Spatial Variability-Based Sample Size Allocation For Stratified Sampling

Stratified sampling is one of the most commonly used sampling strategies for soil survey and mapping. An important issue in stratified sampling is the sample size allocation for each stratum. Neyman allocation is a typical sample size allocation approach in which the main idea is to assign more samples to a stratum with a larger internal standard deviation. By applying the spatial variability for sample size allocation, we proposed a new allocation approach (SVNA) for stratified spatial sampling. In this new approach, more samples were allocated to strata with both a bigger statistical standard deviation and larger spatial variability of the target variable. SVNA was evaluated using a simulated experiment based on real-world soil data of Jiangsu province, China. The target variable was soil organic matter (SOM), and land-use type was utilized for stratification. Simple random sampling (SRS) and spatial simulated annealing algorithm (SSA) were applied to determine sample locations. Results showed that the performance of SVNA generally was superior to Neyman allocation in terms of SOM content prediction at all sampling densities (4.28-0.19 points per km(2)) regardless of the application of SRS or SSA for sample location determination. The maximum reduction of mean squared error (MSE) for the SOM content prediction using SVNA was 11% using SRS and was 10% using SSA. Compared with Neyman allocation, SVNA obtained greater prediction accuracies in strata with large spatial variability and similar or slightly smaller prediction accuracies for strata with small spatial variability. Furthermore, the prediction accuracy of the SVNA approach tended to decrease when the sampling density was 0.37 points per km(2), and this sampling density threshold was not the same for each stratum. We concluded that SVNA is an efficient sample size allocation approach for stratified sampling in soil survey and mapping.