李 毅, 李 敏, Si Bingcheng, 贺缠生. 土壤颗粒分布体积分形维数与数量分形维数之间的关系(英文)[J]. 农业工程学报, 2012, 28(23): 82-91.
    引用本文: 李 毅, 李 敏, Si Bingcheng, 贺缠生. 土壤颗粒分布体积分形维数与数量分形维数之间的关系(英文)[J]. 农业工程学报, 2012, 28(23): 82-91.
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    Li Yi, Li Min, Si Bingcheng, He Chansheng. Relationship between volume-based and number-based fractal dimensions of soil particle size distributions[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2012, 28(23): 82-91.
    Citation: Li Yi, Li Min, Si Bingcheng, He Chansheng. Relationship between volume-based and number-based fractal dimensions of soil particle size distributions[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2012, 28(23): 82-91.
    shu

    土壤颗粒分布体积分形维数与数量分形维数之间的关系(英文)

    Relationship between volume-based and number-based fractal dimensions of soil particle size distributions

      摘要
    • 摘要: 土壤的体积颗粒分布（PSD）可用于同时确定数量分形维数(DN)和体积分形维数(DV)。以往的试验和理论研究均未直接比较DV和DN的关系。为建立DV和DN的关系并分析其参数的敏感程度，在中国各地取了12种不同质地土壤，利用激光粒度仪进行了测定。提出了含3个参数Rupper（颗粒半径的上限），Ri（第i个半径）和 Rlower（半径下限）的DV-DN理论关系，该关系可说明为什么DN可能大于3。在未调整的幂定律范围内（PLR），DV的幂定律半径为38.6～85.8 μm，DN的幂定律半径为53.2～358 μm，估算的DV值（2.18～2.69）比DN值（2.38～3.19）小。调整后的PLR比未调整的窄。在调整的PLRs范围内，估算的DV值变化范围为2.11~2.56，而DN变化范围为2.28～3.02。调整和未调整PLRs得出的DV和DN的差异说明，Rupper, Rlower, Ri和Rlower/Rupper均可能影响DV与DN关系，有必要进行参数的敏感性分析。进行敏感性分析可基于敏感系数（C）来鉴别DV-DN关系中各参数改变所引起的DV和DN相对变化，从而找出对该关系影响最大的参数。就不同情况下计算的C值而言，Rupper是影响DN值的最重要参数，小的Rupper值可能导致估算DN的准确度降低。PLR范围越大，DN的估算越准确。根据DV估算DN的相对误差的绝对值在12%范围内，说明得出的DV-DN理论关系是正确的。

       

      Abstract: A volumetric soil particle size distribution (PSD) can be used to determine volume- (DV) and number (DN)-based fractal dimensions simultaneously. Direct comparisons between DV and DN were not available before by theoretical and experimental methods. To present the theoretical relationship between DV and DN and analyze the sensitivity of parameters, twelve soil samples representing different soil textures were taken at different locations in China and analyzed by laser diffractometry. The theoretical relationship between DV and DN was developed with 3 parameters including Rupper (upper limit of particle radius), Ri (the ith radius) and Rlower (lower limit). The relationship can be used to explain why DN can be greater than 3. The estimated DV values (2.18 to 2.69) were smaller than the DN values (2.38 and 3.19) within unadjusted power-law ranges (PLR) which ranged from 38.6 to 85.8 μm for DV and 53.2 to 358 μm for DN. The adjusted PLR for estimating DV and DN were narrower than the unadjusted PLRs. Within the adjusted PLRs, the estimated DV values were from 2.11 to 2.56 and the DN values were from 2.28 to 3.02. The difference between DV and DN values estimated from adjusted and unadjusted PLRs implied that Rupper, Rlower, Ri and Rlower/Rupper can affect the DV and DN relationship, and sensitivity analysis of parameters is essential. Sensitivity analysis can distinguish the relative variations of the parameters in DV-DN relationship using coefficients of sensitivity (C), through which the most important parameter that affects DV-DN relationship can be determined. Based on the C values at different circumstances, Rupper was found to be the most important factor that influenced the estimation of DN values. A relatively small Rupper may result in a less accurate estimation of DN. Larger PLR can result in more accurate estimation of DN. The relatively small absolute values of relative errors (<12%) between calculated DN and observed DV implied the correctness of relationship between DV and DN. The research can provide a reference for estimating number-based fractal dimension based on volume-based fractal dimension calculated from soil particle size distributions.

       

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