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| Titel |
Comparing and improving proper orthogonal decomposition (POD) to reduce the complexity of groundwater models |
| VerfasserIn |
Moritz Gosses, Wolfgang Nowak, Thomas Wöhling |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250144136
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| Publikation (Nr.) |
 EGU/EGU2017-7925.pdf |
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| Zusammenfassung |
| Physically-based modeling is a wide-spread tool in understanding and management of natural
systems. With the high complexity of many such models and the huge amount of model runs
necessary for parameter estimation and uncertainty analysis, overall run times can be
prohibitively long even on modern computer systems. An encouraging strategy to tackle this
problem are model reduction methods.
In this contribution, we compare different proper orthogonal decomposition (POD,
Siade et al. (2010)) methods and their potential applications to groundwater models.
The POD method performs a singular value decomposition on system states as
simulated by the complex (e.g., PDE-based) groundwater model taken at several
time-steps, so-called snapshots. The singular vectors with the highest information content
resulting from this decomposition are then used as a basis for projection of the
system of model equations onto a subspace of much lower dimensionality than
the original complex model, thereby greatly reducing complexity and accelerating
run times. In its original form, this method is only applicable to linear problems.
Many real-world groundwater models are non-linear, tough. These non-linearities
are introduced either through model structure (unconfined aquifers) or boundary
conditions (certain Cauchy boundaries, like rivers with variable connection to the
groundwater table). To date, applications of POD focused on groundwater models
simulating pumping tests in confined aquifers with constant head boundaries. In
contrast, POD model reduction either greatly looses accuracy or does not significantly
reduce model run time if the above-mentioned non-linearities are introduced. We
have also found that variable Dirichlet boundaries are problematic for POD model
reduction.
An extension to the POD method, called POD-DEIM, has been developed for non-linear
groundwater models by Stanko et al. (2016). This method uses spatial interpolation
points to build the equation system in the reduced model space, thereby allowing
the recalculation of system matrices at every time-step necessary for non-linear
models while retaining the speed of the reduced model. This makes POD-DEIM
applicable for groundwater models simulating unconfined aquifers. However, in our
analysis, the method struggled to reproduce variable river boundaries accurately and
gave no advantage for variable Dirichlet boundaries compared to the original POD
method.
We have developed another extension for POD that targets to address these remaining
problems by performing a second POD operation on the model matrix on the left-hand side of
the equation. The method aims to at least reproduce the accuracy of the other methods where
they are applicable while outperforming them for setups with changing river boundaries or
variable Dirichlet boundaries. We compared the new extension with original POD and
POD-DEIM for different combinations of model structures and boundary conditions. The
new method shows the potential of POD extensions for applications to non-linear
groundwater systems and complex boundary conditions that go beyond the current, relatively
limited range of applications.
References:
Siade, A. J., Putti, M., and Yeh, W. W.-G. (2010). Snapshot selection for groundwater model
reduction using proper orthogonal decomposition. Water Resour. Res., 46(8):W08539.
Stanko, Z. P., Boyce, S. E., and Yeh, W. W.-G. (2016). Nonlinear model reduction of
unconfined groundwater flow using pod and deim. Advances in Water Resources, 97:130 -
143. |
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