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Wayne H. Schubert
,
Michael T. Montgomery
,
Richard K. Taft
,
Thomas A. Guinn
,
Scott R. Fulton
,
James P. Kossin
, and
James P. Edwards

the stage for dynamic instability ( Montgomery and Shapiro 1995 ) and rearrangement of the PV distribution. If, during the rearrangement process, part of the low PV fluid in the eye is mixed into the eyewall, asymmetric eye contraction can occur in conjunction with a polygonal eyewall. While PV maps of hurricanes are beginning to be constructed from various types of available data ( Shapiro and Franklin 1995 ; Shapiro 1996 ), we still need much more observational evidence for the finescale PV

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H. Wexler

studied. In the second, more realistic model,the effect of sudden heating of the ozonosphere upon sea-level pressure is shown to be insignificant.The forty-year series of daily northern-hemisphere sea-level maps has been examined to see if there is asignificant difference in the meridional pressure-profile during periods of sunspot maxima and sunspotminima, the former periods being associated with more frequent ultraviolet outbursts. A comparison withClayton's previous work is made, but the results of

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Ulrich Achatz
and
Gerhard Schmitz

complex conjugate. Different choices are possible for the metric. Here we use as norm the discretized version of total energy, We now ask ourselves what initial perturbation x(0) maximizes for some given finite time τ the ratio || x ( τ )|| 2 /|| x (0)|| 2 . The answer to this question makes use of the propagator matrix Φ, which maps the initial perturbation to its state at t = τ via x ( τ ) = Φ ( τ ) x (0). By variational analysis one can show that the desired perturbation initializing

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Isla Gilmour
,
Leonard A. Smith
, and
Roberto Buizza

) for the perturbations considered. Such a comparison does not verify that the properties of a particular TLM match those of the linearized nonlinear model since ensemble members may evolve linearly even if the particular TLM used is inaccurate. We do not, therefore, test the accuracy of a particular TLM, but rather we extract an upper bound on the duration of its usefulness as an approximation. We wish to define a measure to quantify the error made in assuming linear evolution that is sensitive

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Andrew Roberts
,
John Guckenheimer
,
Esther Widiasih
,
Axel Timmermann
, and
Christopher K. R. T. Jones

regions are shaded in red, while unstable regions are shaded in blue [(b) and (c) only]. c. The reduced problem: Dynamics on the critical manifold Next, we consider the slow dynamics of the reduced problem (7) . In general, a reduced problem describes a flow of reduced dimension restricted to a manifold given by an algebraic condition. Since M is the union of the manifolds and , we need to solve two separate reduced problems—one on each of the two manifolds. The reduced problem on , described

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Wan-Cheng Chiu

1959WAN-CHENG CHIU 357temperature change. This mean seasonal temperaturechange may be large from winter to summer. However, its average contribution to the temperaturechange in a few hours is small in comparison to thatof RZ and so equation (8) is valid to a very goodapproximation. This point will be further examinedin section 3d.b. Selection of radiosonde stations.-The two important criteria for the selection of radiosonde stationsto be used for the study of the temperature variationdue to

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Wayne H. Schubert
,
Joseph S. Wakefield
,
Ellen J. Steiner
, and
Stephen K. Cox

) wepresented a Coupled, convective-radiative, boundary-layer model of marine stratocumulus convection. Under horizontally homogeneous steadystate conditions the governing differential equations reduced to a system of algebraic equationswhich could be easily solved. Solutions were presented for various sea surface temperatures andlarge-scale divergences. In this paper we presentsolutions of the horizontally inhomogeneous version of the model, i.e., we present numericaland approximate analytical solutions of

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Brian F. Farrell
and
Petros J. Ioannou

system as a mapping from the space of input forcings to the space of output states ( Dullerud and Paganini 2000 ). This theory enabled Glover (1984) to obtain the optimal truncation of a dynamical system by using a singular value decomposition of the map between past forcings and future responses of the system (cf. Zhou and Doyle 1998 ). The singular values of this map, called Hankel singular values, have recently been used to truncate the linearized fluid equations and construct a reduced

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John Methven
and
Brian Hoskins

changing most quickly (see Dritschel 1989a ). Note that particle redistribution occurred every 6 h and contour surgery was not used so there was no limitation to the filament widths and the contour was not split. Comparison PV contour simulations were obtained by temporally and spatially truncating the high-resolution life cycle winds to a greater degree. At day 4, when the CA simulations were initiated, the PV field was still wavelike and smooth so that it was virtually unchanged by spatial

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Lian-Ping Wang
and
Davd E. Stock

-half that parallelto va. This was called "the continuity effect" by Csanady (1963). For the purpose of future comparison, itis worth pointing out that Csanady's relations implythat 1)~- -- 1)2- -- l, T~] Tee 1030 v30 T3-~ = T33 = ~' if --u0 -* oo, r~ = 0, (1.4)where v~0 and Tn are ith component of the particlerms fluctuating velocity and ith component of the particle Lagrangian integral time scale, respectively; ra isthe particle aerodynamic response time [ see Eq. (2

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