Assessing the feasibility of copula functions for estimating soil properties: a case study in Hunan Province

Copula functions provide a powerful tool for analyzing and modeling the spatial distribution of environmental data. Consequently, their application in estimating soil properties has the potential to provide more accurate results in this domain. The objective of this study is to compare the accuracy of estimates derived from copula functions with those obtained using geostatistical methods for analyzing and evaluating the spatial distribution of key soil properties, such as soil texture and soil organic matter (SOM). A total of 700 surface soil samples were randomly collected, and soil properties, including sand, silt, clay, and SOM, were measured. Four Archimedean copula functions (Clayton, Frank, Gumbel, and Joe), along with several geostatistical techniques (Simple Kriging, Ordinary Kriging, Indicator Kriging, Disjunctive Kriging, and Inverse Distance Weighting), were utilized for spatial interpolation. The performance of these methods was assessed using statistical indices, including the coefficient of determination (R2), root mean square error (RMSE), and mean bias error (MBE). Spatial analysis of soil properties using geostatistical methods revealed that the degree of correlation between variables diminishes with increasing distance. Notably, no spatial correlation was observed beyond a distance of 30,000 m in the study area. Furthermore, a comparison of copula functions with geostatistical techniques, based on evaluation criteria, indicated that the median copula function outperformed the other methods in estimating soil properties. The R 2 values for estimating sand, silt, clay, and SOM using the median copula method were 0.60, 0.70, 0.53, and 0.71, respectively. Likewise, the RMSE values for these properties were 4.41, 3.30, 4.60, and 0.25 (%), while the MBE values were 2.10, 11.82, 2.14, and 0.50 (%), respectively. Overall, the findings demonstrate that the median copula function provides a more accurate and reliable approach compared to the other methods evaluated in this study for the spatial distribution.