What is the skill of ocean tracers in reducing uncertainties about ocean diapycnal mixing and projections of the Atlantic Meridional Overturning Circulation?

Current projections of the oceanic response to anthropogenic climate forcings are uncertain. Two key sources of these uncertainties are (1) structural errors in current Earth system models and (2) imperfect knowledge of model parameters. Ocean tracer observations have the potential to reduce these uncertainties. Previous studies typically consider each tracer separately, neglect potentially important statistical properties of the system, or use methods that impose rather daunting computational demands. Here we extend and improve upon a recently developed approach using horizontally averaged vertical profiles of chlorofluorocarbon (CFC-11), radiocarbon (Δ¹⁴C), and temperature (T) observations to reduce model parametric and structural uncertainties. Our method estimates a joint probability density function, which considers cross-tracer correlations and spatial autocorrelations of the errors. We illustrate this method by estimating two model parameters related to the vertical diffusivity, the background vertical diffusivity, and the upper Southern Ocean mixing. We show that enhancing the upper Southern Ocean mixing in the model improves the representations of ocean tracers and improves the hindcasts of the Atlantic Meridional Overturning Circulation (AMOC). The most probable value of the background vertical diffusivity in the pelagic pycnocline is between 0.1 and 0.2 cm² s^-1. According to the statistical method, observations of Δ¹⁴C reduce the uncertainty about the background vertical diffusivity mostly followed by CFC-11 and T. Using all three tracers jointly reduces the model uncertainty by 40%, more than each tracer individually. Given several important caveats, we illustrate how the reduced model parametric uncertainty improves probabilistic projections of the AMOC.