Multiple Rotations of Gaussian Quadratures: An Efficient Method for Uncertainty Analyses in Large-Scale Simulation Models

Stepanyan, D., Grethe, H., Zimmermann, G., Siddig, K., Deppermann, A., Feuerbacher, A., Luckmann, J., Valin, H. ORCID: https://orcid.org/0000-0002-0618-773X, Nishizawa, T., Ermolieva, T., & Havlik, P. ORCID: https://orcid.org/0000-0001-5551-5085 (2021). Multiple Rotations of Gaussian Quadratures: An Efficient Method for Uncertainty Analyses in Large-Scale Simulation Models. Environmental Modelling & Software 281 e104929. 10.1016/j.envsoft.2020.104929.

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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 a 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.

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