Journal Article

Water Mass Transformation Budgets in Finite‐Volume Generalized Vertical Coordinate Ocean Models

Krasting, John, Zika, Jan D., Griffies, Stephen M., Bailey, Shanice, Dussin, Raphael, Stanley, Geoffrey, Tesdal, Jan‐Erik, MacGilchrist, Graeme, Drake, Henri F.

2025

Overview

Water Mass Transformation (WMT) 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. Our aim is to demonstrate the feasibility of diagnosing all terms in the water mass budget and to exemplify their usefulness for scientific inquiry and model development by quantitatively relating water mass changes, overturning circulations, boundary fluxes, and interior mixing. We begin with a pedagogical derivation of key results of classical WMT 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 the analysis of a polygonal region of the Greater Baltic Sea in a regional demonstration simulation using the Modular Ocean Model v6 (MOM6). We verify the convergence of our WMT diagnostics by brute‐force, comparing time‐averaged (“offline”) diagnostics on various vertical grids to timestep‐averaged (“online”) 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 (culminating in the new xwmb package), which is intended to be model‐agnostic and available for community use and development. Plain Language Summary A useful tool for characterizing ocean variability and change is water mass analysis, in which the ocean is decomposed into parcels with distinct properties (such as their temperature, density, or dissolved oxygen concentrations). Water Mass Transformation (WMT) theory provides a concise equation for the evolution of these water masses, which can be used to identify the various processes that act to increase or decrease the total mass (or size) of each parcel. In practice, however, calculating the terms in these WMT budget equations from ocean model simulation output is technically challenging, limiting the creativity of applications in the literature. We review the fundamentals of WMT theory, explain how to calculate WMT budgets based on the output of a generic ocean model simulation (with examples generated from a widely used code), and summarize a new publicly available software for doing such calculations: the xwmb Python package. Key Points Water mass budgets provide insights into the processes transforming material water mass properties and how they relate to circulation Spurious water mass transformations due to advection scheme errors can be quantified by combining mass and tracer budget diagnostics We describe best practices for model analysis and present a novel Python stack for model‐agnostic and out‐of‐memory regional calculations

• Publisher: John Wiley & Sons, Inc,American Geophysical Union (AGU)
• Subject: Advection / Best practices / diapycnal mixing / ENVIRONMENTAL SCIENCES / Mass budget / Ocean circulation / ocean mixing / ocean modeling / Ocean models / Oceans / Salinity / spurious numerical mixing / Water / Water mass transformation / Water masses