Estimating Sample Size of Soil Cone Index Profiles by Bootstrapping

ABSTRACT Measurements of the soil cone index are widely used to assess soil resistance to root penetration (SR) and to monitor the soil compaction status of agricultural fields. However, soil sampling for SR estimation is a rather challenging task in view of the high spatial and temporal variability of the soil. This study proposed a bootstrapping method to determine the minimum sample size required to estimate the vertical profile of mean soil cone index (CI) values at different levels of precision and confidence. For this purpose, CI data from a Typic Argiudoll under no-tillage before and after chiseling was used. A total of 151 CI profiles were recorded before and after chiseling in a 3,200 m2 (40 × 80 m) no-tillage area at sampling points distributed on a horizontal 5 × 5 m aligned grid and from the top layer to 0.40 m depth by in 0.02 m intervals. A modified bootstrap routine was developed to estimate the sampling distribution of the sample mean and medians of CI values per layer. The minimum sample size to estimate the vertical profile of mean CI values at different levels of precision and confidence was determined from data of the whole soil profile, including the autocorrelation of CI readings in the vertical direction. Tilling increased the variability of this measurement and thus the sampling efforts to achieve the same level of precision and confidence were different before and after the procedure. The standard errors of sample medians estimated by bootstrapping were higher than those corresponding to sample means. In addition, to achieve the same level of precision and confidence, the estimation of the vertical profile of mean CI values based on sample medians required more observations than based on sample means. This study shows that the viability of the bootstrap approach to determine the implications of soil variability on the sampling efforts required for an accurate estimation of the vertical distribution of resistance in soils under different managements.

摘要：土壤圆锥指数（soil cone index）的测量被广泛应用于评估土壤抗根穿透阻力（soil resistance, SR），以及监测农田土壤压实状态。然而，由于土壤具有显著的时空变异性，通过土壤采样估算抗根穿透阻力是一项极具挑战性的任务。本研究提出一种自举法（bootstrapping method），以确定在不同精度与置信度水平下，估算平均土壤圆锥指数（CI）垂直剖面所需的最小样本量。为此，本研究使用了免耕（no-tillage）农田在深松耕作前后的典型黏化干润软土（Typic Argiudoll）的圆锥指数数据。研究共在3200㎡（40×80m）的免耕区域内，以5m×5m的规则网格布设采样点，从表层至0.40m深度以0.02m为间隔，分别记录了深松耕作前后共151条土壤圆锥指数剖面数据。本研究开发了改进的自举抽样程序，用于估算各土层土壤圆锥指数的样本均值与样本中位数的抽样分布。基于完整土壤剖面的数据（包括垂直方向上土壤圆锥指数读数的自相关性），本研究确定了在不同精度与置信度水平下，估算平均土壤圆锥指数垂直剖面所需的最小样本量。深松耕作会增大该测量指标的变异性，因此为达到相同的精度与置信度水平，耕作前后所需的采样工作量有所差异。通过自举法估算得到的样本中位数标准误高于样本均值的标准误。此外，为达到相同的精度与置信度水平，基于样本中位数估算平均土壤圆锥指数垂直剖面所需的观测样本量多于基于样本均值的情况。本研究证实，自举法可用于明确土壤变异性对不同管理模式下土壤阻力垂直分布精准估算所需采样工作量的影响。