Evaluation of Different Methods for Interpolation of Mean Monthly and Annual Precipitation Data (Case Study: Khuzestan Province)

Introduction
Isohyetal map is the prerequisite of hydrology, meteorology and climatology studies. Precipitation distribution in a region is related to regionalization method of precipitation data. Khuzestan elevation fluctuates from sea level up to 3712 meter while the elevations of meteorological stations fluctuate from 3 meter up to 875 meter. Due to the complex topography of Khuzestan province and the lack of high elevation meteorological stations with long-term data, it is necessary to determine the appropriate interpolation method for monthly and annual precipitation data in this region.

Methodology
In this study, in order to determine the best method for regionalization of precipitation data, seven interpolation methods were compared together. These methods are ordinary kriging, Cokriging, kriging with external drift, regression kriging, inverse distance weighting, spline and three-dimensional linear gradient. The monthly average and annual long-term data were used from 37 meteorological stations (synoptic, climatology and rain gage) over the 22-year period (1984-2005). In variography analysis, five variogram models (spherical, exponential, Gaussian, linear and linear to sill) were fitted to precipitation data and the best one was selected based on higher correlation coefficient and higher structured component to unstructured ratio. Cross validation technique was used to compare the interpolation methods and the best one was chosen based on regression analysis, and calculation of some error indices like as root mean square error and mean bias error.

Results and Discussion
The probability distribution of precipitation data were tested for normality with Anderson Darling (AD) method. The results showed that precipitation data had normal distribution throughout the year except January and December. Non-normal data in other months were normalized with logarithmic transformation.
Variography analysis results showed that structured component in more than 85% of the months was more effective than unstructured component. Our results confirmed that precipitation data had strong spatial structure. Effective ranges of precipitation data vary from 81.1 Km (in warm months) to 250.3 Km (in cold months). Also spatial structure of warm months was weaker than cold months. The goodness of fit results for different variogram models showed that the optimal model was the spherical model.
These results were obtained based on evaluation of different interpolation methods:
• The optimum power in Inverse Distance Weighting method among the five powers
(1-5) was the power 3. It was also found that in this method the variation of adjacent point’s number does not have significant differences in results.
• The Cokriging method was removed from calculations, because spatial correlation was not strong enough in cross variogram models for different months,.
• Altitude variable and altitude, longitude, latitude variables were selected as covariate variables in kriging with external drift and regression kriging methods, respectively.
• The results of three-dimensional linear gradient method showed that meridional, zonal and altitudinal gradients are positive in all months. In other words, precipitation increase from west to east and south to north of region and also increase with increase in altitude.
• Selection of regression kriging and kriging with external drift methods as the best methods based on the regression analysis showed that there is a consistency between results of these methods with real data. So that it can be considered as a result of using elevation as covariate variable.
• Regression kriging was selected as the best interpolation method in monthly precipitation data based on error indices and regression analysis results in Khuzestan province.
• In annual precipitation data, Regression kriging and ordinary kriging methods were selected as the best interpolation methods based on regression analysis and calculation of error indices. But precipitation of highland area was underestimated by using ordinary kriging method. Considering the importance of precipitation in the highland area and slight difference of root mean square error between these two methods, regression kriging was selected as the best interpolation method for annual precipitation data.
In this study, long-term weighted average of annual precipitation data in Khuzestan province was calculated by using regression kriging. It was 391 mm, which is 41 mm more than the amount reported by the Iran meteorological organization.

Conclusion
Among the interpolation methods which were investigated in this study, regression kriging method is introduced as the most suitable interpolation method in Khuzestan province for monthly average and annual precipitation data.
The average annual precipitation obtained from regression kriging map was 41 millimeter more than the average reported by the Iran Meteorological Organization. This difference is due to accurate estimation of precipitation over highland area of this region.