Effect of Parameter Sensitivity of van Genuchten Model on Numerical Simulation of Rainfall Recharge
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摘要: 详细分析不同评价指标下的van Genuchten方程参数敏感性，对于深入认识参数物理意义、合理确定参数值、提高降水入渗数值模拟准确性具有重要意义.用HYDRUS软件建立一维变饱和水分运移模型，以实际补给量、补给过程曲线和极限蒸发深度作为评价指标，采用单因素扰动分析法对van Genuchten方程各参数敏感性进行理论分析，进而选取多组参数实例，分析同一岩性类别下，不同土样土壤水力参数差异及其对入渗补给模拟结果的影响.结果表明：形状系数 (n)、土壤进气值的倒数 (α) 与极限蒸发深度呈负相关关系，是影响极限蒸发深度的显著因素；饱和含水率 (θs)、n、饱和渗透系数 (Ks) 对于入渗补给影响的敏感性较高，三者在实际土样粒径分布、干密度和孔隙性的共同影响下发生同向变动.合理的参数敏感性分析及数值模拟调参过程需结合土壤参数的物理意义来开展.Abstract: The van Genuchten model is frequently used in expression of soil lithology and hydraulic feature of vadose zone. The included soil hydraulic parameters are sensitive factors in numerical simulation of rainfall recharge. It facilitates the understanding of the physical meaning of parameters, improving accuracy of numerical simulation of rainfall recharge and parameters regulation to analyze the sensitivity of each soil hydraulic parameter. In this study, one-dimensional variably saturated flow models were established by using HYDRUS software. Simulations were run under conditions of multiple sets of parameters which are set in the principle of changing one parameter and keeping the others invariant to evaluate parameter sensitivity of van Genuchten model by using actual recharge quantity, recharge process curve and maximum evaporation depth as the index. The case study chose multiple sets of measured parameters to evaluate the influence of parameter variation among different samples of the same lithology. The simulations results show that maximum evaporation depth is significantly affected by the n and α which are negatively related to it; θs, n, and Ks have a high sensibility to the variation of vertical groundwater recharge, however they will change with porosity, grain size distribution and bulk density of soil at the same time. It is concluded that the reasonable analysis of parameter sensitivity can only be done in combination of the study of their physical meaning.
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Key words:
- van Genuchten model /
- parameter sensibility analysis /
- rainfall recharge /
- numerical simulation /
- HYDRUS /
- hydrogeology
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图 2 土壤水力参数对水分特征曲线及非饱和渗透系数的影响
Fig. 2. Effects of soil hydraulic parameters on soil water characteristic curve and unsaturated coefficient of permeability
图 3 土壤水力参数对补给过程曲线的影响
Fig. 3. Effects of soil hydraulic parameters on recharge process curve
图 4 补给过程曲线特征变化程度
Fig. 4. The variation of characteristic indexes of recharge process curve
图 6 土壤水力参数对总水势梯度的影响
Fig. 6. Effects of soil hydraulic parameters on total soil water potential gradient
图 7 土壤水力参数对极限蒸发深度的影响
Fig. 7. Effects of soil hydraulic parameters on maximum evaporation depth
图 8 不同岩性及参数条件下的补给过程曲线
Fig. 8. The corresponding recharge process curve of different instance parameter
表 1 敏感性分析参数设置
Table 1. Parameter list of sensitive analysis
砂质壤土 θr θs α(1/cm) n Ks(cm/d) 原值 0.065 0.410 0.075 0 1.890 106.10 增加 0.097 5(θr+) 0.615(θs+) 0.112 5(α+)
2.835(n+)
2.58(n1+)159.15(Ks+) 减小 0.032 5(θr-) 0.205(θs-) 0.037 5(α-) 1.2(n-) 53.05(Ks-) 注：数值后括号代表相应模型代号，如“n+”、“n1+”、“n-”分别代表在不改变其他参数的前提下，将n值增加50%、增加36.5%和减小36.5%. 
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表 2 华北平原参数实例
Table 2. Measured parameter of North China plain
位置 岩性 编号 粒径分布 干密度 (g/cm3) 土壤水力参数 砂粒 (%) 粉粒 (%) 黏粒 (%) θr θs α(1/cm) n Ks(cm/d) 辛集 1 82.19 13.45 4.38 1.41 0.042 7 0.407 9 0.040 7 1.871 1 193.96 桃园 砂壤土 2 74.04 20.16 5.78 1.58 0.037 4 0.358 5 0.043 7 1.560 9 58.81 藁城 3 56.51 29.65 13.84 1.72 0.039 6 0.325 4 0.033 2 1.289 5 10.28 桃园 粉砂质
黏壤土1 32.19 51.77 15.99 1.46 0.055 0 0.376 1 0.006 9 1.591 6 14.51 正定 2 21.29 60.74 17.92 1.58 0.058 7 0.366 2 0.006 6 1.577 1 8.04 正定 3 20.19 59.68 20.14 1.63 0.060 4 0.360 3 0.007 2 1.535 5 5.43 桃园 壤土 1 54.46 35.67 9.85 1.39 0.041 3 0.384 2 0.017 0 1.464 6 41.60 大河 2 52.96 37.14 9.88 1.47 0.039 8 0.366 7 0.017 9 1.449 4 30.12 藁城 3 41.31 44.04 14.68 1.67 0.043 0 0.328 7 0.015 4 1.385 3 7.40
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