Heat has become an increasingly utilized hydrological tracer for quantifying groundwater flow due to its universal distribution and environmental friendliness. Estimating time-varying groundwater flux is of great significance for understanding the transient behavior of the groundwater system. Most heat tracing models for acquiring transient water flux were specially designed for the near-surface medium that rely on periodic temperature signals, but few can be applicable to deep groundwater flux estimates. Models estimating flux in deep aquifers usually assume constant flow velocity over time, which cannot delineate the temporal patterns of groundwater flow. Here, we propose a numerical approach for automatically quantifying transient vertical groundwater flux from temperature time series at multiple depths. The approach can be applied to deep as well as near-surface homogeneous and heterogeneous media with flexible boundary conditions. The accuracy of the approach is demonstrated through three synthetic experiments and one real case test using data from a field site. Our approach shows fine temporal resolution for rapidly changing flow under various conditions and accurate estimates for a wide range of flow velocities. We conduct analyses to investigate the influence of different strategies to give an initial temperature profile on flux estimates. The results highlight the necessity of accurately giving an initial temperature profile under transient conditions. This study improves the heat tracing approach for estimating time-varying water fluxes, especially in a deep well, which would be beneficial to monitoring and managing groundwater flows with the development of high-resolution temperature observation technology.

中文翻译：

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使用多深度温度时间序列估计垂直地下水通量的时间模式：数值方法


由于其普遍分布和环境友好性，热量已成为越来越多地用于量化地下水流量的水文示踪剂。估算随时间变化的地下水通量对于理解地下水系统的瞬态行为具有重要意义。大多数用于获取瞬态水通量的伴热模型都是专门为依赖周期性温度信号的近地表介质而设计的，但很少有能够适用于深层地下水通量估计的模型。估计深层含水层通量的模型通常假设流速随时间恒定，这无法描绘地下水流的时间模式。在这里，我们提出了一种数值方法，用于根据多个深度的温度时间序列自动量化瞬态垂直地下水通量。该方法可应用于具有灵活边界条件的深层以及近地表均质和异质介质。该方法的准确性通过三个综合实验和一个使用现场数据的真实案例测试来证明。我们的方法显示了各种条件下快速变化的流量的精细时间分辨率以及对各种流速的准确估计。我们进行分析以研究不同策略的影响，以给出初始温度曲线对通量估计的影响。结果强调了在瞬态条件下准确给出初始温度曲线的必要性。这项研究改进了估算时变水通量的热追踪方法，特别是在深井中，随着高分辨率温度观测技术的发展，这将有利于监测和管理地下水流。