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: Annamarie.Hatcher@dal.ca (A. Hatcher),

Paul.Hill@dal.ca (P. Hill), Jon.Grant@dal.ca (J. Grant), Paul.Mac-

Pherson@dal.ca (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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