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Core Information
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| Title: |
The Maximum Likelihood Ensemble Filter as a non-differentiable minimization algorithm |
| Abstract: |
ABSTRACT: The Maximum Likelihood Ensemble Filter (MLEF) equations are derived without the differentiability
requirement for the prediction model and for the observation operators. The derivation reveals that a new non-differentiable
minimization method can be defined as a generalization of the gradient-based unconstrained methods, such as the
preconditioned conjugate-gradient and quasi-Newton methods. In the new minimization algorithm the vector of first-order
increments of the cost function is defined as a generalized gradient, while the symmetric matrix of second-order increments
of the cost function is defined as a generalized Hessian matrix. In the case of differentiable observation operators, the
minimization algorithm reduces to the standard gradient-based form.
The non-differentiable aspect of the MLEF algorithm is illustrated in an example with one-dimensional Burgers model
and simulated observations. The MLEF algorithm has a robust performance, producing satisfactory results for tested
non-differentiable observation operators.
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| Keywords: |
unconstrained minimization, ensemble data assimilation |
Author Information
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Detailed Scientific Article Information
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| Journal Name: |
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY |
| Volume: |
134, Issue 633 |
| Page Range: |
1039-1050 |
Article Number: |
Not Provided |
| Number of Pages: |
Not Provided |
| Year of Publication: |
2008 |
| Refereed: |
Yes |
| Digital Object Identifier (DOI), if available: |
10.1002/qj.251 |
| Official Url: |
http://www3.interscience.wiley.com/journal/113388514/home |
| ISSN: |
1477-870X |
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Subjects Information
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1. Meteorology
2. Mathematics
3. Fluid Dynamics
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