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## Abstract

A quantitative study of the photochemistry of NH_{3} above the Jovian tropopause is given. The NH_{3}, density distribution is described by two relevant vertical scales: *H*
_{av} the scale height of the background atmosphere, and (*K*/*J*
_{net}½ the “photomechanical” scale height, where *K* is the eddy diffusion coefficient and *J*
_{net>} the net destruction rate of NH_{3}.In the case of slow mixing, substantial photochemical destruction of NH_{3} occurs and the NH_{3} density profile departs significantly from a mixed distribution. Comparison of the observed and calculated UV albedos of Jupiter suggests a value of *K*≈2×10^{4} cm^{2} sec ^{−1} is appropriate in the lower stratosphere. Radiative excitation of NH_{2} radicals to the *A* state is unimportant in the NH_{3} photochemistry. A slow circulation that transports N_{2}H_{4} to the hotter, dense regions of the eep atmosphere, where it undergoes thermal decomposition to NH_{2} radicals which react with H2 to form fresh NH_{3}, is invoked to explain the continued presence of NH_{3} on Jupiter. It is suggested that condensation of N_{2}H_{4} is a source of the upper semi-transmitting cloud layer postulated by Axel to explain the low observed UV geometric albedo.

## Abstract

A quantitative study of the photochemistry of NH_{3} above the Jovian tropopause is given. The NH_{3}, density distribution is described by two relevant vertical scales: *H*
_{av} the scale height of the background atmosphere, and (*K*/*J*
_{net}½ the “photomechanical” scale height, where *K* is the eddy diffusion coefficient and *J*
_{net>} the net destruction rate of NH_{3}.In the case of slow mixing, substantial photochemical destruction of NH_{3} occurs and the NH_{3} density profile departs significantly from a mixed distribution. Comparison of the observed and calculated UV albedos of Jupiter suggests a value of *K*≈2×10^{4} cm^{2} sec ^{−1} is appropriate in the lower stratosphere. Radiative excitation of NH_{2} radicals to the *A* state is unimportant in the NH_{3} photochemistry. A slow circulation that transports N_{2}H_{4} to the hotter, dense regions of the eep atmosphere, where it undergoes thermal decomposition to NH_{2} radicals which react with H2 to form fresh NH_{3}, is invoked to explain the continued presence of NH_{3} on Jupiter. It is suggested that condensation of N_{2}H_{4} is a source of the upper semi-transmitting cloud layer postulated by Axel to explain the low observed UV geometric albedo.

## Abstract

A detailed quantitative study of the photochemistry of CH_{4}, C_{2}H_{2}, C_{2}H_{4} and C_{2}H_{6} which includes eddy and molecular diffusion is presented for the Jovian upper atmosphere composed of 90% H_{2}, 10% He with a CH_{4} mixing ratio of 7×10^{−4}. The densities of the following constituents are calculated: CH_{4}, CH, ^{1}CH_{2}, CH_{3}, C_{2}H_{2}, C_{2}H_{3}, C_{2}H_{4}, C_{2}H_{5}, C_{2}H_{6}, H. The C_{2}H_{6} mixing ratio is ∼10^{−5} and the C_{2}H_{2} concentration ∼10^{9} cm^{−3} throughout the upper stratosphere and lower mesosphere. The concentration of C_{2}H_{2} near the mesopause is sufficiently large to make it the most important radiator of infrared energy. C_{2}H_{2} is also an efficient catalyst in the recombination of H atoms. In the region of photolysis approximately 20% of the dissociated CH_{4} molecules are irreversibly converted to heavier hydrocarbons. Density profiles of atomic hydrogen which are needed to interpret Lyman-α albedo measurements of Jupiter are calculated with H_{2} dissociation and ionization and CH_{4} dissociation as sources of H.

## Abstract

A detailed quantitative study of the photochemistry of CH_{4}, C_{2}H_{2}, C_{2}H_{4} and C_{2}H_{6} which includes eddy and molecular diffusion is presented for the Jovian upper atmosphere composed of 90% H_{2}, 10% He with a CH_{4} mixing ratio of 7×10^{−4}. The densities of the following constituents are calculated: CH_{4}, CH, ^{1}CH_{2}, CH_{3}, C_{2}H_{2}, C_{2}H_{3}, C_{2}H_{4}, C_{2}H_{5}, C_{2}H_{6}, H. The C_{2}H_{6} mixing ratio is ∼10^{−5} and the C_{2}H_{2} concentration ∼10^{9} cm^{−3} throughout the upper stratosphere and lower mesosphere. The concentration of C_{2}H_{2} near the mesopause is sufficiently large to make it the most important radiator of infrared energy. C_{2}H_{2} is also an efficient catalyst in the recombination of H atoms. In the region of photolysis approximately 20% of the dissociated CH_{4} molecules are irreversibly converted to heavier hydrocarbons. Density profiles of atomic hydrogen which are needed to interpret Lyman-α albedo measurements of Jupiter are calculated with H_{2} dissociation and ionization and CH_{4} dissociation as sources of H.

## Abstract

A mechanistic, quasi-geostrophic, semi-spectral model with a self-consistent calculation of the mean zonal flow fields is used to numerically simulate sudden stratospheric warmings generated by a single zonal harmonic (*m*) planetary wave. The development of a warming depends critically on the two factors which govern the transmission of planetary waves to the upper stratosphere: 1) the strength of the westerly winds in the lower stratosphere and 2) the magnitude of wave damping in the same region. Major warmings can only develop when the prewarming lower stratospheric winds and tropospheric forcing are strong but insufficient to trap the wave at low altitudes. Damping controls the maximum amplitude that a warming can attain and the time constant for its growth rate. The growth rate of a *m* = 2 warming is accelerated during the westerly zonal wind phase of the quasi-biennial oscillation, but the maximum amplitude of the warming is independent of QBO phase.

The evolution of *m* = 1 and *m* = 2 warmings are very different. An *m* = 1 warming is characterized by pronounced oscillation of wave amplitude and mean flow that result from resonantly trapped, westward propagating planetary waves moving in and out of phase with the tropospherically forced stationary planetary wave. This oscillation can reach sufficient amplitude to decelerate the zonal flow during a cycle to easterlies and create a critical level. Although formation of a *mesopheric* critical level is not required to initiate a warming, the development and propagation of critical levels in the middle atmosphere is central to the evolution of sudden warmings. During an *m* = 1 event the critical level forms initially in the polar region and advances equatorward in its development. But a *m* = 2 critical level first develops in the equatorial region and advances poleward. A *m* = 2 warming is also characterized by a sudden intensification after an initially slow growth in contrast to slowly developing *m* = 1 warmings. Both *m* = 1 and *m* = 2 warmings are accompanied by polar mesospheric cooling, low-latitude stratospheric cooling and equatorial mesospheric heating as a result of the induced secondary circulation in response to eddy heat transport to the polar stratosphere.

Long-term integrations with a steady forced *m* = 1 wave show that the mean flow evolves to a steady, asymptotic state with net cooling in the polar mesosphere from planetary waves. But steady *m* = 2 forcing of greater than approximately 200 m at 300 mb leads to multiple generation of warmings which are similar to stratospheric vacillations.

## Abstract

A mechanistic, quasi-geostrophic, semi-spectral model with a self-consistent calculation of the mean zonal flow fields is used to numerically simulate sudden stratospheric warmings generated by a single zonal harmonic (*m*) planetary wave. The development of a warming depends critically on the two factors which govern the transmission of planetary waves to the upper stratosphere: 1) the strength of the westerly winds in the lower stratosphere and 2) the magnitude of wave damping in the same region. Major warmings can only develop when the prewarming lower stratospheric winds and tropospheric forcing are strong but insufficient to trap the wave at low altitudes. Damping controls the maximum amplitude that a warming can attain and the time constant for its growth rate. The growth rate of a *m* = 2 warming is accelerated during the westerly zonal wind phase of the quasi-biennial oscillation, but the maximum amplitude of the warming is independent of QBO phase.

The evolution of *m* = 1 and *m* = 2 warmings are very different. An *m* = 1 warming is characterized by pronounced oscillation of wave amplitude and mean flow that result from resonantly trapped, westward propagating planetary waves moving in and out of phase with the tropospherically forced stationary planetary wave. This oscillation can reach sufficient amplitude to decelerate the zonal flow during a cycle to easterlies and create a critical level. Although formation of a *mesopheric* critical level is not required to initiate a warming, the development and propagation of critical levels in the middle atmosphere is central to the evolution of sudden warmings. During an *m* = 1 event the critical level forms initially in the polar region and advances equatorward in its development. But a *m* = 2 critical level first develops in the equatorial region and advances poleward. A *m* = 2 warming is also characterized by a sudden intensification after an initially slow growth in contrast to slowly developing *m* = 1 warmings. Both *m* = 1 and *m* = 2 warmings are accompanied by polar mesospheric cooling, low-latitude stratospheric cooling and equatorial mesospheric heating as a result of the induced secondary circulation in response to eddy heat transport to the polar stratosphere.

Long-term integrations with a steady forced *m* = 1 wave show that the mean flow evolves to a steady, asymptotic state with net cooling in the polar mesosphere from planetary waves. But steady *m* = 2 forcing of greater than approximately 200 m at 300 mb leads to multiple generation of warmings which are similar to stratospheric vacillations.

## Abstract

The problem of nonlinear saturation of baroclinic waves in two-layer models is studied and it is shown that Shepherd's rigorous bound on the wavy disturbance growth due to instabilities of parallel shear flow can be improved significantly, in some cases, by exact calculation of the averaged Arnol'd's invariant. Shepherd's bound for the Phillips' β-plane two-layer model with constant potential vorticity gradient is achievable at the minimum critical shear as the supercriticality parameter ε → 0. The underlying reason for such an achievable bound for the wavy disturbance is that the condition leading to the Arnol'd's stability theorem is both necessary and sufficient. Based on such an achievable bound, (2β/3*F*)^{1/2} is deduced as the maximum wave amplitude at the minimum critical shear as the supercriticality parameter ε → 0. When Arnol'd's invariant is applied to an *f*- plane two-layer model, the bound derived from Arnol'd's invariant is not as powerful a constraint on the amplitude of the evolving wavy disturbance. The reason is that the opposite signs of potential vorticity gradients in upper and lower layers are not a sufficient condition for instability.

## Abstract

The problem of nonlinear saturation of baroclinic waves in two-layer models is studied and it is shown that Shepherd's rigorous bound on the wavy disturbance growth due to instabilities of parallel shear flow can be improved significantly, in some cases, by exact calculation of the averaged Arnol'd's invariant. Shepherd's bound for the Phillips' β-plane two-layer model with constant potential vorticity gradient is achievable at the minimum critical shear as the supercriticality parameter ε → 0. The underlying reason for such an achievable bound for the wavy disturbance is that the condition leading to the Arnol'd's stability theorem is both necessary and sufficient. Based on such an achievable bound, (2β/3*F*)^{1/2} is deduced as the maximum wave amplitude at the minimum critical shear as the supercriticality parameter ε → 0. When Arnol'd's invariant is applied to an *f*- plane two-layer model, the bound derived from Arnol'd's invariant is not as powerful a constraint on the amplitude of the evolving wavy disturbance. The reason is that the opposite signs of potential vorticity gradients in upper and lower layers are not a sufficient condition for instability.

## Abstract

The agronomy of hydrogen and its compounds is discussed in a simplified model intended to represent a diurnal and global average. Vertical transport by eddy and molecular diffusion is included for the major components H_{2}O, H and H_{2}. The flow at 100 km is found to be dominated by H_{2}, which is converted to H in the thermosphere and escapes. The flux is insensitive to the details of the chemistry and to large variations in the assumed eddy coefficients. Slightly above the homopause at 100 km, the H_{2} flux is close to its “limiting” value, which is proportional to the H_{2} mixing ratio. This mixing ratio, in terms of total H atoms, is slightly less than that of H_{2}O, H_{2} and CH_{4} at 30 km. Any variation of the latter therefore varies the escape flux in proportion. The model reproduces the observed escape flux fairly well, along with other observations of OH and H in the mesosphere. Reduction of the input mixing ratio by a factor of 2 would improve the agreement. It is suggested that the H_{2}O mixing ratio at 30 km may be low as 1 part per million by volume, and almost certainly no greater than a few ppm.

## Abstract

The agronomy of hydrogen and its compounds is discussed in a simplified model intended to represent a diurnal and global average. Vertical transport by eddy and molecular diffusion is included for the major components H_{2}O, H and H_{2}. The flow at 100 km is found to be dominated by H_{2}, which is converted to H in the thermosphere and escapes. The flux is insensitive to the details of the chemistry and to large variations in the assumed eddy coefficients. Slightly above the homopause at 100 km, the H_{2} flux is close to its “limiting” value, which is proportional to the H_{2} mixing ratio. This mixing ratio, in terms of total H atoms, is slightly less than that of H_{2}O, H_{2} and CH_{4} at 30 km. Any variation of the latter therefore varies the escape flux in proportion. The model reproduces the observed escape flux fairly well, along with other observations of OH and H in the mesosphere. Reduction of the input mixing ratio by a factor of 2 would improve the agreement. It is suggested that the H_{2}O mixing ratio at 30 km may be low as 1 part per million by volume, and almost certainly no greater than a few ppm.

## Abstract

A theoretical study is made to assess the importance of the solar EUV flux in the thermal energy balance of the Jovian thermosphere. A global averaged vertical temperature contrast in the thermosphere of 15K is calculated and the mesopause is located at a particle density of 5×10^{13} cm^{−3}. Thus, the upper atmosphere of Jupiter is approximately isothermal. At the mesopause IR cooling by C_{3}H_{2} is an order of magnitude more important than IR cooling by CH_{4}. Only the location of the mesopause is a sensitive function of the IR cooling agent in the upper atmosphere. The exospheric temperature depends principally on the mesopause temperature and the solar flux. Eddy heat transport plays a negligible role in the thermal energy balance of the Jovian thermosphere. For the thermospheres of Saturn and Titan the global averaged vertical temperature contrasts are estimated to be ∼10K and 90K, respectively, if their compositions are similar to Jupiter's and the same physics is applicable.

## Abstract

A theoretical study is made to assess the importance of the solar EUV flux in the thermal energy balance of the Jovian thermosphere. A global averaged vertical temperature contrast in the thermosphere of 15K is calculated and the mesopause is located at a particle density of 5×10^{13} cm^{−3}. Thus, the upper atmosphere of Jupiter is approximately isothermal. At the mesopause IR cooling by C_{3}H_{2} is an order of magnitude more important than IR cooling by CH_{4}. Only the location of the mesopause is a sensitive function of the IR cooling agent in the upper atmosphere. The exospheric temperature depends principally on the mesopause temperature and the solar flux. Eddy heat transport plays a negligible role in the thermal energy balance of the Jovian thermosphere. For the thermospheres of Saturn and Titan the global averaged vertical temperature contrasts are estimated to be ∼10K and 90K, respectively, if their compositions are similar to Jupiter's and the same physics is applicable.

## Abstract

Radiative damping rates of atmospheric temperature perturbations can be calculated by either an eigenvalue method or a scale-dependent Newtonian cooling method, which we show are equivalent in two limits. One limit is an infinite, homogeneous atmosphere based on Spiegel's model. The other, corresponding to an empirical scale-independent Newtonian cooling coefficient, is the transparent limit to radiation. In the upper mesosphere the damping rate is calculated by both methods using a non-LTE Curtis matrix. If the atmospheric application requires only thermal damping in a narrow altitude region for waves of small vertical wavelength or damping in a thick layer for large vertical wavelength waves, then one of these limits is a valid approximation. Under these circumstances the easily calculated, scale-dependent, Newtonian cooling rate gives a good approximation to the radiative damping rate. Scale-dependent radiative damping rates calculated with non-LTE Curtis matrices and an exact line-by-line integration scheme are presented over the region 60–93 km and supersede the widely used damping rates of Fels in 1984.

## Abstract

Radiative damping rates of atmospheric temperature perturbations can be calculated by either an eigenvalue method or a scale-dependent Newtonian cooling method, which we show are equivalent in two limits. One limit is an infinite, homogeneous atmosphere based on Spiegel's model. The other, corresponding to an empirical scale-independent Newtonian cooling coefficient, is the transparent limit to radiation. In the upper mesosphere the damping rate is calculated by both methods using a non-LTE Curtis matrix. If the atmospheric application requires only thermal damping in a narrow altitude region for waves of small vertical wavelength or damping in a thick layer for large vertical wavelength waves, then one of these limits is a valid approximation. Under these circumstances the easily calculated, scale-dependent, Newtonian cooling rate gives a good approximation to the radiative damping rate. Scale-dependent radiative damping rates calculated with non-LTE Curtis matrices and an exact line-by-line integration scheme are presented over the region 60–93 km and supersede the widely used damping rates of Fels in 1984.

## Abstract

The steady-state, zonally averaged circulation of the middle atmosphere (15–125 km) is studied with a quasigeostrophic, numerical model that explicitly includes a self-consistent calculation of solar radiative heating due to O_{2} and O_{3} absorption, Newtonian cooling, Rayleigh friction, tropopause boundary conditions based on climatological averages, and the effects of vertically propagating planetary waves. We find the direct, radiatively driven pole-to-pole circulation at solstice is sufficient to account for the cold summer mesopause and warm isothermal winter mesosphere with associated zonal jets of realistic magnitude. The climatological heat and momentum fluxes associated with planetary wavenumber 2 have a negligible effect on the mean circulation. With planetary wavenumber 1 no steady-state solution could be obtained due to the formation of easterlies and hence critical layers in the winter mesosphere. We also find that the radiative heating associated with secondary peaks in the O_{3} density at the mesopause could render the polar mesopause region convectively unstable.

## Abstract

The steady-state, zonally averaged circulation of the middle atmosphere (15–125 km) is studied with a quasigeostrophic, numerical model that explicitly includes a self-consistent calculation of solar radiative heating due to O_{2} and O_{3} absorption, Newtonian cooling, Rayleigh friction, tropopause boundary conditions based on climatological averages, and the effects of vertically propagating planetary waves. We find the direct, radiatively driven pole-to-pole circulation at solstice is sufficient to account for the cold summer mesopause and warm isothermal winter mesosphere with associated zonal jets of realistic magnitude. The climatological heat and momentum fluxes associated with planetary wavenumber 2 have a negligible effect on the mean circulation. With planetary wavenumber 1 no steady-state solution could be obtained due to the formation of easterlies and hence critical layers in the winter mesosphere. We also find that the radiative heating associated with secondary peaks in the O_{3} density at the mesopause could render the polar mesopause region convectively unstable.

## Abstract

The effects of various ozone density reductions on the zonally averaged circulation are evaluated with a numerical quasi-geostrophic model. If the ozone perturbation are confined to the polar regions and are minuscule on a global basis as was characteristic of the August 1972 solar proton event, then our calculation indicate a negligible effect on the mean circulation. For global ozone perturbations by predicted halocarbon pollution, we calculate about a 10% reduction in the zonal jet strength and less than a 5% change in global mean stratosphere temperature. Large, uniform ozone reductions (>50%) produce significant effects on the mean circulation: a substantial collapse of the stratosphere due to cooler temperatures, and a weak polar night jet. The reflection and transmission of quasi-stationary planetary waves in the middle atmosphere are computed to be insensitive to solar activity as extreme as the August 1972 solar proton event. It thus seems improbable that planetary waves are a viable mechanism for solar-weather interactions that involve perturbations of the zonally averaged circulation by ozone density reductions.

## Abstract

The effects of various ozone density reductions on the zonally averaged circulation are evaluated with a numerical quasi-geostrophic model. If the ozone perturbation are confined to the polar regions and are minuscule on a global basis as was characteristic of the August 1972 solar proton event, then our calculation indicate a negligible effect on the mean circulation. For global ozone perturbations by predicted halocarbon pollution, we calculate about a 10% reduction in the zonal jet strength and less than a 5% change in global mean stratosphere temperature. Large, uniform ozone reductions (>50%) produce significant effects on the mean circulation: a substantial collapse of the stratosphere due to cooler temperatures, and a weak polar night jet. The reflection and transmission of quasi-stationary planetary waves in the middle atmosphere are computed to be insensitive to solar activity as extreme as the August 1972 solar proton event. It thus seems improbable that planetary waves are a viable mechanism for solar-weather interactions that involve perturbations of the zonally averaged circulation by ozone density reductions.