Adaptive stochastic integrated assessment modeling of optimal greenhouse gas emission reductions

We develop a method for finding optimal greenhouse gas reduction rates under ongoing uncertainty and re-evaluation of climate parameters over future decades. Uncertainty about climate change includes both overall climate sensitivity and the risk of extreme tipping point events. We incorporate both types of uncertainty into a stochastic model of climate and the economy that has the objective of reducing global greenhouse gas emissions at lowest overall cost over time. Solving this problem is computationally challenging; we introduce a two-step-ahead approximate dynamic programming algorithm to solve the finite time horizon stochastic problem. The uncertainty in climate sensitivity may narrow in the future as the behavior of the climate continues to be observed and as climate science progresses. To incorporate this future knowledge, we use a Bayesian framework to update the two correlated uncertainties over time. The method is illustrated with the DICE integrated assessment model, adding in current estimates of climate sensitivity uncertainty and tipping point risk with an endogenous updating of climate sensitivity based on the occurrence of tipping point events; the method could also be applied to other integrated assessment models with different characterizations of uncertainties and risks.