Jacqueline I. Gordon

Overcast sky luminances and directional luminous reflectances of objects and backgrounds under overcast skies.

Two sky luminance distributions are given for overcast sky above snow-covered terrain, and directional luminous reflectance data are presented which were obtained under these skies. Luminous reflectances computed from Krinov spectral reflectance data for a variety of natural terrains measured under overcast are also included.

Atmospheric Properties and Reflectances of Ocean Water and Other Surfaces for a Low Sun

Measurements of illuminance at sea level, directional luminous reflectances of ocean water and other surfaces, atmospheric beam transmittance, and path luminance for a day with an unobscured, low sun are presented. These data are applicable for visibility calculations for downward paths of sight.

Model for a clear atmosphere.

A model of a clear atmosphere is presented based upon two assumptions: (1) the point-function equilibrium radiance for a given path of sight does not change with altitude; (2) there is no absorption. As a result of these assumptions, the equation of transfer can be integrated. The path radiance for any slant path becomes a function of the equilibrium radiance and the beam transmittance of that path. In addition, the equilibrium radiance is a function of the scalar irradiance from the sun, sky, and earth and the proportional directional scattering coefficient for ground level. Sky radiances, and path radiances through the atmosphere for both upward and downward paths are determined by four parameters; the proportional directional scattering function for ground level, the total vertical beam transmittance of the atmosphere, the scalar albedo, and the solar zenith angle.There is evidence that the real atmosphere does on some days conform to the above two assumptions to a useful extent for the visible portion of the spectrum.

Some implications of the equation of transfer

The equation of transfer for radiance as it relates to a scattering, absorbing, and emitting medium is integrated with angle to obtain equations of transfer for irradiance and scalar irradiance. These equations are, in turn, integrated with respect to altitude. One major implication is that a measurement of the 4π radiance distribution at two altitudes in the atmosphere can yield a measure of absorption. Another implication is that there is an emission term in the irradiance equation but not in the scalar-irradiance equation of transfer.

Integrating nephelometer: theory and implications

The Visibility Laboratory integrating nephelometer measures the total volume scattering coefficient and volume scattering functions at 30° and 150° scattering angles. Equations for both measurements and calibration are derived and data reviewed. The ratio of measured to Rayleigh volume scattering function at each scattering angle is a simple function of the ratio of measured to Rayleigh total volume scattering coefficient regardless of altitude or wavelength in the visible spectrum. Methods are developed for obtaining the single scattering albedo from horizon sky radiance and the scattering optical thickness from sky radiance ratios at 55° scattering angle from the sun.

Equilibrium Radiance Model Applications and Comparisons to Atmospheric Measurements and Rayleigh Models

The equilibrium radiance model, which assumes constancy in the source function along the path of sight, predicts equilibrium radiance as a function of the angle from the sun. Measurements made at all altitudes in the troposphere of cloudless sky radiance in the visible spectrum consistently support this prediction. As a result, sky radiances can be used to obtain (1) vertical space-to-sensor scattering transmittance, (2) equilibrium radiance, and (3) path radiance through the atmosphere and in the troposphere. Comparisons are made of the constant equilibrium radiance model predictions of sky radiance, irradiance, and equilibrium radiance to (1) other models for the Rayleigh atmosphere, and (2) to measurements in the troposphere for thin atmospheres. The agreements are good.

Sky Luminances and the Directional Luminous Reflectances of Objects and Backgrounds for a Moderately High Sun

Sky luminance distributions for the upper and lower sky at ground level, 1.52 km and 6.10 km are presented for a clear day with a medium high sun. The directional luminous reflectances of a variety of natural terrains and man-made surfaces measured under a clear sky with a moderately high sun are also presented. These data are applicable for use in visibility calculations and supplement the data presented in an earlier article [S. Q. Duntley, J. I. Gordon, John H. Taylor, C. T. White, A. R. Boileau, J. E. Tyler, R. W. Austin, and J. L. Harris, Appl. Opt. 3, 549 (1964)].

New uses for the solar almucantar

The basic equation for the solar almucantar (same zenith angle as the sun) sky radiance is developed. Methods are reviewed for using the solar almucantar sky radiance to obtain space-to-sensor radiance transmittance and to test the optical stability of the atmosphere. Almucantar sky radiances on optically stable days can also be used to test for spurious sun reflectance in a sky radiance photometer. Examples of such a use are given. A new method is also developed for obtaining the aerosol optical thickness from solar almucantar radiances.

Equilibrium-reflectance model for clear or cloudy atmosphere

Aspects of an earlier equilibrium-radiance model atmosphere for the visible spectrum are extended to the partially cloudy case. Data indicate that in the real atmosphere for some partly cloudy days (60% of the measured paths during one field trip), the point-function equilibrium radiance for a given path of sight is reasonably constant with altitudes up to 6 km for cloud-free path segments. In order for equilibrium radiance to be constant, all path segments must be cloud free and the entire path must be either sunlit or shadowed from the Sun. In an even higher percentage of the partly cloudy and overcast cases (80% during one field trip), the point-function equilibrium reflectance for a path of sight is found to be reasonably constant with altitude. In order for equilibrium reflectance to be constant, all path segments must be cloud free but the path may be partially sunlit and partially shadowed from the Sun. As a result of equilibrium-reflectance constancy, the contrast transmittance for a path of sight with cloud-free path segments in the troposphere can be expressed in the sky–ground-ratio reflectance form.