Hector is a Simple Climate Model (SCM) that contains representations of the major processes governing the earth system. Hector is used as a standalone model and coupled with integrated assessment models and coupled human-natural system models. Calibrating SCMs like Hector is necessary to validate that they can reproduce the behavior of more complicated Earth System Models and set up SCMs as emulators. A variety of calibration procedures have been used to in the past. Here, Hector was calibrated using two different methods. In the first, Hector parameters were tuned using a nonlinear optimization routine to emulate individual Earth System Models (ESMs). During this calibration exercise the optimization routine struggled to identify unique parameterizations of because of symmetries between model parameters. However, this issue was resolved by developing a calibration protocol that uses multiple constraints including additional variables such as atmosphere-ocean heat flux to break the symmetry. We show the results of these optimization calculations, along with insights from these results that proved crucial in developing the protocol used in the second calibration exercise.

In the second calibration exercise we used Bayesian Monte Carlo to calibrate the joint probability distribution of Hector parameters to the CMIP5 ensemble. Results from this calibration revealed that small differences in handling parameter symmetry and assumptions about what it means to calibrate to an ensemble can substantially distort the joint distribution of model parameters, in some cases greatly underestimating the parameter uncertainty, or reversing the sign of correlations between model parameters. This being said, by utilizing novel calibration techniques we were able to avoid the pitfalls of calibrating SCMs. We use these results to produce probabilistic climate pathways, and we offer thoughts on best practices for SCM nonlinear optimization and Bayesian calibration.