Advanced methods for uncertainty quantification in tail regions of climate model predictions.
Conventional methods for uncertainty quantification are generally challenged in the 'tails' of probability distributions. This is specifically an issue for many climate observables since extensive sampling to obtain a reasonable accuracy in tail regions is especially costly in climate models. Moreover, the accuracy of spectral representations of uncertainty is weighted in favor of more probable ranges of the underlying basis variable, which, in conventional bases does not particularly target tail regions. Therefore, what is ideally desired is a methodology that requires only a limited number of full computational model evaluations while remaining accurate enough in the tail region. To develop such a methodology, we explore the use of surrogate models based on non-intrusive Polynomial Chaos expansions and Galerkin projection. We consider non-conventional and custom basis functions, orthogonal with respect to probability distributions that exhibit fat-tailed regions. We illustrate how the use of non-conventional basis functions, and surrogate model analysis, improves the accuracy of the spectral expansions in the tail regions. Finally, we also demonstrate these methodologies using precipitation data from CCSM simulations.