Estimating lateral groundwater inflow to rivers using heat as a tracer

Heat is a natural tracer that can be used to estimate groundwater velocity and fluxes. However, most studies, if not all, are focused on vertical flow due to the existence of a simple closed-form analytical solution that well captures the characteristics of vertical heat transport. In this study, we show that lateral groundwater inflow to rivers can also be inferred from natural heat signals by integrating theoretical development and field observation. A closed-form analytical solution for lateral heat transport in unconfined aquifers is developed and serves as the basis for the inversion of groundwater velocity. Two parameter estimation techniques, Markov Chain Monte Carlo (MCMC) and a trial-and-error method, are applied to estimate groundwater velocity using groundwater temperature observed at wells. The MCMC method requires at least one observation well and its performance increases with the number of wells. The trial-and-error method requires three observation wells and can appropriately represent the groundwater velocity. The performance of both methods is affected by the uncertainty of hydrogeological and thermal parameters, such as porosity, thermal conductivity of the overlying and underlying layers, and aquifer thickness. Porosity is the most sensitive and thermal conductivity is the least sensitive parameter to the accuracy of estimated groundwater velocity. The developed heat tracer method for estimating lateral groundwater inflow to rivers is novel (script provided) and could be a valuable alternative to the widely used environmental tracers.