Learning about parameter and structural uncertainty in carbon cycle models

Uncertainty in the response of the global carbon cycle to anthropogenic emissions plays a key role in assessments of potential future climate change and response strategies. We investigate how fast this uncertainty might change as additional data on the global carbon budget becomes available over the twenty-first century. Using a simple global carbon cycle model and focusing on both parameter and structural uncertainty in the terrestrial sink, we find that additional global data leads to substantial learning (i.e., changes in uncertainty) under some conditions but not others. If the model structure is assumed known and only parameter uncertainty is considered, learning is rather limited if observational errors in the data or the magnitude of unexplained natural variability are not reduced. Learning about parameter values can be substantial, however, when errors in data or unexplained variability are reduced. We also find that, on the one hand, uncertainty in the model structure has a much bigger impact on uncertainty in projections of future atmospheric composition than does parameter uncertainty. But on the other, it is also possible to learn more about the model structure than the parameter values, even from global budget data that does not improve over time in terms of its associated errors. As an example, we illustrate how one standard model structure, if incorrect, could become inconsistent with global budget data within 40 years. The rate of learning in this analysis is affected by the choice of a relatively simple carbon cycle model, the use of observations only of global emissions and atmospheric concentration, and the assumption of perfect autocorrelation in observational errors and variability. Future work could usefully improve the approach in each of these areas.