762 
Zenith angle (degrees) 
Figure 2: Variation of atmospheric radiance (7 a ) with 
zenith angle for radiation at two wavelengths derived 
from LOWTRAN-7 calculations with radiosonde data. 
The curves are based on the parametrisation given by 
Eq. (10) in the text. 
2.3 Emissivity. 
There are only a very few measurements of the angular variation of emissivity over the land 
surface. Barton and Takashima (1986) reported some narrow-band measurements (10-12 /zm) 
over a bare surface and found that the emissivity varied from a value of 0.97 at 30° decreasing to 
a value of 0.95 at 60°. Measurements of the emissivity variation with angle over the sea surface 
do exist (e.g. Saunders, 1967) and calculations have been performed based on modelling the sea 
surface and using the Fresnel reflection coefficients for sea water (Masuda et al., 1988). For the 
land surface it is not obvious how to model the surface nor how to model the physical processes 
contributing to the transfer of radiation at the surface. Takashima and Masuda (1987) have 
performed model calculations for quartz powders and Sahara dust based on radiative transfer 
by assuming that the materials behave like a ‘cloudy’ atmosphere. That is, that the particles 
scatter radiation independently of each other. This is obviously a gross approximation, but it 
has been shown to work quite well for materials such as quartz (e.g. Conel, 1969). Takashima 
and Masuda also computed the variation of emissivity with zenith angle for wavelength bands 
10.5-11.5 /zm and 11.5-12.5 /zm, bands that match AVHRR channels 4 and 5. Figure 3 shows 
results from their computations for both quartz powders with a size distribution of 20 /zm-7.4 
mm and for a plane surface. Results from the experimental study of Baxton and Takashima 
(1986) are also marked on Fig. 3 (As). The results for the 20 /zm-7.4 mm size distribution 
match the experimental measurements quite well but much more experimental data are required 
from many different soil types before these angular variations can be accepted with confidence. 
Nevertheless, here we propose to use a parametrisation for the angular effect of the form, 
£ . w _ (a) 
[1 exp ^ a 0 jJ 
The constants e,(0), d a and di are adjustable. Figure 4 shows the fit obtained using (11) 
e 4 (0)=0.972, d o =5.0 and ¿1 = 1.35 compared with Barton and Takashima’s experimental data 
and Takashima and Masuda’s calculations for the 20 /zm- 7.4 mm size distribution.