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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
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Jun-Ichi Yano

ABSTRACT

Objectively identifying a phenomenon from observation is often difficult. This essay reflects upon this problem from a philosophical perspective by taking the Madden–Julian oscillation (MJO) as an example. I argue that it can be considered as a problem of Gestalt. This concept is introduced by closely following Ludwig Wittgenstein’s two philosophical works, Philosophical Investigations (Philosophische Untersuchungen) and Remarks on the Philosophy of Psychology(Bemerkungen über die Philosophie der Psychologie). Reflections upon the concept of Gestalt suggest why an objective identification of a phenomenon is so difficult. Importantly, the problem should not be reduced to that of “pattern recognition.” Rather a given phenomenon must be considered as a whole, including a question of a driving mechanism.

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Jun-Ichi Yano

Abstract

The present study shows by a linear hydrodynamic stability analysis that an unstable mixed-layer deep circulation can be generated in the dry convective well-mixed layer by the entrainment from the top. The newly identified instability arises under the two competing processes induced by the top entrainment: the destabilization by generating thermal perturbations and the damping by mechanical mixing. The former and the latter, respectively, dominate over the other in the limits of large and small scales. As a result, the instability is realized at the horizontal scales larger than the order of the mixed-layer depth (ca. 1 km), and the time scale for the growth is about 1 day. This study has been motivated from a question of whether the cloud-top entrainment instability (CTEI) can induce a transition of the stratocumulus-topped well-mixed boundary layer into trade cumulus. The present study intends to extend the previous studies based on the local parcel analyses to a full analysis based on the hydrodynamics. Unfortunately, being based on a dry formulation, the present result does not apply directly to the CTEI problem. Especially, the evaporative cooling is totally neglected. Nevertheless, the present result can still be applied to moist systems, to some extent, by redefining certain terms in the formulation.

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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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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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Jun-Ichi Yano
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John L. McBride

Abstract

A hypothesis is proposed that the seasonal evolution of sea surface temperature (SST) is the major forcing to control both the onset and the life cycle of the monsoon. A sensitive coupling of surface heat flux and cumulus convection is the central process and, in the current model, is realized by wind-induced surface-heat exchange. The model adopted is a shallow water analog in dynamics with two vertical levels for thermodynamics. The land forcing effect is neglected as a crucial simplification of the model experiments, along with the absence of the dynamical feedback to the SST in the model.

Experiments with steady SST forcing reveal the presence of three regimes of response. Weak SST forcing realizes two unsteady regimes, depending on the latitude of the forcing: (i) the supercluster regime, characterized by equatorially trapped eastward propagating convective coherencies akin to the Madden–Julian waves, and (ii) the monsoon regime, characterized by an intermittent planetary-scale standing convective oscillation at the subtropics. For a large SST forcing, a steady response is found similar to the earlier solutions of Matsuno, Webster, and Gill.

Experiments with a seasonally varying SST anomaly simulate both the sudden onset and the active–break cycle of the monsoon. In particular the onset is interpreted as the atmosphere undergoing a sudden switch from one dynamical regime to the other. The two unsteady regimes are seen to be in competition, as in the model they cannot coexist. Implications for the atmospheric monsoon are (i) that the SST forcing away from the equator should precede monsoon onset and (ii) that equatorial intraseasonal convective activity should be less active at the time of year when monsoon activity occurs away from the equator.

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Robert S. Plant
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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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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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