基于Kriging估计误差的县域耕地等级监测布样方法

Sampling method for monitoring classification of cultivated land in county area based on Kriging estimation error

为了监测耕地的质量等级,通常采取抽样调查的方法。由于空间样本间存在不独立性等原因,传统抽样方法效率低、精度不高。为此,该文提出基于Kriging估计误差的布样方法,定义了反映Kriging估计情况的统计量作为评估监测网的标准,通过分析样本量与抽样精度的变化趋势确定最优样本容量,将调整过的方形格网作为监测网的基础,在泰森多边形限制下对监测网优化增密,并选用部分标准样地作为监测点。以北京市大兴区为例对该方法进行验证,结果表明,当监测点数同为48时,该文方法均方根误差小于简单随机抽样、分层抽样以及单一使用格网布样的方法,预测总体均值的相对误差为0.07%。因此,该文方法使用较少的监测点反映县域耕地等级的分布状况和变化趋势,能够满足县域耕地等级监测的需求。

China, an agricultural country, has a large population but not enough cultivated land. Until 2011, the cultivated land per capita was 1.38 mu （0.09 ha）, only 40% of the world average, and it is getting worse with industrialization and urbanization. The next task for the Ministry of Land and Resources： Dynamic monitoring of cultivated land classification in which a number of counties will be sampled; in each county, a sample-based monitoring network would be established that reflects the distribution and its tendency of cultivated land classification in county area and estimates of non-sampled locations. Due to the correlation among samples, traditional methods such as simple random sampling, stratified sampling, and systematic sampling are insufficient to achieve the goal. Therefore, in this paper we introduced a spatial sampling method based on the Kriging estimation error. For our case, natural classifications of cultivated land identified from the last Land Resource Survey and Cultivated Land Evaluation are regarded as the true value and classifications of non-sampled cultivated lands would be predicted by interpolating the sample data. Finally, RMSE （root-mean-square error） of Kriging interpolation is redefined to measure the performance of the network. To be specific, five steps are needed for the monitoring network. First, the optimal sample size is determined by analyzing the variation trend between the number and the accuracy of samples. Then, set up the basic monitoring network using square grids. The suitable grid size can be chosen by comparing the grid sizes and the corresponding RMSEs from the Kriging interpolation of the samples data. Because some centers of grids do not overlap the area of cultivated land, the third step is to add some points near the centers of grids to create the global monitoring network. These points are selected from centroids of cultivated land spots which are closest to the centers and inside the searching circles around the centers by a loop algorithm. The fourth step is a procedure of densification, which is needed to build Thiessen polygons through global sampling points. Then, add the point of maximum Kriging estimation error inside polygons whose RMSEs are relatively high to the network only if it makes the global RMSE smaller. This procedure stops when the count of sampling points reaches the optimal sample size. The final step is to replace several monitoring points by standard plots to reduce the sampling cost. Finally, estimate the population mean of cultivated land classification through Kriging interpolation. Experiments in Beijing Daxing district that compared this method to traditional sampling methods in cost （count of sampling points）, estimation accuracy （measured by RMSE）, and prediction accuracy of the population mean illustrate that the estimation accuracy of this method is higher than simple random sampling, stratified sampling, or traditional grids when the number of sampling points is 48. Besides, the prediction accuracy of population mean stays in an accurate level with the relative error of 0.07%. Therefore, this method can meet the needs of monitoring the classification of cultivated land in county area.