A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation
Derivative-based methods are developed for uncertainty quantification (UQ) in large-scale ocean state estimation. The estimation system is based on the adjoint method for solving a least-squares optimization problem, whereby the state-of-the-art MIT general circulation model (MITgcm) is fit to obser...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2014
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| Online Access: | http://hdl.handle.net/1721.1/92547 https://orcid.org/0000-0002-5317-2573 https://orcid.org/0000-0003-3925-6161 |
| _version_ | 1811077516630163456 |
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| author | Heimbach, Patrick Kalmikov, Alex |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Heimbach, Patrick Kalmikov, Alex |
| author_sort | Heimbach, Patrick |
| collection | MIT |
| description | Derivative-based methods are developed for uncertainty quantification (UQ) in large-scale ocean state estimation. The estimation system is based on the adjoint method for solving a least-squares optimization problem, whereby the state-of-the-art MIT general circulation model (MITgcm) is fit to observations. The UQ framework is applied to quantify Drake Passage transport uncertainties in a global idealized barotropic configuration of the MITgcm. Large error covariance matrices are evaluated by inverting the Hessian of the misfit function using matrix-free numerical linear algebra algorithms. The covariances are projected onto target output quantities of the model (here Drake Passage transport) by Jacobian transformations. First and second derivative codes of the MITgcm are generated by means of algorithmic differentiation (AD). Transpose of the chain rule product of Jacobians of elementary forward model operations implements a computationally efficient adjoint code. Computational complexity of the Hessian code is reduced via forward-over-reverse mode AD, which preserves the efficiency of adjoint checkpointing schemes in the second derivative calculation. A Lanczos algorithm is applied to extract the leading eigenvectors and eigenvalues of the Hessian matrix, representing the constrained uncertainty patterns and the inverse of the corresponding uncertainties. The dimensionality of the misfit Hessian inversion is reduced by omitting its nullspace (as an alternative to suppressing it by regularization), excluding from the computation the uncertainty subspace unconstrained by the observations. Inverse and forward uncertainty propagation schemes are designed for assimilating observation and control variable uncertainties and for projecting these uncertainties onto oceanographic target quantities. |
| first_indexed | 2024-09-23T10:44:16Z |
| format | Article |
| id | mit-1721.1/92547 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:44:16Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
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| spelling | mit-1721.1/925472022-09-27T14:36:33Z A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation Heimbach, Patrick Kalmikov, Alex Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Kalmikov, Alex Heimbach, Patrick Derivative-based methods are developed for uncertainty quantification (UQ) in large-scale ocean state estimation. The estimation system is based on the adjoint method for solving a least-squares optimization problem, whereby the state-of-the-art MIT general circulation model (MITgcm) is fit to observations. The UQ framework is applied to quantify Drake Passage transport uncertainties in a global idealized barotropic configuration of the MITgcm. Large error covariance matrices are evaluated by inverting the Hessian of the misfit function using matrix-free numerical linear algebra algorithms. The covariances are projected onto target output quantities of the model (here Drake Passage transport) by Jacobian transformations. First and second derivative codes of the MITgcm are generated by means of algorithmic differentiation (AD). Transpose of the chain rule product of Jacobians of elementary forward model operations implements a computationally efficient adjoint code. Computational complexity of the Hessian code is reduced via forward-over-reverse mode AD, which preserves the efficiency of adjoint checkpointing schemes in the second derivative calculation. A Lanczos algorithm is applied to extract the leading eigenvectors and eigenvalues of the Hessian matrix, representing the constrained uncertainty patterns and the inverse of the corresponding uncertainties. The dimensionality of the misfit Hessian inversion is reduced by omitting its nullspace (as an alternative to suppressing it by regularization), excluding from the computation the uncertainty subspace unconstrained by the observations. Inverse and forward uncertainty propagation schemes are designed for assimilating observation and control variable uncertainties and for projecting these uncertainties onto oceanographic target quantities. National Science Foundation (U.S.) (Collaboration in Mathematical Geosciences Grant 0934404) United States. Dept. of Energy. Office of Science (Scientific Discovery through Advanced Computing (SciDAC). Grant SC0008060) 2014-12-29T22:35:23Z 2014-12-29T22:35:23Z 2014-10 2014-07 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/92547 Kalmikov, Alexander G., and Patrick Heimbach. “A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation.” SIAM Journal on Scientific Computing 36, no. 5 (January 2014): S267–S295. https://orcid.org/0000-0002-5317-2573 https://orcid.org/0000-0003-3925-6161 en_US http://dx.doi.org/10.1137/130925311 SIAM Journal on Scientific Computing Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Heimbach, Patrick Kalmikov, Alex A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation |
| title | A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation |
| title_full | A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation |
| title_fullStr | A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation |
| title_full_unstemmed | A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation |
| title_short | A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation |
| title_sort | hessian based method for uncertainty quantification in global ocean state estimation |
| url | http://hdl.handle.net/1721.1/92547 https://orcid.org/0000-0002-5317-2573 https://orcid.org/0000-0003-3925-6161 |
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