Bidirectional reflectance study on dry, wet, and submerged particulate layers: effects of pore liquid refractive index and translucent particle concentrations

Abstract

We performed extensive bidirectional reflectance measurements on dry, wet, and submerged particulate layers with various albedos to investigate the darkening effect caused by wetting with fluids. It was found that, in addition to the reduction of the refractive index contrast when there is a pore liquid (wetted), the concentration of translucent grains in a particulate layer and the surface roughness conditions of the individual grains make important contributions to the wetting-induced darkening effect. Reflectance measurements on glass–sediment mixtures confirmed that, as the concentration of translucent particles increases, the reflectance of the dry layers increases while that of the wetted layers decreases. Measurements indicate that neither the prediction made by the theory of Twomey et al. [Appl. Opt. 25, 431 (1986)] nor that of Lekner and Dorf [Appl. Opt. 27, 1278 (1988)] is sufficient.

Full text

Bidirectional reflectance study on dry, wet, and submerged
particulate layers: effects of pore liquid refractive index and
translucent particle concentrations
Hao Zhang and Kenneth J. Voss
We performed extensive bidirectional reflectance measurements on dry, wet, and submerged particulate
layers with various albedos to investigate the darkening effect caused by wetting with fluids. It was found
that, in addition to the reduction of the refractive index contrast when there is a pore liquid (wetted), the
concentration of translucent grains in a particulate layer and the surface roughness conditions of the
individual grains make important contributions to the wetting-induced darkening effect. Reflectance
measurements on glass–sediment mixtures confirmed that, as the concentration of translucent particles
increases, the reflectance of the dry layers increases while that of the wetted layers decreases. Measure-
ments indicate that neither the prediction made by the theory of Twomey et al. [Appl. Opt. 25, 431 (1986)]
nor that of Lekner and Dorf [Appl. Opt. 27, 1278 (1988)] is sufficient. © 2006 Optical Society of America
OCIS codes: 010.4450, 280.0280, 120.5700, 290.4210, 030.5620.
1. Introduction
It is well known that many rough and absorbing sur-
faces look darker when wetted by water.
1
A thorough
understanding of the underlying mechanism of this
familiar phenomenon has applications in remote
sensing and other related fields.
2–4
Twomey et al.
2
(TBM) formulated a theory to predict the effect of
wetting on the albedo and reflectance based on the
isotropic multiple-scattering approximation. They
attributed the darkening effect to an increase in
forward scattering by the particulates owing to a
decrease in the refractive index contrast between the
particles and the medium. This decrease allows light
to penetrate farther into the sediment and increases
the probability that the light will be absorbed before
exiting the sediment. Lekner and Dorf
5
(LD) pro-
posed a competing theory based on Angstrom’s geo-
metrical optics model.
6
For this approach diffuse
reflectance from a rough surface will be reflected at
the air–liquid interface, and less light will escape.
Both the TBM and the LD models could qualitatively
explain the darkening of sand and soil. However, the
limited available albedo data and the lack of bidirec-
tional reflectance distribution function (BRDF) data
did not allow a convincing separation of these two
effects. In recent years, we have made extensive
BRDF measurements on various types of sediment
particle, both dry and submerged.
7,8
In our work in-
vestigating predictive and invertible models of natu-
ral benthic sediments it is important to understand
the effect of interstitial water on the BRDF. In this
work we present BRDF measurements on dry, wet,
and submerged particulate layers with varied optical
properties. The albedos calculated from our BRDF
data are compared with model predictions to deter-
mine the mechanisms responsible for the darkening
effect.
2. Experimental Method
The BRDF data were taken with our BRDF meter,
which has been described in greater detail else-
where.
9
Briefly, three colors of incident light (red at
657 nm, green at 570 nm, and blue at 475 nm) can be
directed to the sample surface at zenith angles of 0°,
5°, 15°, 25°, 35°, 45°, 55°, and 65°. The reflected light
is simultaneously measured at 107 viewing direc-
tions with zenith angles from 5° to 65° and azimuth
angles from ⫾5° to ⫾170°. This instrument was
designed to measure submerged benthic sediment
in situ; however, we can also take measurements of
dry and wetted particulate layers. We present the
The authors are with the Department of Physics, University of
Miami, 1320 Campo Sano Drive, Coral Gables, Florida 33146. K. J.
Voss’s e-mail address is voss@physics.miami.edu.
Received 19 May 2006; revised 4 August 2006; accepted 9 August
2006; posted 11 August 2006 (Doc. ID 71165).
0003-6935/06/348753-11$15.00/0
© 2006 Optical Society of America
1 December 2006 兾Vol. 45, No. 34 兾APPLIED OPTICS 8753

BRDF data in terms of the reflectance factor (REFF),
10
which is conveniently compared with a perfect Lam-
bertian surface. The REFF is the ratio of the bidirec-
tional reflectance of the sample rSto that of a perfect
Lambertian diffuser rL, i.e.,
REFF
共
␪i,␾i;␪v,␾v
兲
⫽rS
共
␪i,␾i;␪v,␾v
兲
rL
共
␪i
兲
,
where ␪iand ␪vare the incident and viewing zeniths,
␾iand ␾vare the incident and viewing azimuth an-
gles, respectively; rS共␪i,␾i;␪v,␾v兲is defined as the
ratio of the radiance reflected by the surface in a
given direction, Lr共␪v,␾v兲to the collimated irradiance
incident on the surface, Ei共␪i,␾i兲:
rS
共
␪i,␾i;␪v,␾v
兲
⫽Lr
共
␪v,␾v
兲
Ei
共
␪i,␾i
兲
.
rLis the bidirectional reflectance of a perfect Lam-
bertian diffuser
rL⫽␮0
␲,
where ␮0is cos ␪i. With the above definitions, the
REFF is
REFF
共
␪i,␾i;␪v,␾v
兲
⫽␲rS
共
␪i,␾i;␪v,␾v
兲
␮0
.
We assume that the surfaces are azimuthally symmet-
ric such that the REFF depends not on ␾iand ␾v, but
on ␾i⫺␾
v⫽␾. Then bidirectional quantities defined
above may also be expressed in terms of phase angle
gdefined by
g⫽cos⫺1关cos ␪icos ␪v⫹sin ␪isin ␪vcos
共
␾v⫺␾
i
兲
兴,
with g⫽0 corresponding to the exact backscattering
direction and large g共g⬎90°兲the forward-scattering
direction. The REFF will be displayed against g
throughout this work. Positive phase angles corre-
spond to 0° ⱕ␾ⱕ180°, and the negative phase
angles correspond to 180° ⱕ␾ⱕ360°. For a perfect
surface, the REFF at positive and negative phase
angles should be the same; however, for real surfaces,
differentiating between the two sides allows us to
show how well we made the surface. Asymmetries
would point to problems with the surface geometry.
Note that since we are looking at reflected light, we
are restricted to ␪v⬍90°. If ␪iis zero, g⫽␪
v, and is
less than 90°, if ␪iis greater than zero, larger gvalues
can be measured.
The directional albedo at each incident angle ␪ican
be evaluated by
␣
共
␪i
兲
⫽␲
⫺1
冕
2␲
冕
␲兾2
REFF
共
␪v,␾v
兲
cos ␪vsin ␪vd␪vd␾v
from the measured viewing REFF.
8
We limit our dis-
cussions to red incident light for two reasons: (1) most
particulate samples we have measured in past years
show a very weak, or no, color dependence in the
visible range; and (2) the red REFF has the highest
signal-to-noise ratio among the three colors in the
BRDF meter.
Field samples collected for this work were rinsed
and then bleached with 6%sodium hypochlorite for
24 h to remove organic matter. Most of the samples
were sieved into different size distributions. For the
dry samples, the sample was slowly poured into a
1 cm deep polyvinyl chloride (PVC) sample holder.
The holder was tapped from the side to settle the
sediment until the sediment stabilized, and the sur-
face was then smoothed with a straight edge. Four
rotations of the samples were measured with the
BRDF meter to minimize any remaining surface ori-
entation bias. Due to the stochastic nature of such
particulate layers, we have typically found a 1%–2%
albedo variation between replicate samples because
of different surface layer realizations. After measur-
ing the dry sample, water was slowly applied to the
sand surface with an eyedropper. The wetting process
was started from the edge of the surface to minimize
any surface morphology modifications during the
wetting process. Water was added until the air bub-
bles stopped coming out of the surface and the sample
appeared over saturated. The extra water on the sur-
face was blotted by a soft paper to remove all liquid
puddles. We have found that any extra water left on
the surface caused a strong specular peak especially
at large illumination zenith angles. When doing the
submerged measurement, great care was taken to
preserve the flat surface underwater. The surface
quality was checked both before and after the mea-
surement to ensure that the unavoidable water flow,
caused by putting the BRDF meter down on the sam-
ple, did not disturb the surface. The calibration of the
BRDF meter is described elsewhere,
9
but in essence it
was done with comparison to a Spectralon plaque
(Labsphere).
11
3. Results
A. Shallow Water Benthic Sediments
We started with three typical shallow water sedi-
ments collected near Lee Stocking Island, Exumas,
Bahamas, during Summer 2000. The first sample
was an ooid sand with smooth, round grains, a
lustrous surface, and diameters between 0.25 and
0.5 mm (Sample A). The second sample was mainly
broken shells with a size distribution between 0.125
and 0.25 mm (Sample G). The third sample was com-
posed of large 共1–2 mm兲and rough platelets (Rough).
These samples were chosen because they represented
a variety of the samples measured to date. For exam-
ple, Sample G had the highest albedo values, and
Rough had the strongest backscattering peak (hotspot)
of all the samples.
Figure 1 shows the dry and water-wetted REFF of
these three samples at normal and 65° incidence. The
8754 APPLIED OPTICS 兾Vol. 45, No. 34 兾1 December 2006

REFF versus the positive and negative phase angles
(as defined in Section 2) demonstrates that the an-
gular data are indeed azimuthally symmetric. Also
note that at 65° incidence the phase angle range is
larger than normal incidence, as discussed earlier.
Beginning with the dry measurements, we can see
from Fig. 1 that at normal illumination Sample A is
the most Lambertian while Rough is the most aniso-
tropic among the three. At 65° illumination, both
Sample A and Sample G developed a forward-
scattering peak in addition to the hotspot, while
Rough has only a strong and broad hotspot. At nor-
mal incidence, the effect of wetting is to reduce the
overall reflectance and make the surface more Lam-
bertian than when dry; all three samples have small
variations ranging from 3%(Sample A)to7%(Rough)
for phase angles from 0° to 65°. At 65° incidence,
the wetting decreases the backscattering peak but
relatively increases the forward-scattering peak
共g⬎90°兲. Even for Rough the forward-scattering peak
becomes larger than the hotspot. The angular depen-
dence of the REFF on wetting follows, qualitatively,
the idea of TBM, adding the wetting fluid increased the
forward scattering and decreased the backscattering.
Although wetting with water caused significant
changes in the measured REFF as shown above, visu-
ally these three samples are not appreciably darker
when wet than when dry, especially Sample A. This is
in contrast to our daily experience that many sand or
soil layers appear darker when wet.
According to TBM, increasing the fluid refractive
index should decrease the reflectance. However, for
Sample A, a glycerin 共n⫽1.47兲wetted layer did not
appear significantly darker to the naked eye. In Fig.
2 we show Sample A’s dry, submerged, water wetted,
and glycerin wetted directional albedos at eight illu-
mination angles (we will discuss the submerged mea-
surement in Subsection 3.D). Note that wetting with
water or glycerin decreases the albedo only by ap-
proximately 10%. The slightly higher albedo values of
the glycerin wetted layer were caused by the specular
reflectance produced by residual glycerin on the layer
surface because of its viscid nature. According to TBM,
surfaces with either very high or very low albedos will
have little wetting effect. However, Sample A has a dry
albedo value of 0.6, and hence is expected to have a
more appreciable wetting effect. The lack of an appre-
ciable wetting effect led us to look for other samples
with stronger wetting effects. These samples are de-
scribed below in Subsection 3.B.
B. Beach Sands, Soil Particles, and Glass
We collected four additional samples from different
sites: volcanic black beach sand from the Big Island,
Hawaii (Volcanic), sand from the beach at Crandon
Park, Miami (Crandon); sand from the beach at the
University of Miami’s Rosential School of Marine and
Atmosphere Science (RSMAS), and soil particles
from the University of Miami’s Gifford Arboretum
(Soil). In addition, we measured black silica sand
used as cigarette-urn sand at the University of Miami
(Black Sand) and nonabsorbing broken glass ob-
tained by crushing microscope glass slides (Glass)
(Fisher brand, catalog number 12-550C). These six
samples run the gamut of albedo from nearly 0 (to-
tally absorbing) to approximately 0.7 (weakly absorb-
ing). For Crandon,RSMAS and Soil particles, sieved
grains with a size distribution of 0.25–0.5 mm in di-
ameter were used. For the Volcanic and Black Sand
the size selection was between 0.5 and 1 mm because
this was the dominant size. For Glass the grains were
passed through a 1 mm mesh sieve, as this was the
Fig. 1. Three dry and water wetted typical benthic sediment
samples. Open circles are dry and solid circles are water wetted.
Fig. 2. Albedos of dry, submerged, water, and glycerin wetted
Sample A at eight illumination angles.
1 December 2006 兾Vol. 45, No. 34 兾APPLIED OPTICS 8755

end member of the Sample A–Glass mixture described
in Subsection 3.C.
Figure 3 displays dry, submerged, water, and glyc-
erin wetted albedos for all six samples described above
(again, we will defer the discussion on submerged mea-
surements until Subsection 3.D). It should be noted
that for Glass,a4cmdeep black PVC holder was used
in measurements. As an extra test, a piece of white
paper was placed on the bottom of the holder to test
that the layers were thick enough for BRDF measure-
ment. The results indicated that for dry and water
wetted layers the difference in the measured BRDF
and albedo introduced by placing a white paper on the
bottom, versus no paper and the original black holder,
were within measurement uncertainties, and thus this
holder could be considered optically deep. However,
when glycerin was used as a wetting liquid, a differ-
ence was seen in the wetted layer when the white
paper was added, thus 4 cm is not optically deep. For
this reason, the glycerin wetted albedos for the Glass
are not shown. All other samples were tested and
found to be sufficiently thick to be considered opti-
cally deep.
It is seen that, except for the two very dark samples
(Volcanic and Black Sand), all these samples are sig-
nificantly darker when wetted with water. When we
inspected the natural samples with a stereomicroscope
we discovered that many of the grains were translu-
cent quartz particles. An estimate of the fraction of
translucent (as opposed to opaque) particles was made
Fig. 3. Six sediment samples: dry, submerged, water, and glycerin wetted, symbols as in Fig. 2. For Black Sand the submerged albedo
is not shown.
8756 APPLIED OPTICS 兾Vol. 45, No. 34 兾1 December 2006

from stereomicroscope images. In going from dry to
water wetted, Glass which contained 100% translu-
cent grains, exhibited the greatest reduction in
albedo, followed by Crandon (36% translucent par-
ticles), RSMAS (50% translucent particles), and Soil
(80% translucent particles) at normal incidence. We
also saw that for these three samples the glycerin
wetted layer was significantly darker than the water
wetted one. In this work, “translucent” particles sim-
ply stand for quartzlike particles with a low absorp-
tion coefficient (small imaginary refractive index)
and兾or low internal scattering. For these particles, a
large portion of the light incident on the grains is
transmitted.
For the darker samples we saw that, at normal
incidence, water wetting decreased the dry albedos
by 35% for the Volcanic but there was practically no
effect for the Black Sand. If one looks at the stereo-
microscope images of these two samples, it is evident
that the Volcanic grains have more surface rough-
ness and reflect light more diffusely. The Black Sand
has a shiny surface. If one looks at the REFF of these
two samples, the REFF of the Black Sand had very
little change on wetting, while the Volcanic obviously
decreased backscattering and increased (relatively)
forward scattering when wetted. The difference in
the wetting effect between the Volcanic and the
Black Sand must be attributable to the change in
scattering of the individual grains. The major phys-
ical difference between the two samples is the sur-
face roughness of the individual particles.
The surface roughness of individual particles prob-
ably affects the albedo of the individual particles in a
way similar to that LD predicted for the total surface,
particularly for the particles on the surface of the
layer. Light scattered from the surface of a particle
with a rough surface is scattered more diffusely than
for a particle with a smooth surface. If this surface is
coated with water, then light will interact with a
water–air surface when leaving the particle. For the
diffusely scattering rough surface, more of this light
hits the water–air surface at larger angles, and hence
is reflected back to interact with the particle again
and perhaps be absorbed. Thus the particles with a
rough surface can appear darker, depending on the
albedo of the surface of the individual particles.
The surfaces of the opaque grains found in these
samples are not as smooth as Sample A. In addition, as
mentioned, these samples contain translucent parti-
cles with varying concentrations. These two features
must account for the larger decrease in reflectance
when wetted. In an attempt to quantify the effects
due to translucent particle concentration, we carried
out BRDF measurements on mixtures of Glass and
Sample A.
C. Mixtures of Glass and Ooid Sand
We dispersed Glass in Sample A with varied volume
concentrations. The Glass used in the mixtures were
sieved through a 1 mm mesh sieve. Figure 4 shows the
REFF at normal and at 65° incident angles, for both
dry and wet mixtures. The progressions from pure
Sample A to pure Glass are opposite for dry and wet
mixtures. For the dry samples, increasing the Glass
concentration increases the REFF especially in the
forward-scattering direction 共g⬎90° at 65° incidence).
However, for the wet mixtures, increasing the Glass
concentrations decreases the REFF. This can be better
demonstrated by plotting the albedo variation versus
the Glass concentration, as shown in Fig. 5. For clarity,
only normal and 65° incidence of the dry and water
wetted albedos are displayed in Fig. 5. One can clearly
see that increasing the glass concentrations can indeed
lead to an enhanced darkening effect for the water
wetted mixture. For wet samples, a clear decrease in
the albedo from pure Sample A to pure Glass occurs
at the two illumination angles. In the dry case, for
concentrations of Glass ⬍50%, the albedo does not
change significantly. Above 50%the albedo clearly
increases. Thus the difference between the wet and
the dry albedos clearly increases with increasing
translucent particle concentration.
To quantify the effect of mixing the translucent
particles we applied two mixing formulas
10
to predict
the dry and wet albedos of Sample A–Glass mixtures.
The first one is the areal mixture formula, which
is simply the linear sum of the reflectance of each
component:
␣AM ⫽F1␣1⫹F2␣2, (1)
where Fiand ␣iare the area fraction 共%兲and the
albedo of the individual species, respectively.
The second approach is the intimate mixture for-
mula that is applied to single scattering quantities:
␼⫽␼1⫹␧␼
2
1⫹␧ , (2)
where ␼and ␼jare the single-scattering albedos of
the mixture and the jth type particle, respectively,
and the ratio ␧is given by
␧⫽N2␴2
N1␴1
, (3)
for particles much larger than the wavelength, where
Njis the number density and ␴jis the geometric cross
section of the jth type particle, respectively. For sim-
plicity, the ratio ␧is approximated by
␧⬇1⫺glass%
glass% ,
where glass% is the percent volume of Glass in the
sample. Next, the scaled single scattering albedo ␼*
is given by the similarity relationship
␼*⫽1⫺␰
1⫺␰␼ ␼, (4)
where ␰is the asymmetry parameter of the mixture
10
1 December 2006 兾Vol. 45, No. 34 兾APPLIED OPTICS 8757

␰⫽
共
␼⫺␼
2
兲
␼1␰1⫺
共
␼⫺␼
1
兲
␼2␰2
共
␼1⫺␼
2
兲
␼, (5)
where ␰jis the asymmetry parameter of the jth type
particles. Finally, the diffuse reflectance roof the
mixture is approximated by the albedo at the 60°
zenith angle, and rois related to the scaled single
scattering albedo by
10
␣
共
60°
兲
⬇r0⫽1⫺
冑
1⫺␼*
1⫹
冑
1⫺␼*. (6)
To apply the mixing formula Eq. (5) to a binary
mixture, the values of the asymmetry parameters of
the two end members are needed. Vera et al.
12
mea-
sured the diffuse reflectance of small glass frits
共⬃0.05 mm兲and obtained an asymmetry parameter
value of 0.9 by fitting data to their diffusion reflectance
model. For the large glass frits used in this work, it is
likely ␰has a slightly higher value, which we estimate
to be 0.93. A similar ␰value has been used on highly
forward-scattering snow grains.
13
For pure Sample A,
we use a ␰value of 0.7. This is roughly the asymmetry
parameter of a large ellipsoid with an aspect ratio of
approximately 2 obtained by performing ray-tracing
calculations.
14
When wetted, the ␰values for pure
Sample A and Glass are estimated to be 0.9 and 0.96,
respectively. Using Eq. (4), one obtains the following
single-scattering albedo values for Sample A: 0.981
Fig. 4. REFF versus the Glass concentration and gphase angle: (a) normal incidence, dry; (b) normal incidence, wet; (c) 65° incidence,
dry; (d) 65° incidence, wet.
8758 APPLIED OPTICS 兾Vol. 45, No. 34 兾1 December 2006

(dry), 0.990 (wet), and 0.997 (submerged); for Glass the
values are 0.998 (dry), 0.992 (wet), and 0.996 (sub-
merged). Again, these values are derived from mea-
sured REFF values and the higher submerged values
are discussed in Subsection 3.D.
Figure 6 shows ␣共60°兲of the Sample A–Glass mix-
tures and the predictions made by Eq. (6). The areal
prediction made by Eq. (1) is a simple linear relation-
ship between the end points, does not fit well, and is
not shown for clarity. It is seen that for dry and wet
albedos, the intimate mixing formula fits the data
within 3%and 10%, respectively. For submerged al-
bedos, the measured data have large oscillations, and
the 100% glass measurement is significantly differ-
ent from the 90%value. Thus the mixing prediction
cannot match this drastic change in albedo at higher
glass concentrations.
It should be pointed out that, even if an accurate
prediction of a mixture’s albedo is available, such a
prediction based solely on translucent particle con-
centration is unable to predict the wetting effect of
the natural sand or soil samples used in this work. To
illustrate this, we averaged the ratio of the wet and
dry albedos over the eight illumination angles for the
11 concentrations of Glass and Sample A, and for
Crandon,RSMAS, and Soil. These ratios are dis-
played versus the translucent particle concentrations
in Fig. 7. One can see that the effect of wetting for the
natural samples is much stronger than for the corre-
sponding glass–ooid mixture. Part of this effect is
probably because translucent particles in the natural
samples are often colored. As mentioned in Subsec-
tion 3.B all the natural samples introduced in that
subsection have more surface roughness present in
the grains than does Sample A; as a rough surface
would send some light obliquely enough to be totally
reflected with a wetting liquid film, its surface should
look darker than that of a smooth grain with the
same other conditions. But the main point it shows is
that to understand the mixtures one must have a
good idea of the properties of the end members. Sim-
ply knowing the translucent particle concentration is
not sufficient.
For totally opaque grains such as Sample A, our
previous BRDF measurements
8
demonstrated that
for both dry and wet layers only the top 2–3 mm
layers would have an effect on the BRDF or albedo.
For opaque particles, surface reflection by individual
grains is predominant in the BRDF, and thus decreas-
ing the refractive index contrast between the particles
and the medium would not make the scattering pene-
trate significantly farther into the medium. However,
this is not the case for layers containing translucent
grains, since the decrease of the refractive index con-
trast would increase the forward scattering by the
Fig. 5. Dry, water wetted, and submerged-in-water albedos of
Sample A–Glass mixtures at (a) normal incidence and (b) 65° in-
cidence.
Fig. 6. Predictions of intimate mixture formula for diffuse reflec-
tance (albedo at 60° incidence) of Sample A–Glass mixtures.
Fig. 7. Ratio of dry and wet albedos averaged over eight illumi-
nation angles versus translucent particle concentrations.
1 December 2006 兾Vol. 45, No. 34 兾APPLIED OPTICS 8759

translucent particles, and thus wetting-induced ab-
sorption enhancement should be much stronger.
D. Submerged Bidirectional Reflectance Distribution
Function Measurements
We also investigated the effect of totally submerging
the particles as opposed to simply wetting the surface.
By totally submerging, we mean that the samples are
measured completely underwater, with no water–air
interface between the sample and the measuring de-
vice (the reflectance one would measure if diving in the
water). If one goes back to the original LD and TBM
models, submerged samples would not have an obvious
interface (thus LD would predict no change). However,
there would still be an increased forward scattering
effect (TBM). So it is interesting to contrast the three
cases: dry, wetted, and submerged. Most natural sam-
ples had a submerged effect that was between the
wetted and the dry values, as shown in Fig. 3. How-
ever, Sample A had a submerged albedo at both nor-
mal and 65° incidence that was 16% higher than the
corresponding dry albedo as shown in Fig. 2. This was
verified with two more samples, another ooid sand
from the Bahamas and a benthic sediment collected
from Key Largo. This Key Largo sample was also an
opaque shallow water sediment. To investigate this
effect further we looked at the ooid–glass mixtures
where we found that the submerged albedo decreased
as the glass concentration increased (Fig. 5). The
crossover of submerged and dry albedos occurs at
approximately 80% glass concentration, where the
submerged surface starts to become darker than the
corresponding dry surface. It should be noted that
the absolute REFF value of the sample depends on
the REFF data of the calibration plaque.
9,11
Specifi-
cally, the REFF of a sample is obtained by taking the
ratio of the radiance reflected from the sample to that
from the Spectralon plaque and multiplying it by the
REFF of the plaque. Our measurements of a sub-
merged Spectralon plaque
11
also show that the REFF
共␪i⫽0°, ␪v⬍55°兲is higher when the plaque is sub-
merged than when dry.
E. Comparisons with Wetting Models
The results in Subsection 3.C show that a wetting
prediction may not work well without taking into
account factors such as the translucent particle con-
centration and particle surface roughness. Neverthe-
less, it would be informative to test how well the
current models work when applied to various types of
sediment. In Fig. 8 the wet albedo is plotted versus
the corresponding dry albedo for the six natural sed-
iments described above. The prediction by the TBM
model with a dry asymmetry parameter of 0.7 and a
wet asymmetry parameter of 0.9 is shown as the
dashed curve (note that the TBM prediction made for
60° incidence is approximately 3% lower than for nor-
mal incidence where the dry albedo is between 0.3
and 0.7 and is much closer otherwise). The prediction
made by the LD model with nparticle ⫽1.6 and
nmedium ⫽1.33 is also shown in Fig. 8. These compar-
isons show that the shallow water sediments without
translucent particles have a smaller darkening effect
than predicted by the models; for the other sedi-
ments, the Crandon and RSMAS sands agree well
while Soil is less satisfactory. This demonstrates that
a wetting model needs to incorporate translucent par-
ticle concentration as one of the input parameters.
It should be noted that the TBM theory is based on
the assumption of isotropic multiple scattering, i.e., a
particulate layer’s REFF and albedo are given by
2
REFF ⫽␼*
4
共
␮⫹␮
0
兲
H
共
␮
兲
H
共
␮0
兲
, (7)
where ␮⫽cos ␪v, and the albedo is approximated by
␣
共
␮0
兲
⫽1⫺
冑
1⫺␼*H
共
␮0
兲
, (8)
where the Hfunction is widely used in radiative
transfers.
10,15
However, none of the dry REFF data in
this work could be fitted to Eq. (7). Inferring a single-
scattering albedo from the measured albedo [i.e., fit-
ting to Eq. (8)] could also be unreliable, as all the
information contained in the angular distribution of
light is lost in the albedo data. Thus such a predictive
attempt may only be tentative. Besides the isotropic
Fig. 8. Wetting predictions made by TBM and LD models with
natural sediments. The long dashed straight line is dry ⫽wet.
Table 1. Single-Scattering Albedo (SSALB) and Asymmetry Parameter
␰Values
a
Index of Refraction SSALB ␰
n⫽1.6, k ⫽10
⫺8
0.999981 0.7995
n⫽1.2, k ⫽10
⫺8
0.999984 0.9305
n⫽1.6, k ⫽10
⫺6
0.998184 0.8000
n⫽1.2, k ⫽10
⫺6
0.998388 0.9307
n⫽1.6, k ⫽10
⫺5
0.982443 0.8045
n⫽1.2, k ⫽10
⫺5
0.984285 0.9321
n⫽1.6, k ⫽10
⫺4
0.858256 0.8396
n⫽1.2, k ⫽10
⫺4
0.867680 0.9434
a
The data are derived from Mie scattering by spheres with a
power-law size distribution with a mean radius of 100 ␮m and a
variance of 0.1. The wavelength is 633 nm.
8760 APPLIED OPTICS 兾Vol. 45, No. 34 兾1 December 2006

multiple-scattering assumption made in the TBM
theory, another assumption made is that after wet-
ting, the single-scattering albedo of the grains re-
mains unchanged. This may be a rather accurate
approximation for smooth particles (as shown below)
but remains dubious for a rough particle. When a
rough particle is coated by thin film, the effect of the
thin film on the diffuse reflection could have a signif-
icant impact on its single-scattering albedo.
To further test the numerical accuracy of the
TBM model, we performed radiative transfer calcu-
lations
16,17
on layers of dry and wet spherical par-
ticle layers. The hypothetical sample is a collection
of spherical particles having a power-law size dis-
tribution
18
with a mean radius of 100 ␮m and a
variance of 0.1. The real refractive index is assumed
to be 1.6 when dry and 1.2 when wet (as assumed by
the TBM model). The imaginary index is varied
Fig. 9. Numerical check of the TBM model on hypothetical layers composed of spherical grains having a power-law size distribution with
a mean radius of 100 ␮m and a variance of 0.1: ●, dry layer with refractive index n⫽1.6; , wet layer with n⫽1.2; solid curve, result
of fitting albedos to the TBM model; dashed curve, the predicted values made by TBM. The imaginary refractive index kis indicated in
each plot.
1 December 2006 兾Vol. 45, No. 34 兾APPLIED OPTICS 8761

from 10⫺8to 10⫺4and is not affected by the wetting
process (note that natural particles are unlikely to
have an imaginary refractive index much larger than
10⫺4in the visible wavelength
19
). Table 1 is a sum-
mary of the single-scattering properties (Mie calcu-
lation results
16
), which shows that wetting smooth
spherical particles causes few changes in the single-
scattering albedo: here the biggest change in single-
scattering albedo when going from dry to wet is less
than 2% for k⫽10⫺4.
These single-scattering parameters together with
phase functions are introduced into a radiative trans-
fer code
17
to compute the directional albedo. The pre-
diction procedure is outlined below with the example
data for k⫽10⫺8shown in parenthesis:
(1) Fit the dry albedo calculated by radiative trans-
fer equation (RTE) versus the incident zenith to Eq. (8)
to get a scaled single-scattering albedo ␼*共0.9999兲.
(2) With the known asymmetry parameter for dry
particles (0.7995), use the inverse of Eq. (4) to convert
␼*to obtain the unscaled single-scattering albedo
(0.99998).
(3) With the known asymmetry parameter for
wet particles (0.9305), use Eq. (4) to obtain the scaled
single-scattering albedo when wet (0.9997).
(4) Insert the scaled single-scattering albedo ob-
tained from step (3) into Eq. (8) to get the predicted
wet albedos, and compare with the RTE calculations
made on n⫽1.2.
Figure 9 shows that this prediction results in four
representative kvalues from 10⫺8to 10⫺4. From Fig.
9 it is seen that, when absorption is low, the TBM
prediction works well especially for near-normal illu-
minations. As the absorption increases, the albedo
versus incident zenith becomes more anisotropic,
and Eq. (8) does not fit well, thus causing inaccurate
predictions for wet surfaces. This calculation was
also run for two other size distributions of mean
radii of 50 and 10 ␮m and similar results were ob-
tained.
4. Conclusions and Suggestions
Through this series of measurements of wetted, sub-
merged, and dry natural samples we have shown
that the BRDF–REFF albedo depends on many
factors, and the wetting effect cannot simply be
described by either the LD or TBM models. Our
measurements of the wetted REFF clearly show
that, in some cases, we see enhanced forward scat-
tering and reduced backscattering, evidence of the
effect on which the TBM model is based. However,
the results of the submerged measurements con-
trasted with the wetted results show that the air–
water interface is also important, hence the LD
model is also important. However, we have seen
that an additional two parameters, which must also
be considered in natural samples, can be very im-
portant: specifically, the fraction of translucent par-
ticles and the microscopic surface roughness of the
individual particles. Specifically, the more translu-
cent particles in a particulate layer, the brighter it
is when dry, and the darker it is when wet. Thus the
translucent particle concentration can be a large
proportion of the wetting-induced darkening effect.
The surface roughness of the particles is also im-
portant, as low albedo particles with a rough sur-
face tend to have a larger wetting effect.
These results may have applications in remote
sensing, as when a particulate surface is seen to
have significant variation in reflectance between
dry and wet, it is likely that such a surface contains
translucent particles such as quartz sands. Fur-
thermore, a quantitative model that can account
for both the translucent particle concentrations
and the individual grain surface roughness effects
would be needed to make accurate predictions and
inversions. Such a modeling effort might start with
the current rough surface BRDF models [e.g., Ref.
20] that have both specular and diffuse reflection
components, and by properly taking into consider-
ation the increased forward scattering when wet,
might give an accurate prediction of the wet BRDF
and albedo.
We thank Arthur Gleason and Albert Chapin for
help with the measurements and Michael Feinholz
for providing the volcanic sand sample. This work
was supported by the Office of Naval Research Ocean
Optics Program.
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