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Over half of the greenhouse gas (GHG) emissions in the United States come from the transportation and electricity generation sectors. To analyze the potential impact of cross-sector cooperation in reducing these emissions, we formulate a bi-level optimization model where the transportation sector can purchase renewable energy certificates (REC) from the electricity generation sector. These RECs are used to offset emissions from transportation in lieu of deploying high-cost fuel efficient technologies. The electricity generation sector creates RECs by producing additional energy from renewable sources. This additional renewable capacity is financed by the transportation sector and it does not impose additional cost on the electricity generation sector. Our results show that such a REC purchasing regime significantly reduces the cost to society of reducing GHG emissions. Additionally, our results indicate that a REC purchasing policy can create electricity beyond actual demand.

Available methodologies for model bias identification are mainly regression-based approaches, such as Gaussian process, Bayesian inference-based models and so on. Accuracy and efficiency of these methodologies may degrade for characterizing the model bias when more system inputs are considered in the prediction model due to the curse of dimensionality for regression-based approaches. This paper proposes a copula-based approach for model bias identification without suffering the curse of dimensionality. The main idea is to build general statistical relationships between the model bias and the model prediction including all system inputs using copulas so that possible model bias distributions can be effectively identified at any new design configurations of the system. Two engineering case studies whose dimensionalities range from medium to high will be employed to demonstrate the effectiveness of the copula-based approach.