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- Author or Editor: R. G. Roble x

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## Abstract

The distortions to the image and spectrum of a star being observed during occultation from a satellite are discussed. The primary distortions are shown to be due to refractive dispersion, small and large particle scattering, and absorption by various atmospheric gases. Representative stellar spectra in both the visible and ultraviolet are presented, and various features relating to specific atmospheric constituents are discussed. The possibility of recovering information concerning atmospheric composition from stellar spectra is considered and several distinct processes are used for illustration.

## Abstract

The distortions to the image and spectrum of a star being observed during occultation from a satellite are discussed. The primary distortions are shown to be due to refractive dispersion, small and large particle scattering, and absorption by various atmospheric gases. Representative stellar spectra in both the visible and ultraviolet are presented, and various features relating to specific atmospheric constituents are discussed. The possibility of recovering information concerning atmospheric composition from stellar spectra is considered and several distinct processes are used for illustration.

## Abstract

A time-dependent model that simulates the interaction of a thunderstorm with its electrical environment is introduced. The model solves the continuity equation of the Maxwell current density that includes conduction, displacement, and source currents. Lightning phenomena are neglected and the electric field is assumed to be curl free. Corona, convection, and precipitation currents are not considered in this initial study and their contribution to the source function is not specified explicitly. As a preliminary test of the model we assume that the storm is axially symmetric in spherical geometry, the conductivity depends only on the vertical coordinate, the ground is equipotential, and far from the thunderstorm region the horizontal electric field is zero. These assumptions are for computational efficiency only and can be relaxed in more realistic studies.

The mathematical energy method is applied to the continuity equation to determine boundary conditions that are sufficient to form a well-posed initial-boundary value problem. This ensures the existence of a physical solution that depends continuously on the initial and boundary data. Then analytic techniques are applied to study the dependence of the solution on the properties of the medium. There are two time scales of the problem that are analyzed and discussed: one determined by the background electrical conductivity and the other by the time dependence of the source function. The assumed source function, which represents a mechanism by which charge is separated inside the storm, contributes to a portion of the solution in which the ratio of the displacement current over the conduction current increases with decreasing altitude, i.e., in the lower atmospheric region the displacement current can have an important role in the electrical interaction between the storm and its environment. It is also demonstrated that the source function can induce temporal phase shifts in the solution, which are dependent on altitude.

To obtain details of the solution, which cannot be obtained by analytic techniques. a stable numerical approximation of the continuity equation is introduced and analyzed. The resulting numerical model is used to examine the evolution of the displacement and conduction currents during the charge buildup phase of a developing thunderstorm.

## Abstract

A time-dependent model that simulates the interaction of a thunderstorm with its electrical environment is introduced. The model solves the continuity equation of the Maxwell current density that includes conduction, displacement, and source currents. Lightning phenomena are neglected and the electric field is assumed to be curl free. Corona, convection, and precipitation currents are not considered in this initial study and their contribution to the source function is not specified explicitly. As a preliminary test of the model we assume that the storm is axially symmetric in spherical geometry, the conductivity depends only on the vertical coordinate, the ground is equipotential, and far from the thunderstorm region the horizontal electric field is zero. These assumptions are for computational efficiency only and can be relaxed in more realistic studies.

The mathematical energy method is applied to the continuity equation to determine boundary conditions that are sufficient to form a well-posed initial-boundary value problem. This ensures the existence of a physical solution that depends continuously on the initial and boundary data. Then analytic techniques are applied to study the dependence of the solution on the properties of the medium. There are two time scales of the problem that are analyzed and discussed: one determined by the background electrical conductivity and the other by the time dependence of the source function. The assumed source function, which represents a mechanism by which charge is separated inside the storm, contributes to a portion of the solution in which the ratio of the displacement current over the conduction current increases with decreasing altitude, i.e., in the lower atmospheric region the displacement current can have an important role in the electrical interaction between the storm and its environment. It is also demonstrated that the source function can induce temporal phase shifts in the solution, which are dependent on altitude.

To obtain details of the solution, which cannot be obtained by analytic techniques. a stable numerical approximation of the continuity equation is introduced and analyzed. The resulting numerical model is used to examine the evolution of the displacement and conduction currents during the charge buildup phase of a developing thunderstorm.

## Abstract

Departures from a mean global-scale ionization distribution are commonly found in the ionospheric F region. Global-scale winds experience an acceleration where the ion drag is locally less than its global-scale smooth value and, they likewise, experience a deceleration where the ion drag is locally greater. Thus, a perturbation in the horizontal flow is set up in response to this ion-drag momentum source.

A two-dimensional, steady-state dynamic model of the neutral thermosphere, incorporating thermal conduction, viscosity and ion drag, is used to calculate the temperature perturbation and circulation pattern caused by these ion-drag anomalies. The forcing is given by a momentum source which depends on the interaction of a basic-state neutral wind with the anomaly. For horizontal-scale anomalies of a few hundred kilometers, such as the electron density depression within the stable auroral red arc, the momentum source due to perturbation ion drag is almost completely balanced by a perturbation pressure force. The perturbation temperature and circulation responses are, therefore, negligibly small. For horizontal-scale anomalies of the order of a few thousand kilometers, such as the day-night electron density variation at sunset, the force exerted by the perturbation pressure is not able to cancel the addition of momentum by the ion-drag anomaly. Thus, such a momentum source produces a significant perturbation in the horizontal velocity, vertical motion, and temperature field.

## Abstract

Departures from a mean global-scale ionization distribution are commonly found in the ionospheric F region. Global-scale winds experience an acceleration where the ion drag is locally less than its global-scale smooth value and, they likewise, experience a deceleration where the ion drag is locally greater. Thus, a perturbation in the horizontal flow is set up in response to this ion-drag momentum source.

A two-dimensional, steady-state dynamic model of the neutral thermosphere, incorporating thermal conduction, viscosity and ion drag, is used to calculate the temperature perturbation and circulation pattern caused by these ion-drag anomalies. The forcing is given by a momentum source which depends on the interaction of a basic-state neutral wind with the anomaly. For horizontal-scale anomalies of a few hundred kilometers, such as the electron density depression within the stable auroral red arc, the momentum source due to perturbation ion drag is almost completely balanced by a perturbation pressure force. The perturbation temperature and circulation responses are, therefore, negligibly small. For horizontal-scale anomalies of the order of a few thousand kilometers, such as the day-night electron density variation at sunset, the force exerted by the perturbation pressure is not able to cancel the addition of momentum by the ion-drag anomaly. Thus, such a momentum source produces a significant perturbation in the horizontal velocity, vertical motion, and temperature field.

## Abstract

The mean meridional circulation and latitudinal variation of temperature in the thermosphere are calculated for solstice conditions. The heat and momentum sources that drive the thermospheric circulation are solar EUV and UV heating, high-latitude heating due to auroral processes, and a momentum source due to the correlation of diurnal variations of wind and ion drag. The results show a solar-driven, summer-to-winter circulation that is modified by the high-latitude heat source. The high-latitude heat source reinforces the summer-to-winter circulation in the summer hemisphere, but reverses the circulation in the mid-latitude winter hemisphere at F-layer heights with transition from one cell to another in the midlatitude winter hemisphere. Below about 150 km, however, the summer-to-winter circulation is maintained at all latitudes. The zonal winds at midlatitudes are generally eastward in the winter hemisphere and westward in the summer hemisphere. At F-layer heights, there is a significant temperature decrease from the summer pole to winter pole. Good agreement between the calculated and observed circulations and latitudinal temperature distributions is obtained for a total high-latitude heat source of about 2 × 10^{18} ergs s^{−1}, but with 2½ times as much heating in the summer hemisphere as in the winter hemisphere.

## Abstract

The mean meridional circulation and latitudinal variation of temperature in the thermosphere are calculated for solstice conditions. The heat and momentum sources that drive the thermospheric circulation are solar EUV and UV heating, high-latitude heating due to auroral processes, and a momentum source due to the correlation of diurnal variations of wind and ion drag. The results show a solar-driven, summer-to-winter circulation that is modified by the high-latitude heat source. The high-latitude heat source reinforces the summer-to-winter circulation in the summer hemisphere, but reverses the circulation in the mid-latitude winter hemisphere at F-layer heights with transition from one cell to another in the midlatitude winter hemisphere. Below about 150 km, however, the summer-to-winter circulation is maintained at all latitudes. The zonal winds at midlatitudes are generally eastward in the winter hemisphere and westward in the summer hemisphere. At F-layer heights, there is a significant temperature decrease from the summer pole to winter pole. Good agreement between the calculated and observed circulations and latitudinal temperature distributions is obtained for a total high-latitude heat source of about 2 × 10^{18} ergs s^{−1}, but with 2½ times as much heating in the summer hemisphere as in the winter hemisphere.

## Abstract

The mean meridional circulation and latitudinal variation of temperature in the thermosphere are considered for equinox conditions. With regard to these parameters there have been serious discrepancies between observational indications and theoretical expectations. A numerical model of the zonally symmetric thermospheric circulation is formulated and solved using a finite-difference initial value approach to steady-state solutions. Solutions are obtained for three different prescriptions of forcing terms: solar heating alone, solar heating plus an effective momentum source due to diurnal variations, and inclusion of a high-latitude heat source representing Joule dissipation of electric current systems. It is concluded that the Joule heating is essential for bringing theoretical predictions into agreement with observations but that the global mean of the required heating during geomagnetically quiet periods is necessarily small compared to global mean solar heating at the same levels.

## Abstract

The mean meridional circulation and latitudinal variation of temperature in the thermosphere are considered for equinox conditions. With regard to these parameters there have been serious discrepancies between observational indications and theoretical expectations. A numerical model of the zonally symmetric thermospheric circulation is formulated and solved using a finite-difference initial value approach to steady-state solutions. Solutions are obtained for three different prescriptions of forcing terms: solar heating alone, solar heating plus an effective momentum source due to diurnal variations, and inclusion of a high-latitude heat source representing Joule dissipation of electric current systems. It is concluded that the Joule heating is essential for bringing theoretical predictions into agreement with observations but that the global mean of the required heating during geomagnetically quiet periods is necessarily small compared to global mean solar heating at the same levels.

## Abstract

A model system is established that includes three interactive components: a dynamics model, a turbulence model, and a chemistry model. The dynamics model solves the two-dimensional, nonlinear, nonhydrostatic, compressible, and viscous flow equations, and the turbulence model is adapted from the 2.5-level Mellor–Yamada turbulence model with minor adjustments. The dynamics and the turbulence models are coupled with a chemistry model to study the mesoscale impacts of gravity wave breaking on the atmospheric compositional structures. The present study focuses on the local distribution of atomic oxygen and ozone. The model system is used to study the gravity wave propagation, growth, breakdown, and its impacts on the mean state in the middle and upper atmosphere. The inclusion of a turbulence model makes it possible to study the long-term evolution of the gravity wave after wave breaking and in the presence of nonuniform turbulence, as well as the interaction between a breaking wave and turbulence. The turbulence model parameterizes the three-dimensional mixing due to the flow instability and it eliminates the unrealistically strong supersaturation observed in previous two-dimensional simulations. The modeling result suggests that the induced acceleration due to convective instability may lead to strong shear, which causes dynamical instability at lower altitudes. The result reveals the interdependence of waves and turbulence and shows that the turbulence energy density due to instability has similar temporal and spatial characteristics to previous radar observations. The result is also compared with the linear saturation theory, and it is found that the eddy diffusion coefficients in the wave-breaking region are nonuniform, and the average values are less than those obtained from the linear saturation theory. The result also suggests that the inclusion of the turbulence model could be a valid approach to study the averaged two-dimensional gravity wave and turbulence features after wave breaking. More adjustments of the turbulence model parameters, according to upper-atmosphere observations and turbulence physics studies using large eddy simulation and direct numerical simulation methods for three-dimensional gravity wave–breaking processes, are necessary to improve the model performance in future studies.

## Abstract

A model system is established that includes three interactive components: a dynamics model, a turbulence model, and a chemistry model. The dynamics model solves the two-dimensional, nonlinear, nonhydrostatic, compressible, and viscous flow equations, and the turbulence model is adapted from the 2.5-level Mellor–Yamada turbulence model with minor adjustments. The dynamics and the turbulence models are coupled with a chemistry model to study the mesoscale impacts of gravity wave breaking on the atmospheric compositional structures. The present study focuses on the local distribution of atomic oxygen and ozone. The model system is used to study the gravity wave propagation, growth, breakdown, and its impacts on the mean state in the middle and upper atmosphere. The inclusion of a turbulence model makes it possible to study the long-term evolution of the gravity wave after wave breaking and in the presence of nonuniform turbulence, as well as the interaction between a breaking wave and turbulence. The turbulence model parameterizes the three-dimensional mixing due to the flow instability and it eliminates the unrealistically strong supersaturation observed in previous two-dimensional simulations. The modeling result suggests that the induced acceleration due to convective instability may lead to strong shear, which causes dynamical instability at lower altitudes. The result reveals the interdependence of waves and turbulence and shows that the turbulence energy density due to instability has similar temporal and spatial characteristics to previous radar observations. The result is also compared with the linear saturation theory, and it is found that the eddy diffusion coefficients in the wave-breaking region are nonuniform, and the average values are less than those obtained from the linear saturation theory. The result also suggests that the inclusion of the turbulence model could be a valid approach to study the averaged two-dimensional gravity wave and turbulence features after wave breaking. More adjustments of the turbulence model parameters, according to upper-atmosphere observations and turbulence physics studies using large eddy simulation and direct numerical simulation methods for three-dimensional gravity wave–breaking processes, are necessary to improve the model performance in future studies.

## Abstract

A general circulation model has been developed for the atmosphere above 97 km. It uses a 5° latitude × 5° longitude grid and 24 vertical levels in increments of 0.5 scale height. The prognostic variables are horizontal winds, temperature, and the mass mixing ratios of atomic and molecular oxygen, which are obtained using hydrodynamic equations and which include vertical transport by realistic models of molecular diffusion. All the prognostic variables are in near diffusive equilibrium in the vertical as the top of the model is approached. Realistic ion drag is included in the model equations for horizontal winds, including the rapid polar drifts of magnetic field fines due to magnetospheric convection. Excellent agreement is achieved between the calculated and observed global averaged composition, provided a reasonable amount of vertical eddy mixing is included in the compositional equations over the lowest model scale height. Calculations are carried out for solar minimum equinox conditions. The calculated variation of composition with latitude is opposite to that observed for the model forced only by solar heating but is brought into reasonable agreement with observations with the inclusion of auroral heating. Generally speaking, auroral heating changes significantly the global patterns of wind, temperature, and composition, and brings the model composition in reasonable agreement with that given by the MSIS empirical model. The calculated diurnal variations of composition with auroral heating are in acceptable agreement with observation. Calculated temperature variations in the upper thermosphere are consistent with a tendency for the coupled model to minimize the ratio of temperature to mean molecular mass.

## Abstract

A general circulation model has been developed for the atmosphere above 97 km. It uses a 5° latitude × 5° longitude grid and 24 vertical levels in increments of 0.5 scale height. The prognostic variables are horizontal winds, temperature, and the mass mixing ratios of atomic and molecular oxygen, which are obtained using hydrodynamic equations and which include vertical transport by realistic models of molecular diffusion. All the prognostic variables are in near diffusive equilibrium in the vertical as the top of the model is approached. Realistic ion drag is included in the model equations for horizontal winds, including the rapid polar drifts of magnetic field fines due to magnetospheric convection. Excellent agreement is achieved between the calculated and observed global averaged composition, provided a reasonable amount of vertical eddy mixing is included in the compositional equations over the lowest model scale height. Calculations are carried out for solar minimum equinox conditions. The calculated variation of composition with latitude is opposite to that observed for the model forced only by solar heating but is brought into reasonable agreement with observations with the inclusion of auroral heating. Generally speaking, auroral heating changes significantly the global patterns of wind, temperature, and composition, and brings the model composition in reasonable agreement with that given by the MSIS empirical model. The calculated diurnal variations of composition with auroral heating are in acceptable agreement with observation. Calculated temperature variations in the upper thermosphere are consistent with a tendency for the coupled model to minimize the ratio of temperature to mean molecular mass.