Uncertainty quantification for computer models with spatial output using calibration-optimal bases

TL;DR

This paper introduces calibration-optimal bases to improve uncertainty quantification in spatial computer model outputs, addressing the terminal case problem where standard methods fail to fit observations.

Contribution

It proposes a new optimal rotation algorithm for bases that avoids the terminal case, enhancing calibration accuracy for complex spatial models.

Findings

The optimal rotation algorithm effectively prevents terminal case issues.

Application to climate models demonstrates improved calibration results.

The methodology offers a practical tool for climate model tuning.

Abstract

The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use principal component decomposition to reduce the dimensions of the outputs in order to allow Gaussian process emulators to predict the output for calibration. We introduce the `terminal case', in which the model cannot reproduce observations to within model discrepancy, and for which standard calibration methods in UQ fail to give sensible results. We show that even when there is no such issue with the model, the standard decomposition on the outputs can and usually does lead to a terminal case analysis. We present a simple test to allow a practitioner to establish whether their experiment will result in a terminal case analysis, and a methodology for defining calibration-optimal bases that avoid this whenever it is not inevitable. We present the optimal rotation algorithm for doing this, and demonstrate its efficacy for an idealised example for which the usual principal component methods fail. We apply these ideas to the CanAM4 model to demonstrate the terminal case issue arising for climate models. We discuss climate model tuning and the estimation of model discrepancy within this context, and show how the optimal rotation algorithm can be used in developing practical climate model tuning tools.