On the nudging terms at open boundaries in regional ocean models

For open boundary conditions (OBCs) in regional models, a nudging term added to radiative and/or advective conditions during the wave or flow propagation outward from the model domain of interest is widely used, to prevent the predicted boundary values from evolving to become quite different from the external data, especially for a long-term integration. However, nudging time scales are basically unknown, leading to many empirical selections. In this paper, a method for objectively estimating nudging time scales during outward propagation is proposed, by using internal model dynamics near the boundary. We tested this method and other several commonly used OBCs for cases of both an idealized model domain and a realistic configuration, and model results demonstrated that the proposed method improves the model solutions. Many similarities are found between the nudging and mixing time scales, in magnitude, spatial and temporal variations, since the nudging mainly replaces the effect of the mixing terms in this study. However, the mixing time scale is not an intrinsic property of the nudging term because in other studies the nudging term might replace terms other than the mixing terms and, thus, should reflect other characteristic time scales.