Artificial neural network assisted Bayesian calibration of climate models

We demonstrate and validate a Bayesian approach to model calibration applicable to computationally expensive General Circulation Models (GCMs) that includes a posterior estimate of the intrinsic structural error of the model. Bayesian artificial neural networks (BANNs) are trained with output from a GCM and used as emulators of the full model to allow a computationally efficient Markov Chain Monte Carlo (MCMC) sampling of the posterior for the GCM parameters calibrated against seasonal climatologies of temperature, pressure, and humidity. We validate the methodology by calibrating to targets produced by a model run with added noise. We then demonstrate a calibration of five GCM parameters against an observational data set. The approach accounts for both parametric and structural uncertainties of the model as well as uncertainties associated with the observational calibration data. This enables the generation of statistically rigorous probabilistic forecasts for future climate states. All calibration experiments are performed with emulators trained using a maximum of one hundred model runs, in accord with typical resource restrictions imposed by computationally expensive models. We conclude by summarizing remaining issues to address in order to create a complete and validated operational methodology for objective calibration of computationally expensive models.