On the spatial calibration of imperfect climate models

Abstract. The calibration of Earth System Model parameters is subject to both data, time and computational constraints. The high dimensionality of this calibration problem, combined with errors which arise from model structural assumptions makes it impossible to find model versions fully consistent with historical observations, with the potential for multiple plausible configurations which make different tradeoffs between skill in different variables or spatial regions. In this study, we lay out a formalism for making different assumptions about how ensemble variability in a Perturbed Physics Ensemble (PPE) relates to model error, proposing an empirical but practical solution for finding diverse near-optimal solutions. We argue that the effective degrees of freedom in model performance response to parameter input (the ’parametric component’ ) is, in fact, relatively small, illustrating why manual calibration is often able to find near-optimal solutions. Comparison with a perturbed initial condition ensemble reveals that internal variability associated with this parametric component of model error is negligible. Finally, there is a potential for comparably performing parameter configurations making different trade-offs in model errors. These alternative configurations can inform model development and could potentially lead to significantly different future climate evolution.