Global sensitivity analysis of integrated assessment models with multivariate outputs

Risk assessments of complex systems are often supported by quantitative models. The sophistication of these models and the presence of various uncertainties call for systematic robustness and sensitivity analyses. The multivariate nature of their response challenges the use of traditional approaches. We propose a structured methodology to perform uncertainty quantification and global sensitivity analysis for risk assessment models with multivariate outputs. At the core of the approach are novel sensitivity measures based on the theory of optimal transport. We apply the approach to the uncertainty quantification and global sensitivity analysis of emissions pathways estimated via an eminent open-source climate-economy model (RICE50+). The model has many correlated inputs and multivariate outputs. We use up-to-date input distributions and long-term projections of key demographic and socioeconomic drivers. The sensitivity of the model is explored under alternative policy architectures: a cost-benefit analysis with and without international cooperation and a cost-effective analysis consistent with the Paris Agreement objective of keeping temperature increase below 2°C. In the cost-benefit scenarios, the key drivers of uncertainty are the emission intensity of the economy and the emission reduction costs. In the Paris Agreement scenario, the main driver is the sensitivity of the climate system, followed by the projected carbon intensity. We present insights at the multivariate model output level and discuss how the importance of inputs changes across regions and over time.