332
The second hypothesis, whereby k is independent on par
ticle size, seems to be justified only in cases where
the particle size is greater than the wavelength of
incident radiation (Kortum, 1969). However, for most
soils in natural condition, small particles tend to
cluster in aggregates. Thus, in case of clayey samples
particle size should be interpreted as the smallest
existing aggregate size. The samples used by B&H were
aggregates of clay particles and several times larger
in diameter than the wavelength of incident radiation.
Plots were made of Ln(r) versus wavelength for samples
of different aggregate size and of Ln(r) versus aggre
gate diameter at different wavelengths (Bouman, 1986).
Interpretation of these plots led to the following
formula, equating mean penetrated layer thickness d to
wavelength X and aggregate diameter 0 :
d = \T£*Ln(0/X) (in ) eq.3
This equation was tested on the .(B&H) measured reflec
tance values of the kaolinite and bentonite clay
samples. To this end, the coefficients of absorption
of the clay minerals were calculated as a function
of wavelength, using two samples of different aggre
gate size. With the aid of the values calculated for
k, reflectance r was computed for the other aggregate
sizes and compared with the measured values, see figu
re 1.
Figure 1. Calculated and measured reflectance values
for kaolinite (o) and bentonite (x) clay samples,
(measured values are from Bowers and Hanks, 1965)
On the whole, there seems to be a great consistence
between measured reflectance and reflectance computed
using equation 3. Any decrease in reflectance with
increasing particle size is fairly well predicted. The
total mean deviation computed for the kaolinite and
the bentonite samples is 3.5 % resp. 3.9 % (n = 70).
Boundary conditions for the validity of equation 3
could not be established for lack of data in literatu
re. It should be clear however, that particles or
aggregates infinitely small or very large are beyond
the limits of this formula. In figure 1 it can be seen
that for large values of 0, reflectance r tends to
become overestimated. There appears to be a maximal
particle/aggregate size beyond which reflectance is no
longer significantly reduced (Belonogova, 1959; Stoner
and Baumgardner, 1980).
The influence of mineralogy
It is assumed that the effect of different mineral
composition on reflection can be described by means
of a weighed average of the coefficients of absorption
of the individual components. The coefficients of
weight are based on the percentages of volume of each
component. For a homogeneous mixture of minerals, the
coefficient of absorption k^ is proposed to be :
k = y*c. k. (m 2 ) eq.4
s 1 1
in which : k = coefficient of absorption of the mi
neral mixture
k. = coefficient of absorption of mineral i
c^ = percentage of volume of mineral i
In 1970, Hunt and Salisbury published the results of
extensive reflectance measurements of samples of pure
minerals of various particle sizes. With the aid of
equation 3, the coefficients of absorption of three
minerals quartz, gypsum and calcite, have been calcu
lated as a function of wavelength of incident radia
tion, see table 1.
Table 1. Coefficient of absorption k as a function
of wavelength of incident radiation for quartz, gypsum
and calcite.
Wavelength (^i) Coeff. of absorption (-1 ^ 2 )
Quartz Gypsum Calcite
0.4
i.
086
1,
. 205
1 .
. 188
0.6
0 .
983
1,
. 062
1 .
,062
O
CO
0 .
903
o,
. 974
0 .
,969
1.0
0 .
851
o,
. 899
0 .
, 905
1 . 2
0 .
808
0
.839
0 .
,855
1 . 4
0 .
775
o,
.777
0 .
,82 1
1.6
0 .
748
o,
.739
0 .
,793
1.8
0.
72 1
o,
.7 19
0 .
.771
o
C\1
0 .
705
0
. 557
0 .
.741
2 . 2
0 .
689
0
. 565
0 .
, 724
2.4
o .
675
0
.451
0 .
, 688
For any
dry
mixtu
re of
th
ese m
ine
r a 1 s
in a
well so
r ted
parti
ele s
iz e
c las
S /
r e f 1 e
ctance
r can n
ow be
calc
ulate
d w
ith the
aid o
f equa-
tion 3
and 4
. Table 2
summariz
es
the m
inera-
logical
prop
er ti e
s and
me
an pa
rti
cle s
ize of
two sam
pies
from '
Tunes
ian
soil
su
r f ace
s (van
den Ber
gh, 1
986) .
The
samples
hav
e bee
n air-
dried i
n ord
er to
pres
e rv
e the
ca
leite
and
gypsum
conte
nt an
d wer
e placed
in
smal
1 cups
with a
depth
of about
20
mm .
Table 2
. Min
¡éralo
gical
pr
opert
ies
and
mean
partic1
e s i z
e of
two T
une
■ s ian
soi
1 s am
¡pies .
Property
S amp 1
e A
Sample
B
quartz
(%)
85
70
gypsum
(%)
5
25
calcite
(%)
10
5
organic
matt
er ( %
) 0 .
5
0 .
2
mean pa
rtic 1
e siz
e 75
-12
5
1 2
5-250
(yim)
Sample
ref le
ctanc
es we
re
both
cal
culat
ed and
measure
d with the
NIWARS-
spect
rof
otome
ter ;
results
are
given
in f
igu
res 2
a a
nd 2b
I
100 ..
'-'80 ..
Figur«
of sac
60
50
iiR
40
§ 30
1 20
I I
<D
u 10
Figur«
of sari
In gei
the me
reflec
B is c
dips c
reflec
pronoi
ted r<
tanc e
bratic
ces ii
Hunt i
and tc
struct
and S<
sample
The ii
The ii
from <
many t
dry sc
sorpt;
on it:
which
attemj
water
the ii
ferenc
1965)