Optimal spatial sampling design for monitoring potentially toxic elements pollution on urban green space soil: A spatial simulated annealing and k-means integrated approach

Abstract

Sampling design in soil science is critical because the lack of reliable methods and collecting samples requires tremendous work and resources. The aims were to obtain an optimal sampling design for assessing potentially toxic elements pollution using pilot Pb soil samples from the urban green space area of Shanghai, China. Two general steps have been used. The first step is to determine the optimum sample size against improving the prediction accuracy and monitoring costs using the spatial simulated annealing (SSA) algorithm. Secondly, we evaluated their likely placement of new extra sampling points by integrated SSA with k-means (SSA+ k-means) and expert-based (SSA+ expert-based) sampling methods. The improvement of sampling design by the integrated sampling approaches was evaluated using mean kriging variance (MKV), root mean square error (RMSE), and mean absolute percentage error (MAPE). The findings indicated that adding and placing 350 new monitoring points upon the existing sampling design by SSA increased the prediction accuracy by 64.35%. The MKV for the optimized SSA+ k-means sample was lower than by 4.12 mg/kg, 9.46 mg/kg compared with locations optimized by SSA and SSA+ expert-based method, respectively. Optimizing new sampling locations by SSA+ k-means sampling method was reduced MAPE by 9.26% and RMSE by 7.13 mg/kg compared to optimizing by SSA alone. However, there was no improvement in placing the new sampling points in SSA+ expert-based sampling method; instead, it increased the error by 8.11%. This paper shows integrating optimization approaches to evaluate the existing sampling design and optimize a new optimal sampling design.