Using tracer observations to reduce the uncertainty of ocean diapycnal mixing and climate-carbon cycle projections

What is the uncertainty of climate-carbon cycle projections in response to anthropogenic greenhouse gas emissions, and how can we reduce this uncertainty? We address this question by quantifying the ability of available ocean tracer observations to constrain the values of diapycnal diffusivity in the pelagic ocean (K_v), a key uncertain parameter representing sub-grid-scale diapycnal (vertical) mixing in physical circulation models. We show that model versions with weak mixing (i.e., low K_v) lead to higher projections of atmospheric CO₂ and larger global warming than do models with vigorous mixing. Slower heat uptake and slower carbon uptake by the oceans contribute about equally to the accelerated warming in the low-mixing models. A Bayesian data-model fusion method is developed to quantify the likelihood of different structural and parametric model choices given an array of observed 20th century ocean tracer distributions. These spatially resolved observations provide strong limits on the upper value of K_w whereas global metrics used in previous studies, such as the historical evolution of global average surface air temperature, global ocean heat uptake, or atmospheric CO₂ concentration, provide only poor constraints. We compare different methods to quantify the probability of a particular diffusivity value given the observational constraints. One-dimensional, globally horizontally averaged data result in sharper probability density functions compared with the full 3-D fields. This perhaps unexpected result opens up an avenue to objectively determine the optimal degree of aggregation at which model predictions have skill, and at which observations are most helpful in constraining model parameters. Our best estimate for K_v in the pelagic pycnocline is around 0.05-0.2 cm²/s, in agreement with earlier independent estimates based on tracer dispersion experiments and turbulence microstructure measurements.