Effects of spatial autocorrelation on spatial sampling efficiencies of winter wheat planting areas

Spatial sampling is an important measure for timely and accurate estimation of crop acreage at large-scale regions. There is a common spatial autocorrelation occurring in crop distributions. However, previous studies had paid little attention to the influence of the spatial autocorrelation on the sampling efficiency for crop area estimation. The object of this study was to evaluate the spatial correlation characteristics between the sampling units for crop acreage investigation and analyze the impact of the spatial autocorrelation on the spatial sampling efficiency (i.e., sampling error, sample size, and sample layout). In this study, Fengtai County in Anhui Province, China was selected as the study area. The winter wheat was extracted using 4 GF-1 PMS (Panchromatic and Multispectral Sensor) and Google Earth satellite images in the study area in April 2017, to evaluate the spatial autocorrelation of the winter wheat distribution. Subsequently, the Support Vector Machine (SVM) algorithm was adopted to extract the basic thematic map of winter wheat by combining the fused GF-1 PMS images and ground sample data, to test the accuracy of winter wheat acreage estimation. Ten sampling unit sizes (500, 1 000, 1 500, 2 000, 2 500, 3 000, 3 500, 4 000, 4 500, 5 000 m), three sampling methods (simple random, systematic, and stratified sampling), two permissible limits of the relative error (5% and 10%), and five sample layout patterns (simple random sampling, stratified random sampling, and systematic sampling with three sorting orders) were formulated to construct multiple spatial sampling schemes. Root Mean Squared Error (RMSE), Mean Relative Error (MRE), and Mean Coefficient of Variation (MCV) were used to assess the extrapolation accuracy of the spatial sampling for winter wheat area estimation. The global Moran’s index was employed to evaluate the spatial autocorrelation intensity of the proportion of winter wheat accounting for a sampling unit area. The results demonstrated as follows: The spatial autocorrelation intensity of the proportion of winter wheat to a sampling unit area decreased with sampling unit scale increasing, accordingly, the global Moran’s index fell from 0.75 to 0.50. The proportion of winter wheat to a sampling unit area showed a significant positive spatial autocorrelation, irrespective of the sampling unit scale; the estimation indicators (RMSE, MRE, and MCV) of population extrapolation of the winter wheat acreage firstly decreased and then obviously increased with the spatial autocorrelation intensity decreasing. In terms of ten sampling unit scales, when the sampling unit size was 2 000 m and sampling fraction was 5%, the MRE of population extrapolation of winter wheat area was all the minimum using three sampling methods. Specifically, the MRE from simple random, systematic, and stratified sampling was 17.94%, 9.48%, and 1.82%, respectively; the sample size decreased from 660 to 56 with the spatial autocorrelation intensity of the winter wheat distribution, when the simple random sampling method was used to estimate the winter wheat area and the relative permissible error was 5%. However, the spatial autocorrelation of the winter wheat distribution had little impact on the sample sizes used by the stratified sampling method; As far as five sample layout patterns were concerned, when the stratified random sampling was used for sample layout, the MRE, MCV, and RMSE of population extrapolation of winter wheat acreage were the minimum, which were 1.82%, 3.19%, and 0.11×108 m2, respectively. In this way, this study could provide an important basis for improving the rationality of the spatial sampling scheme for crop acreage estimation.