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- Author or Editor: R. E. Dickinson x
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Abstract
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Abstract
This paper treats the initial value problem of a forced Rossby wave encountering a critical level in a barotropic zonal shear flow which can change in response to the wave momentum flux divergence. The main result of the calculation is that the shape of the zonal flow profile changes with time in such a way as to reduce the potential vorticity gradient (β−U yy ) to zero at the critical level. For this configuration the wave is totally reflected at the critical level and in the absence of dissipation no longer interacts with the zonal flow. Details of the evolution toward the steady state depend on the ratio of two time scales, one a measure of the wave amplitude and the other representing the time it takes for the wave momentum flux to be concentrated in a well-defined critical layer.
The steady-state balance between wave and mean flow probably never occurs in the atmosphere because the time required to set it up is long compared to the expected time scale of natural variability of the zonal flow. More relevant to atmospheric flows is the fact that excursions of (β−U yy ) to negative values during the approach to a steady state are attended by over reflection of the incident wave and a temporary reversal of the wave momentum flux. After the first of these excursions, occurring on a time scale comparable to that required to set up a critical layer, the zonal flow is never far from the final equilibrium profile.
Abstract
This paper treats the initial value problem of a forced Rossby wave encountering a critical level in a barotropic zonal shear flow which can change in response to the wave momentum flux divergence. The main result of the calculation is that the shape of the zonal flow profile changes with time in such a way as to reduce the potential vorticity gradient (β−U yy ) to zero at the critical level. For this configuration the wave is totally reflected at the critical level and in the absence of dissipation no longer interacts with the zonal flow. Details of the evolution toward the steady state depend on the ratio of two time scales, one a measure of the wave amplitude and the other representing the time it takes for the wave momentum flux to be concentrated in a well-defined critical layer.
The steady-state balance between wave and mean flow probably never occurs in the atmosphere because the time required to set it up is long compared to the expected time scale of natural variability of the zonal flow. More relevant to atmospheric flows is the fact that excursions of (β−U yy ) to negative values during the approach to a steady state are attended by over reflection of the incident wave and a temporary reversal of the wave momentum flux. After the first of these excursions, occurring on a time scale comparable to that required to set up a critical layer, the zonal flow is never far from the final equilibrium profile.
Abstract
This analysis treats the transient inertia-gravity wave response of a shallow fluid to an impulsive addition of momentum. The Coriolis parameter varies with latitude, but Rossby waves are not considered. The square of the Coriolis term is approximated by a constant term plus a term linear in the northward coordinate. In this approximation, monochromatic waves, which reach a turning point at the latitude where the wave frequency equals the local Coriolis frequency, are given by Airy functions. A contour integral solution to the initial value problem is expressed as a Fourier integral over wave frequency with an Airy function argument and is evaluated approximately using the stationary phase technique. The solution at a given latitude is first dominated by waves from the source and then waves reflected from turning points poleward of the source. The results are applied to give a qualitative description of the wake of a hurricane moving over a stratified ocean.
Abstract
This analysis treats the transient inertia-gravity wave response of a shallow fluid to an impulsive addition of momentum. The Coriolis parameter varies with latitude, but Rossby waves are not considered. The square of the Coriolis term is approximated by a constant term plus a term linear in the northward coordinate. In this approximation, monochromatic waves, which reach a turning point at the latitude where the wave frequency equals the local Coriolis frequency, are given by Airy functions. A contour integral solution to the initial value problem is expressed as a Fourier integral over wave frequency with an Airy function argument and is evaluated approximately using the stationary phase technique. The solution at a given latitude is first dominated by waves from the source and then waves reflected from turning points poleward of the source. The results are applied to give a qualitative description of the wake of a hurricane moving over a stratified ocean.
Abstract
The vertical motion field in the thermosphere is calculated from the continuity equation. This calculation is based on a field of horizontal winds and an intermediate model of the thermospheric temperature field consistent with the density structure inferred from satellite drag data. The vertical motion consists of a component due to rise and fall of constant pressure surfaces and a component due to horizontal maas divergences, both components being of the order of 1 m. sec.−1 Only the latter component is of importance for thermodynamic considerations. The adiabatic warming associated with the diurnally variable part of the vertical motion due to mass divergence gives a second heat source which is of magnitude comparable to the heating by solar radiation. The time-averaged meridional circulation also implies large adiabatic warming and cooling. This computed mean meridional circulation cannot be reconciled with the heat balance of the thermosphere. The thermospheric temperature field at low levels in high latitudes can be changed so as to reverse the direction of the mean meridional pressure gradient and thus to give a mean meridional circulation consistent with heat balance considerations. Existing global thermospheric models could be improved by adjustment of the temperature field at low levels in such a way that vertical motions computed from horizontal winds give a plausible adiabatic heating field.
Abstract
The vertical motion field in the thermosphere is calculated from the continuity equation. This calculation is based on a field of horizontal winds and an intermediate model of the thermospheric temperature field consistent with the density structure inferred from satellite drag data. The vertical motion consists of a component due to rise and fall of constant pressure surfaces and a component due to horizontal maas divergences, both components being of the order of 1 m. sec.−1 Only the latter component is of importance for thermodynamic considerations. The adiabatic warming associated with the diurnally variable part of the vertical motion due to mass divergence gives a second heat source which is of magnitude comparable to the heating by solar radiation. The time-averaged meridional circulation also implies large adiabatic warming and cooling. This computed mean meridional circulation cannot be reconciled with the heat balance of the thermosphere. The thermospheric temperature field at low levels in high latitudes can be changed so as to reverse the direction of the mean meridional pressure gradient and thus to give a mean meridional circulation consistent with heat balance considerations. Existing global thermospheric models could be improved by adjustment of the temperature field at low levels in such a way that vertical motions computed from horizontal winds give a plausible adiabatic heating field.
Abstract
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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
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.
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 × 1018 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 × 1018 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.
The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) is described and the first stage science plan outlined. PILPS is a project designed to improve the parameterization of the continental surface, especially the hydrological, energy, momentum, and carbon exchanges with the atmosphere. The PILPS Science Plan incorporates enhanced documentation, comparison, and validation of continental surface parameterization schemes by community participation. Potential participants include code developers, code users, and those who can provide datasets for validation and who have expertise of value in this exercise. PILPS is an important activity because existing intercomparisons, although piecemeal, demonstrate that there are significant differences in the formulation of individual processes in the available land surface schemes. These differences are comparable to other recognized differences among current global climate models such as cloud and convection parameterizations. It is also clear that too few sensitivity studies have been undertaken with the result that there is not yet enough information to indicate which simplifications or omissions are important for the near-surface continental climate, hydrology, and biogeochemistry. PILPS emphasizes sensitivity studies with and intercomparisons of existing land surface codes and the development of areally extensive datasets for their testing and validation.
The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) is described and the first stage science plan outlined. PILPS is a project designed to improve the parameterization of the continental surface, especially the hydrological, energy, momentum, and carbon exchanges with the atmosphere. The PILPS Science Plan incorporates enhanced documentation, comparison, and validation of continental surface parameterization schemes by community participation. Potential participants include code developers, code users, and those who can provide datasets for validation and who have expertise of value in this exercise. PILPS is an important activity because existing intercomparisons, although piecemeal, demonstrate that there are significant differences in the formulation of individual processes in the available land surface schemes. These differences are comparable to other recognized differences among current global climate models such as cloud and convection parameterizations. It is also clear that too few sensitivity studies have been undertaken with the result that there is not yet enough information to indicate which simplifications or omissions are important for the near-surface continental climate, hydrology, and biogeochemistry. PILPS emphasizes sensitivity studies with and intercomparisons of existing land surface codes and the development of areally extensive datasets for their testing and validation.
