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.

Motivated by recent advances in mapping mesoscale eddy tracer mixing in the ocean we evaluate the sensitivity of a coarse-resolution global ocean model to a spatially variable neutral diffusion coefficient $\kappa_n(x,y,z)$. We gradually introduce physically-motivated models for the horizontal (mixing length theory) and vertical (surface mode theory) structure of $\kappa_n$ along with suppression of mixing by mean flows. Each structural feature influences the ocean’s hydrography and circulation to varying extents, with the suppression of mixing by mean flows being the most important factor and the vertical structure being relatively unimportant. When utilizing the full theory (experiment “FULL’) the interhemispheric overturning cell is strengthened by $2$ Sv at $26^\circ$N (a $\sim20\%$ increase), bringing it into better agreement with observations. Zonal mean tracer biases are also reduced in FULL. Neutral diffusion impacts circulation through surface temperature-induced changes in surface buoyancy fluxes and non-linear equation of state effects. Surface buoyancy forcing anomalies are largest in the Southern Ocean where decreased neutral diffusion in FULL leads to surface cooling and enhanced dense-to-light surface watermass transformation, reinforced by reductions in cabbeling and thermobaricity. The increased watermass transformation leads to enhanced mid-latitude stratification and interhemispheric overturning. The spatial structure for $\kappa_n$ in FULL is important as it enhances the interhemispheric cell without degrading the Antarctic bottom water cell, unlike a spatially-uniform reduction in $\kappa_n$. These results highlight the sensitivity of modeled circulation to $\kappa_n$ and motivate the use of physics-based models for its structure.

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 median internal variability is reduced in both ocean heat and salt content in T-S space compared to Eulerian coordinates, and that a large proportion of variability in T-S space can be attributed to processes which operate over a timescale greater than 10 years. We show that, as a consequence of the reduced projection of internal variability into T-S space, the signal-to-noise ratio in watermass co-ordinates is at least two times greater than in Eulerian co-ordinate systems, implying that the climate change signal can be more robustly identified.