A particle-tracking scheme for simulating pathlines in coupled surface-subsurface flows

A Lagrangian particle tracking scheme has been extended to simulate advective transport through coupled surface and subsurface flows. This extended scheme assumes a two-dimensional flow field for the overland domain and a three-dimensional flow field for the subsurface domain. Moreover it is assumed that the flow fields are simulated by a cell centered finite difference method. Pathlines in both the subsurface and the overland domain are simulated by classical particle tracking methods. Exchange of particles between the two domains is simulated by newly-developed algorithms presented in this study. Different algorithms are used depending on the direction of the exchange across the interface between the two domains. In the subsurface domain knowledge about a particle’s pathline is enough to detect a transfer to the surface domain and the solution is straightforward. However, in the two-dimensional overland domain pathlines are parallel to the land surface. Therefore the velocity field in the overland domain alone cannot be used to detect a transfer to the subsurface. We propose a relatively simple algorithm to estimate the probability of transfer to the subsurface domain. It is shown that this algorithm can also be used to handle the transfer from the overland domain to the atmosphere domain. The algorithm to estimate the transfer probabilities is based on the mass balance of water on a streamtube aligned with the particle’s pathline. This newly developed technique ensures that transit time distributions can be simulated accurately. These new relationships are implemented in an existing particle tracking code and are verified using analytical solutions for transit times.

► A Lagrangian particle-tracking scheme has been extended.
► The scheme tracks particles trough coupled surface and subsurface flows.
► Particle transfer between the domains is simulated.
► A transfer probability function is used to transfer particles.
► The scheme is verified against an analytical solution.