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Approximate analytical solution and parameter estimation for one‐dimensional horizontal absorption based on the van Genuchten–Mualem model
Soil Science Society of America Journal ( IF 2.9 ) Pub Date : 2020-11-11 , DOI: 10.1002/saj2.20185
Lijun Su 1, 2, 3 , Linfang Hou 2 , Beibei Zhou 1, 3 , Yuyang Shan 1, 3 , Manli Duan 3 , Yan Sun 1, 3 , Songrui Ning 1, 3 , Quanjiu Wang 1, 3
Affiliation  

The van Genuchten–Mualem (VGM) model is used to describe the absorption of water by soil. The model is highly nonlinear, so developing a simple analytical or approximate method to predict the movement of soil water via the VGM model then estimating the model parameters is necessary. We present a approximate functional extremum solution (FES) for the problem of one‐dimensional horizontal absorption (1DHA) of water in soil under constant saturated boundary conditions and uniform initial conditions based on the least action and the variational principles. Simple linear relationships between the infiltration characteristics (distribution of soil water content, cumulative infiltration, infiltration rate, wetting front distance, and infiltration time) and the VGM model parameters were obtained. We developed a simple approximate analytical method for estimating the VGM model parameters by testing 1DHA. Numerical data simulated by HYDRUS‐1D were compared with the analytical results and used to verify our method's feasibility. The results indicated that the FES could accurately predict the infiltration characteristics, with relative errors between the approximate analytical and numerical solutions of 0.8 to 8.5% for the distribution of soil water content, 0.1 to 0.8% for cumulative infiltration, 1.1 to 6.4% for infiltration rate, and 0.1 to 6.9% for wetting front distance. Estimates of the parameters indicated that errors ranged from 3.2 to 28.3% for α (inverse of the mean pore diameter) and 0.4 to 8.0% for n (pore size distribution index). The proposed methods can be used to predict 1DHA and to estimate α and n in the VGM model.

中文翻译:

基于van Genuchten–Mualem模型的一维水平吸收的近似解析解和参数估计

van Genuchten–Mualem(VGM)模型用于描述土壤对水的吸收。该模型是高度非线性的,因此有必要开发一种简单的分析或近似方法,以通过VGM模型预测土壤水分的运动,然后估算模型参数。我们基于最小作用和变分原理,针对恒定饱和边界条件和均匀初始条件下土壤中水的一维水平吸收(1DHA)问题,提出了一种近似函数极值解(FES)。获得了入渗特征(土壤水分的分布,累积入渗,入渗速率,湿润前沿距离和入渗时间)与VGM模型参数之间的简单线性关系。我们开发了一种简单的近似分析方法,通过测试1DHA来估算VGM模型参数。将HYDRUS-1D模拟的数值数据与分析结果进行比较,并用于验证我们方法的可行性。结果表明,FES可以准确地预测入渗特征,近似分析值与数值解之间的相对误差为:土壤水分分布的0.8%至8.5%,累积入渗量为0.1%至0.8%,入渗量为1.1%至6.4%率,润湿前端距离为0.1到6.9%。参数估计表明,α的误差范围为3.2至28.3%(平均孔径的倒数),α的误差范围为0.4至8.0%。将HYDRUS-1D模拟的数值数据与分析结果进行比较,并用于验证我们方法的可行性。结果表明,FES可以准确地预测入渗特征,近似分析值与数值解之间的相对误差为:土壤水分分布的0.8%至8.5%,累积入渗量为0.1%至0.8%,入渗量为1.1%至6.4%率,润湿前端距离为0.1到6.9%。参数估计表明,α的误差范围为3.2至28.3%(平均孔径的倒数),α的误差范围为0.4至8.0%。将HYDRUS-1D模拟的数值数据与分析结果进行比较,并用于验证我们方法的可行性。结果表明,FES可以准确地预测入渗特征,近似分析值与数值解之间的相对误差为:土壤水分分布的0.8%至8.5%,累积入渗量为0.1%至0.8%,入渗量为1.1%至6.4%率,润湿前端距离为0.1到6.9%。参数估计表明,α的误差范围为3.2至28.3%(平均孔径的倒数),α的误差范围为0.4至8.0%。土壤含水量的分布为5%,累积入渗量为0.1至0.8%,入渗速率为1.1至6.4%,湿润前沿距离为0.1至6.9%。参数估计表明,α的误差范围为3.2至28.3%(平均孔径的倒数),α的误差范围为0.4至8.0%。土壤含水量的分布为5%,累积入渗量为0.1至0.8%,入渗速率为1.1至6.4%,湿润前沿距离为0.1至6.9%。参数估计表明,α的误差范围为3.2至28.3%(平均孔径的倒数),α的误差范围为0.4至8.0%。n(孔径分布指数)。所提出的方法可用于预测1DHA并估计VGM模型中的α和n
更新日期:2020-11-11
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