Optimization of spatial sampling schemes for maize planting acreage estimation

Abstract: Sampling fraction, sample layout, and sampling unit scale are three basic elements of a spatial sampling scheme. It plays an important role in optimizing these factors for decreasing the sampling cost and improving the extrapolation accuracy of survey sampling. In this study, spatial analysis, "3S" techniques, and traditional sampling methods were employed to optimize the three basic elements, aiming at the problem that the spatial sampling efficiency is still poor due to only one basic element (e.g. the sampling unit scale) being optimized in the existing spatial sampling studies for crop acreage estimation. DeHui County in Jilin Province was chosen as the study area, maize planting acreage as the study object, and square grids as the shape of the sampling units. First, the sampling unit scale, sampling fraction, and sample layout were formulated based on the Second National land survey data, and the spatial distribution data of maize in the study area in 2009 (derived from SPOT image that the spatial resolution is 10 m). In order to analyze the relationship between the scale and spatial correlation of sampling units, the sampling unit scales were designed to be 8 levels, that is 500 m × 500 m, 1 000 m × 1 000 m, 1 500 m × 1 500 m, 2 000 m × 2 000 m, 2 500 m × 2 500 m, 3 000 m × 3 000 m, 3 500 m × 3 500 m, and 4 000 m × 4 000 m, respectively, the sampling fractions were designed to be 7 levels, that is 0.5%, 1.0%, 1.5%, 2.0%, 2.5%, 3.0%, and 3.5%, and four patterns were selected as the samples layout, they are simple random sampling, system isometric sampling, stratified random sampling, and stratified system isometric sampling respectively to conduct the optimal design of the sampling fractions and samples layouts. Secondly, the optimal sampling unit scales were determined by introducing the global spatial autocorrelation index Moran's I, following the traditional sampling principle that sampling units should be independent of each other; Thirdly, the samples were drawn, and the sample observations measured, population values were extrapolated, and the sampling errors were estimated using the designed spatial sampling scheme. Finally, the relative error of population extrapolation, coefficient of variation (CV) of the population total estimator, and sampling sizes were selected as the evaluation indices to find out the optimal sampling fraction and sample layout. The experimental results demonstrated that the spatial autocorrelation of sampling unit increases with its scales, and that there was a linear positive relationship between the sampling unit scale and spatial autocorrelation. While the sampling units scale was 500 m× 500 m, there was nearly no spatial autocorrelation among sampling units. Therefore, 500 m× 500 m was selected as the optimal sampling unit scale. In order to improve the stratified sampling efficiency, cropland area may be considered as a stratification index due to there being a very significant linear correlation between maize planting acreage and cropland area in sampling units; When the sampling fraction was the same level, the relative error and CV of population extrapolation which the sample layout was the stratified system isometric sampling were the lowest in four layout patterns; The efficiency of spatial sampling scheme in which the sampling fraction was 1% was the highest in the 7 designed levels. In this way, this research can provide a solution for improving the efficiency of a spatial sampling scheme to estimate crop acreage.