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- Author or Editor: Kerry A. Emanuel x
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Abstract
An expression is derived for the critical horizontal gradient of subcloud-layer θ e in radiative-convective equilibrium, sufficient for the onset of thermally direct, zonally symmetric circulations. This corresponds to zero absolute vorticity at the tropopause. The expression is then generalized to nonsymmetric flows under the approximation that the corresponding radiative-convective equilibrium state is in geostrophic balance. Scale analysis shows that actual moist entropy distributions cannot be far from critical in large-scale Hadley, Walker, and monsoon circulations. The balanced component of the surface winds can be calculated from the supercriticality of the surface θ e distribution, and the secondary circulation can then be estimated from the surface stress.
Abstract
An expression is derived for the critical horizontal gradient of subcloud-layer θ e in radiative-convective equilibrium, sufficient for the onset of thermally direct, zonally symmetric circulations. This corresponds to zero absolute vorticity at the tropopause. The expression is then generalized to nonsymmetric flows under the approximation that the corresponding radiative-convective equilibrium state is in geostrophic balance. Scale analysis shows that actual moist entropy distributions cannot be far from critical in large-scale Hadley, Walker, and monsoon circulations. The balanced component of the surface winds can be calculated from the supercriticality of the surface θ e distribution, and the secondary circulation can then be estimated from the surface stress.
Abstract
Recent observations of cumulus clouds strongly support the hypothesis of Squires (1958) that much of the mixing within such clouds is associated with downward propagating currents initiated near their tops. A similarity theory is here proposed to describe the properties of such currents; the use of similarity is defended on the basis of the observed and predicted scale of the downdrafts. The theory suggests that downward-propagating unsaturated thermals are pervasive throughout all but the largest convective clouds and that quasi-steady unsaturated downdraft plumes may exist in the lower portions of cumulonimbi. In addition to providing a reasonable explanation for the microstructure of and liquid water distribution within cumulus clouds, the theory appears to account for certain severe convective phenomena, including down-bursts. A new but related cloud instability is proposed to account for the occurrence of mamma.
Abstract
Recent observations of cumulus clouds strongly support the hypothesis of Squires (1958) that much of the mixing within such clouds is associated with downward propagating currents initiated near their tops. A similarity theory is here proposed to describe the properties of such currents; the use of similarity is defended on the basis of the observed and predicted scale of the downdrafts. The theory suggests that downward-propagating unsaturated thermals are pervasive throughout all but the largest convective clouds and that quasi-steady unsaturated downdraft plumes may exist in the lower portions of cumulonimbi. In addition to providing a reasonable explanation for the microstructure of and liquid water distribution within cumulus clouds, the theory appears to account for certain severe convective phenomena, including down-bursts. A new but related cloud instability is proposed to account for the occurrence of mamma.
Abstract
Numerous budget studies of organized persistent systems of convective clouds outside the tropics suggest that circulations of mesoscale proportions are important in supplying moisture to the convective clouds, though the dynamical nature of mesoscale flows remains poorly defined. In Part I (Emanuel, 1979, hereafter referred to as Part I) it is demonstrated that circulations resulting from symmetric instability of shear flows in rotating fluids have a fundamentally mesoscale character in that both ambient rotation and ageostrophic advection are necessary for instability. The results of Part I are here extended to include the effects of latent heat release in a conditionally unstable atmosphere, using the formalism of the CISK approach. It is found that the presence of shear parallel to the wave fronts introduces new wave-CISK modes which are not strongly dependent on the specified vertical structure of the cumulus heating. The new baroclinic modes are of mesoscale dimensions, have growth rates proportional to the vertical shear of the ambient flow and propagate toward the warm air. These modes compare favorably with observations of squall lines within baroclinic flows.
Abstract
Numerous budget studies of organized persistent systems of convective clouds outside the tropics suggest that circulations of mesoscale proportions are important in supplying moisture to the convective clouds, though the dynamical nature of mesoscale flows remains poorly defined. In Part I (Emanuel, 1979, hereafter referred to as Part I) it is demonstrated that circulations resulting from symmetric instability of shear flows in rotating fluids have a fundamentally mesoscale character in that both ambient rotation and ageostrophic advection are necessary for instability. The results of Part I are here extended to include the effects of latent heat release in a conditionally unstable atmosphere, using the formalism of the CISK approach. It is found that the presence of shear parallel to the wave fronts introduces new wave-CISK modes which are not strongly dependent on the specified vertical structure of the cumulus heating. The new baroclinic modes are of mesoscale dimensions, have growth rates proportional to the vertical shear of the ambient flow and propagate toward the warm air. These modes compare favorably with observations of squall lines within baroclinic flows.
Abstract
A simple model describing the slantwise ascent of a two-dimensional horizontal air tube Subject to moist symmetric instability is developed under the assumptions that the Froude number is small and that mixing is absent. It is shown that, in general, the horizontal velocities attained by the tube are comparable to those of the mean flow and that vertical velocities of up to a few meters per second are possible. The tube ascends slantwise in such a way that its buoyancy remains nearly zero, unless the environment is my very nearly moist adiabatic, in which case ascent at an angle of 45° to the vertical is preferred. Results of the analysis support the contentions of Bennetts and Hoskins and Emanual that moist symmetric instability is the cause of some mesoscale rainbands. In a companion paper, it is demonstrated that the stability of the moist baroclinic atmosphere to two-dimensional slantwise displacements of arbitrary magnitude can be approximately assessed by reversibly lifting parcel along surfaces of constant angular momentum and comparing their density with that of their environment.
Abstract
A simple model describing the slantwise ascent of a two-dimensional horizontal air tube Subject to moist symmetric instability is developed under the assumptions that the Froude number is small and that mixing is absent. It is shown that, in general, the horizontal velocities attained by the tube are comparable to those of the mean flow and that vertical velocities of up to a few meters per second are possible. The tube ascends slantwise in such a way that its buoyancy remains nearly zero, unless the environment is my very nearly moist adiabatic, in which case ascent at an angle of 45° to the vertical is preferred. Results of the analysis support the contentions of Bennetts and Hoskins and Emanual that moist symmetric instability is the cause of some mesoscale rainbands. In a companion paper, it is demonstrated that the stability of the moist baroclinic atmosphere to two-dimensional slantwise displacements of arbitrary magnitude can be approximately assessed by reversibly lifting parcel along surfaces of constant angular momentum and comparing their density with that of their environment.
Abstract
We have constructed a simple, balanced, axisymmetric model as a means of understanding the existence of the threshold amplitude for tropical cyclogenesis discovered by Rotunno and Emanuel. The model is similar to Ooyama's but is phrased in Schubert and Hack's potential radius coordinates.
The essential difference between this and other balanced models lies in the representation of convective clouds. In the present model the cumulus updraft mass flux depends simply and directly on the buoyancy (on angular momentum surfaces) of lifted subcloud-layer air and is not explicitly constrained by moisture convergence. The downdraft mass flux is equal to the updraft flux multiplied by (1−ε), where ε is the precipitation efficiency. The complete spectrum of convective clouds in nature is here represented by two extremes: deep clouds with a precipitation efficiency of one, and shallow, nonprecipitating clouds. The former stabilize the atmosphere both by heating the free atmosphere and drying out the subcloud layer, whereas the shallow clouds stabilize only through drying of the subcloud layer. The two cloud types may coexist. In the crude vertical structure of the model, shallow clouds have the same thermodynamic effect as precipitation-induced downdrafts. Model runs without shallow clouds but with precipitation-induced downdrafts produce the same qualitative features as the runs with shallow clouds.
The existence of low-precipitation-efficiency clouds is crucial to the model hurricane development. When a weak vortex is placed in contact with the sea surface, the enhanced surface fluxes together with adiabatic cooling induced by Ekman pumping destabilize the atmosphere. The initial convective clouds that form have relatively low precipitation efficiency and thus only partially compensate for the adiabatic cooling associated with the Ekman pumping. They do, however, import low θ e air into the subcloud layer. The vortex core therefore cools and the vortex decays. Only when the anomalous surface fluxes are strong enough, and /or the middle troposphere humid enough does the subcloud layer θ e increase, and with it the temperature of the core and the amplitude of the cyclone.
The low-precipitation-efficiency clouds play a dual role, however. Once amplification begins, these clouds continue to dominate the convection outside the eyewall, keeping the boundary layer θ e relatively low. Without low-precipitation-efficiency clouds, large heating occurs in the outer region and the vortex expands and weakens.
Abstract
We have constructed a simple, balanced, axisymmetric model as a means of understanding the existence of the threshold amplitude for tropical cyclogenesis discovered by Rotunno and Emanuel. The model is similar to Ooyama's but is phrased in Schubert and Hack's potential radius coordinates.
The essential difference between this and other balanced models lies in the representation of convective clouds. In the present model the cumulus updraft mass flux depends simply and directly on the buoyancy (on angular momentum surfaces) of lifted subcloud-layer air and is not explicitly constrained by moisture convergence. The downdraft mass flux is equal to the updraft flux multiplied by (1−ε), where ε is the precipitation efficiency. The complete spectrum of convective clouds in nature is here represented by two extremes: deep clouds with a precipitation efficiency of one, and shallow, nonprecipitating clouds. The former stabilize the atmosphere both by heating the free atmosphere and drying out the subcloud layer, whereas the shallow clouds stabilize only through drying of the subcloud layer. The two cloud types may coexist. In the crude vertical structure of the model, shallow clouds have the same thermodynamic effect as precipitation-induced downdrafts. Model runs without shallow clouds but with precipitation-induced downdrafts produce the same qualitative features as the runs with shallow clouds.
The existence of low-precipitation-efficiency clouds is crucial to the model hurricane development. When a weak vortex is placed in contact with the sea surface, the enhanced surface fluxes together with adiabatic cooling induced by Ekman pumping destabilize the atmosphere. The initial convective clouds that form have relatively low precipitation efficiency and thus only partially compensate for the adiabatic cooling associated with the Ekman pumping. They do, however, import low θ e air into the subcloud layer. The vortex core therefore cools and the vortex decays. Only when the anomalous surface fluxes are strong enough, and /or the middle troposphere humid enough does the subcloud layer θ e increase, and with it the temperature of the core and the amplitude of the cyclone.
The low-precipitation-efficiency clouds play a dual role, however. Once amplification begins, these clouds continue to dominate the convection outside the eyewall, keeping the boundary layer θ e relatively low. Without low-precipitation-efficiency clouds, large heating occurs in the outer region and the vortex expands and weakens.
Abstract
Observations of individual convective clouds reveal an extraordinary degree of inhomogeneity, with much of the vertical transport accomplished by subcloud-scale drafts. In view of these observations, a representation of moist convective transports for use in large-scale models is constructed, in which the fundamental entities are these subcloud-scale drafts rather than the clouds themselves. The transport by these small-scale drafts is idealized as follows. Air from the subcloud layer is lifted to each level i between cloud base and the level of neutral buoyancy for undilute air. A fraction (ε i ) of the condensed water is then converted to precipitation, which falls and partially or completely evaporates in an unsaturated downdraft. The remaining cloudy air is then assumed to form a uniform spectrum of mixtures with environmental air at level i; these mixtures ascend or descend according to their buoyancy.
The updraft mass fluxes Mi are represented as vertical velocities determined by the amount of convective available potential energy for undilute ascent to level i, multiplied by fractional areas σ i , which are in turn determined in such a way as to drive the mass fluxes toward a state of quasi-equilibrium with the large-scale forcing. The downdraft mass fluxes are unique functions of the Mi , so that determination of the Mi closes the System.
The main closure parameters in this scheme are the parcel precipitation efficiencies, ε i , which determine the fraction of condensed water in a parcel lifted to level i that is converted to precipitation, and the fraction σ i s of precipitation that falls through unsaturated air. These may be specified as functions of altitude, temperature, adiabatic water content, and so on, and are regarded as explicitly determined by cloud microphysical processes. Specification of these parameters determines the vertical profiles of heating and moistening by cloud processes, given the large-scale (explicitly resolved) forcing. It is argued here that accurate calculation of the moistening by cumulus clouds cannot proceed without addressing the microphysics of precipitation formation, fallout, and reevaporation.
One-dimensional radiative-convective equilibrium experiment with this scheme produce reasonable profiles of buoyancy and relative humidity. When large-scale descent is imposed, a trade-cumulus regime is produced, including a trade inversion and mixing-line structure in the cloud layer.
Abstract
Observations of individual convective clouds reveal an extraordinary degree of inhomogeneity, with much of the vertical transport accomplished by subcloud-scale drafts. In view of these observations, a representation of moist convective transports for use in large-scale models is constructed, in which the fundamental entities are these subcloud-scale drafts rather than the clouds themselves. The transport by these small-scale drafts is idealized as follows. Air from the subcloud layer is lifted to each level i between cloud base and the level of neutral buoyancy for undilute air. A fraction (ε i ) of the condensed water is then converted to precipitation, which falls and partially or completely evaporates in an unsaturated downdraft. The remaining cloudy air is then assumed to form a uniform spectrum of mixtures with environmental air at level i; these mixtures ascend or descend according to their buoyancy.
The updraft mass fluxes Mi are represented as vertical velocities determined by the amount of convective available potential energy for undilute ascent to level i, multiplied by fractional areas σ i , which are in turn determined in such a way as to drive the mass fluxes toward a state of quasi-equilibrium with the large-scale forcing. The downdraft mass fluxes are unique functions of the Mi , so that determination of the Mi closes the System.
The main closure parameters in this scheme are the parcel precipitation efficiencies, ε i , which determine the fraction of condensed water in a parcel lifted to level i that is converted to precipitation, and the fraction σ i s of precipitation that falls through unsaturated air. These may be specified as functions of altitude, temperature, adiabatic water content, and so on, and are regarded as explicitly determined by cloud microphysical processes. Specification of these parameters determines the vertical profiles of heating and moistening by cloud processes, given the large-scale (explicitly resolved) forcing. It is argued here that accurate calculation of the moistening by cumulus clouds cannot proceed without addressing the microphysics of precipitation formation, fallout, and reevaporation.
One-dimensional radiative-convective equilibrium experiment with this scheme produce reasonable profiles of buoyancy and relative humidity. When large-scale descent is imposed, a trade-cumulus regime is produced, including a trade inversion and mixing-line structure in the cloud layer.
Abstract
An exact equation governing the maximum possible pressure fall in steady tropical cyclones is developed, accounting for the full effects of gaseous and condensed water on density and thermodynamics. The equation is also derived from Carnot's principle. We demonstrate the existence of critical conditions beyond which no solution for the minimum central pressure exists and speculate on the nature of hurricanes in the supercritical regime.
Abstract
An exact equation governing the maximum possible pressure fall in steady tropical cyclones is developed, accounting for the full effects of gaseous and condensed water on density and thermodynamics. The equation is also derived from Carnot's principle. We demonstrate the existence of critical conditions beyond which no solution for the minimum central pressure exists and speculate on the nature of hurricanes in the supercritical regime.
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Abstract
We present a linear model of intraseasonal oscillations produced by the interaction of an atmosphere on an equatorial Beta-plane with a fixed ocean. Convection is treated as a means of rapidly redistributing in the vertical heat acquired from the sea surface, rather than as a heat source in and of itself. The model produces a spectrum of equatorially trapped oscillating instabilities, among which is an eastward-propagating wavenumber 1 disturbance with an intrinsic phase speed in the range of 4–20 m s−1, depending on the mean zonal wind, the surface exchange coefficients, the air-sea equivalent potential temperature difference, and the difference of absolute temperature across the depth of the lower troposphere. The three-dimensional structure of this mode is in excellent agreement with observations and recent numerical experiments concerning the 30–60 day oscillation. The phase speed and growth rate of the disturbances depend only on conditions at the equator, while their meridional structure varies with meridional gradients of mean zonal wind, sea surface temperature, and the depth of the moist convective layer. Momentum fluxes by the waves may serve to maintain mean easterlies at the equator. The model also predicts nongeostrophic oscillations with generally shorter periods of around one week.
Abstract
We present a linear model of intraseasonal oscillations produced by the interaction of an atmosphere on an equatorial Beta-plane with a fixed ocean. Convection is treated as a means of rapidly redistributing in the vertical heat acquired from the sea surface, rather than as a heat source in and of itself. The model produces a spectrum of equatorially trapped oscillating instabilities, among which is an eastward-propagating wavenumber 1 disturbance with an intrinsic phase speed in the range of 4–20 m s−1, depending on the mean zonal wind, the surface exchange coefficients, the air-sea equivalent potential temperature difference, and the difference of absolute temperature across the depth of the lower troposphere. The three-dimensional structure of this mode is in excellent agreement with observations and recent numerical experiments concerning the 30–60 day oscillation. The phase speed and growth rate of the disturbances depend only on conditions at the equator, while their meridional structure varies with meridional gradients of mean zonal wind, sea surface temperature, and the depth of the moist convective layer. Momentum fluxes by the waves may serve to maintain mean easterlies at the equator. The model also predicts nongeostrophic oscillations with generally shorter periods of around one week.
Abstract
Observations and numerical simulators of tropical cyclones show that evaporation from the sea surface is essential to the development of reasonably intense storms. On the other hand, the CISK hypothesis, in the form originally advanced by Charney and Eliassen, holds that initial development results from the organized release of preexisting conditional instability. In this series of papers, we explore the relative importance of ambient conditional instability and air-sea latent and sensible heat transfer in both the development and maintenance of tropical cyclones using highly idealized models. In particular, we advance the hypothesis that the intensification and maintenance of tropical cyclones depend exclusively on self-induced heat transfer from the ocean. In this sense, these storms may be regarded as resulting from a finite amplitude air-sea interaction instability rather than from a linear instability involving ambient potential buoyancy. In the present paper, we attempt to show that reasonably intense cyclones may be maintained in a steady state without conditional instability of ambient air. In Part II we will demonstrate that weak but finite-amplitude axisymmetric disturbances may intensify in a conditionally neutral environment.
Abstract
Observations and numerical simulators of tropical cyclones show that evaporation from the sea surface is essential to the development of reasonably intense storms. On the other hand, the CISK hypothesis, in the form originally advanced by Charney and Eliassen, holds that initial development results from the organized release of preexisting conditional instability. In this series of papers, we explore the relative importance of ambient conditional instability and air-sea latent and sensible heat transfer in both the development and maintenance of tropical cyclones using highly idealized models. In particular, we advance the hypothesis that the intensification and maintenance of tropical cyclones depend exclusively on self-induced heat transfer from the ocean. In this sense, these storms may be regarded as resulting from a finite amplitude air-sea interaction instability rather than from a linear instability involving ambient potential buoyancy. In the present paper, we attempt to show that reasonably intense cyclones may be maintained in a steady state without conditional instability of ambient air. In Part II we will demonstrate that weak but finite-amplitude axisymmetric disturbances may intensify in a conditionally neutral environment.
