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- Author or Editor: James J. Hack x

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## Abstract

The implied meridional ocean energy transport diagnosed from uncoupled integrations of two atmospheric general circulation models—the National Center for Atmospheric Research Community Climate Model versions 2 and 3 (CCM2 and CCM3)—shows radically different transport characteristics throughout much of the Southern Hemisphere. The CCM2 simulation requires an equatorward transport of energy by the oceans, and the CCM3 exhibits a poleward energy transport requirement, very similar to what is derived from observational analyses. Previous studies have suggested that errors in the implied ocean energy transport are largely attributable to errors in the simulated cloud radiative forcing. The results of this analysis show that although the proper simulation of the radiative effects of clouds is likely to be a necessary condition for realistic meridional ocean energy transport, it is not sufficient. Important changes in the CCM3 equatorial surface latent heat fluxes, associated with a deep formulation for parameterized moist convection, are primarily responsible for the improved ocean energy transport, where this change in the surface energy budget is much more weakly reflected in top-of-atmosphere differences in cloud radiative forcing.

## Abstract

The implied meridional ocean energy transport diagnosed from uncoupled integrations of two atmospheric general circulation models—the National Center for Atmospheric Research Community Climate Model versions 2 and 3 (CCM2 and CCM3)—shows radically different transport characteristics throughout much of the Southern Hemisphere. The CCM2 simulation requires an equatorward transport of energy by the oceans, and the CCM3 exhibits a poleward energy transport requirement, very similar to what is derived from observational analyses. Previous studies have suggested that errors in the implied ocean energy transport are largely attributable to errors in the simulated cloud radiative forcing. The results of this analysis show that although the proper simulation of the radiative effects of clouds is likely to be a necessary condition for realistic meridional ocean energy transport, it is not sufficient. Important changes in the CCM3 equatorial surface latent heat fluxes, associated with a deep formulation for parameterized moist convection, are primarily responsible for the improved ocean energy transport, where this change in the surface energy budget is much more weakly reflected in top-of-atmosphere differences in cloud radiative forcing.

## Abstract

The accurate treatment of clouds and their radiative properties is widely regarded to be among the most important problems facing global climate modeling. A number of the more serious systematic simulation biases in the NCAR Community Climate Model (CCM2) appear to be related to deficiencies in the treatment of cloud optical properties. In this paper, a simple diagnostic parameterization for cloud liquid water is presented. The sensitivity of the simulated climate to this alternative formulation, both in terms of mean climate metrics and measures of the climate system response, is illustrated. Resulting simulations show significant reductions in CCM2 systematic biases, particularly with respect to surface temperature, precipitation, and extratropical geopotential height-field anomalies. Many aspects of the simulated response to ENSO forcing are also substantially improved.

## Abstract

The accurate treatment of clouds and their radiative properties is widely regarded to be among the most important problems facing global climate modeling. A number of the more serious systematic simulation biases in the NCAR Community Climate Model (CCM2) appear to be related to deficiencies in the treatment of cloud optical properties. In this paper, a simple diagnostic parameterization for cloud liquid water is presented. The sensitivity of the simulated climate to this alternative formulation, both in terms of mean climate metrics and measures of the climate system response, is illustrated. Resulting simulations show significant reductions in CCM2 systematic biases, particularly with respect to surface temperature, precipitation, and extratropical geopotential height-field anomalies. Many aspects of the simulated response to ENSO forcing are also substantially improved.

## Abstract

Under certain circumstances a large fraction of the energy generated by the release of latent heat in a tropical cyclone cab be partitioned to gravity-inertia wave motion rather than to balanced flow. In this way most of the generated energy is radiated away to the far field. If a primitive equation tropical cyclone model is to successfully simulate this process, its lateral boundary condition must be able to transmit the gravity-inertia wave energy generated in the interior of the model. Most present models seem deficient in this regard. As an improvement we explore the possibility of using a cylindrical, pure gravity wave radiation condition. Since there is a wide range of gravity wave phase velocities in a stratified atmosphere, it is necessary to apply the radiation condition vertical mode by vertical mode rather than level by level. The usefulness of this radiation condition and several other conditions in present use is tested both by a reflectivity analysis and by simple numerical time integrations.

## Abstract

Under certain circumstances a large fraction of the energy generated by the release of latent heat in a tropical cyclone cab be partitioned to gravity-inertia wave motion rather than to balanced flow. In this way most of the generated energy is radiated away to the far field. If a primitive equation tropical cyclone model is to successfully simulate this process, its lateral boundary condition must be able to transmit the gravity-inertia wave energy generated in the interior of the model. Most present models seem deficient in this regard. As an improvement we explore the possibility of using a cylindrical, pure gravity wave radiation condition. Since there is a wide range of gravity wave phase velocities in a stratified atmosphere, it is necessary to apply the radiation condition vertical mode by vertical mode rather than level by level. The usefulness of this radiation condition and several other conditions in present use is tested both by a reflectivity analysis and by simple numerical time integrations.

## Abstract

We consider the frictionless, axisymmetric, balanced flow occurring in a thermally forced vortex on an *f*-plane. Following Eliassen (1952) we derive the diagnostic equation for the forced secondary circulation. This equation contains the spatially varying coefficients *A* (static stability), *B* (baroclinity), *C* (inertial stability), and the thermal forcing *Q*. Assuming that *A* is a constant, *B* = 0, and that *C* and *Q* are piecewise constant functions of radius, we obtain analytical solutions for the forced secondary circulation. The solutions illustrate the following points. 1) For a given *Q* an increase in inertial stability leads to a decrease in the forced secondary circulation and a change in the radial distribution of local temperature change, with enhanced ∂θ/∂*t*; in the region of high inertial stability. 2) Lower tropospheric tangential wind accelerations are larger inside the radius of maximum wind, which leads to a collapse of the radius of maximum wind. 3) The fraction of *Q* which ends up as ∂θ/∂*t*; increases during the tropical cyclone development, particularly if the horizontal extent of *Q* is small and close to the region of high inertial stability. 4) One can regard the formation of an eye as a process which tends to stabilize the vortex since it removes *Q* from the protected, highly stable inner region.

## Abstract

We consider the frictionless, axisymmetric, balanced flow occurring in a thermally forced vortex on an *f*-plane. Following Eliassen (1952) we derive the diagnostic equation for the forced secondary circulation. This equation contains the spatially varying coefficients *A* (static stability), *B* (baroclinity), *C* (inertial stability), and the thermal forcing *Q*. Assuming that *A* is a constant, *B* = 0, and that *C* and *Q* are piecewise constant functions of radius, we obtain analytical solutions for the forced secondary circulation. The solutions illustrate the following points. 1) For a given *Q* an increase in inertial stability leads to a decrease in the forced secondary circulation and a change in the radial distribution of local temperature change, with enhanced ∂θ/∂*t*; in the region of high inertial stability. 2) Lower tropospheric tangential wind accelerations are larger inside the radius of maximum wind, which leads to a collapse of the radius of maximum wind. 3) The fraction of *Q* which ends up as ∂θ/∂*t*; increases during the tropical cyclone development, particularly if the horizontal extent of *Q* is small and close to the region of high inertial stability. 4) One can regard the formation of an eye as a process which tends to stabilize the vortex since it removes *Q* from the protected, highly stable inner region.

## Abstract

Using an axisymmetric primitive tropical cyclone model, we first illustrate the way in which nonlinear processes contribute to the development of an atmospheric vortex. These numerical experiment show that nonlinearities allow a given diabatic beat source to induce larger tangential wind (and kinetic energy) changes as the vortex develops and the inertial stability becomes large. In an attempt to gain a deeper theoretical understanding of this process, we consider the energy cycle in the balanced vortex equations of Eliassen. The temporal behavior of the total potential energy *P* is governed by *dP*/*dt*=*H*−*C* where *H* is the rate of generation of total potential energy by diabatic heating, and *C* is the rate of conversion to kinetic energy. We define a time-dependent system efficiency parameter as η¯(*t*)=*C*/*H*. Then, using the dynamical simplifications of balanced vortex theory, we express η¯(*t*) as a weighted average of a dynamic efficiency factor η(*r*, *z*, *t*). The dynamic efficiency factor is a measure of the efficacy of diabatic heating at any point in generating kinetic energy and can be determined by solving a second-order partial differential equation whose coefficients and right-hand side depend only on the instantaneous vortex structure. The diagnostic quantities η¯(*t*) and η(*r*, *z*, *t*) are utilized in the analysis of several balanced numerical experiments with different vertical and radial distributions of a diabatic heat source.

## Abstract

Using an axisymmetric primitive tropical cyclone model, we first illustrate the way in which nonlinear processes contribute to the development of an atmospheric vortex. These numerical experiment show that nonlinearities allow a given diabatic beat source to induce larger tangential wind (and kinetic energy) changes as the vortex develops and the inertial stability becomes large. In an attempt to gain a deeper theoretical understanding of this process, we consider the energy cycle in the balanced vortex equations of Eliassen. The temporal behavior of the total potential energy *P* is governed by *dP*/*dt*=*H*−*C* where *H* is the rate of generation of total potential energy by diabatic heating, and *C* is the rate of conversion to kinetic energy. We define a time-dependent system efficiency parameter as η¯(*t*)=*C*/*H*. Then, using the dynamical simplifications of balanced vortex theory, we express η¯(*t*) as a weighted average of a dynamic efficiency factor η(*r*, *z*, *t*). The dynamic efficiency factor is a measure of the efficacy of diabatic heating at any point in generating kinetic energy and can be determined by solving a second-order partial differential equation whose coefficients and right-hand side depend only on the instantaneous vortex structure. The diagnostic quantities η¯(*t*) and η(*r*, *z*, *t*) are utilized in the analysis of several balanced numerical experiments with different vertical and radial distributions of a diabatic heat source.

## Abstract

Single-column models (SCMs) have been extensively promoted in recent years as an effective means to develop and test physical parameterizations targeted for more complex three-dimensional climate models. Although there are some clear advantages associated with single-column modeling, there are also some significant disadvantages, including the absence of large-scale feedbacks. Basic limitations of an SCM framework can make it difficult to interpret solutions, and at times contribute to rather striking failures to identify even first-order sensitivities as they would be observed in a global climate simulation. This manuscript will focus on one of the basic experimental approaches currently exploited by the single-column modeling community, with an emphasis on establishing the inherent uncertainties in the numerical solutions. The analysis will employ the standard physics package from the NCAR CCM3 and will illustrate the nature of solution uncertainties that arise from nonlinearities in parameterized physics. The results of this study suggest the need to make use of an ensemble methodology when conducting single-column modeling investigations.

## Abstract

Single-column models (SCMs) have been extensively promoted in recent years as an effective means to develop and test physical parameterizations targeted for more complex three-dimensional climate models. Although there are some clear advantages associated with single-column modeling, there are also some significant disadvantages, including the absence of large-scale feedbacks. Basic limitations of an SCM framework can make it difficult to interpret solutions, and at times contribute to rather striking failures to identify even first-order sensitivities as they would be observed in a global climate simulation. This manuscript will focus on one of the basic experimental approaches currently exploited by the single-column modeling community, with an emphasis on establishing the inherent uncertainties in the numerical solutions. The analysis will employ the standard physics package from the NCAR CCM3 and will illustrate the nature of solution uncertainties that arise from nonlinearities in parameterized physics. The results of this study suggest the need to make use of an ensemble methodology when conducting single-column modeling investigations.

## Abstract

We consider the axisymmetric balanced flow occurring in a thermally forced vortex in which the frictional inflow is confined to a thin boundary layer. Above the boundary layer the absolute angular momentum ½*fR*
^{2}=*rv*+½*fr*
^{2} is conserved. We refer to *R* as the potential radius, i.e., the radius to which a particle must be moved (conserving absolute angular momentum) in order to change its tangential component *v* to zero. Using *R* as one of the dependent variables we review the equations of the Eliassen balanced vortex model.

We next reverse the roles of the actual radius *r* and the potential radius *R*, i.e., we treat *R* as an independent variable and *r* as a dependent variable. Introducing transformed components (*u*
^{*}, *w*
^{*}) of the transverse circulation we obtain the transformed Eliassen balanced vortex equations, which differ from the original equations in the following respects: 1) the radial coordinate is *R* which results in a stretching of positive relative vorticity regions and a shrinking of negative relative vorticity regions; 2) the thermodynamic equation contains only the transverse circulation component *w*
^{*}, the coefficient of which is the potential vorticity *q*; 3) the equation for *r* contains only the transverse circulation component *u*
^{*}; 4) the transverse circulation equation contains only two vortex structure functions, the potential vorticity *q* and the inertial stability *s*, where *pq*=(ζ/*f*)(*g*/θ_{0})(∂θ/∂*Z*) and ρ*s*=*f*
^{2}
*R*
^{4}/*r*
^{4}.

The form of the transverse circulation equation leads naturally to a generalized Rossby radius proportional to (*q*/*s*)^{½}. A typical distribution Of (*q*/*s*)^{½} is calculated using the composite tropical cyclone data of Gray. The fundamental dynamical role of (*q*/*s*)^{½} is then illustrated with a simple analytical example.

## Abstract

We consider the axisymmetric balanced flow occurring in a thermally forced vortex in which the frictional inflow is confined to a thin boundary layer. Above the boundary layer the absolute angular momentum ½*fR*
^{2}=*rv*+½*fr*
^{2} is conserved. We refer to *R* as the potential radius, i.e., the radius to which a particle must be moved (conserving absolute angular momentum) in order to change its tangential component *v* to zero. Using *R* as one of the dependent variables we review the equations of the Eliassen balanced vortex model.

We next reverse the roles of the actual radius *r* and the potential radius *R*, i.e., we treat *R* as an independent variable and *r* as a dependent variable. Introducing transformed components (*u*
^{*}, *w*
^{*}) of the transverse circulation we obtain the transformed Eliassen balanced vortex equations, which differ from the original equations in the following respects: 1) the radial coordinate is *R* which results in a stretching of positive relative vorticity regions and a shrinking of negative relative vorticity regions; 2) the thermodynamic equation contains only the transverse circulation component *w*
^{*}, the coefficient of which is the potential vorticity *q*; 3) the equation for *r* contains only the transverse circulation component *u*
^{*}; 4) the transverse circulation equation contains only two vortex structure functions, the potential vorticity *q* and the inertial stability *s*, where *pq*=(ζ/*f*)(*g*/θ_{0})(∂θ/∂*Z*) and ρ*s*=*f*
^{2}
*R*
^{4}/*r*
^{4}.

The form of the transverse circulation equation leads naturally to a generalized Rossby radius proportional to (*q*/*s*)^{½}. A typical distribution Of (*q*/*s*)^{½} is calculated using the composite tropical cyclone data of Gray. The fundamental dynamical role of (*q*/*s*)^{½} is then illustrated with a simple analytical example.

## Abstract

Climatological properties for selected aspects of the thermodynamic structure and hydrologic cycle are presented from a 15-yr numerical simulation conducted with the National Center for Atmospheric Research Community Climate Model, version 3 (CCM3), using an observed sea surface temperature climatology. In most regards, the simulated thermal structure and hydrologic cycle represent a marked improvement when compared with earlier versions of the CCM. Three major modifications to parameterized physics are primarily responsible for the more notable improvements in the simulation: modifications to the diagnosis of cloud optical properties, modifications to the diagnosis of boundary layer processes, and the incorporation of a penetrative formulation for deep cumulus convection. The various roles of these physical parameterization changes will be discussed in the context of the simulation strengths and weaknesses.

## Abstract

Climatological properties for selected aspects of the thermodynamic structure and hydrologic cycle are presented from a 15-yr numerical simulation conducted with the National Center for Atmospheric Research Community Climate Model, version 3 (CCM3), using an observed sea surface temperature climatology. In most regards, the simulated thermal structure and hydrologic cycle represent a marked improvement when compared with earlier versions of the CCM. Three major modifications to parameterized physics are primarily responsible for the more notable improvements in the simulation: modifications to the diagnosis of cloud optical properties, modifications to the diagnosis of boundary layer processes, and the incorporation of a penetrative formulation for deep cumulus convection. The various roles of these physical parameterization changes will be discussed in the context of the simulation strengths and weaknesses.

## Abstract

The spectral cumulus parameterization theory of Arakawa and Schubert is presented in the convective flux form as opposed to the original detrainment form. This flux form is more convenient for use in numerical prediction models. The equations are grouped into one of three categories that are members of a control flow diagram: feedback, static control, and dynamic control. The dynamic control, which determines the cloud base mass flux distribution, is formulated as an optimization problem. This allows quasi-equilibrium to be satisfied as closely as possible while maintaining the necessary nonnegativity constraint on the cloud base mass flux.

Results of two applications of the parameterization are shown. The first illustrates the dependence of the predicted cloud mass flux distribution on the vertical profile of the large-scale vertical motion field. According to the assumption of quasi-equilibrium of the cloud work function, the mass flux associated with deep clouds is controlled by large-scale vertical motion in the middle and upper troposphere, not just by vertical motion at the top of the mixed layer. The second application shows the evolution of the mass flux distribution during the simulated intensification of a tropical vortex using an axisymmetric primitive equation model. A similar sensitivity of deep convection to the development of upper level vertical motion is also observed. These examples demonstrate the inherent potential of this spectral approach for helping to establish a better understanding of the physical nature of the interaction of organized cumulus convection with the large-scale fields not available in more conventional empirical parameterization methods.

## Abstract

The spectral cumulus parameterization theory of Arakawa and Schubert is presented in the convective flux form as opposed to the original detrainment form. This flux form is more convenient for use in numerical prediction models. The equations are grouped into one of three categories that are members of a control flow diagram: feedback, static control, and dynamic control. The dynamic control, which determines the cloud base mass flux distribution, is formulated as an optimization problem. This allows quasi-equilibrium to be satisfied as closely as possible while maintaining the necessary nonnegativity constraint on the cloud base mass flux.

Results of two applications of the parameterization are shown. The first illustrates the dependence of the predicted cloud mass flux distribution on the vertical profile of the large-scale vertical motion field. According to the assumption of quasi-equilibrium of the cloud work function, the mass flux associated with deep clouds is controlled by large-scale vertical motion in the middle and upper troposphere, not just by vertical motion at the top of the mixed layer. The second application shows the evolution of the mass flux distribution during the simulated intensification of a tropical vortex using an axisymmetric primitive equation model. A similar sensitivity of deep convection to the development of upper level vertical motion is also observed. These examples demonstrate the inherent potential of this spectral approach for helping to establish a better understanding of the physical nature of the interaction of organized cumulus convection with the large-scale fields not available in more conventional empirical parameterization methods.

## Abstract

A nonlinear shallow-water model on the sphere is used to study barotropic aspects of the formation of twin tropical disturbances by Madden–Julian oscillation (MJO) convection.

In the model, the effect of MJO convection upon the lower-tropospheric tropical circulation was simulated by an eastward moving, meridionally elongated mass sink straddling the equator. The intensity and propagation speed of the mass sink were chosen to simulate observations that MJO convection intensifies while nearly stationary in the eastern equatorial Indian Ocean, weakens while moving eastward over the Maritime Continent, again intensifies once it reaches the west Pacific Ocean, and finally becomes stationary and dies off near the date line. This mass sink produced twin cyclones in the two regions where it was stationary, namely, where it was initially turned on and where it was turned off. In addition, the mass sink produced two zonally elongated cyclonic potential vorticity anomalies straddling the equator in the region where it propagated eastward.

It is proposed that MJO convection produces twin tropical disturbances in the two regions where it is nearly stationary, namely, its region of formation in the eastern Indian Ocean and its region of decay near the date line. Additional tropical disturbances may arise from the breakdown of the elongated shear regions produced by the eastward propagating MJO convection.

In addition, a series of initial value experiments was performed to determine the conditions under which twin cyclones become so strongly coupled that they propagate directly eastward as a cyclone pair. Apparently, such movement requires the cyclones to be so close together that the situation rarely, if ever, occurs in nature.

## Abstract

A nonlinear shallow-water model on the sphere is used to study barotropic aspects of the formation of twin tropical disturbances by Madden–Julian oscillation (MJO) convection.

In the model, the effect of MJO convection upon the lower-tropospheric tropical circulation was simulated by an eastward moving, meridionally elongated mass sink straddling the equator. The intensity and propagation speed of the mass sink were chosen to simulate observations that MJO convection intensifies while nearly stationary in the eastern equatorial Indian Ocean, weakens while moving eastward over the Maritime Continent, again intensifies once it reaches the west Pacific Ocean, and finally becomes stationary and dies off near the date line. This mass sink produced twin cyclones in the two regions where it was stationary, namely, where it was initially turned on and where it was turned off. In addition, the mass sink produced two zonally elongated cyclonic potential vorticity anomalies straddling the equator in the region where it propagated eastward.

It is proposed that MJO convection produces twin tropical disturbances in the two regions where it is nearly stationary, namely, its region of formation in the eastern Indian Ocean and its region of decay near the date line. Additional tropical disturbances may arise from the breakdown of the elongated shear regions produced by the eastward propagating MJO convection.

In addition, a series of initial value experiments was performed to determine the conditions under which twin cyclones become so strongly coupled that they propagate directly eastward as a cyclone pair. Apparently, such movement requires the cyclones to be so close together that the situation rarely, if ever, occurs in nature.