Spectral optical backscatter of sand in suspension: effects ofparticle size, composition and colour
A. Hatcher*, P. Hill, J. Grant, P. Macpherson
Oceanography Dept., Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J1
Received 24 August 1999; accepted 24 March 2000
Abstract
Optical backscatter sensors (OBS) have been used to estimate in situ concentrations of suspended particulate matter (SPM) in
aquatic systems for about 20 years. The logical next step is to use the differential responses to varying sizes and composition of
the particles across a range of wavelengths to characterize discrete mixtures of sediments. To do this, we examined the response
of the backscatter coef®cients in the optical range 442±671 nm to de®ned mixtures of suspended quartz and carbonate sands in a
turbulent jet. We found positive linear responses of the backscatter coef®cient to the amount of suspended sand at all
wavelengths. The regressions differed among the wavelengths for mixture constituents, but analyses of error propagation
indicated that concentration prediction using mixture component calibration curves was problematic. When the colour of
the sand was changed, the response of backscatter to concentration at some of the wavelengths changed and errors in prediction
of mixture concentration were low. Thus, the differential optical backscatter response of sediment components can provide a
means to estimate suspended sediment concentrations in the ®eld from individual calibration equations when the components
are different colours. Under certain conditions, this approach can be used as an alternative to the traditional calibration
procedure which uses sediment collected from the sampling site during the OBS measurements. q 2000 Elsevier Science
B.V. All rights reserved.
Keywords: Optical properties; Suspended materials; Quartz sand; Calcium carbonate; Concentration; Calibration
1. Introduction
Optical backscatter sensors (OBS) offer a conveni-
ent means for estimating suspended particulate mate-
rial (SPM) concentration in natural waters (Downing
et al., 1981). However, the calibration procedure is
problematic because OBS output co-varies non-
predictably with the refractive index and the particle
size distribution of the SPM as well as with the abso-
lute concentrations (Ludwig and Hanes, 1990). Often,
calibration of output must be accomplished with
quantities of sediment collected at the sampling site
(Downing and Beach, 1989; Lynch et al., 1997).
However, large potential errors exist where environ-
mental variability causes mismatch between the target
volume of suspended particles and the sample used for
calibration.
Most of the work on OBS has used one wavelength,
which is in the infrared range 950 nm. The recent
development of powerful LED's, incorporated into a
multi-spectral optical backscatter sensor (Maf®one
and Dana, 1997) offers new potential for estimating
concentrations of multi-component suspensions by
Marine Geology 168 (2000) 115±128
0025-3227/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
PII: S0025-3227(00)00042-6
www.elsevier.nl/locate/margeo
* Corresponding author. Fax: 1 1-902-494-3877.
E-mail addresses: [email protected] (A. Hatcher),
[email protected] (P. Hill), [email protected] (J. Grant), Paul.Mac-
[email protected] (P. Macpherson).
the simultaneous solution of linear equations that
relate output of optical backscatter sensors operating
at different wavelengths to concentrations of various
constituents of the SPM (Green and Boon, 1993). The
three requirements for this procedure are that: (1)
sensors respond to concentration linearly; (2) consti-
tuent interactions such as grain shielding and multiple
scattering must be negligible; and (3) the linear
responses of the sensors must be fundamentally
different.
As a ®rst step in evaluating this approach, we used
sensor pairs and mixtures composed of two constitu-
ents. Sensor responses are fundamentally different
when the ratios of the slopes relating sensor output
to the concentration of constituents 1 and 2 are not
equal.
Consider a sensor for which
R1 � a1C1 1 b1 �1�
R2 � a2C2 1 b2 �2�where R1 and R2 are sensor responses to constituents 1
and 2, C1 and C2 are concentrations of these constitu-
ents, a1 and a2 are coef®cients of proportionality
(slopes), and b1 and b2 are the intercepts.
Consider a second sensor for which
r1 � a3C1 1 b3 �3�
r2 � a4C2 1 b4 �4�where r1 and r2 are sensor outputs, a3 and a4 are coef-
®cients of proportionality (slopes) and b3 and b4 are
the intercepts. The responses of sensors 1 and 2 are
fundamentally different, satisfying requirement (3)
(above) as long as (Green and Boon, 1993)
a1=a2 ± a3=a4 �5�This study was designed to measure the response of
the optical backscatter coef®cients to increasing
weights of suspended sand at six optical wavelengths.
The relative effects of particle size were quanti®ed
using two size fractions of quartz sand, composition
using the same size of two different types of sand
(quartz and calcium carbonate) and colour by compar-
ing natural quartz sand to a subsample that was dyed
with ¯uorescent pink dye.
This study is divided into two sections. First, to
assess the use of spectral backscatter to measure accu-
rately the concentration in manufactured sediment
mixtures, we used the Hydroscat-6 (HOBI labs) in a
turbulent jet tank with suspended quartz and carbo-
nate sand mixtures. Second, we used the data from
these experiments to expand the criteria that must be
satis®ed to apply component calibration equations,
solved simultaneously, to calculate concentrations of
mixtures. To do this, we concentrated on analysis of
error propagation, which further constrains the
method proposed by Green and Boon (1993).
2. Methods
2.1. Multispectral backscatter sensor
A product of Hydro-Optics, Biology, and Instru-
mentation Laboratories, Inc. (HOBI Labs, Bellevue,
WA), the Hydroscat-6 is a six channel optical back-
scattering sensor measuring at wavelengths of 442,
470, 510, 589, 620, 671 nm with source beams origi-
nating from colour LED's. The geometry gives scat-
tering measurements centered around an angle of
1408. A detailed description of the instrument, the
calibration constants and s correction for water
attenuation is published in Maf®one and Dana (1997).
The backscatter coef®cient (bb; units are m21) is the
product of the geometrical cross-section of the `target'
particles, the dimensionless ef®ciency factor for back-
scattering, and the particle concentration (Morel,
1994). It is a measure of the total amount of light
scattered in the backward direction (from u � 90±
1808, where u is the angle of scattering relative to
the incident beam). It is de®ned mathematically as:
bb � 2pZ 180
90b�u� sin �u�du �6�
In Eq. (6), b(u ) is the volume scattering function of
the target volume, or the angular distribution of
single-event scattering around the direction of a paral-
lel incident beam. Output from the Hydroscat-6 is the
backscattering coef®cient, which is calculated at six
wavelengths using a scaling factor and the measure-
ment of the volume scattering function at 1408.
2.2. Experimental design
The general approach was to generate concentra-
tion/response relationships for suspended sand using
A. Hatcher et al. / Marine Geology 168 (2000) 115±128116
the six sensors of the Hydroscat-6 and a turbulent jet
tank. The in¯uence of grain size was quanti®ed using
two quartz sand samples which had non-overlapping
size distributions (180 and 300 mm diameter; Fig. 1)
in ®ve prescribed mixtures. The relative in¯uence of
composition (i.e. refractive index) was quanti®ed by
comparing backscatter coef®cients of quartz and
carbonate sands which were the same size
(300 mm). The relative in¯uence of colour was quan-
ti®ed by treating a sub-sample of the 300 mm quartz
sand with a ¯uorescent paint pigment.
2.3. Turbulent jet tank
The turbulent jet tank is described in detail in Hay
(1991), and the description that follows is a short
summary of points relevant to the present work. The
turbulent jet maintains a statistically steady suspen-
sion of large sand particles in a compact sampling
volume using a recirculating stream driven by a
pump (Fig. 2). Velocity is maintained with a throttle
in the return system, and after release into the tank, the
suspended sand is captured when it falls into a cone
under the discharge nozzle. Conditions in the jet are
fully turbulent, with a discharge velocity of 93 cm s21
and a discharge Reynolds number of 1.8 £ 104. The
cross-jet distributions of mean velocity and concen-
tration are Gaussian at the target point, 28 cm below
the discharge nozzle, with a centreline velocity of
41 cm s21. At this point, the jet diameter is a function
of the settling velocity of the sand, with a maximum
20% difference expected between the 300 and 180 mm
sand, based on calculations from Hay (1991; see Fig. 9
and Eq. 21). The width of the jet at the sampling point
was expected to be similar at all concentrations (Hay,
1991; see Fig. 9(d)), so a consistent scattering volume
(^20%) was exposed to the sensors of the Hydroscat-6.
The Hydroscat-6 was positioned in the turbulent jet
tank so that the focus beam was perpendicular to the
centreline of the suspended sand stream at a point
28 cm below the discharge nozzle with the sensor
face 8 cm away from the jet centreline (Fig. 2). This
optimal placement, accomplished by a precision x±y±
z planar macro-positioning system, was based on the
need to have the de®ned target volume in an area of
fully developed turbulence, positioned in the area of
peak sensitivity for the Hydroscat-6. At this point, the
jet is approximately 9.7 cm wide. This width is the
distance between points where expected concentrations
are 5% of the centreline concentration, based on an
across-jet Gaussian concentration distribution with
2.2 cm as the standard deviation (Hay, 1991). Based
on calibration with a spectralon sheet (Dana, personal
communication), the scattering volume of the Hydros-
cat-6 (90% of the signal) encompasses 55% of the jet
volume at this placement, spanning approximately
2.65 cm on either side of the jet centreline.
The turbulent jet is a convenient laboratory tool to
examine the response of the optical backscatter coef-
®cient to changes in size and concentration of large
sand grains. It presents a statistically consistent
suspension in a well-constrained sampling volume.
After the jet was established, sand additions were
made using a 5.0 cm diameter acrylic tube. The
bottom of the tube was placed beside the jet within
A. Hatcher et al. / Marine Geology 168 (2000) 115±128 117
Fig. 1. Particle size distributions of 180 and 300 mm quartz sand
from Coulter multi-sizer.
Fig. 2. Turbulent jet tank (drawn from diagram in Hay (1991) with
permission of the author) shown with Hydroscat-6 in position.
the capture cone, and wetted sand was introduced into
the tube at the water surface (Fig. 2). Introduced sand
took 16 s to reappear at the introduction point, and the
jet was then left for 1 min before measurements were
taken. At each new concentration, a mean backscatter
coef®cient was calculated from 240 measurements
taken at a sampling frequency of twice per second.
Each experiment consisted of 5 additions of 2 g sand
(quartz) or 5 additions of 0.5 g (carbonate) while a
particular beam was in place, to achieve a ®nal back-
scatter coef®cient (bb; units are m21) close to 0.100.
This range re¯ected a dilute sand concentration in the
jet, and was chosen to minimize the confounding
effects of multiple scattering and grain shielding
(Maf®one, personal communication). The sand was
then collected using a tube connected to the discharge
nozzle which deposited the sand into a sieve. After
drying, the collected sand was re-sieved to check for
differential loss of size fractions. After collection of
all sand circulating in the jet, a new beam was then
positioned to sample the same volume and the experi-
mental additions were repeated.
2.4. Suspended sand in the target volume
Backscatter measurements always have a high
degree of variability which is often dealt with by
some type of signal averaging. If variability is asso-
ciated with some periodicity in concentration change
associated with the recirculating jet system, measure-
ments may change as a function of time of sampling,
introducing bias. To minimize this bias, auto correla-
tion analysis was used on data collected through
extended logging with 100 g of 300 mm silica sand
circulating in the jet. Using the mixtures of 0.75 and
0.50 silica sand, a weak cycle of 18±21 s was identi-
®ed (autocorrelations between 0.204 and 0.217) in all
beams sampled. The sampling time period of 120 s
was chosen so the cyclic variability of around 20 s
would be encompassed.
The recovery of sand from the jet after exposure
was very ef®cient (100% recovery of the 300 mm and
90% of the 180 mm) so all concentration relationships
are expressed on the basis of amount of sand added to
the jet. Because the sand of both sizes was recovered
with high ef®ciency, the assumption of constant
mixture ratios throughout particular treatments was
justi®ed.
2.5. Sand pretreatment
After washing with a surfactant (10% Calgon
soaked overnight) and repeated rinsing, quartz sand
(from a Nova Scotian pit) and carbonate sand (from a
beach in Barbados) were sieved into two size fractions
using a standard sieve series and a Rotap shaker. The
300±425 mm size fraction was retained for both
quartz and carbonate sands. The 180±250 mm size
fraction was retained for the quartz sand only. In
subsequent discussions, the two size fractions will
be designated as 300 mm (for the 300±425 mm
fraction) or 180 mm (for the 180±250 mm fraction).
After sieving, the sands were washed again with
Calgon, and rinsed 10 times in distilled water before
drying at 508C in a drying oven. Sand was
introduced to the jet either as single grain size incre-
ments or as mixtures. The mixtures consisted of:
(1) 25% 180 mm 1 75% 300 mm (w/w); (2)
50 percent; 180 mm 1 50% 300 mm; and (3) 75%
180 mm 1 25% 300 mm. The mixtures are classi®ed
according to the proportion of 180 mm sand, with 1.0
being 100% 180 mm sand with no 300 mm sand and
0.0 being 100% 300 mm sand with no added 180 mm
sand. Similarly, the two-component mixtures are clas-
si®ed as 0.25, 0.50 and 0.75 signifying proportions of
180 mm sand, as described above.
To obtain sand of a different colour but with the
same shape and composition, sub samples of the
300 mm silica sand were dyed with a ¯uorescent
pink pigment. Previously cleaned samples weighing
600 g (dry weight) were added to a solution of 25 ml
paint pigment (Radiant red-JS-Rd3035 9484, Magru-
der Colour Company, California) dissolved in 400 ml
acetone. The sand was left in the solution for an hour,
and vigorously stirred three times during that period
with a glass rod. The supernatant acetone was
decanted, and the wet sand spread on an enamel tray
for the remaining acetone to evaporate. After the sand
was dry, it was poured into an eluter, which is an
inverted cone with a hose connected to the bottom.
Water was supplied from the bottom, rinsing the dyed
sand and keeping it suspended for 15 min while ®ne
particles were washed out. The rinsed sand was then
collected, spread on a tray and dried overnight at
508C. When dried, it was resieved and used. Using
these techniques, the paint pigment was bonded to
the sand grain surfaces with greater than 90% surface
A. Hatcher et al. / Marine Geology 168 (2000) 115±128118
coverage, no clumping of grains was observed, and all
paint chips were removed. This is a modi®cation of
the technique used by Grant et al. (1997).
To compare the effects of sand composition on the
backscatter coef®cient, carbonate sand was collected
at Brandon's beach on the south coast of Barbados,
and was then treated and sieved in the same way as the
quartz sand. The carbonate sand was predominantly
composed of pieces of eroded coral skeleton. It was
white in appearance, with less than 1% (by number) of
coloured grains, determined from microscopic exam-
ination. All sand grains were rounded, with shapes
virtually indistinguishable from the 300 mm quartz
grains under the stereo microscope. After sieving,
the 300 mm size fraction was collected and used in
the turbulent jet. Because of the strong backscatter
response of the carbonate sand, increments of only
0.5 g were used, giving a ®nal total of 2.5 g in the
jet to give backscatter values near those of the same
size silica sand with a total weight of 10 g.
2.6. Predicted error in concentration estimates
Assuming that sensor outputs Rt and rt equal the
linear sums of sensor responses to mixture constitu-
ents, Eqs. (1)±(4) can be used to calculate total
concentration by solving a set of two linear equations:
a1C1 1 a2C2 � Rt 2 b1 2 b2 �7�
a3C1 1 a4C2 � rt 2 b3 2 b4 �8�
As noted by Green and Boon (1993), a nonsingular
solution to this set of equations requires that a1=a2 ±a3=a4 (Eq. 5). The required magnitude of the differ-
ence in slope ratios is not addressed by Green and
Boon (1993). If the difference is small, the set of
equations is ill-conditioned, so small errors in estima-
tion of any parameter or variable in Eqs. (7) and (8)
can translate to large errors in estimated concentra-
tions. Thus, even if a pair of sensors satis®es the three
criteria of Green and Boon (1993), it may be so sensi-
tive to error as to be rendered useless. Before applying
a particular sensor pair to a monitoring task, this sensi-
tivity must be gauged.
Estimation of error is facilitated by writing Eqs. (7)
and (8) in matrix notation so:
a1 a2
a3 a4
" #C2
C1
" #�
Rt 2 b1 2 b2
rt 2 b3 2 b4
" #�9�
Let
A �a1 a2
a3 a4
" #; x �
C2
C1
" #and y
�Rt 2 b1 2 b2
rt 2 b3 2 b4
" #�10�
Then Eq. (9) becomes
Ax � y �11�To estimate x given A and y
x � A21y �12�A and y both have associated uncertainty, so let
A � A0 1 DA and y � y0 1 Dy �13�where the subscript `0' denotes the true values of A
and y and DA represents associated errors.
Substituting Eq. 13 into Eq. 12 yields
x � �A0 1 DA�21�y0 1 Dy�
� �I 1 A210 DA�21A21
0y0 1 �I 1 A21
0DA�21A21
0 Dy
�14�where I is the identity matrix.
Noting that
�I 1 A210 DA��I 2 A21
0DA� � I 2 �A21
0DA�2 �15�
and assuming that A210DA is small, Eq. (15) can be
approximated as
�I 1 A210 DA�21 . �I 2 A21
0 DA� �16�Substituting Eq. 16 into Eq. 14 yields
x � �I 2 A210 DA�A21
0 y0 1 �I 2 A210 DA�A21
0 Dy �17�Noting that
A210 y0 � x0 �18�
one can rewrite Eq. (17) as
x 2 x0 . 2A210 DAA21
0 y0 1 A210 Dy 2 A21
0 DAA210 Dy
�19�
A. Hatcher et al. / Marine Geology 168 (2000) 115±128 119
Eq. 19 may be rewritten as:
e . A210 Dy 2 A21
0 DAA210 y0 �20�
where e is the vector of uncertainty associated with
estimates of x0.
The actual error in concentration is:
dC ��������������������2C2
ÿ �21 2C1
ÿ �2q�21a�
and the error associated with the estimation of the
constituent concentrations:
� e 0e �21b�Using the parameters estimated from the sand
experiments (presented in Table 1), we calculated
the errors associated with the estimates of concentra-
tion using the above technique, and compared these to
the actual rms error.
A. Hatcher et al. / Marine Geology 168 (2000) 115±128120
Table 1
Regression statistics for lines (Fig. 3) predicting backscatter coef®cients from weight of sand added to jet for mixtures of 180 and 300 mm quartz
sand
Wavelength Constant (intercept) Standard error of intercept Slope Standard error of slope Adjusted multiple
(nm) ( £ 103) ( £ 103) ( £ 103) ( £ 103) (r2)
(a) 0.00 mixture (300 mm)
442 13.367 1.435 8.166 0.216 0.997
470 18.378 5.418 7.628 0.817 0.956
510 18.226 5.731 8.173 0.864 0.957
589 20.015 7.424 15.020 1.119 0.978
620 8.072 2.444 11.938 0.368 0.996
671 8.010 3.860 9.295 0.582 0.985
(b) 0.25 mixture (25% 180 mm 1 75% 300 mm)
442 5.695 3.405 7.789 0.513 0.983
470 4.974 4.640 7.491 0.700 0.966
510 0.896 3.748 8.530 0.565 0.983
589 22.070 7.049 10.365 1.063 0.959
620 0.151 5.195 8.658 0.783 0.968
671 3.105 2.317 6.747 0.349 0.989
(c) 0.50 mixture (50% 180 mm 1 50% 300 mm)
442 11.188 0.431 4.980 0.065 0.999
470 6.270 2.028 7.613 0.306 0.994
510 4.164 3.260 6.568 0.491 0.978
589 2.364 4.114 8.124 0.620 0.977
620 3.822 3.829 6.879 0.577 0.972
671 0.440 3.448 6.942 0.520 0.978
(d) 0.75 mixture (75% 180 mm 1 25 % 300 mm)
442 13.301 1.958 4.891 0.295 0.986
470 11.555 1.927 5.893 0.290 0.990
510 11.185 1.962 5.328 0.296 0.988
589 9.892 2.923 6.706 0.441 0.983
620 9.656 2.296 6.380 0.346 0.988
671 10.332 0.392 5.407 0.059 1.000
(e) 1.00 mixture (180 mm)
442 17.167 1.812 3.605 0.273 0.977
470 14.597 2.117 4.225 0.319 0.978
510 17.563 1.638 3.453 0.247 0.980
589 17.286 2.871 4.927 0.433 0.970
620 19.141 1.219 4.600 0.184 0.994
671 12.842 3.202 4.923 0.483 0.963
3. Results
The sensor responses to sand concentration were
linear at all wavelengths, indicating no effects of grain
shielding or multiple scattering (Fig. 3). The linear
responses varied among wavelength pairs, showing
statistically different slopes for the two (180 and
300 mm) different sizes of quartz sand (Fig. 3; Table
1), the carbonate sand and the dyed quartz sand (Fig. 4;
Table 2). These results, which will be discussed in some
detail below, satisfy the requirements prescribed by
Green and Boon (1993), and lay the groundwork to
explore our analysis of prediction errors.
3.1. Response of backscatter coef®cient to sand
concentration and particle size
The individual data points in Fig. 3 represent the
mean backscatter coef®cients at each of the six wave-
lengths for 240 measurements logged at each of the
®ve sand concentrations. For each wavelength, the
plot contains the regression lines relating the back-
scatter coef®cient (Y) to sand added (X) for the ®ve
mixtures. All of the individual linear regressions
between amount of sand added to the jet and the back-
scatter coef®cient for each mixture at each wavelength
have coef®cients of determination greater than 0.956
(adjusted multiple r2 values in Table 1). At each
wavelength, the regression lines relating the
backscatter coef®cient to sand added to the jet have
signi®cantly different slopes for the 0.00 and the 1.00
single-grain size mixtures but not necessarily for
the two-component mixtures (300 mm 1 180 mm)
(differences considered signi®cant if 95% con®dence
intervals do not overlap; Table 1).
3.2. Response of the backscatter coef®cient to sand
colour and composition for 300 mm sand
The slopes of lines relating the backscatter
A. Hatcher et al. / Marine Geology 168 (2000) 115±128 121
Fig. 3. Regression lines relating the backscatter coef®cient to the amount of sand added to the jet at six wavelengths. Each experiment (30 in
total; ®ve shown on each graph) consisted of ®ve sand additions of 2 g (dry weight) each (x-axis) to the turbulent jet while the backscatter
coef®cient was measured (y-axis) and is shown as a single regression line in one of the panels. Because of overlap among many of the symbols
and/or lines, separate lines are not always apparent in the plots. The weights of sand added were kept constant while the relative proportion of
the two size fractions (180 and 300 mm diameter) was varied. The experiments were repeated at each wavelength using ®ve different sand
mixtures which were named using the proportion of 180 mm sand (y-axis): 0.00� 300 mm sand only; 1.00� 180 mm sand only. Each x±y data
point is the mean of 240 measurements of the backscatter coef®cient at a speci®ed sand concentration of a speci®c sand mixture. Scaling of axes
in all six graphs follows that at 442 (y-axis labelled) and 620 nm (x-axis labelled). Symbols correspond to mixtures identi®ed by the proportion
of 180 mm quartz sand as follows: X (1.00); O (0.75); V (0.50); P (0.25); and B (0.00).
coef®cient to amount of sand in the turbulent jet
(weight) differ signi®cantly among sand types accord-
ing to composition (quartz vs. carbonate) and to
colour (natural vs pink quartz) (Table 1a and Table
2). The slopes of the lines associated with the incre-
mental addition of carbonate sand are more than twice
as high as the slopes associated with the incremental
addition of natural and pink quartz sand of the same
size and with the same number of particles per unit
weight (Fig. 4).
The slopes of lines relating the backscatter coef®cient
to amount of sand (g dry weight) in the turbulent jet
differ among natural and pink quartz sands, with natural
quartz having signi®cantly higher slopes for the 510 and
589 channels (based on lack of overlap in 95% con®-
dence intervals) (Fig. 4 and Tables 1a and 2).
3.3. Error propagation analysis
The predicted errors (Fig. 5) arise from propagation
of error through the simultaneous solution of calibra-
tion equations using the two components of the sand
mixtures. The vertical spread of the predicted errors in
each panel of Fig. 5 is a function of the degree of
divergence in the slopes of the calibration equations,
with a large spread associated with poor predictive
ability irrespective of the mixture composition. The
predicted errors associated with the ®ve mixtures (0.0,
A. Hatcher et al. / Marine Geology 168 (2000) 115±128122
Fig. 4. Regression lines relating the backscatter coef®cients to the
amount of sand (g) added to the jet for three types of sand in the
300 mm size category. At six wavelengths, the x-axes are amount of
sand added to the turbulent jet and the y-axes are the backscatter
coef®cients of natural quartz sand, carbonate sand and ¯uorescent
pink quartz sand. Because of overlap among many of the symbols
and/or lines, separate lines are not always apparent in the plots. The
data for the quartz sand are the same as those presented in Fig. 3 for
the 0.00 category. Symbols correspond to composition as follows: B
(natural quartz); £ (pink quartz); and p (carbonate).
Table 2
Regression coef®cients (slopes) and standard errors of the slopes (se) for lines relating backscatter coef®cients to amount of sand in the turbulent
jet for two types of sand (300 mm diameter)(Fig. 4)
Wavelength Intercept se Slope se Adj. mult.
( £ 103) ( £ 103) ( £ 103) ( £ 103) (r2)
300 mm pink quartz
442 6.370 2.250 6.237 0.339 0.988
470 0.913 4.682 8.660 0.706 0.974
510 12.926 2.364 3.720 0.356 0.964
589 6.033 2.791 8.221 0.421 0.990
620 22.633 3.434 13.601 0.518 0.994
671 24.373 4.027 11.894 0.607 0.990
300 mm carbonate
442 4.546 2.718 27.124 1.639 0.986
470 2.454 3.634 30.857 2.191 0.980
510 5.213 3.868 33.340 2.332 0.981
589 23.340 4.571 43.259 2.756 0.984
620 3.768 2.302 25.283 1.388 0.988
671 3.203 3.998 26.112 2.411 0.967
0.25, 0.50, 0.75 and 1.00) are shown separately, but no
signi®cant trend is observed in any particular mixture.
The change in the vertical spread along the x-axis is a
function of the dependence of predicted error on
concentration, and shows no signi®cant trends, irre-
spective of mixture composition.
Generally, the predicted errors in concentration
estimates agreed well with observed errors in the
quartz sand mixtures (Fig. 5). This correspondence
emphasizes the utility of the error analysis approach
to simplify estimation of suspended particle concen-
tration. On the basis of predicted errors, the best
wavelength pairs were 620, 671 and 589, 671 and
the poorest were 442, 510 and 470, 671. Using this
technique, some predicted errors for the quartz sand
mixtures were very high, and no consistent trend with
A. Hatcher et al. / Marine Geology 168 (2000) 115±128 123
Fig. 5. Quartz sand mixtures of 180 and 300 mm grain size: For each wavelength pair, the observed (closed symbols) and predicted errors (open
symbols) [Y] are plotted against the amount of sand added to the jet [X]. The observed errors are estimated as the square root of the estimated
minus the observed amount of sand squared. The predicted errors are equivalent to the total uncertainty (e 0e) from Eq (21b). Symbols
correspond to mixtures identi®ed by the proportion of 180 mm quartz sand as described for Fig. 3.
concentration was evident across wavelength pairs or
among mixtures.
The slopes of the regression lines relating sand
weight to the backscatter coef®cients for the quartz
and carbonate sands are signi®cantly different (Fig.
4). However, the predicted errors in concentration
estimates are generally high, with signi®cant variation
attributable to weight of sand (horizontal spread) and
mixture composition (vertical spread) (Fig. 6). On the
basis of predicted error, the best wavelength pairs for
the quartz/carbonate mixtures were 470, 510 and 442,
620, while the poorest were 442, 470 and 620, 671.
Predicted errors generally increased with weight of
sand, with some obvious exceptions (i.e. 0.75 mixture
in the 510, 589 pair; Fig. 6).
In contrast to the situations with the quartz grain
size mixtures and quartz/carbonate mixtures, the
predicted errors in concentration estimates for the
natural/pink quartz mixtures clearly pick out optimal
wavelength pairs [(442, 620) and (590, 671)] (Fig. 7).
Generally, predicted errors decrease with weight of
sand and for 9 of the 16 wavelength pairs there is little
effect of mixture composition.
4. Discussion
The results presented here represent the ®rst
published measurements of spectral optical backscat-
ter coef®cients of large sand grains in suspension. In
many previous studies, the relative effects of particle
size and composition on the backscatter coef®cient are
confounded. Our results show that we can see predict-
able responses of the backscatter coef®cient to sand
A. Hatcher et al. / Marine Geology 168 (2000) 115±128124
Fig. 6. Quartz and carbonate sand mixtures of 300 mm grain size: The predicted errors are equivalent to the total uncertainty (e 0e) from Eq.
(21b). The symbols follow Fig. 3 except 300 mm diameter carbonate sand was used instead of 180 mm quartz sand.
concentration and grain size, within the narrow size
range of 180 to 300 mm, when composition is
constant. However, the magnitude of the backscatter
coef®cient at all optical wavelengths is signi®cantly
affected by changing particle composition (refractive
index) when size is constant. Sands of different
composition (carbonate and quartz) have signi®cantly
different backscatter coef®cients as a function of
concentration, but the differences are consistent
across the optical spectrum. However, manipulating
the colour of sand with a ¯uorescent paint pigment
(pink) changes the spectral signature of the sand in the
optical range largely through increased absorption in
the middle of the spectrum (green±orange). It is this
difference in the spectral signatures which determines
whether the model proposed by Green and Boon
(1993) can be used with two sensors measuring back-
scatter coef®cients in the optical range.
The spectral signature of SPM is dependent on
particle size in the size range close to the wavelength
of light. Colour can be important for larger particles,
to cause spectral responses which are strong enough to
allow the application of the Green and Boon (1993)
model with properly conditioned error matrices. The
aims of the earlier study (Green and Boon, 1993) and
our present one are to re®ne calibration procedures for
in situ particle sensors. Re®nements would allow the
application of pre-determined calibration equations
based on the major components of the SPM, thus
obviating the need for in situ calibration. The method
examined in the present study, using backscatter
sensors in the optical range, is useful for systems
with two discrete components exhibiting different
spectral signatures. Some examples include muddy
river discharge mixing with sandy sediments on the
continental shelf or a sedimenting/resuspending
A. Hatcher et al. / Marine Geology 168 (2000) 115±128 125
Fig. 7. Quartz sand mixtures of natural and pink ¯uorescent 300 mm grain size: The predicted errors are equivalent to the total uncertainty (e 0e)
from Eq. (21b). The symbols follow Fig. 3 except 300 mm diameter ¯uorescent pink sand was used instead of 180 mm quartz sand.
phytoplankton bloom in a nearshore sandy embay-
ment. There is further scope to re®ne the technique
to include multi-component systems by developing
calibration equations using the components and
solving them simultaneously. However, when using
backscatter sensors in the optical range, the necessary
constraint is that each of the components exhibit
signi®cantly different spectral signatures.
4.1. Factors which cause error in prediction
Within the experimental ranges (backscatter coef®-
cients ,0.15, less than 15 g of sand in the jet, equiva-
lent to ,0.3 g l21 (approximately)), the responses of
the backscatter coef®cients at six wavelengths to
increasing sand concentration were best described as
linear models with weight of sand in the jet explaining
greater than 96% of the variation in the backscatter
coef®cients in most cases.
The conditions proposed by Green and Boon (1993)
are all met by the multispectral optical backscatter
sensor. Sensor response is proportional to end-
member concentration at all wavelengths, constituent
interactions are not signi®cant because concentrations
are low, and responses differ as a function of wave-
length. However, even though there are signi®cantly
different slopes in the backscatter coef®cient vs.
amount of sand regressions between 180 and
300 mm sand, the slopes of generated mixtures are
not all statistically distinguishable. The reason for
this is partly because of the statistical error involved
with backscatter measurements of all types. In the
paper of Green and Boon (1993), this error was called
`systematic errors in end member sensitivies'. In the
formulation of their predictive model, they identi®ed
this error, D, which was applied to the sensor response
to correct for `prediction errors'. As demonstrated
above, D is not a constant, is not systematic, can be
large, and can lead to serious errors in higher order
calculations, as they put forward in their linear model.
In our consideration of the integrity of the error
matrices associated with the simultaneous solutions
of the linear calibration equations, we found that a
fourfold difference in the slope ratio (as in Eq. (5))
accompanied a change from high predicted error (442/
510 wavelength pairs for quartz grain size mixtures)
to low (442/620 wavelength pairs for the natural/pink
quartz mixtures). Thus, we would suggest that this
limit is a reasonable guideline within which to apply
the model for concentration estimation, given these
experimental conditions. The value of this limit is
prescribed by the magnitude of the difference in the
backscatter coef®cients measured at 442, 510 and
589 nm wavelengths which occurs with the change
in colour from natural to pink quartz sand, as pictured
in Fig. 8. Inherent in this limit is the calculated error in
the slopes of the calibration lines for the mixture
constituents. This error encompasses the precision of
the sensor outputs and the inherent assumptions used
to generate the backscatter coef®cients from integra-
tion of a scattering measurement at a ®xed angle. An
integral contributor to this error is the expected large
range of sensor outputs expected in any measurement
of many individual particles, common to all OBS
measurements. Our experiments were designed to
minimize these measurement errors, using a
uniformly-distributed stream of suspended particles,
a long period of measurement and a de®ned target
volume. Despite the carefully-controlled experimen-
tal conditions, standard errors in the slopes of the
calibration lines were up to 8% and, in the intercepts,
much higher. In a ®eld situation, the measurement
errors are expected to be even higher, so our recom-
mendation of a fourfold limit on the difference in the
slope ratio as in Eq. (5) is considered a minimum.
4.2. Backscatter response to particle composition
The strikingingly different backscatter response of
A. Hatcher et al. / Marine Geology 168 (2000) 115±128126
Fig. 8. Bar chart of the ratio of the backscatter coef®cient at six
optical wavelengths (bbl) for pink quartz sand to (bbl) for natural
quartz sand of the same size (300 mm) and the same amount in the
jet (10 g added).
quartz and carbonate sands in suspension as demon-
strated in this study emphasizes the potential of miner-
alogical changes to alter dramatically the backscatter
characteristics of particulate suspensions, as has
recently been addressed by Balch et al. (1999). The
relative in¯uence of the refractive index of calcite on
the backscatter coef®cient of particulate suspensions
is highly signi®cant, independent of size, as pointed
out by Balch et al. (1996) and as demonstrated in the
present study.
4.3. Spectral responses
The relative in¯uence of absorption and enhanced
scattering on the spectral response of sand is effec-
tively demonstrated by the ¯uorescent pink quartz
sand in our study. There was a signi®cant decrease
in the slope of backscatter coef®cient vs. weight of
sand added in the green±orange region (510±589 nm)
of the visible spectrum because of absorption by the
¯uorescent pigment (Fig. 8). Similarly, Bricaud et al.
(1988) have found an inverse relationship between
absorption and scattering in some algal species.
However, to our knowledge, there have been no paral-
lel manipulations on inorganic particles.
5. Conclusions
Although the infrared OBS (Downing et al., 1981)
provided a signi®cant breakthrough in the measure-
ment of suspended sediments, the accuracy of concen-
tration estimates was often compromised by crude
calibration procedures. The recent availability of a
multispectral optical backscatter sensor made it possi-
ble to measure spectral responses of suspended parti-
cles across the optical range. Using the differential
response of the backscatter coef®cient of suspended
sediment constituents at six wavelengths, we investi-
gated the model proposed by Green and Boon (1993),
which allows carefully-controlled calibration of dual-
sensor output in the lab. This calibration leads to an
accurate estimation of concentration of mixtures in
the ®eld. By analysis of error propagation, we re®ned
the model proposed by Green and Boon (1993). When
the spectral response of two discrete components is
signi®cantly different, concentrations of suspended
mixtures can be con®dently predicted by simulta-
neously solving calibration equations using the
components. This is clearly an improvement on
preceding methods of calibration. Further re®nement
for multi-component suspensions is possible only if
all components exhibit signi®cantly different spectral
signatures. This technique of concentration estimation
is not restricted to measurements of optical backscat-
ter, but is applicable to any two-component suspen-
sion using any pair of sensors.
Acknowledgements
This work is supported by the NSERC of Canada
(strategic grant) and the HMDC (Hibernia Manage-
ment and Development Corporation). Alex Hay
generously gave us access to his turbulent jet tank
and he and Wes Paul helped us use it. Scott Hatcher
collected the carbonate sand from Barbados. John
Cullen provided stimulating ideas. Robert Maf®one
and David Dana helped us to become familiar with
the measurement of optical backscatter in general and
with the interpretation of the output of the Hydroscat-
6 in particular. The manuscript bene®tted from the
comments of Alex Hay and Erin Hildebrand.
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