Fast dimension-reduced climate model calibration

What is the response of the climate system to anthropogenic forcings? This question is addressed typically using projections from climate models. The uncertainty surrounding current climate projections has important policy implications. Characterizing and, if possible, reducing this uncertainty is an area of ongoing research. We consider the problem of making projections of the North Atlantic meridional overturning circulation (AMOC). AMOC projections are of interest because AMOC changes may considerably impact natural and human systems. Uncertainties about climate model parameters play a key role in uncertainties in AMOC projections. When the observational data and the climate model output are high-dimensional spatial data sets, the data are typically aggregated due to computational constraints. The effects of aggregation are unclear because statistically rigorous approaches for model parameter inference have been infeasible for high-resolution data. Here we develop a flexible and computationally efficient approach using principal components and basis expansions to study the effect of spatial data aggregation on parametric and projection uncertainties. Our Bayesian reduced-dimensional calibration approach allows us to study the effect of complicated error structures and data-model discrepancies on our ability to learn about climate model parameters from high-dimensional data. Considering high-dimensional spatial observations reduces the effect of deep uncertainty associated with different priors and results in sharper projections based on our climate model. We demonstrate that our computationally efficient approach may be widely applicable to a variety of high-dimensional computer model calibration problems.