Water mass transformation theory provides conceptual tools that in principle enable innovative analyses of numerical ocean models; in practice, however, these methods can be challenging to implement and interpret, and therefore remain under-utilized. Most prior work evaluates only some of the simpler or more accessible terms in the water mass budget; meanwhile, the few full budget calculations in the literature are either limited to idealized model configurations and geometrically-simple domains or else have required heroic efforts that are neither scalable to large data sets nor portable to other ocean models or research questions. We begin with a pedagogical derivation of key results of classical water mass transformation theory. We then describe best practices for diagnosing each of the water mass budget terms from the output of Finite-Volume Generalized Vertical Coordinate (FV-GVC) ocean models, including the identification of a non-negligible remainder term as the spurious numerical mixing due to advection scheme discretization errors. We illustrate key aspects of the methodology through an example application to diagnostics from a polygonal region of a Baltic Sea regional configuration of the Modular Ocean Model v6 (MOM6). We verify the convergence of our WMT diagnostics by brute-force, comparing time-averaged diagnostics on various vertical grids to timestep-averaged diagnostics on the native model grid. Finally, we briefly describe a stack of xarray-enabled Python packages for evaluating WMT budgets in FV-GVC models, which is intended to be model-agnostic and available for community use and development.

The climatological mean barotropic vorticity budget is analyzed to investigate the relative importance of surface wind stress, topography and nonlinear advection in dynamical balances in a global ocean simulation. In addition to a pronounced regional variability in vorticity balances, the relative magnitudes of vorticity budget terms strongly depend on the length-scale of interest. To carry out a length-scale dependent vorticity analysis in different ocean basins, vorticity budget terms are spatially filtered by employing the coarse-graining technique. At length-scales greater than 10o (or roughly 1000 km), the dynamics closely follow the Topographic-Sverdrup balance in which bottom pressure torque, surface wind stress curl and planetary vorticity advection terms are in balance. In contrast, when including all length-scales resolved by the model, bottom pressure torque and nonlinear advection terms dominate the vorticity budget (Topographic-Nonlinear balance), which suggests a prominent role of oceanic eddies, which are of Ο(10-100) km in size, and the associated bottom pressure anomalies in local vorticity balances at length-scales smaller than 1000 km. Overall, there is a transition from the Topographic-Nonlinear regime at scales smaller than 10o to the Topographic-Sverdrup regime at length-scales greater than 10o. These dynamical balances hold across all ocean basins; however, interpretations of the dominant vorticity balances depend on the level of spatial filtering or the effective model resolution. On the other hand, the contribution of bottom and lateral friction terms in the barotropic vorticity budget remains small and is significant only near sea-land boundaries, where bottom stress and horizontal friction generally peak.