Greenhouse gases and aerosols play a major role in controlling global climate change. Greenhouse gases drive a radiative imbalance which warms the ocean, while aerosols cool the ocean. Since 1980, the effective radiation felt by the planet due to anthropogenic aerosols has levelled off, global ocean cooling due to aerosols has decelerated, and greenhouse gas-driven ocean warming has accelerated. We explore the deceleration of aerosol-driven ocean cooling by quantifying a time- and spatially-varying ocean heat uptake efficiency, defined as the change in the rate of global ocean heat storage per degree of cooling surface temperature. In aerosol-only simulations, ocean heat uptake efficiency has decreased by 69% since the 1900s. The tropics and sub-tropics have driven this decrease, while the coldest fraction of the ocean continues to sustain cooling and high ocean heat uptake efficiency. Our results identify a growing trend towards less efficient ocean cooling due to aerosols.

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.

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.

Projecting fluid systems onto coordinates defined by fluid properties (e.g., pressure, temperature, tracer concentration) can reveal deep insights, for example into the thermodynamics and energetics of the ocean and atmosphere. We present a mathematical formalism for fluid flow in such coordinates. We formulate mass conservation, streamfunction, tracer conservation, and tracer angular momentum within fluid property space (q-space) defined by an arbitrary number of continuous fluid properties. Points in geometric position space (x-space) do not generally correspond in a 1-to-1 manner to points in q-space. We therefore formulate q-space as a differentiable manifold, which allows differential and integral calculus but lacks a metric, thus requiring exterior algebra and exterior calculus. The Jacobian, as the ratio of volumes in x-space and q-space, is central to our theory. When x-space is not 1-to-1 with q-space, we define a generalized Jacobian either by patching x-space regions that are 1-to-1 with q-space, or by integrating a Dirac delta to select all x-space points corresponding to a given q value. The latter method discretises to a binning algorithm, providing a practical framework for analysis of fluid motion in arbitrary coordinates. Considering q-space defined by tracers, we show that tracer diffusion and tracer sources drive motion in q-space, analogously to how internal stresses and external forces drive motion in x-space. Just as the classical angular momentum of a body is unaffected by internal stresses, the globally integrated tracer angular momentum is unaffected by tracer diffusion — unless different tracers are diffused differently, as in double diffusion.

The ocean has absorbed approximately 90% of the accumulated heat in the climate system since 1970. As global warming accelerates, understanding ocean heat content changes and tracing these to surface heat input is becoming increasingly important. We introduce a novel tracer-percentile framework in which we organise the ocean into temperature percentiles from warmest to coldest, allowing us to trace changes in ocean temperature to changes in air-sea heat fluxes and mixing. Applying this framework to observations and historical CMIP6 simulations, we find that 40% of heat uptake between 1970 and 2014 occurs in the warmest 10% ocean volume. However, the coolest 90% ocean volume outcrops over 23% of the ocean’s surface area, implying a disproportionately large heat input per unit area. Additionally, a cold bias in the CMIP6 models is traced to inaccurate sea surface temperatures and surface heat fluxes into the warmest 5 – 20% ocean volume.

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.