An Unsaturated Hydraulic Conductivity Model Based on the Capillary Bundle Model, the Brooks‐Corey Model and Waxman‐Smits Model
An Unsaturated Hydraulic Conductivity Model Based on the Capillary Bundle Model, the Brooks‐Corey Model and Waxman‐Smits Model
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DOI：
10.1029/2022wr034186
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发表时间：
2023-05
影响因子：
5.4
通讯作者：
Yongwei Fu;R. Horton;T. Ren;J. Heitman
中科院分区：
文献类型：
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作者：
Yongwei Fu;R. Horton;T. Ren;J. Heitman
土壤非饱和导电性(K)取决于含水量（θ）和基质势（ψ），在田间尺度上表现出高度的变异性。本文首先基于毛细管束模型和Waxman - Smits模型建立了低盐和高盐条件下的水力电导率（σ）的理论关系，该关系可以解释σ在低盐条件下的非线性行为。然后用Brooks - Corey模型将K - σ关系转换为K（θ, ψ）模型。该模型包括两个参数c和γ。参数c表示(λ + 2)/(λ + 4)项的变化，其中λ为Brooks - Corey模型中的孔径分布参数，m - n项的变化，其中m和n分别为Archie饱和指数和胶结指数。参数γ是考虑水力和电扭度差异的扭度因子与阿奇饱和指数之和。基于从UNSODA数据库中选择的150种土壤的校准数据集，确定了四种质地组的最佳拟合log(c)和γ值为- 2.53和1.92,- 4.39和- 0.14,- 5.01和- 1.34以及- 5.79和- 2.27。新K（θ, ψ）模型估计的log10(K)值与UNSODA数据库中49个土壤独立数据集的实测值比较良好，平均误差（ME）、相对误差（RE）、均方根误差（RMSE）和决定系数（R2）分别为0.02、8.8%、0.80和0.73。对新K（θ, ψ）模型的第二次测试使用了代表23种土壤的数据集，也表明估计值和测量值之间的log10(K)值吻合良好，ME为- 0.01，RE为9.5%，RMSE为0.77，R2为0.85。新的K（θ, ψ）模型优于Mualem - van Genuchten模型和两个最近发表的pedo -传递函数。新的K（θ, ψ）模型可以应用于野外条件下的K估计和水文建模，而不需要对土壤保水曲线数据进行拟合来推导K函数。
Soil unsaturated hydraulic conductivity (K), which depends on water content (θ) and matric potential (ψ), exhibits a high degree of variability at the field scale. Here we first develop a theoretical hydraulic‐electrical conductivity (σ) relationship under low and high salinity cases based on the capillary bundle model and Waxman and Smits model which can account for the non‐linear behavior of σ at low salinities. Then the K‐σ relationship is converted into a K(θ, ψ) model using the Brooks‐Corey model. The model includes two parameters c and γ. Parameter c accounts for the variation of the term (λ + 2)/(λ + 4) where λ is the pore size distribution parameter in the Brooks‐Corey model, and the term m‐n where m and n are Archie's saturation and cementation exponents, respectively. Parameter γ is the sum of the tortuosity factor accounting for the differences between hydraulic and electrical tortuosity and Archie's saturation exponent. Based on a calibration data set of 150 soils selected from the UNSODA database, the best fitting log(c) and γ values were determined as −2.53 and 1.92, −4.39 and −0.14, −5.01 and −1.34, and −5.79 and −2.27 for four textural groups. The estimated log10(K) values with the new K(θ, ψ) model compared well to the measured values from an independent data set of 49 soils selected from the UNSODA database, with mean error (ME), relative error (RE), root mean square error (RMSE) and coefficient of determination (R2) values of 0.02, 8.8%, 0.80 and 0.73, respectively. A second test of the new K(θ, ψ) model using a data set representing 23 soils reported in the literature also showed good agreement between estimated and measured log10(K) values with ME of −0.01, RE of 9.5%, RMSE of 0.77 and R2 of 0.85. The new K(θ, ψ) model outperformed the Mualem‐van Genuchten model and two recently published pedo‐transfer functions. The new K(θ, ψ) model can be applied for estimating K under field conditions and for hydrologic modeling without need for soil water retention curve data fitting to derive a K function.