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- Author or Editor: Donald R. Johnson x
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Abstract
A generalized transport equation for a variety of meteorological coordinate systems is derived. Through its application, the commonality of modes of convective and nonconvective flux of mass, momentum and energy is identified between the specific coordinate systems. Generalized forms for pressure gradient and frictional forces (∇·Π) in the momentum equation are presented that directly integrate to boundary stresses (τ) while in the total energy equation the sum of mechanical [U·(∇·&Pi)] and thermodynamic work (Π:∇U) readily integrates to boundary work (∇·[Π·U]). Additional degrees of freedom for the nonconvective flux of properties are identified with the inclination of information surfaces. The vertical transfer of momentum and energy by this means is discussed in regard to the time rate of change of the dynamic circulation (Bjerknes, 1937). The results reveal that views of the forcing of circulation become coordinate dependent. Variant and invariant aspects of the physical and mathematical meaning of the generalized transport equation and forcing of the circulation are presented.
Abstract
A generalized transport equation for a variety of meteorological coordinate systems is derived. Through its application, the commonality of modes of convective and nonconvective flux of mass, momentum and energy is identified between the specific coordinate systems. Generalized forms for pressure gradient and frictional forces (∇·Π) in the momentum equation are presented that directly integrate to boundary stresses (τ) while in the total energy equation the sum of mechanical [U·(∇·&Pi)] and thermodynamic work (Π:∇U) readily integrates to boundary work (∇·[Π·U]). Additional degrees of freedom for the nonconvective flux of properties are identified with the inclination of information surfaces. The vertical transfer of momentum and energy by this means is discussed in regard to the time rate of change of the dynamic circulation (Bjerknes, 1937). The results reveal that views of the forcing of circulation become coordinate dependent. Variant and invariant aspects of the physical and mathematical meaning of the generalized transport equation and forcing of the circulation are presented.
Abstract
The storm's available potential energy and its rate of change are derived for a vertically walled volume encircling the storm and extending from the surface to the top of the atmosphere. The rate of change includes explicit expressions for the generation of the storm's available potential energy, for its conversion to kinetic energy, and for its change through boundary work and energy flux. The theoretical results in isentropic coordinates show that it is not desirable to conduct available potential studies in a quasi-hydrostatic atmosphere for regions of limited vertical extent. The results also show the difficulty of inferring kinetic energy change from a total potential energy budget of a limited atmospheric domain. Opposite time rates of change for the storm's total and available potential energy are allowed through boundary processes for frictionless isentropic flows within mechanically open regimes. The relation of the available potential energy of storms to the available potential energy of the atmosphere is also established.
Several recent diagnostic studies of the generation of the storm's available potential energy by individual diabatic components are summarized for the hurricane and extratropical cyclone. The amount of available potential energy generated within the storm is a significant fraction of the rate of its kinetic energy production.
Abstract
The storm's available potential energy and its rate of change are derived for a vertically walled volume encircling the storm and extending from the surface to the top of the atmosphere. The rate of change includes explicit expressions for the generation of the storm's available potential energy, for its conversion to kinetic energy, and for its change through boundary work and energy flux. The theoretical results in isentropic coordinates show that it is not desirable to conduct available potential studies in a quasi-hydrostatic atmosphere for regions of limited vertical extent. The results also show the difficulty of inferring kinetic energy change from a total potential energy budget of a limited atmospheric domain. Opposite time rates of change for the storm's total and available potential energy are allowed through boundary processes for frictionless isentropic flows within mechanically open regimes. The relation of the available potential energy of storms to the available potential energy of the atmosphere is also established.
Several recent diagnostic studies of the generation of the storm's available potential energy by individual diabatic components are summarized for the hurricane and extratropical cyclone. The amount of available potential energy generated within the storm is a significant fraction of the rate of its kinetic energy production.
Abstract
Motivated by the circumstantial evidence of the pervasive nature of the “general coldness” of climate model simulations, a theoretical analysis is made of the model response expected from the presence of both physical and aphysical sources of entropy under the joint conditions that the net flux of energy through the upper and lower boundaries of the atmosphere and the isentropic temporally, areally integrated entropy source must vanish. These joint conditions are essential for a simulated global climate state to be without drift. The application of these conditions in the presence of positive definite aphysical entropy sources leads to the conclusion that the model-simulated climate state will be characterized by a general coldness, in particular in the upper polar troposphere and lower tropical troposphere as observed in 104 out of 105 possible outcomes from 35 different simulations by 14 climate models.
In assessing the magnitude of this effect, a 10°C bias in mean temperature corresponds with a relatively small error of 4% in the mean heat addition of an isentropic layer. This correspondence reveals the extreme sensitivity of a climate model’s temperature response to aphysical entropy sources introduced by spurious numerical dispersion/diffusion, Gibbs oscillations, parameterizations, and other factors. In accurately simulating hydrologic and chemical processes, this difficulty is compounded in the sense that the saturation specific humidity doubles for each additional 10°C increase in temperature and the inherent strong dependence of both processes on temperature, pressure, and amount of water substances—vapor, liquid, and ice. A strategy that makes climate simulations tractable is that numerical trade-offs occur among the various parameterizations of the components of heat addition. These trade-offs allow models to be tuned to simulate a reasonable state achievable for given resolution, numerics, and parameterizations. Oreskes et al. label this step “calibration” and suggest that in such situations, “empirical adequacy is forced.”
The results of this analysis in combination with Carathéordary’s statement of the Second Law reveals in the strict sense that the presence of positive definite aphysical sources of entropy in a climate model precludes the simulation of unbiased distributions of the heat addition and temperature. Since in the strict sense the true state cannot be simulated, several questions follow: are reasonable states of global and regional climate change simulated for the right reasons; just what are reasonable states; and how are the right reasons to be determined in view of the trade-offs among the several components of parameterized heat addition?
Abstract
Motivated by the circumstantial evidence of the pervasive nature of the “general coldness” of climate model simulations, a theoretical analysis is made of the model response expected from the presence of both physical and aphysical sources of entropy under the joint conditions that the net flux of energy through the upper and lower boundaries of the atmosphere and the isentropic temporally, areally integrated entropy source must vanish. These joint conditions are essential for a simulated global climate state to be without drift. The application of these conditions in the presence of positive definite aphysical entropy sources leads to the conclusion that the model-simulated climate state will be characterized by a general coldness, in particular in the upper polar troposphere and lower tropical troposphere as observed in 104 out of 105 possible outcomes from 35 different simulations by 14 climate models.
In assessing the magnitude of this effect, a 10°C bias in mean temperature corresponds with a relatively small error of 4% in the mean heat addition of an isentropic layer. This correspondence reveals the extreme sensitivity of a climate model’s temperature response to aphysical entropy sources introduced by spurious numerical dispersion/diffusion, Gibbs oscillations, parameterizations, and other factors. In accurately simulating hydrologic and chemical processes, this difficulty is compounded in the sense that the saturation specific humidity doubles for each additional 10°C increase in temperature and the inherent strong dependence of both processes on temperature, pressure, and amount of water substances—vapor, liquid, and ice. A strategy that makes climate simulations tractable is that numerical trade-offs occur among the various parameterizations of the components of heat addition. These trade-offs allow models to be tuned to simulate a reasonable state achievable for given resolution, numerics, and parameterizations. Oreskes et al. label this step “calibration” and suggest that in such situations, “empirical adequacy is forced.”
The results of this analysis in combination with Carathéordary’s statement of the Second Law reveals in the strict sense that the presence of positive definite aphysical sources of entropy in a climate model precludes the simulation of unbiased distributions of the heat addition and temperature. Since in the strict sense the true state cannot be simulated, several questions follow: are reasonable states of global and regional climate change simulated for the right reasons; just what are reasonable states; and how are the right reasons to be determined in view of the trade-offs among the several components of parameterized heat addition?
Abstract
The earth–atmosphere exchange of storm absolute dynamic circulation by mountain-induced surface pressure stress and the response of the circulation in a Rocky Mountain Ice cyclone is examined. Surface pressure stresses that transfer horizontal momentum across the earth-atmosphere interface stem from the hydrostatic weight of the atmosphere resting against the inclined surfaces of orography. In a Ice cyclone. mass asymmetries must be combined with terrain variability for net transfer across the interface. Within the storm structure, the acceleration of the dynamic circulation by the pressure gradient force is determined by the line integral of the azimuthally directed components of pressure stress, in effect an angular momentum pressure torque. The pressure torque is compared to the tendencies of specific relative circulation and absolute dynamic circulation in a lee cyclone simulated by the eta model.
The mountain-induced pressure torque is found to be negative in the lower layers of the cyclone vortex throughout the simulation. Negative pressure torque, which indicates the transfer of absolute dynamic circulation from the cyclone to the mountain, acts, in conjunction with other processes, to force convergence of the mass transport in the lower layers of the cyclone. The import of absolute angular momentum from the storm's environment by the converging mass circulation exceeds the loss of angular momentum to the earth by pressure and viscous stresses, and thus leads to the spinup of the storm-relative circulation.
The negative pressure torque diagnosed in the simulated cyclone results from an asymmetric distribution of surface pressure stress about the cyclone's circulation center in conjunction with a stronger pressure gradient to the north and northwest of the cyclone than to the south. This asymmetry is shown to be a characteristic of Rocky Mountain Ice cyclones and the results illuminate its relation to the storm's life cycle.
Abstract
The earth–atmosphere exchange of storm absolute dynamic circulation by mountain-induced surface pressure stress and the response of the circulation in a Rocky Mountain Ice cyclone is examined. Surface pressure stresses that transfer horizontal momentum across the earth-atmosphere interface stem from the hydrostatic weight of the atmosphere resting against the inclined surfaces of orography. In a Ice cyclone. mass asymmetries must be combined with terrain variability for net transfer across the interface. Within the storm structure, the acceleration of the dynamic circulation by the pressure gradient force is determined by the line integral of the azimuthally directed components of pressure stress, in effect an angular momentum pressure torque. The pressure torque is compared to the tendencies of specific relative circulation and absolute dynamic circulation in a lee cyclone simulated by the eta model.
The mountain-induced pressure torque is found to be negative in the lower layers of the cyclone vortex throughout the simulation. Negative pressure torque, which indicates the transfer of absolute dynamic circulation from the cyclone to the mountain, acts, in conjunction with other processes, to force convergence of the mass transport in the lower layers of the cyclone. The import of absolute angular momentum from the storm's environment by the converging mass circulation exceeds the loss of angular momentum to the earth by pressure and viscous stresses, and thus leads to the spinup of the storm-relative circulation.
The negative pressure torque diagnosed in the simulated cyclone results from an asymmetric distribution of surface pressure stress about the cyclone's circulation center in conjunction with a stronger pressure gradient to the north and northwest of the cyclone than to the south. This asymmetry is shown to be a characteristic of Rocky Mountain Ice cyclones and the results illuminate its relation to the storm's life cycle.
Abstract
Transverse circulations in the exit and entrance regions of jet streaks are investigated through numerical simulation, a case study, and an application of the isallobaric wind equation in isentropic coordinates, to study the interaction between upper and lower tropospheric jets and the development of severe convective storms. A hybrid isentropic-sigma coordinate numerical model is used to simulate the mass and momentum adjustments associated with a jet streak propagating in a zonal channel. The numerical results depict a two-layer mass adjustment in the exit and entrance region of the jet streak. The results also verify that the isallobaric wind on lower isentropic surfaces is a primary component of the return branches of transverse circulations and is foxed by the two-layer mass adjustment accompanying the propagating jet streak. Results from the case study of a severe weather out- break show that 1) a low-level jet (LLJ) beneath the exit region of an upper tropospheric jet streak is embedded in the lower branch of an indirect circulation, 2) intensification of the lower branch and development of the LLJ is largely a result of an increased isallobaric wind component, and 3) the development of the LLJ is coupled to the upper tropospheric jet streak by the two-layer mass adjustment within the exit region of the streak. The isallobaric wind component of the LLJ is the primary reason for the axis of the LLJ being at a significant angle to the upper jet's axis and the resulting veering of the wind with height. In the exit region, the geometry of this adjustment, combined with warm, moist, lower tropospheric air to the right and ahead of the jet streak and cool, dry air at the jet streak level, produced the differential advections that convectively destabilized the atmosphere. Results of the case study support the concept that the development of conditions favorable for severe convective storms can be forced by mass and momentum adjustments which accompany the propagation of an upper tropospheric jet streak.
Abstract
Transverse circulations in the exit and entrance regions of jet streaks are investigated through numerical simulation, a case study, and an application of the isallobaric wind equation in isentropic coordinates, to study the interaction between upper and lower tropospheric jets and the development of severe convective storms. A hybrid isentropic-sigma coordinate numerical model is used to simulate the mass and momentum adjustments associated with a jet streak propagating in a zonal channel. The numerical results depict a two-layer mass adjustment in the exit and entrance region of the jet streak. The results also verify that the isallobaric wind on lower isentropic surfaces is a primary component of the return branches of transverse circulations and is foxed by the two-layer mass adjustment accompanying the propagating jet streak. Results from the case study of a severe weather out- break show that 1) a low-level jet (LLJ) beneath the exit region of an upper tropospheric jet streak is embedded in the lower branch of an indirect circulation, 2) intensification of the lower branch and development of the LLJ is largely a result of an increased isallobaric wind component, and 3) the development of the LLJ is coupled to the upper tropospheric jet streak by the two-layer mass adjustment within the exit region of the streak. The isallobaric wind component of the LLJ is the primary reason for the axis of the LLJ being at a significant angle to the upper jet's axis and the resulting veering of the wind with height. In the exit region, the geometry of this adjustment, combined with warm, moist, lower tropospheric air to the right and ahead of the jet streak and cool, dry air at the jet streak level, produced the differential advections that convectively destabilized the atmosphere. Results of the case study support the concept that the development of conditions favorable for severe convective storms can be forced by mass and momentum adjustments which accompany the propagation of an upper tropospheric jet streak.
Abstract
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Abstract
No abstract available.
Abstract
The budgets of mass, absolute angular momentum and kinetic energy for two model-generated cyclones and one anticyclone are examined using a sigma-coordinate framework which moves with the center of the MSL pressure extremum. The mass budgets for all three cases show a concentration of lateral mass transport in the surface boundary layer and at a level near 200 mb. The spin up of the low troposphere during cyclogenesis results from the dominance of the mean mode of lateral transport of absolute angular momentum. The spin up of the upper troposphere results from the combined influence of an inward eddy mode of lateral transport and vertical transport of absolute angular momentum. The eddy mode of lateral transport is determined by the configuration of the upper level flow (particularly jet streaks) and is enhanced by frontogenesis in the low and mid-troposphere as these regions spin up. The increase of kinetic energy in the low troposphere during cyclogenesis results from the dominance of local generation by cross-isobar flow toward the center of the developing vortex. In the upper troposphere the kinetic energy budget is not related uniquely to the development or decay of the surface cyclone. While the anticyclone, to a large extent, displays similar behavior to the cyclone, the eddy mode of lateral transport of angular momentum in the upper troposphere is not enhanced by lower level frontogenetic effects, as in the case of the cyclone.
Abstract
The budgets of mass, absolute angular momentum and kinetic energy for two model-generated cyclones and one anticyclone are examined using a sigma-coordinate framework which moves with the center of the MSL pressure extremum. The mass budgets for all three cases show a concentration of lateral mass transport in the surface boundary layer and at a level near 200 mb. The spin up of the low troposphere during cyclogenesis results from the dominance of the mean mode of lateral transport of absolute angular momentum. The spin up of the upper troposphere results from the combined influence of an inward eddy mode of lateral transport and vertical transport of absolute angular momentum. The eddy mode of lateral transport is determined by the configuration of the upper level flow (particularly jet streaks) and is enhanced by frontogenesis in the low and mid-troposphere as these regions spin up. The increase of kinetic energy in the low troposphere during cyclogenesis results from the dominance of local generation by cross-isobar flow toward the center of the developing vortex. In the upper troposphere the kinetic energy budget is not related uniquely to the development or decay of the surface cyclone. While the anticyclone, to a large extent, displays similar behavior to the cyclone, the eddy mode of lateral transport of angular momentum in the upper troposphere is not enhanced by lower level frontogenetic effects, as in the case of the cyclone.
Abstract
The azimuthally averaged transport and budget equations for a translating storm volume are derived in generalized coordinates. The mean and eddy lateral modes of transport by rotational and irrotational motion are contrasted in symmetric and asymmetric vortices. By contrasting the transport relations in isobaric, cartesian, and isentropic coordinates, the results establish that hydrostatic-rotational regimes of atmospheric motion are typified by eddy modes of transport in isobaric and cartesian coordinates, while both mean and eddy modes may be present in isentropic coordinates. This requirement for a “handover” from an eddy mode of transport in the hydrostatic-rotational environment of a vortex to a mean mode of transport via irrotational motion within a vortex is discussed.
Evidence for the existence of mean meridional circulation in isentropic coordinates for the Midwest extratropical cyclone of 22–24 April 1968 is presented. The inward mass transport in the lower troposphere and outward mass transport in the upper troposphere are coupled to vertical mass transport through isentropic surfaces associated with the release of latent heat in the middle troposphere.
Abstract
The azimuthally averaged transport and budget equations for a translating storm volume are derived in generalized coordinates. The mean and eddy lateral modes of transport by rotational and irrotational motion are contrasted in symmetric and asymmetric vortices. By contrasting the transport relations in isobaric, cartesian, and isentropic coordinates, the results establish that hydrostatic-rotational regimes of atmospheric motion are typified by eddy modes of transport in isobaric and cartesian coordinates, while both mean and eddy modes may be present in isentropic coordinates. This requirement for a “handover” from an eddy mode of transport in the hydrostatic-rotational environment of a vortex to a mean mode of transport via irrotational motion within a vortex is discussed.
Evidence for the existence of mean meridional circulation in isentropic coordinates for the Midwest extratropical cyclone of 22–24 April 1968 is presented. The inward mass transport in the lower troposphere and outward mass transport in the upper troposphere are coupled to vertical mass transport through isentropic surfaces associated with the release of latent heat in the middle troposphere.
