Global sensitivity analysis of integrated assessment models with multivariate outputs

Risk assessments of complex systems are often supported by quantitative models. Thesophistication of these models and the presence of various uncertainties call for sys-tematic robustness and sensitivity analyses. The multivariate nature of their responsechallenges the use of traditional approaches. We propose a structured methodology toperform uncertainty quantification and global sensitivity analysis for risk assessmentmodels with multivariate outputs. At the core of the approach are novel sensitivitymeasures based on the theory of optimal transport. We apply the approach to the uncer-tainty quantification and global sensitivity analysis of emissions pathways estimatedvia an eminent open-source climate–economy model (RICE50+). The model has manycorrelated inputs and multivariate outputs. We use up-to-date input distributions andlong-term projections of key demographic and socioeconomic drivers. The sensitivityof the model is explored under alternative policy architectures: a cost-benefit analy-sis with and without international cooperation and a cost-effective analysis consistentwith the Paris Agreement objective of keeping temperature increase below 2◦C. In thecost-benefit scenarios, the key drivers of uncertainty are the emission intensity of theeconomy and the emission reduction costs. In the Paris Agreement scenario, the maindriver is the sensitivity of the climate system, followed by the projected carbon inten-sity. We present insights at the multivariate model output level and discuss how theimportance of inputs changes across regions and over time.