An Improved Copula‐Based Framework for Efficient Global Sensitivity Analysis

• Published in: Water resources research Vol. 60; no. 1
• Main Authors: Liu, Hongli, Clark, Martyn P., Gharari, Shervan, Sheikholeslami, Razi, Freer, Jim, Knoben, Wouter J. M., Marsh, Christopher B., Papalexiou, Simon Michael
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 01.01.2024; Wiley
• Subjects: computationally efficient; Computer applications; computer software; Fluid dynamics; Gaussian mixture copula model; given‐data approach; global sensitivity analysis; Mathematical models; Methods; non‐identifiability; Parameter estimation; Parameter identification; Parameter sensitivity; Parameters; Physical simulation; Python; Random variables; Sensitivity analysis; Sensitivity enhancement; Sobol' sensitivity index; Variance analysis; water
• ISSN: 0043-1397; 1944-7973; 1944-7973
• DOI: 10.1029/2022WR033808

Global sensitivity analysis (GSA) enhances our understanding of computational models and simplifies model parameter estimation. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a variance‐based GSA framework. The advantage of VISCOUS is that it can use existing model input‐output data (e.g., water model parameters‐responses) to estimate the first‐ and total‐order Sobol’ sensitivity indices. This study improves VISCOUS by refining its handling of marginal densities of the Gaussian mixture copula model (GMCM). We then evaluate VISCOUS using three types of generic functions relevant to water system models. We observe that its performance depends on function dimension, input‐output data size, and non‐identifiability. Function dimension refers to the number of uncertain input factors analyzed in GSA, and non‐identifiability refers to the inability to estimate GMCM parameters. VISCOUS proves powerful in estimating first‐order sensitivity with a small amount of input‐output data (e.g., 200 in this study), regardless of function dimension. It always ranks input factors correctly in both first‐ and total‐order terms. For estimating total‐order sensitivity, it is recommended to use VISCOUS when the function dimension is not very high (e.g., less than 20) due to the challenge of producing sufficient input‐output data for accurate GMCM inferences (e.g., more than 10,000 data). In cases where all input factors are equally important (a rarity in practice), VISCOUS faces non‐identifiability issues that impact its performance. We provide a didactic example and an open‐source Python code, pyVISCOUS, for broader user adoption. Plain Language Summary Global sensitivity analysis is a method used to better understand and estimate parameters in computational models. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a framework for this purpose. It estimates the sensitivity of model outcomes to different uncertain model input factors by using the existing input and output data (e.g., water model parameters and responses). This study improved VISCOUS and tested it with various functions. We found that its performance depends on the number of input factors, the amount of input and output data available, and our ability to determine VISCOUS's parameters. VISCOUS is good at estimating the importance of individual input factors, even with limited data (e.g., 200) and numerous input factors. It always correctly ranks input factor importance, whether individually or collectively. When estimating the importance of input factors together, VISCOUS is recommended when the number of input factors is not very high (e.g., <20), as it is challenging to generate enough input and output data for estimating VISCOUS's parameters. When all input factors hold equal importance (though rare in practice), VISCOUS's performance is impacted due to the difficulty of estimating VISCOUS's parameters. To help people use VISCOUS, we provide an example and an open‐source Python code, pyVISCOUS. Key Points We improve the VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) global sensitivity analysis framework in its handling of marginal densities of the Gaussian mixture copula model We evaluate VISCOUS and demonstrate how its performance is affected by function dimension, input‐output size, and non‐identifiability We provide a didactic example and an open‐source Python code called pyVISCOUS to make VISCOUS easier to understand and apply