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

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)