Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/107097
Title: Theory of the norm-induced metric in atmospheric dynamics
Authors: Koh, Tieh-Yong
Wan, F.
Keywords: DRNTU::Science::Geology
Issue Date: 2015
Source: Koh, T.-Y., & Wan, F. (2015). Theory of the norm-induced metric in atmospheric dynamics. Atmospheric chemistry and physics, 15(5), 2571-2594.
Series/Report no.: Atmospheric chemistry and physics
Abstract: We suggest that some metrics for quantifying distances in phase space are based on linearized flows about unrealistic reference states and hence may not be applicable to atmospheric flows. A new approach of defining a norm-induced metric based on the total energy norm is proposed. The approach is based on the rigorous mathematics of normed vector spaces and the law of energy conservation in physics. It involves the innovative construction of the phase space so that energy (or a certain physical invariant) takes the form of a Euclidean norm. The metric can be applied to both linear and nonlinear flows and for small and large separations in phase space. The new metric is derived for models of various levels of sophistication: the 2-D barotropic model, the shallow-water model and the 3-D dry, compressible atmosphere in different vertical coordinates. Numerical calculations of the new metric are illustrated with analytic dynamical systems as well as with global reanalysis data. The differences from a commonly used metric and the potential for application in ensemble prediction, error growth analysis and predictability studies are discussed.
URI: https://hdl.handle.net/10356/107097
http://hdl.handle.net/10220/25316
ISSN: 1680-7324
DOI: 10.5194/acp-15-2571-2015
Rights: © Author(s) 2015. This work is distributed under the Creative Commons Attribution 3.0 License.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EOS Journal Articles
SPMS Journal Articles

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