Water management projects such as stream bed re-naturalization affect the water table, which is relevant, e.g., for flood prediction. These physical processes can be modeled by coupling the Richards equation for groundwater flow to a shallow water model for rivers or lakes (Bastian et al., 2012). We analyzed the fully discrete, linearized formulation of this coupling problem, yielding an optimal choice of the relaxation parameter for sequential Dirichlet-Neumann iterations. Here we followed the techniques previously established in Monge & Birken, 2018. This analysis is closely linked to parallel Dirichlet-Neumann iterations, which are a special case of parallel-in-time waveform relaxation. Waveform relaxation methods have been extensively studied in continuous or semi-discrete formulations. As we will show in this talk, the fully discrete analysis—corresponding to the actual implementation in a numerical model—can give significantly different results. Our theoretical analysis is supported by numerical results for a fully nonlinear test case using DUNE and preCICE.