Craig F. Bohren

An Introduction to Atmospheric Radiation

Fundamentals of Radiation for Atmospheric Applications. Solar Radiation at the Top of the Atmosphere. Absorption and Scattering of Solar Radiation in the Atmosphere. Thermal Infrared Radiation Transfer in the Atmosphere. Light Scattering by Atmospheric Particulates. Principles of Radiative Transfer in Planetary Atmospheres. Application of Radiative Transfer Principles to Remote Sensing. Radiation and Climate.

Multiple scattering of light and some of its observable consequences

Many common observations are inexplicable by single‐scattering arguments: the variation of brightness and color of the clear sky; the brightness of clouds; the whiteness of a glass of milk; the appearance of distant objects; the blueness of light transmitted in snow and other natural ice bodies; the darkening of sand upon wetting. Yet multiple scattering is seldom mentioned in optics textbooks. It is possible to understand many observable phenomena without invoking the complete theory of multiple (incoherent) scattering. A simple two‐stream theory, in which photons are constrained to be scattered in only two directions, forward and backward, is adequate for interpreting many observations, even quantitatively, and it paves the way for advanced study.

How can a particle absorb more than the light incident on it

A particle can indeed absorb more than the light incident on it. Metallic particles at ultraviolet frequencies are one class of such particles and insulating particles at infrared frequencies are another. In the former strong absorption is associated with excitation of surface plasmons; in the latter it is associated with excitation of surface phonons. In both instances the target area a particle presents to incident light can be much greater than its geometrical cross‐sectional area. This is strikingly evident from the field lines of the Poynting vector in the vicinity of a small sphere illuminated by a plane wave.

Reflectance and albedo differences between wet and dry surfaces.

It is commonly observed that natural multiple-scattering media such as sand and soils become noticeably darker when wet. The primary reason for this is that changing the medium surrounding the particles from air to water decreases their relative refractive index, hence increases the average degree of forwardness of scattering as determined by the asymmetry parameter (mean cosine of the scattering angle). As a consequence, incident photons have to be scattered more times before reemerging from the medium and are, therefore, exposed to a greater probability of being absorbed. A simple theory incorporating this idea yields results that are in reasonable agreement with the few measurements available in the literature, although there are differences. Our measurements of the reflectance of sand wetted with various liquids are in reasonably good agreement with the simple theory. We suggest that the difference between reflectances of wet and dry surfaces may have implications for remote sensing.

Backscattering by nonspherical particles: A review of methods and suggested new approaches

Scattering of electromagnetic radiation near the backward direction is more sensitive to particle shape than scattering near the forward direction. Mie theory is therefore of dubious applicability to predicting backscattering by atmospheric particles known to be irregular or to inverting measurements on such particles. An irregular particle is one with an uncertain shape. In the face of uncertainty one must adopt a statistical approach in which scattering properties of ensembles are determined. To obtain ensemble averages, a basis is needed for averaging over a set of electromagnetic microstates. Ensemble averages based on the Rayleigh theory for small ellipsoids and on the T matrix method for spheroids agree better with measurements than Mie theory does. The coupled-dipole method also provides a basis for ensemble averaging. This method also leads to a simple physical interpretation of why backscattering is so sensitive to particle shape and can be used to calculate scattering by one- and two-dimensional analogs to three-dimensional irregular particles.

Light scattering by nonspherical particles: a refinement to the coupled-dipole method

In the coupled-dipole method an arbitrary particle is modeled as an array of N polarizable subunits, each of which gives rise to only electric dipole radiation. The Clausius-Mosotti relation is widely used to calculate the polarizability of the subunits that correspond to the dielectric function of the particle that the array represents. We replace the Clausius-Mosotti relation with an exact expression for the electric dipole polarizability and find improvement in extinction calculations for spheres as compared with Mie theory. Near a Frohlich frequency the coupled-dipole method yields extinction cross sections for spheres and spheroids that compare favorably with the continuous distribution of ellipsoids method and measured values.

Microwave-absorbing chiral composites: Is chirality essential or accidental?

Suspensions of wire helices are absorbing at microwave frequencies. Although such suspensions are chiral, this may be accidental rather than essential for absorption in coatings. Nonchiral suspensions of connected loop arrays behave similarly to suspensions of helices.

Backscattering by Nonspherical Hydrometeors as Calculated by the Coupled-Dipole Method: An Application in Radar Meteorology

Abstract The severest test of a theory of scattering by particles is how well it calculates scattering in the backward direction. The coupled-dipole method can be used for accurately calculating backscattering at 94 GHz by hexagonal ice crystals. Backscattering by columns is markedly different from that by plates, which indicates that it might be possible to infer size and shape distributions of ice crystals using recently developed millimeter wave radar.

Forward-scattering corrected extinction by nonspherical particles

Measured extinction of light by particles, especially those much larger than the wavelength of the light illuminating them, must be corrected for forward-scattered light collected by the detector. Near-forward scattering by arbitrary nonspherical particles is, according to Fraunhofer diffraction theory, more sharply peaked than that by spheres of equal projected area. The difference between scattering by a nonspherical particle and that by an equal-area sphere is greater the more diffusely the particles projected area is distributed about its centroid. Snowflakes are an example of large atmospheric particles that are often highly nonspherical. Calculations of the forward-scattering correction to extinction by ice needles have been made under the assumption that they can be approximated as randomly oriented prolate spheroids (aspect ratio 10:1). The correction factor can be as much as 20% less than that for equal-area spheres depending on the detectors acceptance angle and the wavelength. Randomly oriented oblate spheroids scatter more nearly like equal-area spheres.

Colors of snow, frozen waterfalls, and icebergs

Snow presents more than just a uniformly white face. Beneath its surface a vivid blueness, the purity of which exceeds that of the bluest sky, may be seen. This subnivean blue light results from preferential absorption of red light by ice; multiple scattering by ice grains, which is not spectrally selective, merely serves to increase the path length that photons travel before reaching a given depth. Although snow is usually white on reflection, bubbly ice, which can be found in frozen waterfalls and icebergs, may not be. To a first approximation, bubbly ice is equivalent to snow with an effective grain size that increases with decreasing bubble volume fraction. Ice grains in snow are too small to give it a spectrally selective albedo, but the much larger effective grain sizes of bubbly ice can give it bluish-green hues of low purity on reflection.