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\begin{document}

\title{Calibration and Uncertainty Quantification of Convective Parameters in
an Idealized GCM}



\author[1]{Oliver Dunbar}%
\author[1]{Tapio Schneider}%
\author[1]{Andrew Stuart}%
\author[2]{Alfredo Garbuno-Inigo}%
\affil[1]{California Institute of Technology}%
\affil[2]{Instituto Tecnologico Autonomo de Mexico,}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
Parameters in climate models are usually calibrated manually, exploiting
only small subsets of the available data. This precludes an 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(10\^{}5)\$ model runs, rendering
them infeasible for climate models. Here we demonstrate an approach to
model calibration and uncertainty quantification that requires only
\$O(10\^{}2)\$ model runs and can accommodate internal climate
variability. The approach consists of three stages: (i) a calibration
stage uses variants of ensemble Kalman inversion to calibrate a model by
minimizing mismatches between model and data statistics; (ii) an
emulation stage emulates the parameter-to-data map with Gaussian
processes (GP), using the model runs in the calibration stage for
training; (iii) a sampling stage approximates the Bayesian posterior
distributions by using the GP emulator and then samples using 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 data surrogates 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.%
\end{abstract}%



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