中文摘要：

将封丘县3608个土壤样点分为3463和145个点,分别构成制图数据总集和验证数据总集,再从制图数据总集中通过4%~96%的多尺度随机抽样,构成17个制图子集。分别按Kriging、IDW和以点代面法对土壤有机质、有效磷和速效钾进行预测制图,基于地图直接对比计算制图子集和制图数据总集制图结果的相关系数以评价土壤属性图变化的尺度效应,并与验证数据集评价的多尺度制图结果进行了对比。最后,采用多子集制图结果的变异系数指示多尺度地图表达的不确定性,并将其与基于Kriging估值方差及随机模拟的不确定性表达进行了对比。研究表明,基于地图直接对比可发现,制图效果与样本数量具有显著的分形关系,且分形维数受制图方法和土壤属性空间可变性的双重影响：同样条件下以Kriging方法最小,而以点代面法最大;以土壤速效钾最小,而土壤有效磷最大。验证数据集实测值和估计值的相关系数及均方根误差没有表现预期的分形特征。Kriging估值方差及随机模拟表达的单一尺度制图不确定性明显受采样点分布与Kriging估值大小影响,而基于地图直接对比的多尺度制图的不确定性更客观地反映土壤自然变异,其中土壤有机质、土壤速效钾有较强规律可循,而土壤有效磷则没有规律。

英文摘要：

In Fengqiu County of Henan Province, topsoil samples were collected from 3 608 sampling sites, of which 3 463 sampling sites were chosen to form a master dataset for soil attribute mapping, while the remaining 145 sampling sites were to form a master verification dataset. Then, through 4% - 96% multi-scaled stochastic sampling of the former, 17 subsets were formed for mapping of soil organic matter, soil available phosphate and soil readily available potassium using kriging interpolation, inverse distance weight interpolation （IDW） and Polygon value represented by point value （PRP） , respectively. Based on direct map comparison between the computerized mapping subsets and the master mapping dataset, correlation coefficients were obtained to evaluate effects of scaling on soil attribute maps, and further more com- parison was made with the multi-scaled mapping evaluated with the verification dataset. In the end, variable coefficient of the multi-subset mapping was used to indicate uncertainty of the expression of muhi-scaped mapping and comparison was made of this uncertainty with that of the kriging variance and that of the stochastic simulation. Through the direct map comparison, it was found that the relationship between mapping quality and volume of samples was fractal and the fractal dimension was affected dually by mapping method and spatial variability of soil attributes. In the same conditions, the fraetal dimension was the smallest with the kriging method and the largest with the PRP method, and the smallest with soil available potassium and the largest with soil available phosphate. The correlation coefficients and Root mean square error （RMSE） between the measured values and forecasted values in the verification dataset did not show any fraetal feature as expected. The uncertainty of single-scale mapping expressed by kriging variance and stochastic simulation was significantly influenced by distribution of the sampling sites and value of the kriging estimation, while the uncertainty of the m