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Donald R. Johnson

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?

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Donald R. Johnson
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Donald R. Johnson
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Donald R. Johnson

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.

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Donald R. Johnson

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.

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Donald R. Johnson and Akio Arakawa

Abstract

Professor Yale Mintz's contributions in combining theory, diagnostic analysis, and modeling in scientific studies across a broad range of interests over more than four decades are reviewed. His studies include diagnostic analysis of the general circulation and modeling of atmospheric circulation, planetary atmospheres, stratospheric ozone transport, ocean circulations, and hydrospheric and biospheric processes. The focus of the review is to examine some of the early interests of this illustrious individual during the formative year of his career in atmospheric science, to document Mintz's creative insight concerning the development of the Mintz-Arakawa General Circulation Model (GCM), and to summarize briefly his scientific contributions. Much of his scientific work involved collaborations with an unusually talented array of younger scientists.

His descriptions of the field of mean motion, the zonally averaged state, and poleward angular momentum flux must be regarded as classic contributions to meteorology. The Mintz-Arakawa GCM was also a remarkable contribution to atmospheric science, both with respect to the development of early general circulation models and its range of applications to varied scientific challenges.

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BEN R. BULLOCK and DONALD R. JOHNSON

Abstract

The theory of available potential energy applied to a “translating” atmospheric volume is used to estimate the generation of available potential energy for the cyclogenetic, mature, and occluding stages of a mid-latitude cyclone. Primary attention is focused upon the importance of the diabatic process of latent heat release in generating the storm's available potential energy. In addition, preliminary estimates for the process of infrared cooling are presented.

Total latent heat release is determined from observed precipitation rates. Three different models for the vertical distribution of latent heat release together with the storm's structure provided by isentropic analyses are utilized to estimate the contribution by latent heat release to the available potential energy of the disturbance. For each stage of the storm, variations in the generation estimates between models were extremely small. For the cyclogenetic, mature, and occluding stages, generation estimates of approximately 1, 8, and 6 W m−2, respectively, reflected changes in the horizontal distribution of precipitation about the storm.

Two simplified cooling distributions were assumed to evaluate the importance of infrared cooling in the generation. The first was one of uniform cooling at the rate of 1.4°C day−1 thoughout the volume, and the second was one in which the clear air was cooled at a greater rate than the cloudy air. Positive generation estimates on the order of 1 to 2 W m−2 resulted from these calculations.

The results of this study indicate that the diabatic process of latent heat release is very likely an important factor in the subsequent behavior of the system. It is speculated that an energy supply of this magnitude, available for immediate conversion to kinetic energy, is sufficient to offset a major portion of the storm's frictional dissipation. Generation estimates for the process of infrared cooling, while less reliable than those for latent heat release, indicate that this process also contributes to the storm's available potential energy supply.

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Donald R. Johnson and William K. Downey

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The concept of absolute angular momentum and its time rate of change is developed for a translating vortex. Storm absolute angular momentum is defined to be the moment of the velocity about an origin translating with the center of the vortex. With this development in generalized coordinates, sources by transport and by internal torques are isolated. An integration over a storm volume reveals that for hydrostatic atmospheres, pressure, viscous, gravitational and inertial torques sum to boundary integrals.

After the vector relations are established for storm absolute angular momentum, the component along the storm axis of rotation through the vortex is determined. By a systematic analysis, the physical basis for a geostrophic torque in an asymmetric baroclinic vortex is established. The role of the geostrophic torque is to transfer angular momentum vertically in isentropic coordinates. Angular momentum is extracted from an isentropic layer with an inward geostrophic mode of mass transport and given to a layer with an outward geostrophic mode. The vertical transfer across the isentropic layer occurs through pressure stresses. Two examples for the Midwest cyclone of 23 April 1968 are presented. Finally, the modes of mean and eddy transport of earth and relative angular momentum as well as sources for the azimuthally averaged storm absolute angular momentum are studied in isobaric, cartesian, and isentropic coordinates.

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Bart J. Wolf and Donald R. Johnson

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A kinetic energy (KE) analysis of the forcing of a mesoscale upper-tropospheric jet streak by organized diabaaic processes within the simulated convective system (SCS) that was discussed in Part I is presented in this study. The relative contributions of the ageostrophic components of motion to the generation of KE of the convectively generated jet streak are compared, along with the KE generation by the rotational (nondivergent) and irrotational (divergent) mass transport. The sensitivity of the numerical simulations of SCS development to resolution is also briefly examined. Analysis within isentropic coordinates provides for an explicit determination of the influence of dramatic processes on the generation of KE.

The upper-level production of specific KE is due predominantly to the inertial advective ageostrophic component (IAD), and as such represents the primary process through which the KE of the convectively generated jet streak is realized. A secondary contribution by the inertial diabatic (IDI) term is observed. Partitioning the KE generation into its rotational and irrotational components reveals that the latter, which is directly linked to the diabatic heating within the SCS through isentropic continuity requirements, is the ultimate source of KE generation as the global area integral of generation by the rotational component vanishes. Comparison with an identical dry simulation reveals that the net generation of KE must be attributed to latent beating. Both the IAD and IDI ageostrophic components play important roles in this regard.

Examination of results frown simulations conducted at several resolutions supports the previous findings in that the effects of diabatic processes and ageostrophic motion on KE generation remain consistent. Resolution does impact the location and timing of SCS development, a result that has important implications in forecasting the onset of convection that develops from evolution of the large-scale flow and moisture transport. Marked differences are observed in the momentum field aloft subsequent to the lift cycle of the SCS in the 1°, 30-level base case (MP130) simulation discussed in Part I versus its 2° counterparts in that the MP130 simulation with higher spatial resolution contains from 14% to 30% more total KE.

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Donald R. Johnson and Louis W. Uccellini

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Five methods for computing the pressure gradient force within a sigma domain of a hybrid model are compared for flow over a steeply sloped terrain. The comparison includes pressure gradient calculations determined from a direct transformation to sigma coordinates, an application of an atmospheric deviation state to the direct transformation (Phillips, 1974), an evaluation within isobaric coordinates (Janjić, 1977), a flux form (Johnson, 1980), and a flux prime form that applies the Phillips' deviation state to the flux form. The results from a numerical simulation establish that the Janjić, Phillips and flux prime methods reduce truncation errors substantially, and successfully predict the surface anticyclonic circulation that develops within vertically and horizontally sheared baroclinic flow over elevated terrain. A discussion of the generation of kinetic energy and elimination of a spurious kinetic energy source through reduction of the truncation error by the flux prime method is presented.

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