An Investigation of Annual Rainfall Spatial Distribution Using Geostatistical Methods (A Case Study: Qom Province)

Introduction
The rate of average precipitation specifically its regional average is one of the significant factors in the field of natural resources studies. There are different estimation methods to estimate the precipitation such as geostatistic technique. This method is important with concerning to correlation and data spatial structure. Spatial location of the samples can be analyzed with the purposed quantity together. In other word the relationship between different quantitative rates is required to the community, samples distance and their situation dime. This spatial relationship (distance and community) is possible to describe in mathematical method between the rates of quantities in sampled community. In this research Kriging and inverse distance methods with power of 1 to 3 used to investigate the annual precipitation rate in Qom province.

Methodology
The study area
This study is focused on Qom province with an area of 1123800 hectares. For the data control and their accuracy 12 climatology stations were used as the coved points in the study area. After determining the stations, data homogeneity is sorted based on run test to make sure data quality and also the recorded data series homogeneity. According to table 1 the average rainfall was extracted based on IDW method for 30 years from 1978-2007 in GS+ environment.


Table 1: Characteristics of the rainfall in Qom Province
Rainfall Ave. Max. Min. St.D.
P/mm 180.03 250.90 117.40 40.639


For that reason the related data and information were collected for the software environment of GS+ and Arc GIS v.10 to produce isohyets map and analysis of variogram. The cross validation, MAE and MBE parameters techniques were used to validate IDW methods.
Analysis of Variogram
Simi-variogram method is one of the sensible methods for the spatial variations. Calculation of semi-variogram curve is the most significant operation of geostatistical which based on variation of two points in distinctive distance.

Method and criteria of validation
Cross validation technique and statistical two parameters of MAE and MBE were used to validate the IDW methods. In this study different models such as linear, spherical were used to calculate Kriging coefficient as a geostatistical estimator.

Results and Discussion
For investigation on spatial structure of the annual rainfall, the rate of empirical semi-variogram was calculated to draw the curve which processed with a appropriate model (table 2).


Table 2: The results of different semi-variogram model investigation in Kriging for the rainfall investigation
Model P/mm
MBE MAE
Gosian 14.1 30.23
Linear 24.6 93.24
Exposure 8.8 32.5
Spherical 11.82 35.12


Table 3 indicates different parameter of the model than the spatial structure.


Table 3: The effective parameter in spatial structure model
RSS
(mm2) R
(km) Co
Effect of segment (mm2) Co+C
Threshold effect (mm2) Ao
Distance (km) Co + C /C Model
7.38 31.46 0.6 5.20 75.9 0.885 Gaussian
8.38 33.70 0.01 5.02 77.9 0.998 Exposure
7.8 62.10 0.06 5.12 162.1 0.99 Spherical
51.2 80.64 0.08 3.63 80.64 0.997 Linear

Final results of the validated different methods of IDW are also indicated in table 4.

Table 4: The final validated results of different IDW methods
Division Precision IDW methods
14.1 30.23 Kriging
5.9 32.23 IDW1
11.1 33.55 IDW2
13.6 35.1 IDW3

The results shown that the annual semi-variogram of Gaussian is indicated with the best precision and the annual rainfall variations are mostly following Gaussian model. Empirical variogram of height and rainfall at the large scale of the study area were indicated an extension of 75.9 km between stations with a meaningful relationship to the height. After this distance the relationship between them is random with an average distance of 31.46 km for the effective rainfall which tends to a radial form of the rainfall correlation for the stations. Therefore distances between the stations are limited to 31.46 to 75.9 kilometer.

Conclusion
According to the gained results in this study Kriging method is specified with the highest precision (MAE of 30.23 mm) and the lowest precision is related to the inverse distance with power 3 (MAE of 35.5 mm) which are shown as follow:
Kriging method >?IDW?^3>?IDW?^2>?IDW?^1
Statistically the extracted results from the selected stations with 30 years recorded data can be concluded that the form of rainfall is distributed with 210, 205, 180 and 165 millimeters in Khalajestan district in west, Kahak district in south, Salafchagan in south west, central part and North West parts respectively.