dc.contributor.author | Kalmikov, Alexander G. | |
dc.contributor.author | Heimbach, Patrick | |
dc.date.accessioned | 2020-02-13T22:08:30Z | |
dc.date.available | 2020-02-13T22:08:30Z | |
dc.date.issued | 2014 | |
dc.identifier.citation | Kalmikov, A.G. and Heimbach, P. (2014) A Hessian-based method for uncertainty quantificiation in gllobal ocean state estimation. SIAM Journal of Scientific Computing, 36(5), pp. S267–S295. DOI: 10.1137/130925311 | en_US |
dc.identifier.uri | http://hdl.handle.net/11329/1216 | |
dc.identifier.uri | http://dx.doi.org/10.25607/OBP-733 | |
dc.description.abstract | Derivative-based methods are developed for uncertainty quantification (UQ) in largescale 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 | en_US |
dc.language.iso | en | en_US |
dc.rights | Attribution 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject.other | Uncertainty propagation | en_US |
dc.subject.other | Principal uncertainty patterns | en_US |
dc.subject.other | Posterior error reduction | en_US |
dc.subject.other | Hessian method | en_US |
dc.subject.other | Algorithmic differentiation (AD) | en_US |
dc.subject.other | MIT general circulation model (MITgcm) | en_US |
dc.subject.other | Drake Passage transport | en_US |
dc.subject.other | Large-scale ill-posed inverse problem | en_US |
dc.title | A Hessian-based method for uncertainty quantification in global ocean state estimation. | en_US |
dc.type | Journal Contribution | en_US |
dc.description.refereed | Refereed | en_US |
dc.format.pagerange | pp. S267–S295 | en_US |
dc.identifier.doi | 10.1137/130925311 | |
dc.subject.parameterDiscipline | Parameter Discipline::Physical oceanography | en_US |
dc.bibliographicCitation.title | SIAM Journal of Scientific Computing | en_US |
dc.bibliographicCitation.volume | 36 | en_US |
dc.bibliographicCitation.issue | 5 | en_US |
dc.description.sdg | 14.A | en_US |
dc.description.bptype | Manual (incl. handbook, guide, cookbook etc) | en_US |
obps.contact.contactname | Alexander Kalmikov | |
obps.contact.contactemail | kalex@alum.mit.edu | |
obps.resourceurl.publisher | https://epubs.siam.org/doi/pdf/10.1137/130925311 | en_US |