A. E. S. Green

THE MIDDLE ULTRAVIOLET REACHING THE GROUND

Abstract— We present a semi‐empirical analytic formula for calculating the direct, diffuse and global solar middle‐ultraviolet radiation (280–340 nm) reaching the ground. The formula accommodates variations in wavelength, solar angle, ozone thickness, aerosol thickness, ground albedo, ground elevation, and cloudiness. Analytic representations of biological action spectra are also presented for use in calculations of effective dose at any time of day. Our purpose is to provide a basis for estimating approximate changes in middle‐ultraviolet radiation levels reaching the ground caused by anthropogenic changes in the intervening atmosphere.

IMPROVED ANALYTIC CHARACTERIZATION OF ULTRAVIOLET SKYLIGHT

Abstract— We present an improved analytic characterization of diffuse spectral irradiance (skylight) for the wavelength range 280–380 nm and solar zenith angle range from 0 to 85°. The formulas achieve greater accuracy by (a) focusing on ratio representations and (b) adjusting the parameters to the more precise radiative transfer calculations of Dave, Braslau and Halpern.

Efficiencies for production of atomic nitrogen and oxygen by relativistic proton impact in air

Relativistic electron and proton impact cross sections are obtained and represented by analytic forms which span the energy range from threshold to 109 eV. For ionization processes, the Massey–Mohr continuum generalized oscillator strength surface is parametrized. Parameters are determined by simultaneous fitting to (1) empirical data, (2) the Bethe sum rule, and (3) doubly differential cross sections for ionization. Branching ratios for dissociation and predissociation from important states of N2 and O2 are determined. The efficiency for the production of atomic nitrogen and oxygen by protons with kinetic energy less than 1 GeV is determined using these branching ratio and cross section assignments.

MIDDLE ULTRAVIOLET RADIATION REACHING THE OCEAN SURFACE

Abstract— Direct measurements of the downwelling spectral irradiance in the middle UV (280–340 nm) have been made for a range of solar zenith angles (20°‐70°). These measurements were made for a marine atmosphere at equatorial latitudes. We fit these data to two semi‐empirical analytic representations, from which quantitative calculations of spectral irradiance in the middle UV incident at the ocean surface can be made. The formulae accommodate variation in wavelength, solar zenith angle, ozone thickness, aerosol thickness and surface albedo. Our purpose is to provide marine photobiologists and photochemists with a basis for estimating middle UV radiation levels reaching the ocean surface and the approximate changes caused by manmade alterations of the ozone layer.

Influence of Clouds, Haze, and Smog on the Middle Ultraviolet Reaching the Ground

We extend the multiple scattering formalism of Shettle and Green using a turbid atmosphere of uniform horizontal layers with vertical nonhomogeneities by introducing uniform cloud, haze, and smog layers. Our solution follows the rigorous equations of Chandrasekhar. The fact that it is capable of handling a cloud layer of large optical thickness with minimal subdivision of that layer permits a fast computer solution. A formalism for treating a fractional cloud layer is presented, and this allows the interesting possibility of an increase in the global flux over the clear-sky case that was not allowed by the uniform layers. The uv spectral and dose results are then compared with existing experimental data, and averaged effects are presented and parameterized.

Multiple scattering calculation of the middle ultraviolet reaching the ground.

We use a multiple channel solution to the radiative transfer equation, a computationally fast method which achieves reasonable accuracy. The method is applied to the problem of light scattering in a turbid atmosphere in the 280-340 nm wavelength region to calculate the direct, downward diffuse and global flux reaching the ground. This spectral region is of particular interest in studies of the biological effects of possible depletion of the ozone layer by a future fleet of supersonic transport planes. We input atmospheric conditions in terms of analytic models chosen to encompass standard ozone and aerosol distributions.We examine the changes in the results with respect to the variations of the solar zenith angle, wavelength ozone thickness, aerosol thickness, ground albedo, and ground height level. The results are fairly well represented by a semiempirical analytic formula which may be used for the purposes of interpolation and communication.

AVERAGE LATITUDINAL VARIATION IN ULTRAVIOLET RADIATION AT THE EARTH'S SURFACE

Abstract— Tabulated values are presented for ultraviolet radiation at the earths surface as a function of wavelength, latitude, and season, for clear sky and seasonally and latitudinally averaged ozone amounts. These tabulations can be combined with any biological sensitivity function in order to obtain the seasonal and latitudinal variation of the corresponding effective doses. The integrated dosages, based on the erythemal sensitivity curve and on the Robertson‐Berger sunburn‐meter sensitivity curve, have also been calculated, and these are found to vary with latitude and season in very nearly the same way as 307 and 314 nm radiation, respectively.

ANALYTICAL CHARACTERIZATION OF SPECTRAL ACTINIC FLUX and SPECTRAL IRRADIANCE IN THE MIDDLE ULTRAVIOLET

Abstract— We present an analytic characterization of upward and downward diffuse spectral irradiance for the wavelength range 280–380 nm, solar zenith angle range from 0 to 86, altitude range from 0 to 5 km and for non‐zero surface albedo. This work is a modification and extension of the previous work of Green, Cross and Smith based upon the radiative transfer calculations of Braslau, Dave and Halpern. Guided by these irradiance systematics we develop an analytic characterization of diffuse spectral scalar irradiance or actinic flux also broken down into upward and downward components for the above wavelengths, solar zenith angles and altitudes, for non‐zero surface albedo utilizing the actinic flux calculations of Peterson.

Interpretation of the Sun’s Aureole Based on Atmospheric Aerosol Models

Theoretical calculations of forward scattered sunlight are carried out assuming single scattering. Analytic models for the altitude-size distribution of atmospheric aerosols are used of the separable form eta(y,r) = rho(y)n(r), where rho(y) is a vertical density profile and n(r) is the differential aerosol size distribution. The functions considered for n(r) include the models of Junge, Deirmendjian, a generalized distribution function, and a mathematical spline model. For rho(y), we use an exponential model, a mixing height model involving a step function profile, and a two-term generalized distribution function. The theory is set up so that optimum fits to the experimental data at several wavelengths can be achieved by adjusting the parameters of the aerosol model. Both photoelectric and photographic measurements of daytime sky brightness are made, and the data are analyzed with several different aerosol models.

Attenuation by Ozone and the Earth’s Albedo in the Middle Ultraviolet

An approximate analytical expression is developed for the attenuation of middle ultraviolet radiation along slant paths through the atmosphere. The independent variables are wavelength, altitude of source (the detector is assumed to be above the atmosphere), angle of path with respect to zenith, and three parameters which characterize the ozone distribution. An approximate analytical expression is also developed for the scattered solar radiance seen by a satellite. Here the independent variables are the wavelength, the look angle and the sun angle with respect to the zenith, the scattering angle, and again three parameters which characterize the ozone distribution. The results based upon the formula are compared with previous studies and an experimental measurement.