Inferring likelihoods and climate system characteristics from climate models and multiple tracers

Characterizing the risks of anthropogenic climate change poses considerable statistical challenges. A key problem is how to combine the information contained in large-scale observational data sets with simulations of Earth system models in a statistically sound and computationally tractable manner. Here, we describe a statistical approach for improving projections of the North Atlantic meridional overturning circulation (AMOC). The AMOC is part of the global ocean conveyor belt circulation and transfers heat between low and high latitudes in the Atlantic basin. The AMOC might collapse in a "tipping point" response to anthropogenic climate forcings. Assessing the risk of an AMOC collapse is of considerable interest because it may result in major impacts on natural and human systems. AMOC projections rely on simulations from complex climate models. One key source of uncertainty in AMOC projections is uncertainty about background ocean vertical diffusivity (K_v), an important model parameter. K_v cannot be directly observed but can be inferred by combining climate model output with observations on the oceans (so-called tracers). Here, we combine information from multiple tracers, each observed on a spatial grid. Our two-stage approach emulates the computationally expensive climate model using a flexible hierarchical model to connect the tracers. We then infer K_v using our emulator and the observations via a Bayesian approach, accounting for observation error and model discrepancy. We utilize kernel mixing and matrix identities in our Gaussian process model to considerably reduce the computational burdens imposed by the large data sets. We find that our approach is flexible, reduces identifiability issues, and enables inference about K_v based on large data sets. We use the resulting inference about K_v to improve probabilistic projections of the AMOC.