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Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM

Dunbar, Oliver R. A. and Garbuno-Inigo, Alfredo and Schneider, Tapio and Stuart, Andrew M. (2021) Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM. Journal of Advances in Modelling Earth Systems, 13 (9). Art. No. e2020MS002454. ISSN 1942-2466. doi:10.1029/2020MS002454.

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Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that allow uncertainty quantification are too expensive for climate models; they are also not robust in the presence of internal climate variability. For example, Markov chain Monte Carlo (MCMC) methods typically require O(10⁵) model runs and are sensitive to internal variability noise, rendering them infeasible for climate models. Here we demonstrate an approach to model calibration and uncertainty quantification that requires only O(10²) model runs and can accommodate internal climate variability. The approach consists of three stages: (a) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (b) an emulation stage emulates the parameter-to-data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (c) a sampling stage approximates the Bayesian posterior distributions by sampling the GP emulator with MCMC. We demonstrate the feasibility and computational efficiency of this calibrate-emulate-sample (CES) approach in a perfect-model setting. Using an idealized general circulation model, we estimate parameters in a simple convection scheme from synthetic data generated with the model. The CES approach generates probability distributions of the parameters that are good approximations of the Bayesian posteriors, at a fraction of the computational cost usually required to obtain them. Sampling from this approximate posterior allows the generation of climate predictions with quantified parametric uncertainties.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper Paper
Dunbar, Oliver R. A.0000-0001-7374-0382
Garbuno-Inigo, Alfredo0000-0003-3279-619X
Schneider, Tapio0000-0001-5687-2287
Stuart, Andrew M.0000-0001-9091-7266
Additional Information:© 2021 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: 09 September 2021; Version of Record online: 09 September 2021; Accepted manuscript online: 19 August 2021; Manuscript accepted: 17 August 2021; Manuscript revised: 13 July 2021; Manuscript received: 24 December 2020. This work was supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF, award AGS-1835860). Andrew M. Stuart was also supported by the Office of Naval Research (award N00014-17-1-2079). The authors thank Emmet Cleary for his preliminary work underlying some of the results shown here. The authors would like to thank the reviewers for their insightful comments and suggestions which have lead to the improvement of this article. Data Availability Statement: All computer code used in this paper is open source. The code for the idealized GCM, the Julia code for the CES algorithm, the plot tools, and the slurm/bash scripts to run both GCM and CES are available at
Funding AgencyGrant Number
Schmidt Futures ProgramUNSPECIFIED
Paul G. Allen Family FoundationUNSPECIFIED
Office of Naval Research (ONR)N00014-17-1-2079
Subject Keywords:uncertainty quantification; model calibration; machine learning; general circulation model; parametric uncertainty; inverse problem
Issue or Number:9
Record Number:CaltechAUTHORS:20210113-143919927
Persistent URL:
Official Citation:Dunbar, O. R. A., Garbuno-Inigo, A., Schneider, T., & Stuart, A. M. (2021). Calibration and uncertainty quantification of convective parameters in an idealized GCM. Journal of Advances in Modeling Earth Systems, 13, e2020MS002454.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107459
Deposited By: Tony Diaz
Deposited On:13 Jan 2021 22:53
Last Modified:15 Sep 2021 21:06

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