Numerical mixing, defined here as the physically spurious diffusion of tracers due to the numerical discretization of advection, is known to contribute to biases in ocean circulation models. However, quantifying numerical mixing is non-trivial, with most studies utilizing specifically targeted experiments in idealized settings. Here, we present a precise, online water-mass transformation-based method for quantifying numerical mixing that can be applied to any conserved variable in global general circulation models. Furthermore, the method can be applied within individual fluid columns to provide a spatially-resolved metric. We apply the method to a suite of global ocean-sea ice model simulations with differing grid spacings and sub-grid scale parameterizations. In all configurations numerical mixing drives across-isotherm heat transport of comparable magnitude to that associated with explicitly-parameterized mixing. Numerical mixing is prominent at warm temperatures in the tropical thermocline, where it is sensitive to the vertical diffusivity and resolution. At colder temperatures, numerical mixing is sensitive to the presence of explicit neutral diffusion, suggesting that much of the numerical mixing in these regions acts as a proxy for neutral diffusion when it is explicitly absent. Comparison of equivalent (with respect to vertical resolution and explicit mixing parameters) $1/4^\circ$ and $1/10^\circ$ horizontal resolution configurations shows only a modest enhancement in numerical mixing at $1/4^\circ$. Our results provide a detailed view of numerical mixing in ocean models and pave the way for future improvements in numerical methods.

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.