Taimoor Sohail

and 2 more

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.

A. J. George Nurser

and 3 more

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.

Taimoor Sohail

and 2 more

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.