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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

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
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Donald R. Johnson
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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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Bart J. Wolf
and
Donald R. Johnson

Abstract

The mutual forcing of a midlatitude upper-tropospheric jet streak by organized mesoscale adiabatic and diabatic processes within a simulated convective system (SCS) is investigated. Using isentropic diagnostics, results from a three-dimensional numerical simulation of an SCS are examined to study the isallobaric flow field, modes of dominant ageostrophic motion, and stability changes in relation to the mutual interdependence of adiabatic processes and latent heat release. Isentropic analysis affords an explicit isolation of a component of isallobaric flow associated with diabatic processes within the SCS.

Prior to convective development within the simulation, atmospheric destabilization occurs through adiabatic ageostrophic mass adjustment and low-level convergence in association with the preexisting synoptic-scale upper-tropospheric jet streak. The SCS develops in a baroclinic zone and quickly initiates a vigorous mass circulation. By the mature stage, a pronounced vertical couplet of low-level convergence and upper-level mass divergence is established, linked by intense midtroposphoric diabatic heating. Significant divergence persists aloft for several hours subsequent to SCS decay. The dominant mode of ageostrophic motion within which the low-level mass convergence develops is the adiabatic isallobaric component, while the mass divergence aloft develops principally through the diabatic isallobaric component. Both components are intrinsically linked to the convectively forced vertical mass transport.

The inertial diabatic ageostropiiic component is largest near the level of maximum heating and is responsible for the development of inertial instability to the north of the SCS, resulting in this quadrant being preferred for outflow. The inertial advective component, the dominant term that produces the new downstream wind maximum, rapidly develops north of the SCS and through mutual adjustment creates the baroclinic support for the new jet streak.

The results establish the synergistic relationship between the synoptic and mesoscale ageostrophic flow in the organization and maintenance of the SCS, as well as in the subsequent three-dimensional modification of the environmental flow field. The findings reinforce the need for operational models to accurately and explicitly simulate the effects of organized midlatitude convection on the larger-scale environment.

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Bart J. Wolf
and
Donald R. Johnson

Abstract

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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Alan C. Czarnetzki
and
Donald R. Johnson

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.

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Linda M. Keller
and
Donald R. Johnson

Abstract

Time series of hemispheric available potential (A) and kinetic (K) energies were used to examine the results of a series of observing system simulation experiments that were performed with the Goddard Laboratory for Atmospheres model to determine the impact of the proposed space-based wind profiler on forecast accuracy. The simulated data for the series of 5-day forecasts were produced from a 20-day integration using the ECMWF model, which was also used to produce the verification forecast for the 5-day period. The three simulated observational sets of data that represented conventional observations, satellite-retrieval temperatures, and wind profiles were produced by NMC.

The results in the Northern Hemisphere show that the magnitudes of A and K from the simulation forecasts are quite similar to each other and are uniformly higher than the verification forecast, reflecting systematic differences in the energy levels of the two models. In the Southern Hemisphere, differences in magnitude of A between simulation and verification forecasts are larger than in the Northern Hemisphere. The time series for K shows greater diversity in magnitude among the simulation forecasts, with all the simulation forecasts for K being higher than the verification forecast. The S 1 skill scores and root-mean-square (rms) differences reveal little variation in the accuracy of the forecasts among the three simulation datasets in the Northern Hemisphere. In the Southern Hemisphere, however, forecasts using satellite temperature and wind-profiler data have much smaller rms differences and S 1 scores, indicating an improvement in forecast accuracy over conventional observations. The addition of wind-profiler data provides the greatest improvement in forecast accuracy.

Geographical distributions of vertically integrated eddy A (Ae and K in the Northern Hemisphere reveal that these quantities in the three simulation forecasts are more similar to each other than with the verification forecast. In the Southern Hemisphere, the geographical distributions of Ae and K are more varied with the wind-profiler dataset producing a forecast closest to the verification forecast. In general, the impact of the addition of wind-profiler data on forecast accuracy of energy parameters is negligible in the Northern Hemisphere but distinctly positive in the Southern Hemisphere.

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Donald R. Johnson
and
Louis W. Uccellini

Abstract

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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