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Christopher A. Davis

large region of parameterspace. However, such an analysis can only providequalitative information; hence, in section 3, idealizedinversions of perturbations are considered using thefull balance equations. The ultimate comparison ofmethods is in the context of inverting observed atmospheric EPV anomalies, two examples of which arepresented in section 4. Our primary result is that therelative differences between most of the inversionmethods are small, generally less than 25% even at largeRossby number

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Shian-Jiann Lin
and
Raymond T. Pierrehumbert

basis functions in an infinitedomain (y-direction) or semi-infinite domain (z-direction) one encounters the difficulty of satisfying theboundary conditions at infinity. Grosch and Orszag(1977) employed both algebraic and exponential map~_. 1.0 tLLI 0.8.-r 0.6 0.4 0.20.0 ~jl= 0 l= 1 ' 2-D I I I I I I0.0 4. 16. 36. EDDY VISICOSITY vI I I IFIG. 3. Maximum

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K. Pflug
,
S. Lovejoy
, and
D. Schertzer

algebraic behavior in threedimensions but to exponential behavior in two (Larchevesque and Lesieur 1981). On the contrary, thereis now considerable experimental evidence indicatingthat the (power law) energy spectra of horizontal fluctuations of the horizontal wind continue through the Corresponding author address.' Dr. Shaun Lovejoy, Departmentof Physics, McGill University, Ernest Rutherford Physics Bldg., 3600University St., Montreal, H3A 2T8 Quebec, Canada.mesoscale unchanged for scales ranging

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Roberto Buizza

( Buizza et al. 1993 ). The singular vector approach to the study of atmospheric instabilities has been related to other methods by Buizza and Palmer (1995) , who have described, at least in some restrictive conditions, the relationship between singular vectors, eigenmodes, and Lyapunov vectors. The reader is also referred to Toth and Kalnay(1993) for a comparison of the characteristics of the singular vectors and of the so-called bred modes. Singular vectors depend, by definition, on the choice of

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D. L. Hartmann
,
T. N. Palmer
, and
R. Buizza

vertical diffusion,horizontal diffusion, and surface drag schemes (Buizza1994). The horizontal diffusion is fourth power or biharmonic, with a coefficient chosen to give an e-foldingtimescale at the maximum total wavenumber of 5 days.for T21 and 1.25 days for T42. Equation (2) can be written in the integral form x'(t) = L(t, to)X'(to). (3)The operator L(t, to) is referred to as the forward tangent propagator; it maps small perturbations along the

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Guosen Chen

-level circulation in the CCER wave, as the convection of wave-CISK occurs in the low-level convergence region predicted by the corresponding dry waves. The observed fact that tropical atmosphere is nearly convectively neutral further questions the wave-CISK theory ( Xu and Emanuel 1989 ). Recent studies have shown that the CCER wave has stronger coherence between column moisture and precipitation than the gravity-type waves ( Yasunaga and Mapes 2012 ), indicating the importance of moisture variation in the

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Carl Youngblut
and
Takashi Sasamori

that algebraically the term can be cancelledfrom each side. In numerical simulations of planetary-waves (e.g., Matsuno, 1970) a similar term oftenappears on only the left-hand side of the wave equation as a Rayleigh friction and/or Newtonian cooling.For our study, a0* is added to both sides of (2.4) toretain the diagnostic balance and as discussed inSection 5, to suppress a resonance in the numerical solution. The term may be simply interpreted asa mathematical device which, allows the comput

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Shyh-Chin Chen
and
Kevin E. Trenberth

must be forced by some persistent set offorcings. A comparison of the time-mean flow betweenthe Northern and Southern hemispheres indicates that * The National Center for Atmospheric Research (NCAR) issponsored by the National Science Foundation (NSF). Corresponding author address: Dr. Shyh-Chin Chen, Scripps Institution of Oceanography--A024, University of California, SanDiego, La Jolla, CA 92023.the origin of the quasi-stationary planetary waves isattributable to the earth's orography and

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J. Weinstock

comparison of our results with thoseof Dewan and Good (1986) and Smith et al. (1987)is given in Section 5.1. We also note that, aside fromwave saturation derivations, k-3 spectra (where k isthe scalar wave number) were previously derived fromstratified turbulence theory by accounting for the influence of buoyancy on random fluctuations and tur 2 While it is true that one particular wave may have saturatedbefore the others, it is also true that after a steady-state saturationspectrum is established each

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Claude Fischer

optimally growing modes, without referring explicitly to “singular vectors” (see his section 4 ). Joly (1995) displays numerical solutions of singular modes for several norms within a uniform potential vorticity flow. It is of interest that the shapes of the solutions depend on the norm, so that the singular vectors are found to be either baroclinic or barotropic modes. In Joly’s study, the time T is set somewhat arbitrarily to 48 h by comparison with typical timescales for secondary cyclogenesis

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