Evaluation of the Performance of Copula Function in Estimating Some Soil Properties

The study of spatial distribution of soil properties for optimal soil management and proper utilization of non-renewable soil resources is of particular importance. The copula function is one of the new interpolation techniques that are widely used in various sciences such as hydrology. Thus, the aim of this study was to evaluate the spatial variation of some soil properties using the copula function and to compare with geostatistics techniques. Sampling by regular networking was done in a 484 ha area in the west of Baft city, Kerman province, and 121 surface soil samples were collected. After air drying and passing through a 2 mm sieve, the percentage of organic matter and clay were determined in soil samples. To interpolate, four functions of the Archimedean copula including the Clayton, Frank, Gumbel and Joe functions, and geostatistics techniques including simple kriging, ordinary kriging, universal kriging and disjunctive Kriging and the Inverse Distance Weighting (IDW) method were used. The results were analyzed using Root Mean Square Error (RMSE), determination coefficient (R2), mean absolute error (MAE), and Mean Bias error (MBE). In order to fit the copula function on the data, the distribution function of the studied variables was determined. The results showed that the distribution of each of the studied variables is different and is explained by different distribution functions. Also, with increasing distance, the value of correlation for all studied variables decreased so that after a distance of 2000 meters, they do not show any spatial correlation. Comparison of the Copula function and geostatistical techniques based on evaluation criteria showed that the Copula function had a better performance in estimating the studied variables and the estimation error for the Copula function were calculated less. In general, the results of this study showed that due to the skewed nature of soil data, Copula function have the ability to fully express the probabilistic dependence and can be considered in spatial studies.