed amount around the assumed point 
(xi) 
= 
The position of the observed points 
λi 
= 
The amount of weights of the observed points 
N 
= 
No. of the measurement points 
To evaluate interpolation methods, the cross validation technique (Moore,
2007) and two MAE (Mean Absolute Error) and MBE (Mean Bias Error) statistical
parameters were used. The MAE is an indicator of errors in the results and MBE
indicates the bias of the results obtained through the applied method. When
MAE and MBE are 0.00 or near to naught, the applied method simulates the fact
well. However, as far as its amount is farer than 0.00, it implies to less precise
and more bias. How the parameters MAE and MBE are calculated, has been indicated
as Eq. 2 and 3.
Where:
R_{s} 
= 
The estimated amount 
R_{o} 
= 
The measured amount 
n 
= 
No. of the data 
RESULTS AND DISCUSSION
To generalize the results obtained from point rates in profile sites to the regional one, the normal distribution of the data was checked with ShapiroWilk test. If test coefficient and skew ness are, respectively less than 0.5 and 1.0, the data will be of normal distribution. The results indicated that the data related to soil nitrogen and phosphorus were of such a characteristic, however, those related to the rates of soil potash were not normally distributed and therefore, these data were logarithmically converted and normalized (Table 1).
The distribution of the studied profiles, together with the measured rates of nitrogen has been shown for example in Fig. 2.
Table 1: 
Results of the ShapiroWilk test of normality 


Fig. 2: 
The rates of nitrogen measured in each of the profile sites 
Table 2: 
Rates of geostatistical interpolation parameters 


Fig. 3: 
Empirical semi variogram of nitrogen obtained based on Kriging
method 

Fig. 4: 
Nitrogen empirical semi variogram with potassium based on
Cokriging method 
Then, the spatial variations of soil fertility parameters in the nonsampled points were studied. In Kriging method, the effect radiance of this semi variogram was determined as equal as 1323 m; the nugget effect was calculated as 0.008 and sill was equal to 0.65 milliequivalent per 100 grams of soil. The summary of the results related to other nutrients has been presented in Table 2.
To use Cokriging method, the empirical semi variogram curve of nitrogen was drawn taking advantage of potassium as an auxiliary factor with the most rate of mutual correlation. An example of Kriging and Cokriging method based on Gaussian model to semi variogram in relation to nitrogen cross taking advantage of auxiliary variable of potassium has been presented in Fig. 3 and 4.
The radius of the effect of this method was calculated as equal to 2510 m, the nugget effect was determined as equal as 0.01 and sill was calculated as 21.6 milliequivalent per 100 g of soil. The correlation coefficient for the presented model was calculated as 1. The results related to other nutrients have been indicated in Table 2.
The weighted moving average approach was taken in use with three of soil properties, that an example of the calculation of the rates of organic carbon and its comparison with the measured rates with this method has been indicated in Fig. 5.

Fig. 5: 
Weighted moving average based evaluation of soil nitrogen 

Fig. 6: 
Empirical semivariogram model of real soil potassium rates
based on Kriging method 

Fig. 7: 
Empirical semivariogram model of soil logarithmic rates of
potassium based on Kriging method 
The results of geostatistical analyses of studied fertility factors have been presented in Table 2. Based on this table, the empirical semi variogram models of most of the factors have been obtained as of Gaussian type. There are also exponential and spherical models obtained to Phosphorus and Potassium by Kriging method. Considering to the nugget effect, it is revealed that the lowest rate of it calculated based on Kriging method, is related to nitrogen with the rate of 0.008 Meq/100 g of soil and its highest rate calculated based on the same method, is related to potassium with the rate of 93 Meq/100 g. The distance of efficiency of models ranges between 1228 for Phosphorus and 6220 m for Potassium.
As shown in Table 2, the logarithmic amounts of potassium
were used in Kriging model. Differences of the fitted semivariogram to the
actual potassium rates and its logarithmic amounts are shown in Fig.
6 and 7. The change of origin has been conducted to normalize
data of potassium and to decrease nugget effects as Fig. 7.
Accordingly the correlation coefficient increased from 0.23 to 0.998.
Table 3: 
The preciseness and deviation rates of the methods applied
for the estimation of some soil nutrients 

To evaluate and select the most proper geostatistical method for the estimation of soil major nutrients, the rates of preciseness and deviation for each of the methods were investigated with each of the individual fertility nutrients, the results from which have been indicated in Table 3.
Based on the Table 3, it was revealed that with all cases, Kriging method was of less error and deviation rates compared with Cokriging approach. Also, it was notable that weighted moving average method was of more error and deviation rates compared with Kriging approach but still of deviation rate less than that of Cokriging method.
Thus, Kriging method with high preciseness and less deviation was selected as the suitable model for the regional estimation of soil fertility nutrients and their rates in the different points of the region were estimated and their maps of regional distribution were prepared in GIS medium. The results showed that the rate of organic carbon is generally low in the region so that most of the regional areas are of very low to low organic carbon rates and only some spots around Orumia city are of high organic carbon contents (Fig. 8). With phosphorus, the region is totally classified as in the range of high to very high (Fig. 9). From the standpoint of potassium content, the region is evaluated as one of low to mediate contents of potassium (Fig. 10). In some limited points around the city, the regional content of potassium rises to high to very high amounts.
The present investigation was carried out in order to have a better understanding
of the local variation in the rates of soil major nutrients as the prerequirement
for programming and management of fertilization and fertilizer provision in
vast regions. Scharf et al. (2002) have suggested
next studies on the determination of the local distribution of nitrogen in order
to understand its variation in vast ranches and this investigation has been
necessarily performed to respond to this necessity and the question of this
type but with other major nutrients. The results related to phosphorus got through
this research are in accordance with those obtained by Nazarizade
et al. (2003). Also present results agree well with the results
of Amini and his collaborators studies on the subject of soil pollution and
the selection of Kriging method as the proper approach, however, in our studies,
the semivariogram was Gaussian model. In contrast in the study conducted by
Amini et al. (2003), the calculated variograms
were mostly exponential and spherical. Washburn et al.
(2002) investigated the oneranged variability of phosphorus distribution
but they did not use landstatistical approaches to make fertilizer recommendations
and to manage fertilization.

Fig. 8: 
Spatial variability map of Nitrogen by Kriging 

Fig. 9: 
Spatial variability map of exchangeable phosphor by Kriging 

Fig. 10: 
Spatial variability map of exchangeable potassium by Kriging 
Kamaruzaman and Tamaluddin (2001) have recommended
the mapping of soil variation with the use of Gs+ for agricultural production
purposes, however, they have not applied geographical information system to
compensate the existent limitations of the software they used.