Multiple rotations of Gaussian quadratures: An efficient method for uncertainty analyses in large-scale simulation models

Concerns regarding the impacts of climate change, food price volatility and uncertain macroeconomic conditions have motivated users of large-scale simulation models addressing agricultural markets to consider uncertainty in their projections. One way to incorporate uncertainty in such models is the integration of stochastic elements, thus turning the model into a problem of numerical integration. In most cases, such problems do not have analytical solutions, and researchers apply methods of numerical approximation. This article presents a novel approach to uncertainty analysis as an alternative to the computationally burdensome Monte Carlo or quasi-Monte Carlo methods, also known as probabilistic approaches. The method developed here is based on Stroud’s degree three Gaussian quadrature (GQ) formulae. It is tested in three different large-scale simulation models addressing agricultural markets. The results of this study demonstrate that the proposed approach produces highly accurate results using a fraction of the computation capacity and time required by probabilistic approaches. The findings suggest that this novel approach, called the multiple rotations of Gaussian Quadratures (MRGQ), is highly relevant to increasing the quality of the results since individual GQ-rotations tend to produce results with rather large variability/approximation errors. The MRGQ method can be applied to any simulation model, but we believe that the main beneficiaries will be users of large-scale simulation models who struggle to apply probabilistic methods for uncertainty analyses due to their high computational, data management and time requirements.