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. Analysing temperature and salinity change in watermass-based coordinate systems has been proposed as an alternative to traditional Eulerian (e.g., fixed-depth, zonally-averaged) co-ordinate systems. The impact of internal variability is thought to be reduced in watermass co-ordinates, 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 co-ordinate 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 co-ordinate systems in a 500 year pre-industrial 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 co-ordinates. A large proportion of variability in 𝑇 − 𝑆 and latitude-depth space can be attributed to processes which operate over a timescale greater than 10 years. Overall, the signal-to-noise ratio in 𝑇 − 𝑆 co-ordinates is roughly comparable to latitude-depth co-ordinates, but is greater in regions of high historical temperature change. Conversely, latitude-depth co-ordinates 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 watermass-co-ordinates.