Water flux characterization through hydraulic head and temperature data assimilation: Numerical modeling and sandbox experiments

Spatial distribution of groundwater recharge/discharge fluxes has an important impact on mass and energy exchanges in shallow streambeds. During the last two decades, extensive studies have been devoted to the quantification of one-dimensional (1-D) vertical exchange fluxes. Nevertheless, few studies were conducted to characterize two-dimensional (2-D) heterogeneous flux fields that commonly exist in real-world cases. In this study, we used an iterative ensemble smoother (IES) to quantify the spatial distribution of 2-D exchange fluxes by assimilating hydraulic head and temperature measurements. Four assimilation scenarios corresponding to different potential field applications were tested. In the first three scenarios, the heterogeneous hydraulic conductivity fields were first inferred from hydraulic head and/or temperature measurements, and then the flux fields were derived through Darcy's law using the estimated conductivity fields. In the fourth scenario, the flux fields were estimated directly from the temperature measurements, which is more efficient and especially suitable for the situation that a complete knowledge of flow boundary conditions is unavailable. We concluded that, the best estimation could be achieved through jointly assimilating hydraulic head and temperature measurements, and temperature data were superior to the head data when they were used independently. Overall, the IES method provided more robust and accurate vertical flux estimations than those given by the widely used analytical solution-based methods. Furthermore, IES gave reasonable uncertainty estimations, which were unavailable in traditional methods. Since temperature can be accurately monitored with high spatial and temporal resolutions, the coupling of heat tracing techniques and IES provides promising potential in quantifying complex exchange fluxes under field conditions.