冬小麦种植面积空间抽样单元尺寸优化设计

抽样单元尺寸是空间抽样调查方案设计过程中的关键要素。合理的抽样单元尺寸对降低抽样调查费用、改善抽样外推总体精度具有重要意义。为实现农作物种植面积空间抽样调查中抽样单元尺寸的优化设计,论文以河南省为研究区,以冬小麦种植面积为研究对象,选取正方形网格作为抽样单元,遵循传统抽样理论中抽样单元间相互独立原则,通过分析不同抽样单元尺寸与对应该尺寸下的抽样框内总体单元间全局空间自相关指数(Moran’s I)的相关关系,进行了抽样单元尺寸的初选。为最终实现抽样单元尺寸优选,基于初选的8种抽样单元尺寸,分别构建抽样框,采用以抽样单元内冬小麦面积占单元面积比例(麦土比)为分层标志的分层抽样方法进行了研究区冬小麦种植面积空间抽样样本抽选、总体外推及误差估计试验研究,结果表明:抽样比随抽样单元尺寸的增大而增大;8种抽样单元尺寸下的外推总体相对误差和变异系数均较小,变化范围分别为3.82%~5.75%和3.76％~4.69％;以抽样调查费用和抽样误差为抽样效率评价指标,优选出抽样单元尺寸为20 000 m×20 000 m时,进行研究区冬小麦种植面积抽样调查的效率最高。

Optimizing the Size of Spatial Sampling Units for Estimating Winter Wheat Sown Acreage

The formulation of sampling unit size is essential in spatial sampling schemes for estimating crop sown area. Reasonable sampling unit size plays an important role for reducing sampling cost and improving population extrapolation accuracy. The experiment on optimizing sampling unit size was conducted to improve the efficiency of spatial sampling for winter wheat sown acreage estimation. Henan Province was selected as a study area and square grids as sampling units. Following the principle that sampled units are independent each other, sampling unit size is preliminarily selected through analyzing the relationships between different sampling unit sizes and corresponding global spatial autocorrelation index (Moran’s I) of all population units in the sampling frame. Furthermore, in order to find the optimal sampling unit size, eight kinds of sampling frames are constructed using the preliminarily selected sampling unit sizes and stratified sampling method. The stratification symbol is the ratio of winter wheat sown area accounting for that of a sampling unit, which is used to draw samples, and then extrapolate population value as well as estimate sampling errors. The experimental results demonstrate that, sampling fraction increases with the increase of sampling unit size; both the relative errors and coefficients of variation (C_V) of population extrapolation are small at eight sampling unit size levels (relative errors vary from 3.82% to 5.75%, C_V vary from 3.76% to 4.69%). It is found that the efficiency of stratified sampling method used to estimate the population of winter wheat sown area is the maximum, when the sampling unit size is 20000 m×20000 m.