Determining optimum sampling numbers for survey of soil heavy metals in decision-making units: taking cadmium as an example

A three-dimensional sampling design based on the coefficient of variation method for soil environmental damage investigation

A traditional grid model for soil sampling may suffer from poor efficiency and low accuracy. With a nonferrous metal processing plant as the study area, a three-dimensional kriging interpolation model was built based on this plant's preliminary investigation data for arsenic (As), and a detailed survey sampling programme was proposed. The sampling density at the pollution interval of the surface soil was estimated by the coefficient of variation method, and the sampling depth was determined by the pollution interval of the vertical prediction results. The results showed that the encrypted soil sampling distribution optimisation method obtains greater pointing accuracy with fewer points. The sampling accuracy was 87.62% after optimising the depth of pointing. Moreover, this approach could save 66.13% of the sampling costs and 56.93% of the testing costs compared to a full deployment programme. This study provides a new and cost-effective method for predicting the extent of contamination exceedance at a site and provides valuable information to guide post-remediation strategies for contaminated sites.

Improving the mapping accuracy of soil heavy metals through an adaptive multi-fidelity interpolation method

Soil heavy metal pollution poses a serious threat to environmental safety and human health. Accurately mapping the soil heavy metal distribution is a prerequisite for soil remediation and restoration at contaminated sites. To improve the accuracy of soil heavy metal mapping, this study proposed an error correction-based multi-fidelity technique to adaptively correct the biases of traditional interpolation methods. The inverse distance weighting (IDW) interpolation method was chosen and combined with the proposed technique to form the adaptive multi-fidelity interpolation framework (AMF-IDW). In AMF-IDW, sampled data were first divided into multiple data groups. Then one data group was used to build the low-fidelity interpolation model through IDW, while the other data groups were treated as high-fidelity data and used for adaptively correcting the low-fidelity model. The capability of AMF-IDW to map the soil heavy metal distribution was evaluated in both hypothetical and real-world scenarios. Results showed that AMF-IDW provided more accurate mapping results compared with IDW and the superiority of AMF-IDW became more evident as the number of adaptive corrections increased. Eventually, after using up all data groups, AMF-IDW improved the R² values for mapping results of different heavy metals by 12.35-24.32%, and decreased the RMSE values by 30.35%-42.86%, indicating a much higher level of mapping accuracy relative to IDW. The proposed adaptive multi-fidelity technique can be equally combined with other interpolation methods and provide promising potential in improving the soil pollution mapping accuracy.

Evaluating sample sizes and design for monitoring and characterizing the spatial variations of potentially toxic elements in the soil

Cost-effective, representative and spatial coverage sampling designs are required to monitor the effects of potentially toxic elements (PTEs) in the soil. This study aims to evaluate the minimum sample sizes and placement of soil sampling designs to monitor and characterize the spatial variation of the PTEs (Cu, Zn, Cd, Cr, Pb, and Ni) in the soils. However, there is no standardized approach for evaluating the optimum soil sample size and monitoring location because of the spatial heterogeneity of PTEs in the soil. As a result, three broad techniques were applied. The first step was to use Global Moran's I and q-statistic values to describe the variability of soil PTEs and select appropriate evaluation methods. Second, using simple random sampling (SRS), ordinary kriging (OK), and Mean of Surface with Non-homogeneity (MSN), we estimated and evaluated soil PTEs in the current soil sampling schemes. Finally, MSN and spatial simulated annealing (SSA) optimization techniques were used to assess the required sample sizes and placements in the existing designs. Method performance was evaluated using a standard error (SE) and a relative standard error of the mean (RSE). Except for Zn and Cd, all PTEs tested showed heterogeneous distributions over the area. The MSN lowered the predicted SE by 79-86 % compared with SRS. The OK approach also outperformed the SRS method regarding mean estimated values of soil PTEs by 42-57 %. After SSA refined the initial design, the predicted SE by MSN of Cr and Zn was lowered by 13 % and 39 %, respectively. The MSN was effective with small sample sizes, reducing sample sizes and surveying costs by 39 % after SSA optimized the existing sample numbers. Thus, integrating various sampling strategies may be efficient for building optimal sample designs to monitor PTEs in the soil.

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

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.

A simple method to determine the sampling numbers in decision-making units with unknown variations of soil cadmium

Sampling number is one critical issue to achieve credible results when surveying soil contamination and making remediation decisions. Traditional methods based on a normal distribution for determining numbers of samples are not always optimal because most distributions of soil heavy metal concentrations followed a log-normal distribution. Moreover, the variation of soil heavy metal concentrations is a prerequisite for previous methods to determine sampling numbers. Unfortunately, the variation is often unknown before soil sampling. Therefore, a simple method under the log-normal distribution without relying on variation to determine quickly the sampling number (QSN) was developed for soil cadmium and compared with other methods based on classical statistics and Chebyshev inequality. Results showed that an equation as a function of sampling areas could be used to determine QSN (QSN = 18.44 × A^0.54 + 8.69, A is sampling areas, km²), with acceptable errors ranging from 13 to 33% at the sampling areas of 0.03-10 km². The developed simple method for QSN was easy to use and cost-effective without prerequisite on the estimation of variation. Moreover, when the sampling cost was enough and the improved accuracy was requested, the increased sampling numbers were recommended as 1.53 times as the number calculated by the simple method. Therefore, the proposed method is believed as a simple and cost-effective method to determine the sampling numbers of soil Cd in decision-making units with unknown variations.