Application of Polynomial Chaos Expansion for Climate Economy Assessment

Abstract: In climate economics integrated assessment models (IAMs) are used to predict economic impacts resulting from climate change. These IAMs attempt to model complex interactions between human and geophysical systems to provide quantifications of economic impact, typically using the Social Cost of Carbon (SCC) which represents the economic cost of a one ton increase in carbon dioxide. Another difficulty that arises in modeling a climate economics system is that both the geophysical and economic submodules are inherently stochastic. Even in frequently cited IAMs, such as DICE and PAGE, there exists a lot of variation in the predictions of the SCC. These differences stem both from the models of the climate and economic modules used, as well as from the choice of probability distributions used for the random variables. Seeing as IAMs often take the form of optimization problems these nondeterministic elements potentially result in heavy computational costs. In this thesis a new IAM, FAIR/DICE, is introduced. FAIR/DICE is a discrete time hybrid of DICE and FAIR providing a potential improvement to DICE as the climate and carbon modules in FAIR take into account feedback coming from the climate module to the carbon module. Additionally uncertainty propagation in FAIR/DICE is analyzed using Polynomial Chaos Expansions (PCEs) which is an alternative to Monte Carlo sampling where the stochastic variables are projected onto stochastic polynomial spaces. PCEs provide better computational efficiency compared to Monte Carlo sampling at the expense of storage requirements as a lot of computations can be stored from the first simulation of the system, and conveniently statistics can be computed from the PCE coefficients without the need for sampling. A PCE overloading of FAIR/DICE is investigated where the equilibrium climate sensitivity, modeled as a four parameter Beta distribution, introduces an uncertainty to the dynamical system. Finally, results in the mean and variance obtained from the PCEs are compared to a Monte Carlo reference and avenues into future work are suggested.