Ming Cai is supported in part by research grants from the National Science Foundation (Grant ATM-0833001), the NOAA CPO/CPPA program (Grant NA10OAR4310168), and the DOE Office of Science’s Regional and Global Climate Modeling (RGCM) program (Grant DE-SC0004974). B. Huang is supported by the COLA omnibus grant from NSF (ATM-0830068), NOAA (NA09OAR4310058), and NASA (NNX09AN50G). The authors are benefited from discussions with Drs. Mankin Mak, Yi Deng, Zhaohua Wu, and Huug van den Dool, and Mr. Sergio Sejas on the earlier version of the paper. The authors greatly appreciate the constructive and informative comments and suggestions from Dr. Qin Xu and the anonymous reviewer during the peer review process.
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Alternatively, we could set up the coordinate for the 1D model in such a way that the geostrophic flow is aligned with contours of planetary vorticity. However, with this alternative setting, the β-plane model is reduced to an f-plane model and the only possible solution is a time-independent geostrophic mode because the flow does not cross planetary vorticity contours. The negligence of tendencies of ua and υa in (1) is in accordance with the QG approximation.
In a nondivergent barotropic model, the notion of Rossby radius of deformation is no longer relevant, corresponding to the case λ = 0, in which