Parameter Uncertainty Quantification in an Idealized GCM With a Seasonal Cycle.

Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top‐of‐atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and parameters. Bayesian calibration can estimate climate model parameters and their uncertainty using a larger fraction of the available data and automatically exploring the parameter space more broadly. In Bayesian learning, it is natural to exploit the seasonal cycle, which has large amplitude compared with anthropogenic climate change in many climate statistics. In this study, we develop methods for the calibration and uncertainty quantification (UQ) of model parameters exploiting the seasonal cycle, and we demonstrate a proof‐of‐concept with an idealized general circulation model (GCM). UQ is performed using the calibrate‐emulate‐sample approach, which combines stochastic optimization and machine learning emulation to speed up Bayesian learning. The methods are demonstrated in a perfect‐model setting through the calibration and UQ of a convective parameterization in an idealized GCM with a seasonal cycle. Calibration and UQ based on seasonally averaged climate statistics, compared to annually averaged, reduces the calibration error by up to an order of magnitude and narrows the spread of the non‐Gaussian posterior distributions by factors between two and five, depending on the variables used for UQ. The reduction in the spread of the parameter posterior distribution leads to a reduction in the uncertainty of climate model predictions. Plain Language Summary: Climate models rely on empirical representations of physical processes that cannot be resolved with available computational resources. Empirical representations of physical processes, such as turbulence and cloud physics, reduce the computational cost of simulations, but introduce new unknown parameters into the climate model. The unknown parameters contribute to uncertainties associated with climate model predictions. Historically, fixed values of the model parameters have been hand‐tuned using scientific intuition and a limited amount of available data. We develop methods for the computationally efficient estimation of the unknown climate model parameters and their uncertainty from data, by using optimization and machine learning. Many processes and observable statistics of Earth's climate used to produce this data are influenced by seasonal variations. We demonstrate that the incorporation of seasonal information into these statistics significantly improves the resulting calibration of climate model parameters, in contrast to using annually averaged information alone. We show that including seasonal information also reduces the uncertainty associated with the model parameters, which consequently reduces the uncertainty of climate model predictions. Key Points: We use time‐averaged climate statistics to calibrate and quantify uncertainty of model parameters in an idealized general circulation model with a seasonal cycleWe show a reduction in parameter error up to 10x by using seasonally averaged statistics for Bayesian learning, compared to annual averagesWe demonstrate a 2–5 factor reduction in parametric uncertainty when including seasonal information, compared to annual averages [ABSTRACT FROM AUTHOR]