Impact of non-smooth observation operators on variational and sequential data assimilation for a limited-area shallow-water equation model
We investigate the issue of variational and sequential data assimilation with nonlinear and non‐smooth observation operators using a two‐dimensional limited‐area shallow‐water equation model and its adjoint. The performance of the four‐dimensional variational approach (4D‐Var: two dimensions plus ti...
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| Published in | Quarterly journal of the Royal Meteorological Society Vol. 138; no. 663; pp. 323 - 339 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Chichester, UK
John Wiley & Sons, Ltd
01.01.2012
Wiley |
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| Abstract | We investigate the issue of variational and sequential data assimilation with nonlinear and non‐smooth observation operators using a two‐dimensional limited‐area shallow‐water equation model and its adjoint. The performance of the four‐dimensional variational approach (4D‐Var: two dimensions plus time) compared with that of the maximum‐likelihood ensemble filter (MLEF), a hybrid ensemble/variational method, is tested in the presence of non‐smooth observation operators.
Following the work of Lewis & Overton and Karmitsa, we investigate minimization of the data‐assimilation cost functional using the limited‐memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) quasi‐Newton algorithm originally intended for smooth optimization and the limited‐memory bundle method (LMBM) algorithm specifically designed to address large‐scale non‐smooth minimization problems.
Numerical results obtained for the MLEF method show that the LMBM algorithm yields results superior to the L‐BFGS method. Results for 4D‐Var suggest that L‐BFGS performs well when the non‐smoothness is not extreme, but fails for non‐smooth functions with large Lipschitz constants. The LMBM method is found to be a suitable choice for large‐scale non‐smooth optimization, although additional work is needed to improve its numerical stability. Finally, the results and methodologies of 4D‐Var and MLEF are compared and contrasted. Copyright © 2011 Royal Meteorological Society |
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| AbstractList | Abstract
We investigate the issue of variational and sequential data assimilation with nonlinear and non‐smooth observation operators using a two‐dimensional limited‐area shallow‐water equation model and its adjoint. The performance of the four‐dimensional variational approach (4D‐Var: two dimensions plus time) compared with that of the maximum‐likelihood ensemble filter (MLEF), a hybrid ensemble/variational method, is tested in the presence of non‐smooth observation operators.
Following the work of Lewis & Overton and Karmitsa, we investigate minimization of the data‐assimilation cost functional using the limited‐memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) quasi‐Newton algorithm originally intended for smooth optimization and the limited‐memory bundle method (LMBM) algorithm specifically designed to address large‐scale non‐smooth minimization problems.
Numerical results obtained for the MLEF method show that the LMBM algorithm yields results superior to the L‐BFGS method. Results for 4D‐Var suggest that L‐BFGS performs well when the non‐smoothness is not extreme, but fails for non‐smooth functions with large Lipschitz constants. The LMBM method is found to be a suitable choice for large‐scale non‐smooth optimization, although additional work is needed to improve its numerical stability. Finally, the results and methodologies of 4D‐Var and MLEF are compared and contrasted. Copyright © 2011 Royal Meteorological Society We investigate the issue of variational and sequential data assimilation with nonlinear and non‐smooth observation operators using a two‐dimensional limited‐area shallow‐water equation model and its adjoint. The performance of the four‐dimensional variational approach (4D‐Var: two dimensions plus time) compared with that of the maximum‐likelihood ensemble filter (MLEF), a hybrid ensemble/variational method, is tested in the presence of non‐smooth observation operators. Following the work of Lewis & Overton and Karmitsa, we investigate minimization of the data‐assimilation cost functional using the limited‐memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) quasi‐Newton algorithm originally intended for smooth optimization and the limited‐memory bundle method (LMBM) algorithm specifically designed to address large‐scale non‐smooth minimization problems. Numerical results obtained for the MLEF method show that the LMBM algorithm yields results superior to the L‐BFGS method. Results for 4D‐Var suggest that L‐BFGS performs well when the non‐smoothness is not extreme, but fails for non‐smooth functions with large Lipschitz constants. The LMBM method is found to be a suitable choice for large‐scale non‐smooth optimization, although additional work is needed to improve its numerical stability. Finally, the results and methodologies of 4D‐Var and MLEF are compared and contrasted. Copyright © 2011 Royal Meteorological Society |
| Author | Navon, I. M. Zupanski, M. Steward, J. L. Karmitsa, N. |
| Author_xml | – sequence: 1 givenname: J. L. surname: Steward fullname: Steward, J. L. email: jls07c@fsu.edu organization: Department of Scientific Computing, The Florida State University, Tallahassee, USA – sequence: 2 givenname: I. M. surname: Navon fullname: Navon, I. M. organization: Department of Scientific Computing, The Florida State University, Tallahassee, USA – sequence: 3 givenname: M. surname: Zupanski fullname: Zupanski, M. organization: Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, USA – sequence: 4 givenname: N. surname: Karmitsa fullname: Karmitsa, N. organization: Department of Mathematics, University of Turku, Turku, Finland |
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| Keywords | algorithms MLEF Four dimensional calculations Limited area model LMBM extreme value maximum likelihood L-BFGS Variational calculus 4D-Var non-smooth optimization performances Numerical stability Data assimilation Shallow-water equations |
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| Snippet | We investigate the issue of variational and sequential data assimilation with nonlinear and non‐smooth observation operators using a two‐dimensional... Abstract We investigate the issue of variational and sequential data assimilation with nonlinear and non‐smooth observation operators using a two‐dimensional... |
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| SubjectTerms | 4D-Var Earth, ocean, space Exact sciences and technology External geophysics L-BFGS LMBM Meteorology MLEF non-smooth optimization Physics of the high neutral atmosphere |
| Title | Impact of non-smooth observation operators on variational and sequential data assimilation for a limited-area shallow-water equation model |
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