平原与丘陵区土壤地球化学调查的优化采样尺度：1:50,000尺度验证与克里金插值优选

Optimized Sampling Scale for Soil Geochemical Surveys in Plain and Hilly Areas: Validation of the 1:50,000 Scale and Kriging Interpolation Preference

摘要: 为确定不同地貌条件下满足精度要求的成本最优采样尺度，研究选取湖南省临澧县南部丘陵区和北部平原区各6 km²典型区域，对比分析了1:10,000与1:50,000两种采样尺度数据。基于《土地质量地球化学评价规范》(DZ/T 0295-2016)，以镉(Cd)为指示元素，采用径向基函数法(RBF)和普通克里金法(Ordinary Kriging)进行空间插值与交叉验证，并以相对误差(RE= |预测值 − 实测值|/实测值) ≤ 30%的样本比例 ≥ 85%作为精度达标判据。结果表明：1) 1:50,000尺度下两地貌精度均超规范要求(RE ≤ 30%比例 > 92%)；2) 平原区尺度缩减未显著降低精度(RE比例降幅 < 1 %)；3) 丘陵区1:50,000尺度精度反超1:10,000尺度(RE比例提升6%~8%)，揭示稀疏采样在复杂区具“降噪提精”效应；4) 普通克里金法在丘陵区抗噪性更优。综合技术经济性，建议全域采用1:50,000采样尺度 + 普通克里金法，可降本72.3%~72.7%，且保障成果可用性。

Abstract: To identify the cost-optimal sampling scale meeting accuracy requirements under different topographic conditions, this study selected two representative 6 km² areas—a hilly region in the south and a plain region in the north of Linli County, Hunan Province. Comparative analysis was conducted on data collected at 1:10,000 and 1:50,000 sampling scales. Following the Specification of Land Quality Geochemical Assessment (DZ/T 0295-2016), we selected cadmium (Cd) as the indicator element. Spatial interpolation and cross-validation were performed using Radial Basis Function (RBF) and Ordinary Kriging methods. Accuracy compliance was judged based on the criterion that the proportion of samples with a relative error (RE = |Predicted − Measured|/Measured) ≤ 30% must reach or exceed 85%. Key findings reveal that: 1) The 1:50,000 scale achieves compliance (> 92% RE ≤ 30%) in both terrains; 2) Plain areas tolerate scale reduction with negligible accuracy loss (ΔRE < 1%); 3) Hilly areas exhibit counterintuitive gains at 1:50,000 scale (↑6%~8% RE compliance), indicating noise suppression by sparser sampling; 4) Ordinary Kriging outperforms RBF in complex topography. This cost-optimal protocol (1:50,000 + Kriging) reduces sampling costs by 72.3%-72.7% while meeting accuracy standards (DZ/T 0295-2016).