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Youmin Tang, Richard Kleeman, and Andrew M. Moore

utility and proposes a practical algorithm for its computation. Section 4 describes the strategy and methodology used in the ensemble experiments, while a reduced space in which the utility is evaluated is discussed in section 5 . Utility analyses for two coupled models are presented in sections 6 and 7 . A summary and discussion are given in section 8. 2. The coupled models and initialization scheme a. The coupled models Two hybrid coupled models (HCMs), an ocean general circulation model (OGCM

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R. L. Walterscheid and G. Schubert

from theturbulence model of wave saturation have no rigorous justification and could give erroneous results if employedin studies of middle atmosphere circulation and minor constituent mixing. The immediate consequence ofwave overturning is small-scale convection (regular, cellular structures with length scales of several to tens ofkilometers) in the moving unstable phases of the wave. Cellular convection grows at the expense of the waveand provides a stabilization of the gross stratification

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R. T. Pierrehumbert and H. Yang

discussed in a separate paper. We conclude with a few remarks putting the mixingresults in context within the broader setting of the general circulation. The approach that is emerging is similar to that extant in ocean thermocline theory, withthe 315-K isentropic surface regarded as being "ventilated'' in the tropics (see, e.g., Hoskins 1989). In thepresent terrestrial climate, the northern extratropicshave generally high positive potential vorticity on the315-K surface, the southern extratropics

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Joseph J. Barsugli and David S. Battisti

mathematical or statistical model. At the complex end of the modeling spectrum, studies using realistic atmospheric general circulation models (AGCMs) have been used to examine the impacts of coupling on the natural climate variability in the midlatitudes (e.g., Schneider and Kinter 1994 ; Manabe and Stouffer 1996 ; Lau and Nath 1996 ; Bhatt et al. 1998 ; Bladé 1997 ; Nitsche 1996 ). The methodology used in each of these studies involves the comparison of two integrations of the AGCM. First, the AGCM

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Steven A. Smith, David C. Fritts, and Thomas E. Vanzandt

instabilities and turbulence would act to limitgravity wave amplitudes in the middle atmosphere.More recently, Lindzen (1981) argued that gravitywaves could account for appreciable drag and diffusionin the mesosphere and thus contribute substantially tothe large-scale circulation and structure of this region.The theory and observations relating to gravity wavesaturation were reviewed by Fritts (1984). The basic idea of this saturation theory is that amonochromatic gravity Wave will achieve a state

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O. Bokhove

horizontal coordinates and time, while in the latter the positions of the fluid parcels are functions of the fluid labels and time. Boussinesq models in isopycnic coordinates are often used in ocean circulation models, such as the Miami Isopycnic Coordinate Ocean Model (MICOM) model (e.g., Bleck and Smith 1990 ). In contrast, material coordinates have been less popular in atmospheric numerical models, since the use of terrain-following or sigma coordinates in numerical models appears to be more

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David C. Fritts and Timothy J. Dunkerton

gravity waves. J. Geophys. Res., 74, 4087-4090.Holton, J. R., 1982: The role of gravity wave-induced drag and diffusion in the momentum budget of the mesosphere. J. Atmos. Sci., 39, 791-799.--., 1983: The influence of gravity wave breaking on the general circulation of the middle atmosphere. J. Atmos. Sci., 40, 2497-2507.Ingersoll, A. P., 1966: Thermal convection with shear at high Rayleigh number. J. Fluid Mech., 25, 209-228.Koop, C. G., 1981: A preliminary investigation of the interaction

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K-M. Lau and Suhung Shen

circulation arises from the so-called "mobile" wave-CISKwhich combines the above mechanism together witha positive-only heating, thus providing an upscale cascade of energy from the convection scale to the planetary scale. Recently studies by Yamagata. (1987),Takahashi (1987) and Miyahara (1987) further confirmthe importance of wave-CISK in leading to intraseasonal oscillations of the tropical atmosphere. While many basic features of intraseasonal oscillations are explained by the mobile wave

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David S. Battisti and Anthony C. Hirst

nonlinearity in the full numerical model is shown to be the dependence of the temperature of theupwelled water on the thermocline depth. However, we find the essential processes that describe the localinstability growth rate and period 0fthe interannual oscillations in the coupled system are linear. Nonlinearitiesprimarily act as a bound on the amplitude of the final state oscillations, and decrease the period of the finalstate oscillations by about I0 percent from that obtained in the small amplitude

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Frank B. Lipps

f0 we take the value of theCoriolis parameter at 38 deg which is 0.897X 10-4 sec-1.Hence we find for the Rossby number Ro = 0.540. The value of F: is somewhat more difficult to findsince it is evident from Fig. 33 of Stommel that themean density varies continuously with depth and is notdiscontinuous as assumed in the above model. We therefore find F~ by the following somewhat indirect procedure. Stommel states that the main thermocline (10Cisotherm) slopes from 200 m below the surface to

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