Propagation of hydropeaking waves in heterogeneous aquifers: effects on flow topology and uncertainty quantification

Topological flow properties are proxies for mixing processes in aquifers and allow us to better understand the mechanisms controlling transport of solutes in the subsurface. However, topological descriptors, such as the Okubo-Weiss metric, are affected by the uncertainty in the solution of the flow problem. While the uncertainty related to the heterogeneous properties of the aquifer has been widely investigated in the past, less attention has been given to the one related to highly transient boundary conditions. We study the effect of different transient boundary conditions associated with hydropeaking events (i.e., artificial river stage fluctuations due to hydropower production) on groundwater flow and the Okubo-Weiss metric. We define deterministic and stochastic modeling scenarios applying four typical settings to describe river stage fluctuations during hydropeaking events: a triangular wave, a sine wave, a complex wave that results of the superposition of two sine waves, and a trapezoidal wave. We use polynomial chaos expansions to quantify the spatiotemporal uncertainty that propagates into the hydraulic head in the aquifer and the Okubo-Weiss. The wave-shaped highly transient boundary conditions influence not only the magnitude of the deformation and rotational forces of the flow field but also the temporal dynamics of dominance between local strain and rotation properties. Larger uncertainties are found in the scenario where the trapezoidal wave was imposed due to sharp fluctuation in the stage. The statistical moments that describe the propagation of the uncertainty highly vary depending on the applied boundary condition.