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- Author or Editor: S. Twomey x
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Abstract
Scaling principles can be used to transform problems of radiative transfer in media that scatter anisotropically to equivalent isotropic problems with exact solutions. By using such scaling principles together with geometric optics to relate the albedo for single scattering to drop radius and bulk absorption coefficient, very simple relationships can be obtained to calculate absorption of solar radiation by optically thick clouds. The results predict a dependence of absorption on the square root of cloud drop radius and thereby a dependence on air mass and pollution. Although these formulas are approximate, they are probably as good as the exact theory to within the limits of experimental accuracy, and they have the virtue of being exceedingly simple while retaining in their derivation the physics underlying the dependences that they indicate.
Abstract
Scaling principles can be used to transform problems of radiative transfer in media that scatter anisotropically to equivalent isotropic problems with exact solutions. By using such scaling principles together with geometric optics to relate the albedo for single scattering to drop radius and bulk absorption coefficient, very simple relationships can be obtained to calculate absorption of solar radiation by optically thick clouds. The results predict a dependence of absorption on the square root of cloud drop radius and thereby a dependence on air mass and pollution. Although these formulas are approximate, they are probably as good as the exact theory to within the limits of experimental accuracy, and they have the virtue of being exceedingly simple while retaining in their derivation the physics underlying the dependences that they indicate.
Abstract
Spectral reflectances have been calculated by accepted methods for water cloud layers having various microphysical properties.
We show that spectral reflectance measurements carried out with realistic accuracy at wavelengths free from interference by absorbers other than water, can yield information about scaled optical thickness [τ′=(1−gτ] and mean drop radius R̄
Abstract
Spectral reflectances have been calculated by accepted methods for water cloud layers having various microphysical properties.
We show that spectral reflectance measurements carried out with realistic accuracy at wavelengths free from interference by absorbers other than water, can yield information about scaled optical thickness [τ′=(1−gτ] and mean drop radius R̄
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This paper presents the results of measurements of size distributions of particulate matter in the atmosphere. The general shape of the distributions is discussed, particularly the appearance of maxima corresponding to particles with radii about 6×10−6 cm and the sizeable fraction of the total particle population in the region r≤10−6 cm. Size distributions obtained from the same air mass before and after fog formation show apparent removal of smaller particles (r≤10−6 cm) which is consistent with Smoluchowski's coagulation law. Several representations of size distributions are presented in order to compare the results obtained with those of other researchers.
Abstract
This paper presents the results of measurements of size distributions of particulate matter in the atmosphere. The general shape of the distributions is discussed, particularly the appearance of maxima corresponding to particles with radii about 6×10−6 cm and the sizeable fraction of the total particle population in the region r≤10−6 cm. Size distributions obtained from the same air mass before and after fog formation show apparent removal of smaller particles (r≤10−6 cm) which is consistent with Smoluchowski's coagulation law. Several representations of size distributions are presented in order to compare the results obtained with those of other researchers.
Abstract
An apparatus for the determination of the size distribution of an heterogeneous aerosol is described. The apparatus employs two diffusion batteries (series of narrow rectangular channels) through which an aerosol sample is passed to obtain attrition of its particle population by diffusion to the walls of the channels. Observations of particle concentrations after successive stages of “decay” produce a decay curve which represents an integral transform of the distribution function with respect to diffusion coefficient. After mathematical manipulation the size distribution of the aerosol is obtained.
Abstract
An apparatus for the determination of the size distribution of an heterogeneous aerosol is described. The apparatus employs two diffusion batteries (series of narrow rectangular channels) through which an aerosol sample is passed to obtain attrition of its particle population by diffusion to the walls of the channels. Observations of particle concentrations after successive stages of “decay” produce a decay curve which represents an integral transform of the distribution function with respect to diffusion coefficient. After mathematical manipulation the size distribution of the aerosol is obtained.
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Abstract
Automated equipment has been used to obtain hourly counts of cloud nuclei at Robertson, N.S.W., Australia (34°36′S, 50°36′E). The experiment is described and some results from the first year of continuous observations are given.
Abstract
Automated equipment has been used to obtain hourly counts of cloud nuclei at Robertson, N.S.W., Australia (34°36′S, 50°36′E). The experiment is described and some results from the first year of continuous observations are given.
Abstract
An extension of the Chahine relaxation method for inverting the radiative transfer equation is presented. This method is superior to the original method in that it takes into account in a realistic manner the shape of the kernel function, and its extension to nonlinear systems is much more straightforward.
A comparison of the new method with a matrix method due to Twomey (1965), in a problem involving inference of vertical distribution of ozone from spectroscopic measurements in the near ultraviolet, indicates that in this situation this method is stable with errors in the input data up to 4%, whereas the matrix method breaks down at these levels. The problem of non-uniqueness of the solution, which is a property of the system of equations rather than of any particular algorithm for solving them, remains, although it takes on slightly different forms for the two algorithms.
Abstract
An extension of the Chahine relaxation method for inverting the radiative transfer equation is presented. This method is superior to the original method in that it takes into account in a realistic manner the shape of the kernel function, and its extension to nonlinear systems is much more straightforward.
A comparison of the new method with a matrix method due to Twomey (1965), in a problem involving inference of vertical distribution of ozone from spectroscopic measurements in the near ultraviolet, indicates that in this situation this method is stable with errors in the input data up to 4%, whereas the matrix method breaks down at these levels. The problem of non-uniqueness of the solution, which is a property of the system of equations rather than of any particular algorithm for solving them, remains, although it takes on slightly different forms for the two algorithms.
Abstract
Instability limits the usefulness of indirect sounding, i.e. the deduction of a physical distribution from a set of observations which represent an integral transform of the former. A method is presented which allows a stable, but smoothed, solution to be obtained in certain cases. As an illustration of the application of the method, the deduction of vertical ozone distribution from measurements of the spectral distribution of scattered ultraviolet radiation is discussed. Graphs showing results from several possible methods of inversion are included to show the difficulties associated with such indirect measurements.
Abstract
Instability limits the usefulness of indirect sounding, i.e. the deduction of a physical distribution from a set of observations which represent an integral transform of the former. A method is presented which allows a stable, but smoothed, solution to be obtained in certain cases. As an illustration of the application of the method, the deduction of vertical ozone distribution from measurements of the spectral distribution of scattered ultraviolet radiation is discussed. Graphs showing results from several possible methods of inversion are included to show the difficulties associated with such indirect measurements.
