Water-Mass Coordinates Isolate the Historical Ocean Warming Signal
Authors: Sohail T. , Holmes R. M. , Zika J.D. 
Published: January 2023

Abstract
Persistent warming and water cycle change due to anthropogenic climate change modifies the temperature and salinity distribution of the ocean over time. This “forced” signal of temperature and salinity change is often masked by the background internal variability of the climate system. Analyzing temperature and salinity change in water-mass-based coordinate systems has been proposed as an alternative to traditional Eulerian (e.g., fixed-depth, zonally averaged) coordinate systems. The impact of internal variability is thought to be reduced in water-mass coordinates, enabling a cleaner separation of the forced signal from background variability—or a higher “signal-to-noise” ratio. Building on previous analyses comparing Eulerian and water-mass-based one-dimensional coordinates, here we recast two-dimensional coordinate systems—temperature–salinity (T–S), latitude–longitude, and latitude–depth—onto a directly comparable equal-volume framework. We compare the internal variability, or “noise” in temperature and salinity between these remapped two-dimensional coordinate systems in a 500-yr preindustrial control run from a CMIP6 climate model. We find that the median internal variability is lowest (and roughly equivalent) in T–S and latitude–depth space, compared with latitude–longitude coordinates. A large proportion of variability in T–S and latitude–depth space can be attributed to processes that operate over a time scale greater than 10 years. Overall, the signal-to-noise ratio in T–S coordinates is roughly comparable to latitude–depth coordinates, but is greater in regions of high historical temperature change. Conversely, latitude–depth coordinates have greater signal-to-noise ratio in regions of historical salinity change. Thus, we conclude that the climatic temperature change signal can be more robustly identified in water-mass coordinates.

Significance Statement
Changes in ocean temperature and salinity are driven both by human-induced climate change and by modes of natural variability in the climate system, such as El Niño–Southern Oscillation. It can be difficult to isolate the human-induced “signal” of climate change from the natural fluctuations or “noise” in the climate system. Water-mass-based methods, which “follow” a parcel of water around the ocean, have been thought to improve on “Eulerian” (i.e., analyses performed at fixed latitude, longitude, and depth) frames of reference as they are less impacted by the noise. However, it is difficult to cleanly compare between water-mass-based methods and Eulerian methods. Here, we aim to quantify the extent to which water-mass-based frameworks improve on Eulerian frameworks in isolating the climate signal from the noise. We recast water-mass and Eulerian methods onto an equivalent grid, enabling a clean comparison between them, and find that doing so increases the signal-to-noise ratio in water-mass-based coordinates in regions of ocean warming. These results emphasize the utility of water-mass-based methods in analyzing long-term climatic temperature change in the ocean.