stage, the prior PDF is updated with specific data. The prior and posterior PDFs are related based on Bayes’ theorem. Based on our purpose of estimation, different conditions such as mean and mode (known as BMEmean and BMEmode) of the posterior PDF can be obtained. The BMEmean minimizes the mean square error, and the BMEmode is the most probable realization.
Kriging is one of the optimum classical geostatistical methods which can estimate unsampled stations with the contribution of sampled measurements. Kriging is a special case of BME. Under some assumptions (considering mean and covariance as general knowledge and hard/ soft data as site-specific knowledge), kriged and BME predictions become the same. Kriging is used in this study as a base for comparison.
One hundred and five rain gauge stations are located in and around the study area, out of which 44 have full records of observations for the period of 1977 through 2008. The records of these stations are considered as the hard dataset. The remaining stations have some missing data and therefore observations in these stations are classified as the soft dataset.
The stages of spatial modeling in this paper are as follows: (1) The primary processing of raw data, which includes investigating statistical missing data; the hard and soft data are distinguished in this stage. (2) The determination of variograms; the primary fitting of experimental variograms was done using GS+ software based on the maximum correlation coefficient and then these parameters are optimized by the Iterated Non-linear Weighted Least Squares (INWLS) method for univariate cases and Iterated Least Squares (ILS) method for multivariate cases. (3) The application of the optimum theoretical variograms obtained through the Kriging, Cokriging and BME methods, and, finally, (4) the estimation of precipitation.
The cross validation technique was used to evaluate the results of these two methods. The results of this study have shown that BME estimates were less biased and more accurate than those of the classical OK.