Analysis of Heterogeneous Soil Water Using Information Entropy and Multifractal Theory
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摘要: 根据粘土和壤土中非均匀水流运动的示踪试验, 研究了土壤水非均匀流动模式, 并基于信息熵与多重分形理论探讨了多孔介质中流动的非均匀性质.不同土质试验研究的分析结果表明, 各深度信息熵与特征长度具有相反的变化趋势.非均匀流动多重分形特性分析表明, 非均匀流动分布具有很强的自相似性, 但并不是在所有研究尺度范围内都满足标度不变性, 在显色比例相近的情况下, 壤土和粘土中水流运动标度不变性的范围表现出显著的差异.Abstract: The major objective of this study is to investigate the heterogeneity of soil water flow. Field experiments were performed in loam and clay soil and an iodine-starch staining method was applied to visualize flow paths in the soil. Heterogeneous flow patterns were described by using information entropy and multifractal theory.Resultsshow that information entropy increases with decreasingly characteristic length, which is a scale used to characterize flow stained patterns. The soil flow heterogeneity is similar at different measurement scales. However, the variance of flow distributions change with scales. In the loam soil, scaling invariance of water flow distributions is in a larger range than that in the clay soil.
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图 2 不同土壤深度显色模式
a.粘土深度为5cm、10cm、20cm、40cm和80cm显色模式; b.壤土深度为5cm、10cm、20cm、30cm和50cm深度显色模式
Fig. 2. Heterogeneous stained patterns at various depths
图 3 显色比例、流动模式相关程度R的比较
Fig. 3. Comparison of dye coverage, correlativity of water flow pattern in stained regions after infiltration
图 4 不同土壤深度下标准化信息熵随尺度变化分析
Fig. 4. Normalized configuration entropy (H * (r)) versus box size (r) from horizontal sections at different depths
图 5 特征长度(a)与信息熵最大值(b)随土壤深度变化
Fig. 5. The change of characteristic length (a) and information entropy (b) at different depths
图 6 壤土和粘土lnχ(r, q)- In(r)曲线
Fig. 6. Bi-log plot of χ(r, q) versus box size (r) for the loam and clay soil
图 7 基质熵、信息维数与显色面积关系比较
Fig. 7. (a) Potential entropy (H* (r)/ L) vs. information dimension; (b) fractal dimension vs. iodine stained coverage for different soils
表 1 试验土壤物理和水动力性质
Table 1. Physical and hydraulic properties of the experimental soils
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