Computer Model Calibration with Multivariate Spatial Output: A Case Study

Computer model calibration involves combining information from simulations of a complex computer model with physical observations of the process being simulated by the model. Increasingly, computer model output is in the form of multiple spatial fields, particularly in climate science. We study a simple and effective approach for computer model calibration with multivariate spatial data. We demonstrate the application of this approach to the problem of inferring parameters in a climate model. We find that combining information from multiple spatial fields results in sharper posterior inference than obtained from a single spatial field. In addition, we investigate the effects of including a model discrepancy term and compare the use of a plug-in versus a fully Bayesian approach for accounting for emulator variances. We find that usually, although not always, inclusion of the model discrepancy term results in more accurate and sharper inference of the calibration parameter, and estimating emulator spatial variances in a fully Bayesian model results in wider posterior distributions.