### Abstract

The stochastic multicloud model (SMCM) was recently developed [B. Khouider, J. Biello, and A. J. Majda, Commun. Math. Sci., 8 (2010), pp. 187-216] 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. We formulate the calibration problem 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. We develop a parallel version of a preconditioning technique 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 via the standard Markov chain Monte Carlo. The robustness of the calibration procedure is tested using synthetic data produced by a simple toy climate model. A sensitivity study to the length of the data time series and to the prior distribution is presented, and a sequential learning strategy is also tested.

Original language | English (US) |
---|---|

Journal | SIAM Journal on Scientific Computing |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Bayesian inference
- Climate models
- High performance computing
- Inverse problem
- Large sparse matrix exponential
- Monte carlo markov chain
- Parallel uniformization method
- PETSc
- Stochastic cumulus parameterization

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Scientific Computing*,

*36*(3). https://doi.org/10.1137/13094267X

**Calibration of the stochastic multicloud model using bayesian inference.** / De La Chevrotiére, Michéle; Khouider, Boualem; Majda, Andrew J.

Research output: Contribution to journal › Article

*SIAM Journal on Scientific Computing*, vol. 36, no. 3. https://doi.org/10.1137/13094267X

}

TY - JOUR

T1 - Calibration of the stochastic multicloud model using bayesian inference

AU - De La Chevrotiére, Michéle

AU - Khouider, Boualem

AU - Majda, Andrew J.

PY - 2014

Y1 - 2014

N2 - The stochastic multicloud model (SMCM) was recently developed [B. Khouider, J. Biello, and A. J. Majda, Commun. Math. Sci., 8 (2010), pp. 187-216] 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. We formulate the calibration problem 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. We develop a parallel version of a preconditioning technique 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 via the standard Markov chain Monte Carlo. The robustness of the calibration procedure is tested using synthetic data produced by a simple toy climate model. A sensitivity study to the length of the data time series and to the prior distribution is presented, and a sequential learning strategy is also tested.

AB - The stochastic multicloud model (SMCM) was recently developed [B. Khouider, J. Biello, and A. J. Majda, Commun. Math. Sci., 8 (2010), pp. 187-216] 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. We formulate the calibration problem 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. We develop a parallel version of a preconditioning technique 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 via the standard Markov chain Monte Carlo. The robustness of the calibration procedure is tested using synthetic data produced by a simple toy climate model. A sensitivity study to the length of the data time series and to the prior distribution is presented, and a sequential learning strategy is also tested.

KW - Bayesian inference

KW - Climate models

KW - High performance computing

KW - Inverse problem

KW - Large sparse matrix exponential

KW - Monte carlo markov chain

KW - Parallel uniformization method

KW - PETSc

KW - Stochastic cumulus parameterization

UR - http://www.scopus.com/inward/record.url?scp=84903631358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903631358&partnerID=8YFLogxK

U2 - 10.1137/13094267X

DO - 10.1137/13094267X

M3 - Article

VL - 36

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 3

ER -