Estimating temporal patterns of vertical groundwater flux using multidepth temperature time series: A numerical method

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.