空间自相关性对冬小麦种植面积空间抽样效率的影响

空间抽样是实现区域农作物面积高效估算的重要手段,农作物分布受自然条件等因素影响普遍存在空间自相关性,但以往针对空间相关性对农作物面积抽样效率的影响研究明显不足。该研究选取安徽省凤台县为研究区,通过2017年4月4景GF-1全色多光谱影像(Panchromatic and Multispectral, PMS)与Google Earth高空间分辨率影像相结合提取研究区冬小麦。设计10种抽样单元尺度、3种抽样外推方法、2种相对允许误差和5种样本布局方式,构建多种冬小麦面积空间抽样方案。利用全局莫兰指数(global Moran’s index)评价不种尺度下抽样单元内冬小麦面积比的空间自相关强度,分析空间自相关性对冬小麦面积抽样效率(抽样误差、样本容量和空间布局)的影响。研究结果表明,抽样单元内冬小麦面积比的空间自相关强度随单元尺度的增大而减小,全局莫兰指数相应地由0.75降至0.50。无论在何种尺度下抽样单元内冬小麦面积比都呈显著的空间正相关性;抽样外推冬小麦面积总体的误差随空间自相关强度的减小呈先减小后明显增大的趋势。在10种抽样单元尺度中,当抽样单元尺度为2000m且抽样比为5%时,无论采用何种抽样方法外推总体的误差均为最小(简单随机抽样、系统和分层抽样外推总体的相对误差分别为17.94%、9.48%和1.82%);当相对允许误差设计为5%时,简单随机抽样外推总体所需样本容量随空间自相关强度的降低从660降至56。而分层抽样的样本容量不受空间自相关性的影响;5种样本布局方式中,采用分层随机抽样方式外推冬小麦面积总体的平均相对误差、平均变异系数和均方根误差最小,分别为1.82%、3.19%和0.11×108 m2。该研究可为有空间自相关存在下的农作物面积空间抽样方案合理设计提供参考依据。

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 0.5. 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.