Abstract In this paper, we introduce 2D profile analytical models describing advection solute transport induced by a recharge boundary condition in a catchment-scale aquifer represented by a sediment or rock with permeability changing with depth. The suggested mathematical formulation is based on the concept of transit time distribution (TTD), according to which the concentration trend can be derived directly from the cumulative travel time frequency or from the convolution of TTD (considered as a transfer function) with a solute input function. This approach is shown to be applicable to water flow and solute transport in an aquifer characterized by a vertical hydraulic conductivity profile, k(z), which can be described by either continuous (e.g., massive rock exhibiting an exponential or power-law dependence of k on depth) or discrete (a stratified aquifer) analytical functions. A special focus is on the problem related to advection solute transport in a rectangular anisotropic flow domain bounded by a shallow stream of finite width (downflow-converging area). The suggested analytical models and solutions, utilizing new transfer functions and accounting for different inflow and solute flux conditions, can be involved in several applications, including the assessment of the impacts of spatially variable nonpoint contamination sources on groundwater quality; groundwater dating based on the observation of environmental tracers; and the study of groundwater recharge itself. The models were shown to be applicable not only to simulating the impact on groundwater due to the contaminated recharge, but also to predicting aquifer contamination caused by a source located below the water table within the aquifer domain. Such source can be associated with a radioactive material leachate generated within a deep geological repository of nuclear waste. A relevant modeling example is given.

中文翻译：

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各向异性和深度相关导水率对非点源污染浓度曲线响应的影响

摘要 在本文中，我们介绍了二维剖面分析模型，该模型描述了在以渗透率随深度变化的沉积物或岩石为代表的流域尺度含水层中，由补给边界条件引起的平流溶质运移。建议的数学公式基于传输时间分布 (TTD) 的概念，根据该概念，浓度趋势可以直接从累积旅行时间频率或从 TTD（视为传递函数）与溶质输入的卷积得出功能。这种方法被证明适用于含水层中的水流和溶质输送，其特征是垂直水力传导率剖面 k(z)，可以用连续的（例如，大块岩石表现出 k 对深度的指数或幂律依赖性）或离散（分层含水层）分析函数。特别关注与有限宽度浅流（下流会聚区）界定的矩形各向异性流域中的平流溶质输运相关的问题。建议的分析模型和解决方案利用新的传递函数并考虑不同的流入和溶质通量条件，可用于多种应用，包括评估空间可变的非点污染源对地下水质量的影响；基于环境示踪剂观察的地下水测年；以及地下水补给本身的研究。这些模型不仅适用于模拟受污染补给对地下水的影响，还可以预测由位于含水层域内地下水位以下的源引起的含水层污染。这种源可能与在核废料的深层地质处置库内产生的放射性物质渗滤液有关。给出了一个相关的建模示例。