Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM

Abstract

We use time averaged climate statistics to calibrate convective parameters and quantify their uncertainties.• We demonstrate use of the calibrate-emulate-sample algorithm to provide efficient 10 calibration and uncertainty quantification.

Parameter Uncertainty Quantification in an Idealized GCM With a Seasonal Cycle

“…Harnessing the input‐output pairs as training points, GP regression is used (Rasmussen, 2003) to create an emulator, composed of a mean function and covariance function pair, where $${\mathcal{G}}_{\text{GP}}(\boldsymbol{\theta })\approx {\mathcal{G}}_{\infty }(\boldsymbol{\theta })$$ and Σ GP ≈ Σ . Since, the input‐output pairs are subject to different realizations of the chaotic system, the emulator mean approximates $${\mathcal{G}}_{\infty }(\boldsymbol{\theta })$$ rather than $$\mathcal{G}(\boldsymbol{\theta },\xi )$$ (Cleary et al., 2021; Dunbar et al., 2021).…”

“…Instead, we perform calibration and UQ using the recently developed CES methodology (Cleary et al., 2021), which consists of three steps: (a) Ensemble Kalman processes (Garbuno‐Inigo et al., 2020; Schillings & Stuart, 2017) are used to calibrate parameters and to generate input‐output pairs of the mapping $$\boldsymbol{\theta }{\mapsto}\mathcal{G}(\boldsymbol{\theta })$$; (b) Gaussian process (GP) regression, or other machine learning tools, are used to train an emulator $${\mathcal{G}}_{\text{GP}}(\boldsymbol{\theta })$$ of the mapping $$\boldsymbol{\theta }{\mapsto}\mathcal{G}(\boldsymbol{\theta })$$ using the training points generated in the calibration step; and (c) MCMC sampling with the computationally efficient emulator $${\mathcal{G}}_{\text{GP}}(\boldsymbol{\theta })$$ rather than the expensive forward model $$\mathcal{G}(\boldsymbol{\theta })$$ is used to estimate the posterior distribution $$\mathbb{P}(\boldsymbol{\theta }\vert \boldsymbol{y})$$. The CES methodology has previously been used for calibration and UQ of parameters in simple model problems such as Darcy flow and Lorenz systems (Cleary et al., 2021) and for convective parameters in a statistically stationary GCM (Dunbar et al., 2021). More recent methodological developments by Lan et al.…”

“…Instead, we perform calibration and UQ using the recently developed CES methodology (Cleary et al, 2021), which consists of three steps: (a) Ensemble Kalman processes (Garbuno-Inigo et al, 2020;Schillings & Stuart, 2017) are used to calibrate parameters and to generate input-output pairs of the mapping 𝐴𝐴 𝜽𝜽↦(𝜽𝜽) ; (b) Gaussian process (GP) regression, or other machine learning tools, are used to train an emulator 𝐴𝐴 GP(𝜽𝜽) of the mapping 𝐴𝐴 𝜽𝜽↦(𝜽𝜽) using the training points generated in the calibration step; and (c) MCMC sampling with the computationally efficient emulator 𝐴𝐴 GP(𝜽𝜽) rather than the expensive forward model 𝐴𝐴 (𝜽𝜽) is used to estimate the posterior distribution 𝐴𝐴 ℙ(𝜽𝜽|𝒚𝒚) . The CES methodology has previously been used for calibration and UQ of parameters in simple model problems such as Darcy flow and Lorenz systems (Cleary et al, 2021) and for convective parameters in a statistically stationary GCM (Dunbar et al, 2021). More recent methodological developments by Lan et al (2021) enabled the CES framework to perform simultaneous UQ on 𝐴𝐴 (1000) parameters using deep neural network-based emulation and MCMC suited to high-dimensional spaces (Beskos et al, 2008(Beskos et al, , 2011.…”

“…As a step toward automating and augmenting this process, here, we further develop algorithms for model calibration and uncertainty quantification (UQ) that in principle allow models to learn from large datasets and that scale to high‐dimensional parameter spaces. In previous work, these algorithms have been demonstrated in simple conceptual models (Cleary et al., 2021) and in a statistically stationary idealized GCM (Dunbar et al., 2021). We take the next step and demonstrate how these algorithms can exploit seasonal variations, which for many climate statistics are large relative to the climate changes expected in the coming decades and contain exploitable information about the response of the climate system to perturbations (Knutti et al., 2006; Schneider et al., 2021).…”

Derivative-Free Bayesian Inversion Using Multiscale Dynamics

“…In a number of important applications of inverse problems, such as parameter estimation in climate models [16], the derivatives of the forward operator G are unavailable or too computationally expensive to obtain, so, in this literature review, we only briefly review gradient-based methods and we focus mostly on derivative-free methods.…”