Feasibility of using Copula function in predicting soil available phosphorus and potassium

Spatial and temporal variations of soil characteristics occur in large and small scales. Investigating the variability of soil parameters is considered as one of the requirements for proper management of fertilizer resources in a sustainable agricultural system. Studying of these variation is very time-consuming and costly especially in large scales. In order to the fast and reliable determination of the soil properties, various interpolation techniques have been developed and applied. The most widely used interpolation technique is the different Kriging types. The copula function is one of the new interpolation techniques that are recently used in sciences such as hydrology. Thus, the aim of this research was to evaluate the spatial variation of some soil chemical properties using the copula function and comparisons with geostatistics techniques.

Sampling by regular networking was done in an area of 484 ha located in 10 km far from the west of Baft city, located in Kerman province, central Iran (latitude of 29° 15′ N and longitude of 56° 29′ E). In the studied area, three agricultural, pasture and industrial sites are located nearby. The common crops of the region are wheat, barley, alfalfa, legumes and orchards of walnuts, pomegranates, almonds and grapes. The average height of the studied area is 2270 meters above sea level, the average annual temperature of the area is 16 degrees Celsius, and the average annual precipitation of the area is 247 mm. The soil used for the experiment was collected from 0 to 20 cm depth of the field. 121 soil samples were air-dried and, some physical and chemical properties were measured. In order to fit the Copula function to the data, first the appropriate marginal distribution function should be fitted to the data. For this purpose, three tests were used: Kolmogorov-Smirnov, Anderson-Darling and Chi-Square. The mentioned tests were carried out in the EasyFit 5.5 statistical software. By fitting the best marginal distribution function, the cumulative value of the marginal distribution function is calculated for each data. After calculating the above values, detailed functions can be fitted to the data. Finally, the accuracy of each interpolation method was evaluated according to the root mean square Error (RMSE), coefficient of determination (R2), mean absolute error (MAE) and mean biass error (MBE) indices.

In all types of geostatistical methods, the first step in interpolation is to fit the semivaiogram to the measured data, so after normalizing the data and validating the models, the appropriate model was selected for fitting the semivaiogram. Among the measured parameters, Pava and Kava semivaiogram followed spherical model and the interpolation of the above variables was done on the basis of this model. Copula analysis showed that the available phosphorous and potassium variables followed from the Wakeby and gamma distribution function, respectively. Also, based on the Pearson correlation coefficient, the correlation between pairs of points was less than 2000 m and the distance more than 2000 m was known as an independent distance. Based on the validation criteria for Pava parameter, Median copula function, Average copula function, IDW, Ordinary Kriging, Disjunctive Kriging, Universal Kriging and Simple Kriging have better estimates, respectively, and in the same way, the best interpolator for Kava parameter Median copula function, Average copula function, Ordinary Kriging, Universal Kriging, Disjunctive Kriging, Simple Kriging and IDW were determined, respectively. The estimation performance based on the coefficient of determination (R2) showed that value of this coefficient for copula function for available phosphorous and potassium were 5% and 4% greater than conventional geostatistics techniques. Also, the error of estimation was less for copula function indicating the better performance of copula to estimate the mentioned soil properties

This study was performed to investigate the Feasibility study of Copula function in predicting some soil nutrients and comprising this method with widely used methods of geostatistics. Our results demonstrated that the copula function method is more capable than the classical geostatistical methods in estimating soil properties due to the non-dependence of this method on the normality of the data distribution and outlier data. Therefore, with the help of this method, having a reliable and high-quality data bank of soil characteristics, acceptable maps of other soil characteristics can be presented at various scales.