CHEN Wen, LIANG Yingjie, YANG Xu. Soil Infiltration Rates and Hydrology Model Classifications Based on the Hausdorff Fractal Derivative Richards Equation[J]. Applied Mathematics and Mechanics, 2018, 39(1): 77-82. doi: 10.21656/1000-0887.380101
 Citation: CHEN Wen, LIANG Yingjie, YANG Xu. Soil Infiltration Rates and Hydrology Model Classifications Based on the Hausdorff Fractal Derivative Richards Equation[J]. Applied Mathematics and Mechanics, 2018, 39(1): 77-82.

# Soil Infiltration Rates and Hydrology Model Classifications Based on the Hausdorff Fractal Derivative Richards Equation

##### doi: 10.21656/1000-0887.380101
Funds:  The National Natural Science Foundation of China（11402214;51375402;11572264;61773004）
• Rev Recd Date: 2017-05-31
• Publish Date: 2018-01-15
• The time-dependent soil infiltration rate was derived based on the Hausdorff fractal derivative Richards equation. This model requires only 2 parameters, among which the Hausdorff derivative order characterizes the underlying water transport environment property in heterogeneous soil, while the pore size distribution index categorizes different hydrological models. Two applications show that a fractal order α≠1 of the Hausdorff derivative indicates the history-dependent process. Namely, a lower α exhibits slower decay of the infiltration rate with time evolution, reflecting stronger memory and further departure from the classical integer-order models. It is also observed that a smaller pore size distribution index indicates slower decay of the infiltration rate, making a fundamental index of soil infiltration.
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