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Jun-Ichi Yano

Abstract

Arakawa and Schubert’s cumulus parameterization is formulated under the two asymptotic limits: σ → 0 and τ c/τ L → 0, where σ is the fractional area occupied by cumulus convection, and τ c and τ L are the characteristic timescales for convection and large scales, respectively. The present note shows that the two asymptotic limits tend to contradict each other, so that the smallness of these two quantities is established only under a compromise. This contradiction is formally established by referring to the heat engine theories by Rennó and Ingersoll, and by Emanuel and Bister. The climatological estimate for σ indicates that the timescale separation is only marginally satisfied with respect to the tropical planetary-scale circulation.

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Jun-Ichi Yano

Abstract

The basic idea of the maximum entropy principle is presented in a succinct, self-contained manner. The presentation points out some misunderstandings on this principle by Wu and McFarquhar. Namely, the principle does not suffer from the problem of a lack of invariance by change of the dependent variable; thus, it does not lead to a need to introduce the relative entropy as suggested by Wu and McFarquhar. The principle is valid only with a proper choice of a dependent variable, called a restriction variable, for a distribution. Although different results may be obtained with the other variables obtained by transforming the restriction variable, these results are simply meaningless. A relative entropy may be used instead of a standard entropy. However, the former does not lead to any new results unobtainable by the latter.

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Jun-Ichi Yano
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Jun-Ichi Yano and Kerry Emanuel

Abstract

The Wind-Induced Sea–Air Heat Exchange (WISHE) Model of the 30–60-day oscillation developed by Emanuel is improved by adding downdrafts to the representation of convection and by coupling the troposphere to a passive stratosphere into which equatorial waves may propagate. The downdrafts are associated with a precipitation efficiency that is less than unity; this means that not all of the adiabatic cooling due to ascent in a wave disturbance can be countered by condensation heating, and the wave therefore “feels” a stable stratification as in the work of Neelin et al. As in the latter's model, growth rates of eastward-propagating Kelvin-like modes asymptote to a constant at large zonal wavenumber.

The presence of the stratosphere is shown to have a profound effect on the unstable tropospheric modes. As the upward group velocity is larger for smaller zonal wavelengths, short waves in the troposphere are strongly damped and the most unstable mode shifts to low wavenumbers.

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Jun-Ichi Yano and Robert Plant

Abstract

The present paper presents a simple theory for the transformation of nonprecipitating, shallow convection into precipitating, deep convective clouds. To make the pertinent point a much idealized system is considered, consisting only of shallow and deep convection without large-scale forcing. The transformation is described by an explicit coupling between these two types of convection. Shallow convection moistens and cools the atmosphere, whereas deep convection dries and warms the atmosphere, leading to destabilization and stabilization, respectively. Consequently, in their own stand-alone modes, shallow convection perpetually grows, whereas deep convection simply damps: the former never reaches equilibrium, and the latter is never spontaneously generated. Coupling the modes together is the only way to reconcile these undesirable separate tendencies, so that the convective system as a whole can remain in a stable periodic state under this idealized setting. Such coupling is a key missing element in current global atmospheric models. The energy cycle description used herein is fully consistent with the original formulation by Arakawa and Schubert, and is suitable for direct implementation into models using a mass flux parameterization. The coupling would alleviate current problems with the representation of these two types of convection in numerical models. The present theory also provides a pertinent framework for analyzing large-eddy simulations and cloud-resolving modeling.

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Jun-Ichi Yano and Marine Bonazzola

Abstract

A systematic scale analysis is performed for large-scale dynamics over the tropics. It is identified that two regimes are competing: 1) a dynamics characterized by balance between the vertical advection term and diabatic heating in the thermodynamic equation, realized at horizontal scales less than L ∼ 103 km given a velocity scale U ∼ 10 m s−1, and 2) a linear equatorial wave dynamics modulated by convective diabatic heating, realized at scales larger than L ∼ 3 × 103 km given U ∼ 3 m s−1. Under the first dynamic regime (balanced), the system may be approximated as nondivergent to leading order in asymptotic expansion, as originally pointed out by Charney.

Inherent subtleties of scale analysis at large scales for the tropical atmosphere are emphasized. The subtleties chiefly arise from a strong sensitivity of the nondimensional β parameter to the horizontal scale. This amounts to qualitatively different dynamic regimes for scales differing only by a factor of 3, as summarized above. Because any regime under asymptotic expansion may have a wider applicability than a formal scale analysis would suggest, the question of which one of the two identified regimes dominates can be answered only after extensive modeling and observational studies. Preliminary data analysis suggests that the balanced dynamics, originally proposed by Sobel, Nilsson, and Polvani, is relevant for a wider range than the strict scale analysis suggests.

A rather surprising conclusion from the present analysis is a likely persistence of balanced dynamics toward scales as small as the mesoscale L ∼ 102 km. Leading-order nondivergence also becomes more likely the case for the smaller scales because otherwise the required diabatic heating rate becomes excessive compared to observations by increasing inversely proportionally with decreasing horizontal scales.

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Jun-Ichi Yano and Mitchell W. Moncrieff

Abstract

The vertical transport of horizontal momentum by organized convection is a prominent process, yet its impact on the large-scale atmospheric circulation has not even been qualitatively assessed. In order to examine this problem in a simple framework the authors incorporate a nonlinear dynamical model of convective momentum flux into a linear model of the large-scale tropical atmosphere. This model has previously been used to investigate the WISHE (wind-induced surface-heat exchange) instability.

In order to implement the dynamically determined fluxes as a parameterization, a closure assumption is required to relate the relevant mesoscale parameters to the large-scale variables. The most straightforward method is to relate the low-level large-scale pressure (p L) to the mesoscale pressure perturbation (p M), which is linked to the mesoscale momentum flux by the dynamical model. The mesoscale momentum transport under this closure reduces the effective pressure gradient in the large-scale momentum equation and, consequently, the effective stratification. A sufficiently large p M may even cause an effectively unstable stratification (convective instability by mesoscale momentum transport), which is marginally realizable according to a scale analysis.

In general, the WISHE instability is suppressed by the mesoscale momentum flux under this closure because a larger effective stratification can provide a more efficient mass redistribution and, in turn, a larger potential energy for WISHE. This demonstrates that momentum transport by mesoscale convective systems can substantially modify the large-scale tropical dynamics through the WISHE mechanism.

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Robert S. Plant and Jun-Ichi Yano

Abstract

In a recent paper, Wagner and Graf derived a population evolution equation for an ensemble of convective plumes, an analog with the Lotka–Volterra equation, from the energy equations for convective plumes provided by Arakawa and Schubert. Although their proposal is interesting, as the present note shows, there are some problems with their derivation.

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Danyang Wang, Jun-Ichi Yano, and Yanluan Lin

Abstract

The vorticity variability associated with the Madden–Julian oscillation (MJO) is examined. The analysis is focused on the 150-hPa pressure level, because a clear dipolar-vortex signal, reminiscent of the theoretically proposed strongly nonlinear solitary Rossby wave solution (albeit with the opposite sign), is seen in raw data at that level. A local empirical orthogonal function (EOF) analysis over the equatorial region of the Eastern Hemisphere (0°–180°E) identifies the two principal components representing an eastward propagation of a dipolar vortex trapped to the equator. Association of this propagation structure with the moist convective variability of the MJO is demonstrated by regressing the outgoing longwave radiation (OLR) against this EOF pair. The obtained evolution of the OLR field is similar to the one obtained by a direct application of the EOF to the OLR. A link of the local vorticity variability associated with the MJO to the global dynamics is further investigated by regressing the global vorticity field against the time series of the identified local EOF pair. The Rossby wave trains tend to propagate toward the Indian Ocean from higher latitudes, just prior to an initiation of the MJO, and in turn, they propagate back toward the higher latitudes from the MJO active region over the Indian Ocean. A three-dimensional regression reveals an equivalent barotropic structure of the MJO vortex pair with the signs opposite to those at 150 hPa underneath. A vertical normal mode analysis finds that this vertical structure is dominated by the equivalent height of about 10 km.

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