Transit Times and StorAge Selection Functions in Idealized Hillslopes With Steady Infiltration
Transit Times and StorAge Selection Functions in Idealized Hillslopes With Steady Infiltration
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DOI：
10.1029/2019wr025917
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发表时间：
2022-02
影响因子：
5.4
通讯作者：
Minseok Kim;C. Harman
中科院分区：
文献类型：
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作者：
Minseok Kim;C. Harman
空间集成的输运模型已广泛应用于水文输运模拟。然而，我们缺乏简单的和基于过程的理论工具来预测运输关闭-运输时间分布（TTD）和存储选择（SAS）功能。这限制了我们从示踪观测推断水文系统特征的能力，以及在没有示踪数据的流域中对SAS函数进行一阶估计的能力。在这里，我们提出了一个理论框架，TTD和SAS功能的水力地下水理论在山坡尺度。对于饱和导水率随深度呈指数下降的山坡，封闭的解析解，可用作假设来测试对数据。在最简单的形式中，山坡SAS函数类似于均匀或指数分布（对应于饱和带中的流动路径），通过非饱和带中的存储从零偏移，该存储对排放没有贡献。对9个理想化的虚拟山坡使用2-D理查兹方程为基础的模型，并对两个人工山坡的示踪剂实验数据的框架进行了验证。模拟的内部年龄，预期寿命和过境时间结构重现理论预测。实验数据也支持这一理论，但需要进一步的工作来解释时变性的影响。讨论了TTD的形状、拖尾及其功率谱。理论框架产生几个无量纲的数字，可用于分类山坡规模的流量和运输动力学，并建议不同的水年龄结构高或低山坡数。
Spatially integrated transport models have been applied widely to model hydrologic transport. However, we lack simple and process‐based theoretical tools to predict the transport closures—transit time distributions (TTDs) and StorAge Selection (SAS) functions. This limits our ability to infer characteristics of hydrologic systems from tracer observations and to make first‐order estimates of SAS functions in catchments where no tracer data is available. Here we present a theoretical framework linking TTDs and SAS functions to hydraulic groundwater theory at the hillslope scale. For hillslopes where the saturated hydraulic conductivity declines exponentially with depth, analytical solutions for the closures are derived that can be used as hypotheses to test against data. In the simplest form, the hillslope SAS function resembles a uniform or exponential distribution (corresponding to flow pathways in the saturated zone) offset from zero by the storage in the unsaturated zone that does not contribute to discharge. The framework is validated against nine idealized virtual hillslopes constructed using a 2‐D Richards equation‐based model, and against data from tracer experiments in two artificial hillslopes. Modeled internal age, life expectancy, and transit time structures reproduce theoretical predictions. The experimental data also support the theory, though further work is needed to account for the effects of time‐variability. The shape and tailing of TTDs and their power spectra are discussed. The theoretical framework yields several dimensionless numbers that can be used to classify hillslope scale flow and transport dynamics and suggests distinct water age structures for high or low Hillslope number.