NASA's Orbiting Carbon Observatory-2 (OCO-2) collects tens of thousands of observations of reflected sunlight daily, and the mission's retrieval algorithm processes these indirect measurements (radiance spectra) into estimates of atmospheric CO2 and other states. The retrieval is an inverse problem and consists of a physical forward model for the transfer of radiation through the atmosphere. The model and other algorithm inputs introduce key sources of uncertainty into the retrieval problem. Here we focus on a Bayesian approach where the posterior distribution of the state given the observed spectra is used to quantify the uncertainties in the model inputs. Due to the nonlinear forward model, the posterior is intractable and Markov chain Monte Carlo method is used to sample from the posterior. But this approach requires a large number of evaluations of the expensive forward model. So, here we focus on the emulator approach where a statistical representation of the forward mode, based on Gaussian process, is built using some simulation runs of the forward model. The fitted emulator is used to link the atmospheric state vector to the observed radiance in the MCMC sampling.