Drag parameter estimation using gradients and hessian from a polynomial chaos model surrogate

Ihab Sraj, Mohamed Iskandarani, W. Carlisle Thacker, Ashwanth Srinivasan, Omar M. Knio

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model's (HYCOM's) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian's inverse yields an estimate of the uncertainty in the solution when the latter's probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed

Original languageEnglish (US)
Pages (from-to)933-941
Number of pages9
JournalMonthly Weather Review
Volume142
Issue number2
DOIs
StatePublished - Feb 2014

Fingerprint

chaotic dynamics
drag
Markov chain
inverse problem
cost
parameterization
methodology
sampling
ocean
parameter estimation
distribution

ASJC Scopus subject areas

  • Atmospheric Science

Cite this

Drag parameter estimation using gradients and hessian from a polynomial chaos model surrogate. / Sraj, Ihab; Iskandarani, Mohamed; Carlisle Thacker, W.; Srinivasan, Ashwanth; Knio, Omar M.

In: Monthly Weather Review, Vol. 142, No. 2, 02.2014, p. 933-941.

Research output: Contribution to journalArticle

Sraj, Ihab ; Iskandarani, Mohamed ; Carlisle Thacker, W. ; Srinivasan, Ashwanth ; Knio, Omar M. / Drag parameter estimation using gradients and hessian from a polynomial chaos model surrogate. In: Monthly Weather Review. 2014 ; Vol. 142, No. 2. pp. 933-941.
@article{0fd0bcbd285a4b009e18a5fa6f287eaa,
title = "Drag parameter estimation using gradients and hessian from a polynomial chaos model surrogate",
abstract = "A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model's (HYCOM's) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian's inverse yields an estimate of the uncertainty in the solution when the latter's probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed",
author = "Ihab Sraj and Mohamed Iskandarani and {Carlisle Thacker}, W. and Ashwanth Srinivasan and Knio, {Omar M.}",
year = "2014",
month = "2",
doi = "10.1175/MWR-D-13-00087.1",
language = "English (US)",
volume = "142",
pages = "933--941",
journal = "Monthly Weather Review",
issn = "0027-0644",
publisher = "American Meteorological Society",
number = "2",

}

TY - JOUR

T1 - Drag parameter estimation using gradients and hessian from a polynomial chaos model surrogate

AU - Sraj, Ihab

AU - Iskandarani, Mohamed

AU - Carlisle Thacker, W.

AU - Srinivasan, Ashwanth

AU - Knio, Omar M.

PY - 2014/2

Y1 - 2014/2

N2 - A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model's (HYCOM's) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian's inverse yields an estimate of the uncertainty in the solution when the latter's probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed

AB - A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model's (HYCOM's) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian's inverse yields an estimate of the uncertainty in the solution when the latter's probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed

UR - http://www.scopus.com/inward/record.url?scp=84893854293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893854293&partnerID=8YFLogxK

U2 - 10.1175/MWR-D-13-00087.1

DO - 10.1175/MWR-D-13-00087.1

M3 - Article

VL - 142

SP - 933

EP - 941

JO - Monthly Weather Review

JF - Monthly Weather Review

SN - 0027-0644

IS - 2

ER -