Diagnosing spurious diapycnal mixing and its spatial distribution due to advection in Z-coordinate ocean models using discrete variance decay

Ocean models relying on geopotential (Z) vertical coordinates suffer from spurious diapycnal mixing created by advection due to the misalignment of isopycnal and grid-layer surfaces. Given the delicateness of diapycnal mixing in ocean models, several studies have been performed to determine its impact, mainly by means of global analyses. Here we present a local analysis of spurious diapycnal mixing based on tracer variance decay. We apply the discrete variance decay (DVD) method proposed by Klingbeil et al. (2014) to diagnose numerical mixing created by several third-order advection schemes used in FESOM (Finite volumE Sea ice Ocean Model). The analysis is applied for an idealized channel flow test setup with Z* vertical coordinates and a linear equation of state. This ensures numerical DVD to be entirely diapycnal enabling identification of its spatial distribution. Further modification of the DVD method is proposed which allows for splitting of total diapycnal mixing into individual contributions from advection and diffusion. The new modifications are then used to compare spurious diapycnal mixing due to advection and explicit horizontal diffusion with parameterized physical diapycnal mixing due to vertical diffusion.