the theory, as applied to a pure molecular atmosphere, gives results 
which seem to be in approximate agreement with experiment. However, 
as noted earlier, it has been discovered in recent years that Earth's 
atmosphere cannot be treated as a pure molecular atmosphere because of 
the presence of a global background distribution of aerosols. Most 
radiative transfer models use simple approximations to the highly 
anisotropic single-scattering phase functions of aerosols when they are 
included. Furthermore, those models cannot readily be adapted to 
handle the variety of aerosol distributions needed. Another complica- 
tion for remote sensing work in this spectral region is the fact that 
the properties of Earth's atmosphere are such that we are not able to 
make simplifying assumptions in our analysis and calculations like those 
possible in many other modeling effects in which the atmospheres have 
been either much clearer or denser. Also, investigators particularly 
in astronomy and astrophysics, usually only consider radiation emerging 
from the top and bottom of the atmosphere. This is not sufficient for 
remote sensing from aircraft. Another limitation of some models is 
their failure to deal with the calculation of irradiance, transmittance, 
and path radiance in a unified way throughout the atmosphere; that is, 
each radiometric quantity is usually computed independently of the others. 
Turner [19, 20, 21] has developed a simple, working radiative- 
transfer model to calculate the basic radiation quantities (irradiance, 
transmittance, path radiance, and sky radiance) in a unified way 
including an analytical capability for very accurately describing and 
using the theoretically exact phase functions corresponding to an 
aerosol-type atmosphere with any desired aerosol distribution profile. 
The scattering phase function plays an important role in determining 
the angular dependencies of atmospherically scattered radiation. One 
of the features of the model is the use of time as an independent 
parameter which allows simulation of temporal variations that would be 
present in aircraft area survey data. 
The next nine figures and the discussion taken from [22] present 
graphs that are representative of the model's output and illustrate the 
sources of systematic variation in scanner data. Figure 3 shows the 
dependence of transmittance on scan angle for four different visual ranges. 
V-2 km corresponds to a dense haze and V-23 km represents a normal clear 
day (bordering on a light haze). The airborne scanners generally collect 
data at scan angles of + 45° or smaller, and it is clear that the path 
transmittance for these angles varies substantially. The transmittance 
and all other quantities depend on the altitude of the sensor, and the 
data in this figure are for an altitude of 3 km. While the data 
presented herein are for aircraft altitudes, the model also can be 
used to simulate data collected from spacecraft. 
Irradiance is another quantity of interest. Figure 4 shows the 
spectrum of the irradiance that would be detected by a sun sensor on an 
aircraft flying at an altitude of 1 km. Note the increase in levels for 
hazy conditions, that is, for short visual ranges. Information of this 
sort is of value in using "sun sensor" signals for signature extension 
away from known areas.