Calibration of the stochastic multicloud model using Bayesian inference
type: Item
instance of: scholarly article
zbMATH Open document ID: 1298.86003
DOI: 10.1137/13094267X
author: Michèle De La Chevrotière
author: Boualem Khouider
author: Andrew J. Majda
published in: SIAM Journal on Scientific Computing
publication date: 2014-09-05T00:00:00Z
Mathematics Subject Classification ID: 86-08
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 82D30
Mathematics Subject Classification ID: 86A10
Mathematics Subject Classification ID: 86A32
zbMATH DE Number: 6340655
zbMATH Keywords: stochastic cumulus parametrization
zbMATH Keywords: stochastic multi-cloud model
zbMATH Keywords: inverse problem
zbMATH Keywords: Bayesian inference
zbMATH Keywords: large sparse matrix exponential
zbMATH Keywords: parallel uniformization method
zbMATH Keywords: high performance computing
zbMATH Keywords: PETSc
zbMATH Keywords: Monte Carlo Markov chain
zbMATH Keywords: climate models
zbMATH Keywords: general circulation model
describes a project that uses: PETSc
MaRDI profile type: Publication
full work available at URL: 13094267x
OpenAlex ID: W2033749523
title: Calibration of the stochastic multicloud model using Bayesian inference
review text: The stochastic multicloud model (SMCM) was recently developed [\textit{B. Khouider} et al., Commun. Math. Sci. 8, No. 1, 187--216 (2010; Zbl 1190.86003)] to represent the missing variability in general circulation models due to unresolved features of organized tropical convection. This research aims at finding a robust calibration methodology for the SMCM to estimate key model parameters from data. The SMCM model considered in the present work is in essence a three-dimensional birth-death process with immigration whose population species track the time evolution of the area fractions of three types of clouds, congestus, deep penetrative cumulus and stratiform ones, which are observed to describe tropical convective systems. Transition rates between the different cloud states depend on the convective potential energy and the middle tropospheric humidity. The calibration problem is formulated within a Bayesian framework to derive the posterior distribution over the model parameters. The main challenge here is due to the likelihood function which requires solving a large system of differential equations (the Kolmogorov equations) as many times as there are data points, which is prohibitive in terms of both computation time and storage requirements. The most attractive numerical techniques to compute the transient solutions to large Markov chains are based on matrix exponentials, but none is unconditionally acceptable for all classes of problems. A parallel version of a preconditioning technique is developed, which is known as the uniformization method, using the PETSc (Portable, Extensible Toolkit for Scientific computation) suite of sparse matrix-vector operations. The parallel uniformization method allows for fast and scalable approximations of large sparse matrix exponentials, without sacrificing accuracy. Sampling of the high-dimensional posterior distribution is achieved using the standard Markov chain Monte Carlo technique. The robustness of the calibration proce…
reviewed by: Claudia-Veronika Meister
description: scientific article; zbMATH DE number 6340655