Abstract The streamtube approximation has been commonly used for upscaling of flow and transport in spatially heterogeneous unsaturated soils. This study investigates the prediction ability of streamtube approach to model flow in heterogeneous unsaturated sandy soils under a rainfall event at a plot scale. Towards this aim, a numerical model for solving 3-D Richards’s equation was developed and verified for 1-D and 3-D cases. Turning band method was used to generate the random field of soil hydraulic parameters. The 3-D soil field heterogeneity was represented by considering variation in both van Genuchten parameter (α) and K s . For streamtube models, two cases of heterogeneity were investigated: i) variability in K s only, and ii) variability in both K s and α. Both the parameters were assumed to follow a log-normal distribution. For different boundary conditions at the soil surface and varying soil heterogeneity, the average Darcy's flux and mean field-scale soil moisture obtained using streamtube approach were compared with 3-D numerical solutions. The results identify that for high recharge rate at the soil surface, streamtube model is a good approximation of the 3-D heterogeneous soil field, and the average difference in mean soil moisture obtained from 3-D model and streamtube based 1-D model was below 10% when variability in both K s and α was considered for all timesteps. The inclusion of variability in α leads to improvement in prediction capability of streamtube model. Further, regression equations were developed that can be utilized to predict the mean field soil moisture for heterogeneous 3-D sandy soil fields given the mean field soil moisture obtained from streamtube approach for both the cases. The regressions equations follow exponential model for case-1 and linear model for case-2 with R 2 values 0.80 and 0.99, respectively. The developed equations can be reliably used to predict mean field soil moisture for heterogeneous sandy soil fields.

中文翻译：

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非均质不饱和砂土中流管法模拟流动的数值研究

摘要 在空间非均质非饱和土壤中，流管近似常用于放大流动和输运。本研究调查了在样地尺度下降雨事件下流管方法模拟非均质非饱和砂质土壤中流动的预测能力。为此，开发了一个用于求解 3-D Richards 方程的数值模型，并针对 1-D 和 3-D 情况进行了验证。采用转带法生成土壤水力参数随机场。3-D 土壤田间异质性通过考虑 van Genuchten 参数 (α) 和 K s 的变化来表示。对于流管模型，研究了两种异质性情况：i) 仅 K s 的变异性，以及 ii) K s 和 α 的变异性。假设这两个参数都遵循对数正态分布。对于土壤表面的不同边界条件和不同的土壤异质性，将使用流管方法获得的平均达西通量和平均田间尺度土壤水分与 3-D 数值解进行比较。结果表明，对于土壤表面的高补给率，流管模型是 3-D 异质土壤场的良好近似，从 3-D 模型和基于流管的 1-D 模型获得的平均土壤水分的平均差异为当所有时间步长都考虑 K s 和 α 的可变性时，低于 10%。α 中包含可变性导致流管模型预测能力的提高。更多，给出了两种情况下通过流管方法获得的平均田间土壤水分，开发了回归方程，可用于预测异质 3-D 沙质土壤田的平均田间土壤水分。回归方程遵循案例 1 的指数模型和案例 2 的线性模型，其中 R 2 值分别为 0.80 和 0.99。开发的方程可以可靠地用于预测异质砂质土壤田的平均田间土壤水分。