类别辅助变量参与下的土壤无偏采样布局优化方法

摘要

The unbiasedness in feature space and geographical space is generally used for evaluating the samples’ representation in measure region. Although auxiliary variables are often used for mapping soil variables, problems associated with categorical variables are rarely mentioned. In this paper, a method of unbiased sampling of soil which compromise ing between spreading in geographical space and feature space is presented for optimization of the sample pattern based on multidimensional categorical auxiliary variables. In this method, the feature space is constructed of categorical auxiliary variables;the optimization function which blends the uniform distributions of feature space and geographical space is minimized. The optimal pattern is obtained using simulated annealing. In addition, Feature Divation Index (FDI) is defined in the paper to measure the unbiasedness in feature space of samples. The method was tested through a case study on the soil heavy metal in farmland in Shunyi District, Beijing. As basis data of experiment, the spatial distribution data of samples in the study area were selected in 2007, 2008, 2009 years. The original sample size was 1139, from which the calculated optimal sampling number without considering spatial correlation was 450. Taking 100 as lower limit and 450 as upper limit, eight datasets of sampling number were set, which were 100, 150, 200, 250, 300, 350, 400, 450, respectively. According to scale transformation, the sampling scales were 0.225, 0.239, 0.255, 0.275, 0.302, 0.337, 0.389, 0.477, respectively. Two patterns were selected as the sampling layout to compare with the unbiased sampling: the patterns of uniform sampling in feature space (feature uniform sampling) and of uniform sampling in geographic space (geographical uniform sampling). Land type, soil texture and parent material as categorical auxiliary variables were used to represent the feature space of soil variables. The performances in the overall estimates, the uniformity in feature space and the mapping accuracy were compared between the 3 types of designs. It can be concluded that in the case of global estimation, based on relative error of mean, range, coefficient of skewness and kurtosis, the precision of geographical uniform sampling is worst; when the sampling scale is larger than 0.275, feature uniform sampling achieves best results;as the sampling scale becomes smaller, unbiased sampling can get better results. What’s more, the sampling designs by geographical uniform sampling have the worst feature presentation. When the sampling scale is larger, the representative of samples by feature uniform sampling in feature space is the best;when sampling scale is less than 0.302, unbiased sampling is suggested as a prudent sampling strategy. Finally, in the case of forming geostatistical map, root mean square error (RMSE) between basis data and the Kriging predicted data is used. Unbiased sampling is shown to be competitive in reproducing area with high accuracy. In a word, among the methods of optimizing sampling based on auxiliary variable, the feature uniform sampling is suitable in the situation of large sampling scale or fewer sample points and can only be used in global estimation; the unbiased sampling is a good compromise between spreading in geographical space and feature space, and it can achieve better result in the case of small sampling scale or more sample points.%为了提高采样点在地理空间和辅助变量特征空间中的代表性，该文提出特征空间偏离指数用以测度采样点在特征空间中的无偏性，采用类别型辅助变量参与下的多维特征空间构建方法，融合地理空间和特征空间均匀分布的多目标优化目标函数，并利用空间模拟退火的方法实现采样点布局优化。以北京顺义区农田土壤重金属采样为例，选取土地利用类型、土壤质地和母质为辅助变量进行样点布局优化，并与特征空间均匀和地理空间均匀采样方法比较，结果表明：用于区域变量总体估计时，地理空间均匀采样估计精度最低，在采样尺度大于0.275时以特征空间均匀采样估计精度最好，而在采样尺度小于0.275时，无偏采样能获得更好的估计结果；在特征空间代表性方面，采样尺度较大时特征空间均匀采样样点代表性最好，采样尺度小于0.302时，无偏采样与特征空间均匀采样的代表性基本一致，地理空间采样点的代表性最差；用于空间制图时，无偏采样总体上比其他2种方法具有更好的制图精度。可见，在辅助变量支持的采样优化中，当采样尺度大且样点数较少时，适合采用特征空间均匀方法，且只能用于总体估计；采样尺度较小，样点数多时，适合采用无偏采样方法。该研究为利用辅助变量设计区域采样布局提供参考。