This paper analyzes the surface/subsurface flow coupled with transport. The flow is modeled by the coupling of Stokes and Darcy equations. The transport is modeled by a convection-dominated parabolic equation. The two-way coupling between flow and transport is nonlinear and it is done via the velocity field and the viscosity. This problem arises from a variety of natural phenomena such as the contamination of the groundwater through rivers. The main result is existence and stability bounds of a weak solution.