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Brian V. Smoliak
and
John M. Wallace

Dunkerton 1995 ). Rotation alleviates these problems, at the price of some loss of efficiency in explaining variance. Most published studies are based on varimax rotation of the principal component time series, which yields mutually orthogonal “expansion coefficient” time series but spatially correlated maps as explained in Horel (1981) and Kushnir and Wallace (1989) . The rotation is performed in a truncated EOF space whose dimension needs to be prescribed by the user: the larger the space, the

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Jerome Weinstock

and the action of the turbulence back onthe wave. The turbulence closures are also similar. Thedifference is that they considered a dynamical instability triggered by a wave with a mean background gradient Richardson number approaching the "thresholdvalue" % over some height range, whereas we considera convective instability triggered by a wave with themean background Richardson number everywheremuch larger than %. A detailed comparison of resultsis not practicable because of the different

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Klaus Fraedrich
and
John L. McBride

instability has both abalanced and an unbalanced solution. The balanced solution gives growth rates on the timescale of a day, andon length scales of several hundred kilometers. Boththe growth rate and horizontal scale are related to thevertical structure of the initial perturbation. By comparison with vertical structures and horizontal scales ofincipient tropical cyclones in nature, we propose thatthe balanced version of the model may be a viablemechanism for either tropical cyclone or tropical

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Anna Trevisan
and
Francesco Pancotti

small number of iterations of the Poincaré map. Therefore, the study of the stability of periodic orbits is a tool to unfold the structure of the whole attractor. Periodic solutions of the Lorenz (1963) system: where r = 28, b = 8/3, and σ = 10 can be found, given a sufficiently accurate first guess of the orbit and itsperiod, using a Newton–Raphson scheme on the residual of the return map ( Ghil and Tavantzis 1983 ). Consider now the stability problem and linearize (1) about a closed

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Craig H. Bishop
and
Zoltan Toth

: On extending the limits of variational assimilation in chaotic systems. Tellus, 48A, 96–121. Strang, G., 1988: Linear Algebra and Its Applications. Harcourt, Brace and Jovanavitch, 505 pp. Szunyogh, I., E. Kalnay, and Z. Toth, 1997: A comparison of Lyapunov and optimal vectors in a low-resolution GCM. Tellus, 49A, 200–227. Thorpe, A. J., 1998: Predictability studies with FASTEX data using the ECMWF IFS. Proc. ECMWF Workshop on Predictability, Reading, United Kingdom, ECMWF

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E. C. Neven

blocks, and strongly nonlinear coherent structures known as modons as models for atmospheric blocks. The observed patterns include wavelike structures in one-point correlation maps of geopotential height known as teleconnections ( Wallace and Gutzler 1981 ). These patterns resemble the most unstable linear barotropic modes as shown in the normal mode analysis of a January-mean 300-mb observed basic state in a barotropic model ( Simmons et al. 1983 , hereafter SWB). The insight into the spectrum and

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Peter P. Sullivan
,
James C. McWilliams
, and
Edward G. Patton

2d . b. Coordinate transformation We adapt our LES model with a flat boundary ( Sullivan and Patton 2011 ) to the situation with a three-dimensional time-dependent lower boundary with shape h = h ( x , y , t ) by applying a transformation to the physical space coordinates x i ≡ ( x , y , z ) that maps them onto computational coordinates ξ i ≡ ( ξ , η , ζ ). The computational mesh in physical space is surface following, nonorthogonal, and time varying. Vertical gridlines are held

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Christopher A. Jeffery
and
Jon M. Reisner

) PDF schemes that utilize the ICE assumption ( section 2a ) and (ii) microphysics models that resolve S and ignore subgrid correlations ( section 2b ). In section 2c we introduce the Damköhler number—the ratio of mixing and reaction (evaporation) time scales—which facilitates a comparison of PDF and resolved evaporation rates for a range of atmospheric conditions. In section 3 we study the evaporation rate predicted numerically by a simple 1D eddy diffusivity model for various initial

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Manuel S. F. V. de Pondeca
,
Albert Barcilon
, and
Xiaolei Zou

is the reference time. The first-order change δR in the response function, brought about by adding the perturbation δ x ( t 0 ) to the model’s initial condition x 0 ( t 0 ), can be evaluated as the inner product: In (1) , δ x ( t ) is the departure from the reference trajectory x 0 ( t ) and (∂ R /∂ x ) x 0 ( t ) is the gradient of the response function evaluated on that reference trajectory at time t. Equation (1) follows from simple calculus and vector algebra considerations. The

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Xun Zhu

found that the algebraic approximation of the saturated vertical wavenumber spectrum of horizontal winds, F(/z), cab be written as ~/z_3(0 2.5 F(/~)where/~ is the dimensionless vertical wavenumber, and 0 is a parameter measuring the ratio of the dynamiceffect to the radiative effect on the dissipation. The theory predicts the widely cited -3 power law for both smalland large vertical

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