s of absorption 
icients of 
volume of each 
minerais, the 
d to be : 
eq. 4 
on of the mi- 
on of minerai i 
minerai i 
he results of 
amples of pure 
.h the aid of 
.ion of three 
ive been calcu- 
icident radia- 
a function 
quartz, gypsum 
don ( - 1 p 2 ) 
licite 
. . 188 
. .062 
). 969 
) . 905 
) .855 
). 8 2 1 
). 793 
). 77 1 
). 7 4 1 
3.724 
3.688 
erals in a 
reflectance 
aid of equa- 
the minera- 
icle size of 
urfaces (van 
ve been air- 
alcite and 
n small cups 
>s and mean 
) i1 s ample s. 
¡ample B 
'O 
!5 
). 2 
.25-250 
ilculated and 
>fotometer; 
and 2b. 
L, 
100 _ 
"-'80 .. 
o 
<1> 
£40 ‘ 
0) 
u 
20 ■■ 
# ! measured 
X * : calculated 
_i i i 1 . i . i . i i L u i 1 I 
' 1.0 1.4 1.8 2.2 
wavelength 
tyumf 
Figure 2a. Calculated and measured reflectance 
of sample A. 
1.0 1.4 1.8 2.2 
wavelength (um) 
Figure 2b. Calculated and measured reflectance 
of sample B. 
In general, the same trend is observed for 
the measured reflectance and the calculated 
reflectance. The presence of gypsum in sample 
B is clearly recognised in the characteristic 
dips around 1.4 and 1.9 um in the measured 
reflectance curve. These dips, although less 
pronounced, are also observed in the calcula 
ted reflectance curve. Differences in reflec 
tance value are due to differences in cali 
bration of the two spectrometers; to differen 
ces in sample preparation (the depth of the 
Hunt and Salisbury samples was only 3.5 mm); 
and to differences in shape and surface 
structure between the minerals used by Hunt 
and Salisbury and those in the Tunesian soil 
samples. 
The influence of soil water 
The influence of soil water on reflection 
from soil surfaces is complex and involves 
many variables. Adding water to a sample of 
dry soil introduces an extra component of ab 
sorption which optical characteristics depend 
on its solute content and on the tension at 
which it is bound to the soil mass (pF). An 
attempt has been made here to include soil 
water as a single parameter in modelling at 
the intrinsic soil surface level. Again, re 
ference is made to Bowers and Hanks (B&H, 
1965): "The effect of moisture content on re 
flection from a Newtonian Silt Loam". Plots 
of Ln(r) versus moisture content at different 
wavelengths showed a linear relation between 
Ln(r) and moisture content. It is assumed 
that the influence of soil water on mean pe 
netrated layer thickness can be neglected 
when compared to its effect on the coeffi 
cient of absorption. On this assumption, the 
following formula for the coefficient of ab 
sorption of the total soil mass is proposed : 
2 
k = k + 9 k (m ) eq.5 
s w w 
in which : k = coefficient of absorption of 
the total soil mass 
k = coefficient of absorption of 
the dry soil mass 
k = coefficient of absorption of 
the soil water 
9 = moisture content in percentage 
of volume 
Applying this equation to the measurements 
of Bowers and Hanks raised the problem of 
finding some input for the mean penetrated 
layer thickness d. Since no specifications 
concerning aggregate size of the Newtonian 
Silt Loam could be found, arbritary values 
for the mean aggregate diameter 0 have been 
chosen. In figure 3,calculated values for 
k , using equation 5 and 3 with 0 = 100, 500 
and 1000 |im,are plotted against wavelength 
of incident radiation. 
Figure 3. Calculated values of k 
tion of wavelength, and k derived 
et al. , 1965 . W 
as a fune- 
from Allen 
The shape of these curves compares well with 
that of the water absorption curve of Allen 
et al. , 196-5. Considering the method used for 
obtaining some value for mean penetrated la 
yer thickness, no comparison between absolute 
values for k can be made. Also, the influen- 
■i w 
ce of soil water composition and soil water 
tension on k has not been taken into ac 
count. 
CONCLUDING REMARKS 
The combination of equation 3, equation 4 
and equation5 leads to the following formu 
la, describing reflectance from a moist mix 
ture of mineral matter in a specific parti 
cle size class : 
r = exp ( - ( Y*c . k . + 9 k ) (vf^Ln ( 0/X) ) ) eq.6 
11 w w 
Modelling of intrinsic soil surface reflec 
tion has to include more variables such as 
shape and surface structure of the particles 
and aggregates, nature and content of organic