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An efficient Bayesian approach to learning droplet collision kernels: Proof of concept using "Cloudy", a new n-moment bulk microphysics scheme

Bieli, Melanie and Dunbar, Oliver R. A. and De Jong, Emily K. and Jaruga, Anna and Schneider, Tapio and Bischoff, Tobias (2022) An efficient Bayesian approach to learning droplet collision kernels: Proof of concept using "Cloudy", a new n-moment bulk microphysics scheme. . (Unpublished)

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The small-scale microphysical processes governing the formation of precipitation particles cannot be resolved explicitly by cloud resolving and climate models. Instead, they are represented by microphysics schemes that are based on a combination of theoretical knowledge, statistical assumptions, and fitting to data ("tuning"). Historically, tuning was done in an ad-hoc fashion, leading to parameter choices that are not explainable or repeatable. Recent work has treated it as an inverse problem that can be solved by Bayesian inference. The posterior distribution of the parameters given the data---the solution of Bayesian inference---is found through computationally expensive sampling methods, which require over O(10⁵) evaluations of the forward model; this is prohibitive for many models. We present a proof-of-concept of Bayesian learning applied to a new bulk microphysics scheme named "Cloudy", using the recently developed Calibrate-Emulate-Sample (CES) algorithm. Cloudy models collision-coalescence and collisional breakup of cloud droplets with an adjustable number of prognostic moments and with easily modifiable assumptions for the cloud droplet mass distribution and the collision kernel. The CES algorithm uses machine learning tools to accelerate Bayesian inference by reducing the number of forward evaluations needed to O(10²). It also exhibits a smoothing effect when forward evaluations are polluted by noise. In a suite of perfect-model experiments, we show that CES enables computationally efficient Bayesian inference of parameters in Cloudy from noisy observations of moments of the droplet mass distribution. In an additional imperfect-model experiment, a collision kernel parameter is successfully learned from output generated by a Lagrangian particle-based microphysics model.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper Itemcode for the Calibrate-Emulate-Sample algorithm ItemCloudy repositorry ItemJournal Article
Bieli, Melanie0000-0002-2056-9486
Dunbar, Oliver R. A.0000-0001-7374-0382
Jaruga, Anna0000-0003-3194-6440
Schneider, Tapio0000-0001-5687-2287
Bischoff, Tobias0000-0003-3930-2762
Additional Information:Attribution-NonCommercial 4.0 International This work was supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by the Hopewell Fund, and the Paul G. Allen Family Foundation. Open Research. The code for the Calibrate-Emulate-Sample algorithm is available at The Cloudy repository can be found at
Group:Division of Geological and Planetary Sciences
Funding AgencyGrant Number
Schmidt Futures ProgramUNSPECIFIED
Paul G. Allen Family FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20220207-89642000
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113312
Deposited By: George Porter
Deposited On:08 Feb 2022 16:36
Last Modified:11 Nov 2022 18:33

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