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 calibration and uncertainty quantification.• The algorithm leverages ensemble simulations, over convective parameters, to quantify parametric uncertainties in climate predictions.

Parameter uncertainty quantification in an idealized GCM with a seasonal cycle

“…(2) Gaussian process (GP) regression is used to train an emulator G GP (θ) of the mapping θ → G(θ) using the training points generated in the calibration step; and (3) MCMC sampling with the computationally efficient GP emulator G GP (θ) rather than the expensive forward model G(θ) is used to estimate the posterior distribution P(θ|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, 2020). More recent methodological developments by enabled the CES framework to perform simultaneous UQ on O(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, 2020). 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).…”

“…EKI is guaranteed to find the optimal parameters in linear problems (Schillings & Stuart, 2017) and has empirical success in nonlinear problems (Dunbar et al, 2020). Several other approaches exist for estimation in nonlinear problems.…”

“…The number of ensemble members and EKI iterations are hyperparameters; they are set to standard values of N ens = 100 and N it = 5 in this study (Schillings & Stuart, 2017;Dunbar et al, 2020;Cleary et al, 2021). Each ensemble member is run through the GCM, initialized from the same initial conditions.…”

“…This focuses the learning problem on quantities of interest in climate predictions (i.e., climate statistics, including higher-order statistics such as precipitation extremes), and it avoids the need to estimate uncertain atmospheric initial conditions on which trajectories of states depend (Cleary et al, 2021). Calibration and UQ of climate models on the basis of time-averaged statistics smooths the prediction-error based objective function and enables the use of data that have different resolution than the climate simulations (Schneider, Lan, et al, 2017;Dunbar et al, 2020).…”