Multiple rotations of Gaussian quadratures: An efficient method for uncertainty analyses in large-scale simulation models. (February 2021) - Stepanyan, Davit; Grethe, Harald; Zimmermann, Georg; Siddig, Khalid; Deppermann, Andre; Feuerbacher, Arndt; Luckmann, Jonas; Valin, Hugo; Nishizawa, Takamasa; Ermolieva, Tatiana; Havlik, Petr
Abstract: Concerns regarding the impact of climate change, food price volatility, and weather uncertainty have motivated users of simulation models to consider uncertainty in their simulations. One way to do this is to integrate uncertainty components in the model equations, thus turning the model into a problem of numerical integration. Most of these problems do not have analytical solutions, and researchers, therefore, apply numerical approximation methods. This article presents a novel approach to conducting an uncertainty analysis as an alternative to the computationally burdensome Monte Carlo-based (MC) methods. The developed method is based on the degree three Gaussian quadrature (GQ) formulae and is tested using three large-scale simulation models. While the standard single GQ method often produces low-quality approximations, the results of this study demonstrate that the proposed approach reduces the approximation errors by a factor of nine using only 3.4% of the computational effort required by the MC-based methods in the most computationally demanding model. Highlights: Conventional methods of uncertainty/sensitivity analysis suffer from poor computational efficiency. Gaussian quadrature (GQ) is an efficient method for uncertainty/sensitivity analysis. The standard single GQ method often produces low-quality approximations. The proposed novel method, called MRGQ, overcomes the problem of insufficient accuracy of traditional GQ approaches. The MRGQ method is especially relevant for computationally intensive models.