Modeling Coupled Surface–Subsurface Flow Processes: A Review

Surface and subsurface flow systems are inherently unified systems that are often broken into sections for logical (e.g., time scales) and technical (e.g., analytical and computational solvability) reasons. While the basic physical laws are common to surface and subsurface systems, spatial and temporal dimensions as well as the continuum approach used for the subsurface lead to different formulations of the governing partial differential equations. While in most applications such decoupling of the systems works well and allows a very accurate and efficient description of the individual system by treating the adjacent system as a boundary condition, in the case of water flow over a porous medium, it does not. Therefore coupled models are in increasing use in this field, led mostly by watershed and surface irrigation modelers. The governing equations of each component of the coupled system and the coupling physics and mathematics are reviewed first. Three different coupling schemes are identified, namely the uncoupled (with the degenerated uncoupled scheme being a special case of the uncoupled), the iteratively coupled, and the fully coupled. Next, the different applications of the different coupling schemes, sorted by field of application, are reviewed. Finally, some research gaps are discussed, led by the need to include vertical momentum transfer and to expand the use of fully coupled models toward surface irrigation applications.