Numerical algorithms are proposed, analyzed and tested for improved efficiency and reliabil-
ity of the dynamic core of climate codes. The commonly used rigid lid hypothesis is assumed,
which allows instantaneous response of the interface to changes in mass. Additionally, mois-
ture transport is ignored, resulting in a static interface. A central algorithmic feature is the
numerical decoupling of the atmosphere and ocean calculations by a semi-implicit treatment
of the interface data, i.e. partitioned time stepping. Algorithms are developed for simpli-
fied continuum models retaining the key mathematical structure of the atmosphere-ocean
equations.
The work begins by studying linear parameterization of momentum flux in terms of wind
shear, coupling the equations. Partitioned variants of backward-Euler are developed allowing
large time steps. Higher order accuracy is achieved by deferred correction. Adaptations are
developed for nonlinear coupling. Most notably an application of geometric averaging is
used to retain unconditional stability. This algorithm is extended to allow different size time
steps for the subcalculations. Full numerical analyses are performed and computational
experiments are provided.
Next, heat convection is added including a nonlinear parameterization of heat flux in
terms of wind shear and temperature. A partitioned algorithm is developed for the atmo-
sphere and ocean coupled velocity-temperature system that retains unconditional stability.
Furthermore, uncertainty quantification is performed in this case due to the importance of
reliably calculating heat transport phenomena in climate modeling. Noise is introduced in two coupling parameters with an important role in stability. Numerical tests investigate the
variance in temperature, velocity and average surface temperature.
Partitioned methods are highly efficient for linearly coupled 2 fluid problems. Exten-
sions of these methods for nonlinear coupling where the interface data is processed properly
before passing yield highly efficient algorithms. One reason is due to their strong stability
properties. Convergence also holds under time step restrictions not dependent on mesh size.
It is observed that two-way coupling (requiring knowledge of both atmosphere and ocean
velocities on the interface) generates less uncertainty in the calculation of average surface
temperature compared to one-way models (only requiring knowledge of the wind velocity).
| Identifer | oai:union.ndltd.org:PITT/oai:PITTETD:etd-05052010-180427 |
| Date | 28 September 2010 |
| Creators | Connors, Jeffrey Mark |
| Contributors | William J. Layton, Ivan Yotov, Noel J. Walkington, Catalin Trenchea |
| Publisher | University of Pittsburgh |
| Source Sets | University of Pittsburgh |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.pitt.edu/ETD/available/etd-05052010-180427/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Pittsburgh or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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