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| Titel |
Numerical Error Estimation with UQ |
| VerfasserIn |
Jan Ackmann, Peter Korn, Jochem Marotzke |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250096882
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| Publikation (Nr.) |
 EGU/EGU2014-12412.pdf |
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| Zusammenfassung |
| Ocean models are still in need of means to quantify model errors, which are inevitably made
when running numerical experiments. The total model error can formally be decomposed into
two parts, the formulation error and the discretization error. The formulation error arises from
the continuous formulation of the model not fully describing the studied physical process.
The discretization error arises from having to solve a discretized model instead of the
continuously formulated model. Our work on error estimation is concerned with the
discretization error. Given a solution of a discretized model, our general problem
statement is to find a way to quantify the uncertainties due to discretization in physical
quantities of interest (diagnostics), which are frequently used in Geophysical Fluid
Dynamics.
The approach we use to tackle this problem is called the "Goal Error Ensemble method". The
basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated
into a weighted sum of local model errors, which makes it conceptually based on the Dual
Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual
Weighted Residual method these local model errors are not considered deterministically but
interpreted as local model uncertainty and described stochastically by a random process. The
parameters for the random process are tuned with high-resolution near-initial model
information. However, the original Goal Error Ensemble method, introduced in [1], was
successfully evaluated only in the case of inviscid flows without lateral boundaries in a
shallow-water framework and is hence only of limited use in a numerical ocean
model. Our work consists in extending the method to bounded, viscous flows in a
shallow-water framework. As our numerical model, we use the ICON-Shallow-Water
model.
In viscous flows our high-resolution information is dependent on the viscosity parameter,
making our uncertainty measures viscosity-dependent. We will show that we can choose a
sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss
is the choice of the underlying distribution of the random process. This is especially of
importance in the scope of lateral boundaries.
We will present resulting error estimates for different height- and velocity-based diagnostics
applied to the Munk gyre experiment.
References
[1]F. RAUSER: Error Estimation in Geophysical Fluid Dynamics
through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010
[2]F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical
uncertainty quantification from single model integrations; SIAM/ASA
Journal on Uncertainty Quantification, submitted |
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