Additional Sampling Layout Optimization Method for Environmental Quality Grade Classifications of Farmland Soil

Farmland soil environmental quality is important for farmland management. To precisely classify the environmental quality grades of farmland soil, additional samples may be required for multistage sampling or supplementary investigations. Compared with the sampling optimization methods used for mapping or estimating global means, environmental quality grade classifications are primarily focused on estimating the relationships between the values of unsampled locations and the thresholds that classify the environment quality grades. Such classifications must use a sampling layout optimization method to distribute additional sampling units into areas with a high risk of misclassification. To resolve such problems, this paper provides an additional sampling layout optimization method that initially develops a classification error index by building a multi-Gaussian model with the predicted values and error variances of unsampled locations and then calculates the probability of a threshold value occurring in the standardized Gaussian distribution. The average error indexes of all locations in the study area are then set as the objectivity function of the additional sampling layout optimization, and the spatial simulated annealing is adopted to obtain the optimized sampling layout by minimizing the objectivity function. The performance of the error index sampling layout optimization method was demonstrated in a case study using chromium concentration data for Hunan Province, China. The results showed that the additional samples generated by the proposed method produce lower and more stable classification error rates than the minimization of the mean of the shortest distances and spatially random sample methods. The proposed method can be used to improve the efficiency of additional sampling for environmental quality grade classifications of farmland soil.