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Parameter Uncertainty Quantification in an Idealized GCM With a Seasonal Cycle

Howland, Michael F. and Dunbar, Oliver R. A. and Schneider, Tapio (2022) Parameter Uncertainty Quantification in an Idealized GCM With a Seasonal Cycle. Journal of Advances in Modelling Earth Systems, 14 (3). Art. No. e2021MS002735. ISSN 1942-2466. doi:10.1029/2021MS002735.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper ItemJulia implementation of CES
Howland, Michael F.0000-0002-2878-3874
Dunbar, Oliver R. A.0000-0001-7374-0382
Schneider, Tapio0000-0001-5687-2287
Additional Information:© 2022 The Authors. Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Issue Online: 10 March 2022; Version of Record online: 10 March 2022; Accepted manuscript online: 14 January 2022; Manuscript accepted: 07 January 2022; Manuscript revised: 22 December 2021; Manuscript received: 26 July 2021. This work was supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program and by the National Science Foundation (NSF, award AGS-1835860). The authors thank Andrew Stuart for thoughtful comments on the work and the manuscript. The authors would also like to thank the anonymous referees for their thoughtful comments and contribution to this work. The simulations were performed using resources from the Resnick High Performance Computing Center, which is partially supported by the Gordon and Betty Moore Foundation. Data Availability Statement: All computer code used in this paper is open source. The code is available at ( An open-source Julia implementation of CES is accessible at (
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Schmidt Futures ProgramUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:uncertainty quantification; Bayesian learning; GCM; seasonal cycle
Issue or Number:3
Record Number:CaltechAUTHORS:20210823-173258629
Persistent URL:
Official Citation:Howland, M. F., Dunbar, O. R. A., & Schneider, T. (2022). Parameter uncertainty quantification in an idealized GCM with a seasonal cycle. Journal of Advances in Modeling Earth Systems, 14, e2021MS002735.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110383
Deposited By: Tony Diaz
Deposited On:24 Aug 2021 18:58
Last Modified:25 Mar 2022 22:51

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