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| Titel |
The effects of the model errors generated by discretization of "on-off'' processes on VDA |
| VerfasserIn |
Q. Zheng, M. Mu |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 13, no. 3 ; Nr. 13, no. 3 (2006-07-25), S.309-320 |
| Datensatznummer |
250011775
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| Publikation (Nr.) |
 copernicus.org/npg-13-309-2006.pdf |
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| Zusammenfassung |
| Through an idealized model of a partial differential equation with
discontinuous "on-off'' switches in the forcing term, we investigate the
effect of the model error generated by the traditional discretization of
discontinuous physical "on-off'' processes on the variational data
assimilation (VDA) in detail. Meanwhile, the validity of the adjoint
approach in the VDA with "on-off'' switches is also examined. The
theoretical analyses illustrate that in the analytic case, the gradient of
the associated cost function (CF) with respect to an initial condition (IC)
exists provided that the IC does not trigger the threshold condition. But in
the discrete case, if the on switches (or off switches) in the forward model
are straightforwardly assigned the nearest time level after the threshold
condition is (or is not) exceeded as the usual treatment, the discrete CF
gradients (even the one-sided gradient of CF) with respect to some ICs do
not exist due to the model error, which is the difference between the
analytic and numerical solutions to the governing equation. Besides, the
solution of the corresponding tangent linear model (TLM) obtained by the
conventional approach would not be a good first-order linear approximation
to the nonlinear perturbation solution of the governing equation.
Consequently, the validity of the adjoint approach in VDA with parameterized
physical processes could not be guaranteed. Identical twin numerical
experiments are conducted to illustrate the influences of these problems on
VDA when using adjoint method. The results show that the VDA outcome is
quite sensitive to the first guess of the IC, and the minimization processes
in the optimization algorithm often fail to converge and poor optimization
retrievals would be generated as well. Furthermore, the intermediate
interpolation treatment at the switch times of the forward model, which
reduces greatly the model error brought by the traditional discretization of
"on-off'' processes, is employed in this study to demonstrate that when the
"on-off'' switches in governing equations are properly numerically treated,
the validity of the adjoint approach in VDA with discontinuous physical
"on-off'' processes can still be guaranteed. |
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