Li, Yong
(2016)
TIME FILTERS FOR NUMERICAL WEATHER PREDICTION.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
The Robert-Asselin (RA) time filter combined with leapfrog scheme is widely used in numerical models of weather and climate. The RA filter suppresses the spurious computational mode associated with the leapfrog method, and successfully stabilizes the numerical solution. However, it also weakly dampens the physical mode and degrades the formal second-order accuracy of the leapfrog scheme to first order. There is a natural intention to reduce the time-stepping error as it has proven to be a substantial part of the total forecast error. Yet a new scheme must be non-intrusive, i.e., easily implementable in legacy codes in order to avoid significant programming undertaking.
The object of this work is the development, analysis and validation of novel Robert-Asselin type time filters, addressing both of the above problems. Specifically, we first propose and analyze a higher-order Robert-Asselin (hoRA) type time filter. The analysis reveals that the filtered leapfrog scheme exhibits second- or third-order accuracy depending on the filter parameter. We then investigate its behavior when used in conjunction with the implicit-explicit integration, which is commonly used in weather and climate models to relieve the severe time step restriction induced by unimportant high-frequency waves. Next, we build a framework of constructing a family of hoRA filters with any pre-determined order of accuracy. In particular, we focus on the fourth-order time filter. Finally, we present supplemental analysis for several filters developed by Williams. For each direction, we present comprehensive error and stability analysis, and perform numerical tests to verify theoretical results.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
30 September 2016 |
| Date Type: |
Publication |
| Defense Date: |
28 April 2016 |
| Approval Date: |
30 September 2016 |
| Submission Date: |
14 June 2016 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
64 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
numerical weather prediction, time filters, Robert-Asselin-Williams, higher-order Robert-Asselin, leapfrog scheme, Crank-Nicolson, G-stability |
| Date Deposited: |
30 Sep 2016 19:24 |
| Last Modified: |
15 Nov 2016 14:33 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/28208 |
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