The estimation of historical CO2 trajectories is indeterminate: Comment on “A new look at atmospheric carbon dioxide”

A paper by Hofmann et al. (2009, this journal) is critiqued. It is shown that their exponential model for characterizing CO2 trajectories for historical data is not estimated properly. An exponential model is properly estimated and is shown to fit over the entire 51 year period of available data. Further, the entire problem of estimating models for the CO2 historical data is shown to be ill-posed because alternate model forms fit the data equally well. To illustrate this point the past 51 years of CO2 data were analyzed using three different time-dependent models that capture the historical pattern of CO2 increase. All three fit with R2 > 0.98, are visually indistinguishable when overlaid, and match each other during the calibration period with R2 > 0.999. Projecting the models forward to 2100, the exponential model comes quite close to the Intergovernmental Panel on Climate Change (IPCC) best estimate of 836 ppmv. The other two models project values far below the IPCC low estimates. The problem of characterizing historical CO2 levels is thus indeterminate, because multiple models fit the data equally well but forecast very different future trajectories.