Using ensemble data assimilation to estimate transient hydrologic exchange flow under highly dynamic flow conditions

Quantifying dynamic hydrologic exchange flows (HEFs) within river corridors that experience high-frequency flow variations caused by dam regulations is important for understanding the biogeochemical processes at the river water and groundwater interfaces. Heat has been widely used as a tracer to infer steady-state flow velocities through analytical solutions of heat transport defined by the diurnal temperature signals. Under sub-daily dynamic flow conditions, however, such analytical solutions are not applicable due to the violation of their fundamental assumptions. In this study, we developed a data assimilation-based approach to estimate the sub-daily flux under highly dynamic flow conditions using multi-depth temperature observations at a 5-min resolution. If the hydraulic gradient is measured, Darcy's law was used to calculate the flux with permeability estimated from temperature responses below the riverbed. Otherwise, flux was estimated directly by assimilating multi-depth temperature data at 1- or 2-hr time intervals assuming one-dimensional flow and heat transport governing equation. By comparing estimated fluxes with model-generated synthetic truth, we demonstrated that both schemes have robust performance in estimating fluxes under highly dynamic flow conditions. This data assimilation-based flux estimation method was able to capture the vertical sub-daily fluxes using multi-depth high-resolution temperature data alone, even in the presence of multi-dimensional flow. This approach has been successfully applied to real field temperature data collected at the Hanford site, which experiences highly dynamic HEFs. Our study shows the promise of adopting distributed 1-D temperature monitoring to capture spatial and temporal exchange dynamics in river corridors at a watershed scale or beyond.