Assessment Of Operational Techniques For Estimating Visible Spectrum Contrast Transmittance

AbstractApproximate solutions appropriate for real time calculations of directional path radiance and atmospheric contrast transmittance were developed and tested using an extensive data base gathered with a specially instrumented aircraft. The high-resolution, simultaneous optical and meteorological measurements were made in a broad range of environmental conditions and diverse geographical areas in the United States and western Europe. Modelling techniques based upon these data yield computationally fast and consistent results of reasonable accuracy. The effects of the natural variations in environmental physical parameters upon the calculations of spectral contrast transmittance are examined through systematic application of the modelling techniques. Comparative analyses are made of the changes in the visible spectrum contrast transmittance associated with typical changes in some of the relevant parameters such as the depth and density of the low-level haze layer, aerosol absorption, surface spectral reflectance, solar zenith angle and viewing path.IntroductionThe degredation of visible image contrast along a viewing path of increasing length is governed by (1) the attenuation of the inherent background and object radiances by air molecule and aerosol particle scattering and absorption, and (2) the generation of path radiance by molecular and aerosol scattering of ambient light into the path of sight. Direct measurements of radiance and aerosol concentration profiles for selected path segments cannot be made simply arid inexpensively. Thus, operational estimates of contrast transmittance must be derived from model calculations that are based upon estimated variables, including the distribution of aerosol particles and their directional scattering and absorption properties. In this paper, we present the results of a systematic series of calculations designed to help identify the relative effects of the changes or uncertainties in relevant physical parameters upon the contrast transmittance of hazy, cloud free paths of sight.Model for the calculation of contrast transmittanceThe equation for apparent spectral radiance of the background b at altitude z and range r in the direction defined by zenith angle 0 and azimuth angle 0 is1 :b Lr (z,0, ) = Tr (z,0) b L0 (zt ,9, ) + L,*(z,0,0) 0)where b L0 is the inherent background radiance at target altitude z,, Tr is path transmittance, and L* is the spectral path radiance generated by the scattering of light reaching the path from all directions.The spectral contrast transmittance is given1 directly by the product of ratio of the inherent and apparent (b Lr ) background radiances and the path transmittance as follows,C(z,0,0)/C0 (z,,0,0) = Tr (z,9)b L0 (zt ,9, )/b Lr (z,9, ) (2)where Cr = (,Lr - b Lr }/b Lr is the apparent target contrast at path length r and C0 (zt ,9, ) = ({ L0 - h L0 )/b L0 is the inherent target contrast at altitude z,.A computationally fast technique for the calculation of atmospheric path radiance and contrast transmittance was developed ' through analysis of an extensive series of optical/meteorological measurements gathered by the Visibility Laboratory with an instrumented aircraft deployed in the United States and Europe. Model input parameters are the number of atmospheric layers, the average optical scattering ratio and single scattering albedo for each layer, solar zenith angle, representative wavelength, extra-terrestrial solar irradiance and surface reflectance. The computer code calculates the path radiance and contrast transmittance for any selected slant path.Modelling approximations include the representation of the vertical profile of total volume scattering coefficient, 5(1,X) by the profile of optical scattering ratio, (Hz,\) = S(Z,\)/SR (Z,\) where SR is the Rayleigh scattering coefficient, thus normalizing with respect to wavelength and pressure altitude. Under conditions of complete mixing within a given atmospheric layer, (Hz, A) would be constant in the layer. The aircraft measurements reveal large variability in (Hz) depending upon the aerosol particle source strength and the nature of the convective and turbulent mixing processes. The model computer code will accept specification of as many layers as warranted by available observations. However, a prominent feature of most aircraft measured profiles in the daytime, following the dispersion of surface ground based temperature inversions, is the strong tendency for good mixing with constant (Hz) in the primary haze layer and again in the overlying troposphere. So that a simple 2-layer troposphere model assuming a constant Q(z) in each layer provides a good first approximation of the scattering ratio profile on a majority of sunny days over inland areas.