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## Abstract

New formulas for the backscattered fraction in two-stream theory are derived. They express this fraction, for either isotropically or monodirectionally incident radiation, as a single integral over the scattering phase function, thereby effecting a substantial simplification over the customary multiple-integral definitions. From these formulas the globally averaged backscatter of the earth due to typical aerosols is shown to depend primarily on the *forward* part (0° to 90°) of the scattering phase function, where the disagreement between spherical-and nonspherical-particle scattering is smallest. The new formulas also lead to connections, in terms of standard elliptic integrals, between the backscatter and the phase function asymmetry factor; while rigorously correct only for the Henyey-Greenstein phase function, these relations are shown to be remarkably accurate for *all* spherical-particle phase functions. The detailed relationship between backscatter and asymmetry factor is shown to be multi-valued; thus two-stream and Eddington approximations cannot be uniquely related.

The common approximation of the globally averaged backscatter, or Bond albedo, by the backscatter for radiation incident at solar zenith angles of O° or 60° is shown to lead, for a wide range of particle sizes and optical properties, to systematic and often large underestimates. The solar-spectrum-integrated enhancement of the Bond albedo due to a uniform, optically thin aerosol layer is examined, holding the total mass of aerosol fixed and varying the particle radii and optical properties over wide ranges. The particle radius at which maximum albedo enhancement occurs decreases from 0.3 µm down to about 0.08 µm as the particle absorptivity increases. Also, increasing the absorption of particles smaller than 0.1 µm actually raises the albedo in contrast to the usual situation where absorption suppresses backscattering.

## Abstract

New formulas for the backscattered fraction in two-stream theory are derived. They express this fraction, for either isotropically or monodirectionally incident radiation, as a single integral over the scattering phase function, thereby effecting a substantial simplification over the customary multiple-integral definitions. From these formulas the globally averaged backscatter of the earth due to typical aerosols is shown to depend primarily on the *forward* part (0° to 90°) of the scattering phase function, where the disagreement between spherical-and nonspherical-particle scattering is smallest. The new formulas also lead to connections, in terms of standard elliptic integrals, between the backscatter and the phase function asymmetry factor; while rigorously correct only for the Henyey-Greenstein phase function, these relations are shown to be remarkably accurate for *all* spherical-particle phase functions. The detailed relationship between backscatter and asymmetry factor is shown to be multi-valued; thus two-stream and Eddington approximations cannot be uniquely related.

The common approximation of the globally averaged backscatter, or Bond albedo, by the backscatter for radiation incident at solar zenith angles of O° or 60° is shown to lead, for a wide range of particle sizes and optical properties, to systematic and often large underestimates. The solar-spectrum-integrated enhancement of the Bond albedo due to a uniform, optically thin aerosol layer is examined, holding the total mass of aerosol fixed and varying the particle radii and optical properties over wide ranges. The particle radius at which maximum albedo enhancement occurs decreases from 0.3 µm down to about 0.08 µm as the particle absorptivity increases. Also, increasing the absorption of particles smaller than 0.1 µm actually raises the albedo in contrast to the usual situation where absorption suppresses backscattering.

## Abstract

A compact law-radar system has been developed for use on an airborne platform. Of particular interest is the use of a flashlamp-pumped dye laser as the radiation source and a plastic Fresnel lens in the receiver to collect the radiation backscattered by the atmosphere. These novel features resulted in a laser probing system that is less expensive, more reliable, and more compact than systems incorporating ruby laser and more conventional receiver optics.

## Abstract

A compact law-radar system has been developed for use on an airborne platform. Of particular interest is the use of a flashlamp-pumped dye laser as the radiation source and a plastic Fresnel lens in the receiver to collect the radiation backscattered by the atmosphere. These novel features resulted in a laser probing system that is less expensive, more reliable, and more compact than systems incorporating ruby laser and more conventional receiver optics.

## Abstract

A simple radiative energy balance model has been developed to assess the impact of stratospheric aerosols on the global climate through their effect on the equilibrium global mean surface temperature. With the assumptions that the radiation in the atmosphere can be treated as diffuse radiation and that the effect of the gases in the stratosphere can be approximated by equivalent gray absorbers and scatterers, an analytic expression which depends only on the optical properties of the aerosol and the planetary albedo is derived for the fractional change in the upward flux of terrestrial infrared radiation at the base of the stratospheric aerosol layer. The fractional change in the upward flux of infrared radiation is then directly related to changes in the global mean surface temperature by using existing results of climate model and radiative convective model calculations. Mie theory is used to compute the scattering and absorbing properties of the aerosol for a range of visible and infrared indices of refraction. Sample calculations are presented that show the fractional change in the upward flux of infrared radiation at the base of the layer as a function of particle size for a specified mass concentration of stratospheric aerosols. The results indicate that both small particles (radii ≲0.05 *μ*m) and large particles (radii ≳ 1.0 *μ*m) generally have a greater influence on terrestrial infrared radiation than on incident solar radiation; therefore, these particles contribute to warming at the surface. Particles of intermediate sizes affect the incident solar radiation more strongly than they affect the terrestrial radiation and thereby contribute to cooling at the surface. The results also demonstrate the feasibility of estimating the largest possible surface temperature response to a given increase in the mass concentration of stratospheric aerosols. Calculations were also performed to enable comparison of the results from the present model with those obtained by approximating the effect of an increase in stratospheric aerosols by means of an equivalent reduction in the solar constant. It is shown that the effects of the aerosols on terrestrial radiation must be negligible, and the aerosols must be nonabsorbing at solar wavelengths in order for the results of the present model to agree with those obtained by assuming a reduction in the solar constant.

## Abstract

A simple radiative energy balance model has been developed to assess the impact of stratospheric aerosols on the global climate through their effect on the equilibrium global mean surface temperature. With the assumptions that the radiation in the atmosphere can be treated as diffuse radiation and that the effect of the gases in the stratosphere can be approximated by equivalent gray absorbers and scatterers, an analytic expression which depends only on the optical properties of the aerosol and the planetary albedo is derived for the fractional change in the upward flux of terrestrial infrared radiation at the base of the stratospheric aerosol layer. The fractional change in the upward flux of infrared radiation is then directly related to changes in the global mean surface temperature by using existing results of climate model and radiative convective model calculations. Mie theory is used to compute the scattering and absorbing properties of the aerosol for a range of visible and infrared indices of refraction. Sample calculations are presented that show the fractional change in the upward flux of infrared radiation at the base of the layer as a function of particle size for a specified mass concentration of stratospheric aerosols. The results indicate that both small particles (radii ≲0.05 *μ*m) and large particles (radii ≳ 1.0 *μ*m) generally have a greater influence on terrestrial infrared radiation than on incident solar radiation; therefore, these particles contribute to warming at the surface. Particles of intermediate sizes affect the incident solar radiation more strongly than they affect the terrestrial radiation and thereby contribute to cooling at the surface. The results also demonstrate the feasibility of estimating the largest possible surface temperature response to a given increase in the mass concentration of stratospheric aerosols. Calculations were also performed to enable comparison of the results from the present model with those obtained by approximating the effect of an increase in stratospheric aerosols by means of an equivalent reduction in the solar constant. It is shown that the effects of the aerosols on terrestrial radiation must be negligible, and the aerosols must be nonabsorbing at solar wavelengths in order for the results of the present model to agree with those obtained by assuming a reduction in the solar constant.

## Abstract

Simultaneous visibility observations and size-number distribution measurements of airborne soil particles were made during incidents of soil erosion in west Texas. Visibilities were calculated by applying Mie scattering theory to measured size distributions and were compared with observed visibilities. Agreement was found, and similar comparison with artifical modicications to the observed size distributions demonstrated that any major changes in the observed size distributions would result in significant discrepancies between the observed and the calculated visibilities. These comparisons confirm that under our experimental conditions the optically important particles are those in the size range 0.62 < *r* < 20 *μ*m. The sensitivity of the calculated visibility to modifications in the measured size distribution implies that such comparisons between calculated and observed visibility provide a means of confirming size distribution measurements under a variety of conditions.

## Abstract

Simultaneous visibility observations and size-number distribution measurements of airborne soil particles were made during incidents of soil erosion in west Texas. Visibilities were calculated by applying Mie scattering theory to measured size distributions and were compared with observed visibilities. Agreement was found, and similar comparison with artifical modicications to the observed size distributions demonstrated that any major changes in the observed size distributions would result in significant discrepancies between the observed and the calculated visibilities. These comparisons confirm that under our experimental conditions the optically important particles are those in the size range 0.62 < *r* < 20 *μ*m. The sensitivity of the calculated visibility to modifications in the measured size distribution implies that such comparisons between calculated and observed visibility provide a means of confirming size distribution measurements under a variety of conditions.

## Abstract

Hemispherical backscattering cross sections *σ _{b}
* of spherical particles are calculated using a recently derived analytic expression. Results are compared with

*σ*values obtained by numerical integration. It is found that the analytic formula gives exact values of the hemispherical backscattering cross sections and also saves computer time. The behavior of

_{b}*σ*in the limits of very small and very large spheres is discussed. As an aid in utilizing simple models of climate change due to aerosols, the percentage of incident solar radiation scattered into the backward hemisphere is calculated for a range of particle sizes and complex refractive indices. Similar results are also presented for the ratio of absorption to hemispheric backscattering, a critical parameter in many aerosol climate models.

_{b}## Abstract

Hemispherical backscattering cross sections *σ _{b}
* of spherical particles are calculated using a recently derived analytic expression. Results are compared with

*σ*values obtained by numerical integration. It is found that the analytic formula gives exact values of the hemispherical backscattering cross sections and also saves computer time. The behavior of

_{b}*σ*in the limits of very small and very large spheres is discussed. As an aid in utilizing simple models of climate change due to aerosols, the percentage of incident solar radiation scattered into the backward hemisphere is calculated for a range of particle sizes and complex refractive indices. Similar results are also presented for the ratio of absorption to hemispheric backscattering, a critical parameter in many aerosol climate models.

_{b}## Abstract

On 30 September 1970, the National Center for Atmospheric Research (NCAR) obtained data on the vertical distribution of particulate material over Boulder, Colo., from laser radar soundings and simultaneous airborne particle collections. A layer of particulate material at about 13 km was of special interest. Particles in this layer differed from normal tropospheric particles and were probably fly ash created by forest fires in California during the previous week. A technique for determining the complex index of refraction of atmospheric particles has been applied to the 13-km data. By assuming the real part of the refractive index to be 1.55, the imaginary part (the absorption parameter) is estimated to be 0.044±0.011.

## Abstract

On 30 September 1970, the National Center for Atmospheric Research (NCAR) obtained data on the vertical distribution of particulate material over Boulder, Colo., from laser radar soundings and simultaneous airborne particle collections. A layer of particulate material at about 13 km was of special interest. Particles in this layer differed from normal tropospheric particles and were probably fly ash created by forest fires in California during the previous week. A technique for determining the complex index of refraction of atmospheric particles has been applied to the 13-km data. By assuming the real part of the refractive index to be 1.55, the imaginary part (the absorption parameter) is estimated to be 0.044±0.011.

## Abstract

The angular variation of the intensity of light scattered from a collimated beam by airborne soil particles and the size distribution of the particles were measured simultaneously 1.5 m above the ground. These measurements gave an estimate of the complex index of refraction *m=n*
_{RE}−*n*
_{IM}
*i* of airborne soil particles, where *n*
_{RE} is the real part and *n*
_{IM} the imaginary part of the refractive index.

Standard microscopic analysis procedures were employed to determine *n*
_{RE}. Although a wide range of values was observed, the value 1.525 was taken as representative. By applying Mie scattering theory to each of the observed distributions of particle size, the expected angular variation of the intensity of the scattered light was calculated for a fixed value of *n*
_{RE} and a wide range of values of *n*
_{IM}. For each set of simultaneous measurements, the value of *n*
_{IM} was taken to be that value which provided the best fit to the experimental data. The upper limit of the value of *n*
_{IM} for the airborne particles studied in the experiment was determined to be 0.005 with an uncertainty factor of about 2. The estimate of *n*
_{IM} was found to be fairly insensitive to the assumed value of *n*
_{RE}.

## Abstract

The angular variation of the intensity of light scattered from a collimated beam by airborne soil particles and the size distribution of the particles were measured simultaneously 1.5 m above the ground. These measurements gave an estimate of the complex index of refraction *m=n*
_{RE}−*n*
_{IM}
*i* of airborne soil particles, where *n*
_{RE} is the real part and *n*
_{IM} the imaginary part of the refractive index.

Standard microscopic analysis procedures were employed to determine *n*
_{RE}. Although a wide range of values was observed, the value 1.525 was taken as representative. By applying Mie scattering theory to each of the observed distributions of particle size, the expected angular variation of the intensity of the scattered light was calculated for a fixed value of *n*
_{RE} and a wide range of values of *n*
_{IM}. For each set of simultaneous measurements, the value of *n*
_{IM} was taken to be that value which provided the best fit to the experimental data. The upper limit of the value of *n*
_{IM} for the airborne particles studied in the experiment was determined to be 0.005 with an uncertainty factor of about 2. The estimate of *n*
_{IM} was found to be fairly insensitive to the assumed value of *n*
_{RE}.