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Brian Reinhold

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Brian Reinhold

Abstract

The linear evolution of arbitrarily specified perturbations in a zonally homogeneous, two-layer model is analyzed in a dynamical system which describes the disturbances in terms of the phase difference and amplitude ratio between the temperature and streamfunction components. The stationary equilibria of this system are equivalent to the individual eigenmodes of normal mode analysis and in the inviscid case, simple analytical expressions for these equilibria are possible. These expressions allow us to quantitatively examine the physical processes that determine the normal mode structures in the inviscid case and how the processes of friction then affect them. The advantage to this approach is that a conceptual understanding for the processes determining the so-called “preferred structure” and their characteristics (e.g., growth rates) of normal mode analysis is obtained in terms of the basic Quid flow properties of advection, dispersion and dissipation. But the most important conceptual property we find is that in the presence of dissipation the normal modes are indeed “preferred structure” or deterministic, in the sense that any arbitrarily specified initial perturbation evolves asymptotically to that structure. This is not always the case in the inviscid problem or certain cases of symmetrically applied dissipation. However, the occurrence of determinism in this simple case allows us to conceptually investigate and understand the equilibrated truncated nonlinear state in terms of the linear solution.

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Brian Reinhold

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A single baroclinic normal mode is perturbed by small orography. The method of analysis considered here allows one to conceptually, understand how the orography modifies the characteristics of the normal mode, and how the modulations depend upon the structural and diagnostic properties of the normal mode (such as the phase speed and the growth rate). It is found that slow phase speeds and growth rates enhance the orographically induced zonal flows, which accounts for the long-wave sensitivity to orography. In addition, the structural modulations are shown to be proportional to the square of the induced zonal wind speeds, which allows the orography to dramatically influence the flow without entering strongly into the energetics. The modulations of the phase speed can easily mitigate that due to the baroclinic wave itself at the long waves, leading to orographic instability.

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Shuting Yang and Brian Reinhold

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An objective break criterion is utilized to investigate the manner in which the slowly varying component of the atmosphere ( 10-90 day frequency band) actually varies. It is found that a great deal of the behavior appears to be made up of relatively infrequent large amplitude transitions between quasi-persistent states. The most frequent time interval over which these transition events occur is between five and six days. The rapid speed of these events strongly suggests that some type of baroclinic instability mechanism is involved in the transition process.

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Brian Reinhold and Shuting Yang

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Transition of weather regimes is examined in a highly simplified model. Two completely distinct internal methods of transition are identified. The first is a synoptically triggered large-scale instability, while the second is an energy inconsistency between the large-scale and synoptic scales that does not allow the two scales to equilibrate. In the atmosphere, the first case appears as a sudden propagation and damping (or vice versa) of the large-scale pattern with no obvious warning, while the second is consistent with the synoptician's description of a regime being disrupted by a single catastrophic event such as explosive cyclogenesis. The first method is always fast (on a synoptic time scale), while the second does not have to be, though often is. By examining what causes the regimes to fail, one can better understand the role of the transients during all phases of weather regimes.

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Shuting Yang, Brian Reinhold, and Erland Källén

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Systematically recurrent, geographically fixed weather regimes forced by a single isolated mountain in a two-layer, high-resolution, quasigeostrophic model modified for the sphere are found to be robust phenomena. While the climatological stationary wave is often confined to (or has maximum amplitude in) the region just downstream of the orography, giving the appearance of a wave train propagating into the Tropics, the regional maximum centers of low-frequency variance appear around the hemisphere, giving the appearance of zonal resonance or some type of zonally confined propagation. This result is not anticipated in light of Rossby wave dispersion theory on the sphere. On the other hand, baroclinic disturbances developing on a meridional temperature gradient of finite extent force subtropical and polar easterlies as well as a sharpened midlatitude westerly jet, which provides a zonal waveguide (by refraction and/or reflection) for the Rossby waves. These conditions are favorable for the establishment of multiple weather regimes. The baroclinicity of the atmosphere is then continuously forcing a mean state that favors forced zonal propagation, counteracting the meridional dispersion generated by the spherical geometry alone. These ideas suggest that the multiple-equilibria theories may be more applicable to the atmosphere than originally suggested by linear dispersion theory on the sphere. It may also help explain why channel models work as well as they do even for the largest scales.

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Ake Johansson, Brian Reinhold, and Suranjana Saha

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The climate drift of various quantities associated with deep, planetary-scale, equilibrated, transient Rossby waves are estimated for the Southern Hemisphere extratropical summer as revealed by the DERF II (Dynamical Extended Range Forecasting) dataset. It is found that the vertical structures of these waves systematically become too baroclinic during the course of integration. There are two time scales associated with this climate drift. There is one very short time scale, estimated to be of the order of one day, when the waves become more barotropic. It is followed by a period when the wave baroclinicity monotonically increases, and after roughly 10 days the model structures appear to have reached their statistically equilibrated state.

In the meantime, the kinetic energy of the transient waves decreases substantially to roughly half the observed value. After this initial drop, however, the transient kinetic energy increases again, and it is not clear if an equilibrium value has been reached after 30 days, which is the limit of the DERF II dataset. This third time scale is not found in the quantities directly associated with the vertical structures per se, but it is hypothesized to be a consequence of these errors.

A theory is utilized that in a simplified way takes into account the processes that determine the vertical structure of baroclinic waves as well as their robustness as a means of understanding the processes leading to these errors. The implications from this theory are that the formulation and magnitude of the dissipative and diffusive processes in the model are the most likely problem, but there are other possibilities.

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Brian B. Reinhold and Raymond T. Pierrehumbert

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We hypothesize that periods of quasi-stationary behavior in the large scales are integrally associated with an organized behavior of the synoptic scales, thus the terminology “weather regime.” To investigate our hypothesis, we extend the model of Charney and Straus (1980) to include an additional wave in the zonal direction which is highly baroclinically unstable and can interact directly with the externally forced large-scale wave. We find that such a model aperiodically vacillates between two distinct weather regime states which are not located near any of the stationary equilibria of the large-scale state; thus, we cannot ascertain the qualitative behavior of the large-scale flow in our model knowing only the large-scale equilibria and their respective stabilities to perturbations on the scale of the equilibria. The state of the model flow may remain in either one of the two regime states for several synoptic periods. During each of the two regimes, the net transports by the transient disturbances are found to have consistent, zonally inhomogeneous structure, the form of which depends upon the regime. This result implies that the transports appear as a net additional external forcing mechanism to the large-scale wave, accounting for the differences between the time-mean regime state and the stationary equilibria.

Following the analysis procedure of Frederiksen (1979), we show that the observed structure of these net transports can be accounted for by the spatial modulation of the baroclinically most unstable eigenmodes by the large-scale wave. We then consider only the tendency equations of the large-scale variables where the effects of the transients are parameterized by solving the stability problem at each time step. We find that such a dynamical system possesses two absolutely stable “regime-equilibria” which are very close in phase space to the time mean states of the regimes appearing in the full model. We then demonstrate that the instantaneous component of the transients are also capable of transferring the state of the model flow from the attractor basin of one of the stable regime-equilibria to the attractor basin of the other. Our experiments thus indicate that the transients are important in determining the qualitative behavior of both the instantaneous and time-mean components of the large-scale flow in our system, and suggest that the very different short-range climates in the atmosphere can result from entirely internal processes.

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