Identification of spatial distributions and uncertainties of multiple heavy metal concentrations by using spatial conditioned Latin Hypercube sampling

• We introduce spatial structures of environmental variables in sampling procedure.
• The approach efficiently captures spatial structures of environmental variables.
• Optimally selected samples efficiently capture variability of monitored variables.
• The proposed approach effectively selects samples without a reconnaissance survey.
• The approach efficiently selects samples — especially small samples.

This work develops spatial conditioned Latin hypercube sampling (scLHS), a novel advance on conditioned Latin hypercube sampling (cLHS) [Minasny and McBratney, Computers & Geosciences (2006) 1378–1388]. The difference between cLHS and scLHS is that the latter introduces variograms of ancillary variables into the objective function of the optimization procedure that selects sampling locations. The improvement of scLHS was evaluated by applying both scLHS and cLHS to simulated samples of multiple heavy metals (Cr, Cu, Ni, and Zn) in the soil of Changhua County in Taiwan. Simulation was done by using sequential indicator simulation (SIS), which generated 1000 realizations of spatial distributions of the heavy metals, based on existing sample data, to represent the real distributions of heavy metals. The results of the Ripley K analysis show that the locations of samples obtained by both approaches were not significantly spatially segregated. The sampling results show that the declustering of sample locations may dominate the optimization process in cLHS and scLHS. Statistical analysis indicated that compared with cLHS, the means, standard deviations and contamination proportions of scLHS samples captured more efficiently the variability of the SIS realizations. Moreover, the experimental variograms of scLHS samples, especially for small sample sizes, captured the experimental variograms of the SIS realizations more efficiently. Therefore, the use of the scLHS approach is recommended as a novel alternative sampling approach without the need for a reconnaissance survey to increase the efficiency of capturing the spatial structures of soil heavy metals and delineating contaminated sites.