SEPA
United States
Environmental Protection
Agency
Environmental Monitoring
Systems Laboratory
PO Box 15027
Las Vegas NV89114
EPA 600/4 80-019
March 1980
Research and Development
Multispectral Techniques
for Remote Monitoring
of Sediment in Water:
A Feasibility Investigation
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EPA-600/4-80-019
March 1980
MULTISPECTRAL TECHNIQUES FOR REMOTE
MONITORING OF SEDIMENT IN UATER:
A Feasibility Investigation
by
Ronald J. Holyer
Lockheed Electronics Company, Inc.
Remote Sensing Laboratory
Las Vegas, Nevada 89114
Contract No. EPA 68-03-2153
Project Officer
Gary A. Shelton
Advanced Monitoring Systems
Environmental Monitoring Systems Laboratory
Las Vegas, Nevada 89114
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
LAS VEGAS, NEVADA 89114
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DISCLAIMER
This report has been reviewed by the Environmental Monitoring Systems
Laboratory—Las Vegas, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily reflect
the views and policies of the U.S. Enviornmental Protection Agency, nor does
mention of trade names or commercial products constitute endorsement or
recommendation for use.
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FOREWORD
Protection of the environment requires effective regulatory actions based
on sound technical and scientific information. This information must include
the quantitative description and linking of pollutant sources, transport
mechanisms, interactions, and resulting effects on man and his environment.
Because of the complexities involved, assessment of exposure to specific
pollutants in the environment requires a total systems approach that
transcends the media of air, water, and land. The Environmental Monitoring
Systems Laboratory— Las Vegas contributes to the formation and enhancement of
a sound monitoring data base for exposure assessment through programs designed
to:
• develop and optimize systems and strategies for
monitoring pollutants and their impact on the
envi ronment
• demonstrate new monitoring systems and technologies
by applying them to fulfill special monitoring needs
of 'the Agency's operating programs
This report considers a method of remotely measuring suspended sediment
concentrations in water using multispectral techniques having sufficient
accuracy to be feasible for regulatory purposes without the need for continual
ground truth support. Federal and state agencies should find this approach
promising for large area coverage with a minimum of cost and time. Further
information can be obtained from the Remote Sensing Operations Branch of the
Environmental Monitoring Systems Laboratory in Las Vegas, Nevada.
George B. Morgan
Di rector
Environmental Monitoring Systems Laboratory
Las Vegas
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ABSTRACT
A data acquisition and analysis program has been undertaker to
demonstrate the feasibility of remote multispectral techniques for monitoring
suspended sediment concentrations in natural water bodies. Two hundred
surface albedo measurements (400 to 1,000 nanometers) were made at Lake Mead
with coincident water sampling for laboratory analysis. Water volume
spectral reflectance was calculated from the recorded surface albedo, and
volume reflectance-suspended sediment relationships were investigated.
Statistical analysis has shown that quantitative estimates of nonfilterable
residue - 105°C and nephelometric turbidity can be made from volume spectral
reflectance data with sufficient accuracy to make the multispectral technique
feasible for sediment monitoring.
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CONTENTS
Foreword ................................ iii
Abstract ................. ...... ......... iv
Figures ................................ vii
Tables ................................. xl
Abbreviations and Symbols ....................... xii
Acknowledgments ............................ xiii
I Introduction .......................... 1
Statement of the problem .......... . ....... 1
State-of-the-art overview ................. 2
Significance of this study as related to
previous work ...................... 4
EPA guidelines ....................... 5
II Summary and Recommendations ................... 7
Conclusion regarding feasibility .............. 7
Recommendations ...................... 8
III Turbidity ............................ 10
Definition ......................... 10
Methods of measurement ................... 12
IV Peripheral Effects ....................... 14
General discussion ............... ...... 14
Mathematical discussion .................. 15
Magnitude of peripheral effects .............. 32
V Instrumentation ......................... 36
Spectrometer ........................ 36
Spectrometer mounting ................... 38
Calibrated reflectance standards .............. 38
VI Error Analysis ......................... 43
Instrumental uncertainties ................. 43
Conceptual uncertainties .................. 57
Laboratory accuracy .................... 67
Error summary ....................... 69
VII Data Acquisition ........................ 72
Lake Mead test sites .................... 72
Sampling stations ..................... 75
Field procedures ...................... 75
Data reduction ....................... 80
VIII Data Description ........................ 85
Suspended sediment concentrations ............. 85
Variability of sediment types ............... 85
Color interferences .................... 88
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CONTENTS (Continued)
IX Data Analysis 94
Introduction to data analysis 94
Verification of the particle size hypothesis 97
Polynomial fits to residue/turbidity vs.
volume reflectance 100
A statistical method for obtaining multispectral
quadratic algorithms 109
Evaluation of statistical algorithms 114
Single channel algorithms for verification
of error analysis results 115
Multispectral algorithms 119
Signature transferability 126
Universal nephelometric turbidity algorithms 127
X References . . . 132
Appendix A - Conversion Table 135
Appendix B - VOLREF Program Listing 136
Appendix C - ALGOR Program Listing 153
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FIGURES
Number
1 Geometry of measurement points and definition of
variables used in removing peripheral effects ......... 17
2 Correction factor to be applied to approximate alpha
for sunlight on a flat water surface ............. 22
3 Surface slope distribution function for several wind
velocities .......................... 24
4 Mean o correction factors as a function of wind velocity
for several sun zenith angles and for skylight ........ 25
5 Radiance distribution for a clear sky (Jerlov, 1968) ...... 28
6 Percent of total underwater energy density attributable
to skylight .......................... 33
7 Comparison of surface albedo and calculated water volume
reflectances for a typical overcast sky ............ 34
8 Comparison of surface albedo and calculated water volume
reflectances for a typical clear sky ............. 35
9 Spectrometer head, periscope, mounting platform, and
reflectance panel holder installed on boat .......... 39
10 Reflectance panel holder in use ................. 40
11 Typical reflectance values for MgO, Kodak neutral test
cards, and painted calibration panels ............. 42
12 Experimental setup for measuring water reflectance ....... 44
13 Spectral reflectance data for Krylon Gray Primer
calibration panels ...................... 47
14 Experimental setup for measuring gain of last
amplification stage of spectrometer electronics ........ 48
15 Variance in gain measurements as a function of wavelength. ... 50
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FIGURES (Continued)
Number Page
16 Average strip chart deflection as a function of
wavelength for data used in calculating aQ 51
17 Variance in illumination and spectrometer electronics
as a function of wavelength 52
18 Typical volume spectral reflectance curves for water
containing suspended sediment concentrations of
25 and 250 mg/1 54
19 Normalized variance in volume spectral reflectance
resulting from instrumental uncertainties 55
20 Sensitivity of reflectance to changes in sediment
concentration as a function of wavelength 56
21 Instrumental uncertainties expressed in units of
sediment concentration for 25 mg/1 water 57
22 Instrumental uncertainties expressed in units of
sediment concentration for 250 mg/1 water 58
23 Instrumental uncertainties expressed in units of
nephelometric turbidity for 15 and 150 NTU water 59
24 Maximum depth of water penetration by sunlight assuming
reflectance from a panel with a typical sediment
spectral reflectance and a two percent return to
the surface 62
25 Least-squares linear fits to filterable and non-
filterable residue values from the analysis of
the Lake Mead water samples 64
26 Albedos, peripheral effects, and volume reflectances of a
clear and an overcast day at station MV1 66
27 Uncertainties in the Lake Mead data as a function of
residue and turbidity values 71
28 Lake Mead test sites 73
29 Sampling stations at the Colorado River site 76
30 Sampling stations at the Las Vegas Wash and
Government Wash sites 77
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FIGURES (Continued)
Number £§S§
31 Sampling stations at the Virgin River and Muddy
River sites 78
32 Casting a shadow on the calibration panel 79
33 Field observations form filled out at each
sampling station 81
34 Spectrometer video outputs as recorded on strip chart
for sample 35175-1 82
35 Computer printout for the data shown in Figure 34 83
36 Histogram of nonfilterable residue (105°C) values
in the 200 Lake Mead samples 86
37 Spectral reflectance curves for the moistened
sediment samples 87
38 Nonfilterable residue (105°C) vs. nephelometric
turbidity for all Lake Mead samples in the 50
to 500 mg/1 range 89
39 Spectral absorption curve of a natural phytoplankton
population (Yentsch, 1960) 91
40 Statistical estimates of volume spectral reflectance for
0 and 20 NTU turbidity levels 92
41 Six "best fit" curves for volume reflectance at 652 nm
vs. nonfilterable residue (105°C) for silt-sized
particles in Lake Mead 96
42 Typical nonfilterable residue-nephelometric turbidity
relationships for various particle sizes 98
43 Particle size distribution for Muddy, Virgin, and
Colorado River sediment samples 101
44 Particle size distribution for Las Vegas and Government
Wash sediment samples 102
45 Volume reflectance at 480 nm as a function of
nonfilterable residue (105°C) 104
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FIGURES (Continued)
Page
Volume reflectance at 550 run as a function of
nonfilterable residue (105°C) 105
47 Volume reflectance at 652 nm as a function of
nonfilterable residue (105°C) 106
48 Volume reflectance at 782 nm as a function of
nonfilterable residue (1Q5°C) 107
49 Volume reflectance at 480 nm as a function of
nephelometric turbidiy 108
50 Volume reflectance at 550 nm as a function of
nephelometric turbidity 109
51 Volume reflectance at 652 nm as a function of
nephelometric turbidity 110
52 Volume reflectance at 782 nm as a function of
nephelometric turbidity Ill
53 Effects of random noise addition on training set
and test set accuracy evaluations 116
54 Uncertainties in remote measurements based on red or
near-IR volume reflectance 118
55 Accuracies of multispectral algorithms for predicting
nonfilterable residue (105°C) 124
56 Accuracies of multispectral algorithms for predicting
nephelometric turbidity 125
57 Comparison between accuracies of correct and misapplied
six-wavelength algorithms 129
58 Expected accuracy of universal nephelometric turbidity
algorithms 131
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TABLES
Number Page
1 Turbidity-Related Parameters Used in EPA Permits 12
2 JPL Supplied Filter Data 37
3 Size Ranges of Various Particulates 60
4 Sky and Water Condition at Station MV1 on
8/8/75 and 11/14/75 65
5 Uncertainties in Laboratory Analysis Results 68
6 Summary of Uncertainties in the Lake Mead Data in
Units of Suspended Sediment 69
7 Summary of Uncertainties in the Lake Mead Data in
Units of Nephelometric Turbidity 69
8 Platinum-Cobalt Color Averages by Site 90
9 Grouping of Samples by Site and Particle Size 99
10 Single-Wavelength Algorithms - Particle Size Known 117
11 Multispectral Algorithm Coefficients Fine Sand -
Nonfilterable Residue (105°C) 120
12 Multispectral Algorithm Coefficients Silt -
Nonfilterable Residue (105°C) 121
13 Multispectral Algorithm Coefficients Fine Sand -
Nephelometric Turbidity 122
14 Multispectral Algorithm Coefficients Silt -
Nephelometric Turbidity 123
15 Multispectral Algorithm - Nonfilterable Residue
(0 to 50 mg/1 Silt) 128
16 Multispectral Algorithm - Nephelometric Turbidity
(0 to 40 NTU Silt) 128
17 Universal Nephelometric Turbidity Algorithms 130
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ABBREVIATIONS AND SYMBOLS
APHA American Public Health Association
ASTM American Society for Testing and Materials
AWWA American Mater Works Association
deg., degree
EIFAB European Inland Fisheries Advisory Board
EMSL/LV Environmental Monitoring and Support Laboratory—Las Vegas
EPA U.S. Environmental Protection Agency
FET Field Effect Transistor
IR infrared
JPL Jet Propulsion Laboratory of the University of California
mg/1 milligrams per liter
m/sec meters per second
Mfl Megohm
N/A Not available
nm nanometers
NOIC National Oceanographic Investigation Committee
NTU nephelometric turbidity units
OEGC Office of Enforcement General Counsel
Pt-Co platinum-cobalt
rms root mean square
SCS Scene Color Standard
USDI U.S. Department of the Interior
VAC Volts, Alternating Current
VDC Volts, Direct Current
WPCF Water Pollution Control Federation
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ACKNOWLEDGMENTS
Recognition is given to Mr. John Novotny and Mr. Chuck Lanska of Lockheed
Electronics Company, Inc. who redesigned and modified several portions of the
EPA spectrometer to increase its sensitivity and reliability to levels
acceptable for the requirements of this project.
The quality of the data acquired in the field, and hence the success of
this study, was greatly dependent upon proper care in exercising field
procedures and upon careful attention to assure proper spectrometer operation.
Messrs. Mike Ensminger, Chuck Lanska, and Wilbur McAllister of Lockheed are
thanked for their conscientious efforts in assisting the author in performing
the field work reported here.
xiii
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SECTION I
INTRODUCTION
STATEMENT OF THE PROBLEM
Sediment has been defined as soil material which, erodes from the surface
of the land and Is transported to streams and reservoirs by runoff water
(USEPA 1973). Suspended sediment Is that part of the total fluvial sediment
which remains In suspension In water owing to the upward components of
turbulent currents or by colloidal suspension (USDI 1959). Suspended sediment
In natural water bodies Is an environmental problem of major consequence for
many reasons. The following are among the more significant effects:
Suspended sediment directly affects light penetration, water
temperature, and oxygen transfer which in turn can create
unfavorable habitats for aquatic life.
Suspended sediment serves as a mechanism of transport for
sorbed minerals and organic substances including many toxic
materials.
The aesthetic and recreational value of a water body is reduced
by the turbidity resulting from suspended sediment.
Agriculture, silviculture, construction, and mining are among the more
important activities of man that contribute sediment to waterways. These
sources of sediment loading are not point sources but can involve processes
occurring over an entire watershed. This type of nonpoint source pollution is
not easily monitored by conventional ground-based sampling techniques. Thus
aerial remote sensing techniques are drawing increased attention from the
United States Environmental Protection Agency (EPA) as useful tools for
monitoring nonpoint source surface water pollution. It has been suggested
(USEPA 1975) that remote sensing techniques for measuring suspended sediment
concentration could be valuable aids in the following areas:
Identification of sources and potential sources of sediment loading.
Determination of the extent of areas affected.
Quantitative assessment of the distribution of sediment in waterways.
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Assessment of the contributions of sediment to waterways from
various point and nonpoint sources.
Study of relationships between sediment loading rates and land
use practices.
This report covers the first phase of a long-range study the ultimate
objective of which is the development of remote sensing techniques for the
routine monitoring of suspended sediments. The work performed in this first
phase consists of the acquisition of coincident spectral reflectance data and
water samples from five sites in Lake Mead, Nevada-Arizona, and the analysis
of that data to determine the feasibility of monitoring suspended sediments
remotely. Speaking in broad terms, the problem of determining feasibility is
thought to consist of the following:
From the Lake Mead data, statistically define the relationships
between sediment concentration and the spectral reflectance of
the water body.
Based on these statistical relationships, estimate the accuracy,
precision, analytical range, and other parameters describing the
confidence levels to be expected in remote measurements.
Determine the degree of variability of the reflectance/suspended
sediment relationships from site to site in order to evalute the
possibility of developing universally applicable multispectral
algorithms which would estimate sediment concentrations without
the need for extensive ground truth at each monitoring site.
STATE-OF-THE-ART OVERVIEW
The relationship between water spectral reflectance and suspended solids
has been the topic of numerous investigations. Conventional and multispectral
photography, spectrometers, multispectral scanners, and LANDSAT have all been
used as remote sensing systems for previous studies. A small representative
sample of some recent work in this field is briefly summarized in the
following paragraphs.
Photographic Studies
Color-infrared photography was employed by Rosgen (1975) in a study of the
West Fork of the Madison River in southwestern Montana. The concentrations
and sources of sediment produced during peak snowmelt runoff were determined
by photo densitometric analysis coupled with specifically located ground-truth
stations. His conclusion was that, with proper attention to the controls
necessary to minimize spectral variability in photographic procedures and
microdensitometer analysis, reliable sediment concentrations may be obtained
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through photo analysis. He reports a 71.5-milligrams-per-liter (mg/1)
standard error in his statistical estimates of suspended sediment
concentrations which ranged from 22 to 660 mg/1.
The Upper Truckee River sediment plume in Lake Tahoe was the subject of a
recent remote sensing study by Goldman (1974). Aerial color and multispectral
photography and simultaneous ground-truth measurements in the lake were
subjected to a statistical analysis. Their procedure was to assign a four- or
five-level visual density scale to the imagery of the plume. It was found
that the correlation coefficients were high between these density values and
surface measurements of suspended sediment.
Another recent-study involving col or-infrared photographs and simultaneous
water sampling was performed by Lillesand et al. (1975) in the mixing zone
resulting from the discharge of paper mill effluent. The objective was to
quantitatively delineate the mixing zone by photographic photometry. It was
concluded that, if predicated on a limited amount of ground sampling, these
methods could be used to measure and delineate waste distributions as reliably
as conventional surface-measuring techniques. Although the authors made no
specific statements concerning accuracy, data from this paper have been used
to infer a variance at the 25-mg/l level of approximately 0.16. They stated
that variations between observed and modeled concentrations could be
attributed to the experimental error inherent in collecting and processing the
suspended solids ground truth.
The Ross Barnett Reservoir near Jackson, Mississippi, was the test site
for a study in which multispectral photography and ground-truth were combined
to give a model relating measured turbidities with the spectral responses at
the various sample sites. Data from two areas within the reservoir were
analyzed and it was noted that the spectral response-turbidity relationship
was not the same for both sites.
Other photographic studies include Klooster and Scherz (1974) and
Lillesand (1973).
Spectrometer Studies
Ritchie et al. (1974) conducted an in situ measurements program of special
interest because of its similarity with the present study. The reflected
solar radiation from the surface waters of six northern Mississippi lakes was
measured using a portable spectrometer. Their objective was to determine the
relationship between the reflected solar radiation and the concentration of
total solids in the surface waters. This study indicated that a quantitative
relationship existed, but the relationships apparently were not the same for
all six lakes. The need is pointed out for further studies to determine if
separate regression models are needed for each lake or if a composite model
could be used on all lakes.
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Multispectral Scanner Studies
An aircraft-borne multispectral scanner study has been conducted by Pionke
and Blanchard (1975) leading to the conclusion that the suspended sediment
concentrations of 14 Oklahoma impoundments were related to spectral
reflectance. They investigated the transferability of the relationships from
one area to another and concluded that a relationship can be applied to other
areas providing sediment characteristics controlling reflectance are similar.
Soil color or geologic origin were thought to be the most important factors
influencing transferability and that textural differences are of little
significance.
LANDSAT Studies
Klemas et al. (1974) related ground-truth sediment concentration values to
LANDSAT band 5 radiance values with an exponential function and found good
correlation between modeled and ground-truth values. They go on to state that
such a method promises not only to yield a mathematically expressible
relationship between concentration and radiance but also, by identification of
typical spectral signatures, allows identification of sediment and certain
pollutants. If this method is refined by using a greater number of bands,
they feel it may even be capable of distinguishing between different sediment
types.
LANDSAT data have been widely used in studies of such water clarity
indicators as secchi disc extinction depth, Jackson candle turbidity, and the
mass/volume of suspended solids. Other investigators applying LANDSAT data to
these types of problems include Kritikos et al. (1974), and Bowker et al.
(1975).
SIGNIFICANCE OF THIS STUDY AS RELATED TO PREVIOUS WORK
Most previous studies, including those just cited, share a common "case
study" approach to the sediment/water reflectance problem. This approach
consists of the coincident acquisition of remote and ground-truth data.
Remote statistical algorithms are derived based on the ground-truth and then
applied back to that same data set to evaluate performance. The result is a
case study demonstrating the existence of relationships between suspended
solids and reflected radiance.
The desire of EPA to use remote sensing techniques as routine monitoring
tools demands a departure from the traditional case study approach to a more
universal understanding of the reflectance properties of sediment-bearing
water-bodies. If extensive ground truth is required at each monitoring site
for purposes of calibrating the remote algorithm, the use of remote methods
would be greatly reduced. The objective of this study is to examine the
variability of sediment/reflectance relationships to determine the need for
local calibration of remote algorithms.
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Ritchie et al. (1974), Pionke and Blanchard (1975), and Blanchard and
Learner (1973) have Investigated the transferability of signatures but not in
sufficient depth to evaluate realistically the feasibility of remote methods
for EPA monitoring. Thus the present study is seen as a logical and
significant extension of the state-of-the-art from a case study understanding
toward a more general knowledge of suspended sediment signatures which would
permit quantitative remote monitoring with little or no ground truth.
EPA GUIDELINES
The feasibility of a remote technique for some specific application is
generally not a case of yes or no; the answer lies in a set of trade-off
relationships between many variables. Sensitivity, accuracy, ground-truth
requirements, spatial resolution, cost effectiveness, data processing
requirements and many other variables can normally be improved at the expense
of one or more of the others. The complexity of the trade-off relationships
can be reduced if a priori knowledge is available concerning acceptable limits
on some of the variables. Therefore, it is necessary to consider certain
guidelines which have been established by the EPA.
Requirements have been issued (USEPA 1975) for four parameters related to
the problem of remote monitoring of suspended sediments. One of these,
spatial resolution, is not considered in the present study, but the other
three, which are discussed briefly below, are related to the problem at hand.
Sensitivity
The sensitivity criterion is based on the philosophy that suspended
sediments should be detectable down to the lowest concentration at which a
measurable effect on water uses or aquatic life is first produced. The
European Inland Fisheries Advisory Board reports the minimum level which has
any harmful effects on fisheries is 25 mg/1 (EIFAB 1965). This level has,
therefore, been established as the detection threshold for suspended sediment.
Accuracy and Precision
Accuracy is a measurement of how close the result of an experiment comes
to the "true" value. Precision is a measure of the spread of sample values
about their own mean. If there is no bias in experimental and estimation
procedures, accuracy and precision can be considered synonymous.
The EPA (USEPA 1975) requirement does not establish values for accuracy
and precision individually because the "true" value of sediment measurements
is difficult to determine. Therefore, the guideline is that the sum of the
inaccuracy and imprecision shall result in a variance of the remote estimate
not to exceed 0.05. It is assumed that this value is a normalized variance
which is not to be exceeded over the entire analytical range down to the
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25-mg/l detection threshold. To prevent any ambiguity, the EPA accuracy
requirement, as interpreted for purposes of this project, can be expressed
mathematically as
where Sj is the ith remote estimate of suspended sediment concentration
s\ is the ground truth value at the ith point
N is the number of estimates.
This requirement corresponds to a ±5.6-mg/l standard deviation in remote
estimates at a 25-mg/l concentration.
Laboratory measurements of nonfilterable residues in the 25-mg/l range
have uncertainties ranging from ±4.3 to ±8.2 mg/1 depending on the drying
temperature (see Table 7). Thus the accuracy guideline for remote
measurements is comparable to the accuracy of standard laboratory techniques.
This requirement may be too stringent to lie within the capability of a remote
sensing system. The question arises as to whether this type of accuracy is
really needed when evaluated in the light of the intended applications for
remote sediment monitoring systems.
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SECTION II
SUMMARY AND RECOMMENDATIONS
CONCLUSION REGARDING FEASIBILITY
The objective of this study was to demonstrate the feasibility of
multispectral techniques for remote monitoring of sediment in water. The
introductory section of this report stated that feasibility would be
demonstrated by following a three-part approach consisting of defining
relationships, estimating accuracies, and investigating signature
transferability. Each of these three study areas is dealt with in Section IX
of this report. The findings regarding each question are summarized in
general terms below:
Quadratic least-squares fits relating volume spectral reflec-
tance to nephelometric turbidity and nonfilterable residue
(105°C) have been statistically defined for single and multiple
wavelengths. Thus the existence of sediment-reflectance re-
lationships has been demonstrated.
These statistically defined relationships were cast into a form
suitable for predicting nephelometric turbidity and nonfilter-
able residue values from spectral reflectance data. The
accuracy of these prediction algorithms depended upon which
parameter was being predicted, number of wavelengths used,
range of parameter values, etc. However, in most cases
accuracy evaluations resulted in values close to the a2 = 0.05
EPA requirement.
It was discovered that nonfilterable residue algorithms could
be transferred among sites with a relatively small reduction
in accuracy if the size of the suspended particles was known.
However, nephelometric turbidity algorithms were found to be
transferable between all Lake Mead test sites with virtually
no loss in accuracy and without knowing particle size. Thus
the possibility seems promising for operational implementation
of remote techniques without the need for continual ground
truth support.
Answers in each of these three fundamental question areas were
encouraging. It is concluded that the evidence presented here speaks strongly
in favor of the feasibility of remote multispectral techniques for EPA
monitoring purposes.
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RECOMMENDATIONS
Promotion of Nephelometric Turbidity
One of the more important results of this study has been the emergence of
nephelometric turbidity as a much more desirable parameter for remote
monitoring than is nonfilterable residue which is now the most widely used
measurement. It is expected that EPA will concur with the conclusions of this
report and pursue a long-range program to bring remote multispectral
techniques to an operational status. If this be the case, it is strongly
recommended that nephelometric turbidity be promoted within the environmental
community as the primary suspended sediment related parameter.
In some situations the mass/volume value may be important and it may not
be possible to substitute nephelometric turbidity for nonfilterable residue.
However, it is suspected that nonfilterable residue is often specified in dis-
charge permits because it is traditional to do so and not because the
mass/volume is really significant. In these cases if permits could be written
in units of nephelometric turbidity it would definitely facilitate the
eventual implementation of remote monitoring.
The big advantage of nephelometric turbidity is its signature transfer-
ability. However, there are several other important advantages associated
with this parameter.
This study has shown that nephelometric turbidity is more
accurately related to volume spectral reflectance than is non-
filterable residue.
Nephelometric turbidity can also be more accurately measured
on the water samples collected for accuracy verification.
Nephelometric turbidity can be measured in the field using an
inexpensive turbidimeter, whereas, nonfilterable residue
necessitates sample storage, transportation, and laboratory
analysis.
Future Studies
The study reported here was only a first step toward the long-range
objective of operational remote monitoring of suspended sediment. The
feasibility of this goal has been demonstrated, but continuing study will be
required to gain the additional knowledge necessary for upgrading these
techniques to the status of an operational monitoring tool. Many areas need
further investigation but there are two of primary importance that are
recommended for the next phase of study.
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Geographical Expansion of the Data Base
The conclusions resulting from this study are significant if they are true
in general and not just a peculiarity of Lake Mead. To verify these
conclusions in the general sense it is recommended that additional data
acquisition be performed at several other water bodies in geographically
diverse locations.
Atmospheric Effects
Data acquisition for this project was performed from a boat. Therefore,
we could not investigate the effects that the intervening atmosphere would
have on a remotely sensed surface albedo. Indications are that the magnitude
of atmospheric effects can be larger than the surface albedo itself. Thus
accurate removal of atmospheric effects from airborne data will be a
necessity.
It is recommended that the extension of data acquisition to other
geographical locations be accomplished from an airborne platform so that the
resulting data can serve as input to the analysis of the atmospheric effects
problem.
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SECTION III
TURBIDITY
DEFINITION
Light scattered by sediment particles gives water a cloudy or turbid
appearance. In discussing the optical properties associated with the presence
of particles in water, the term "turbidity" arises constantly. Unfortunately
the topic of water turbidity is not clearly defined. There are three
authoritative sources of guidelines for the measurement and definition of
turbidity: American Public Health Association's (APHA) "Standard Methods ..."
(1971); EPA's "Methods ..." (1973); ASTM's "Annual Book of ..." (1973). These
sources do not agree with each other in all respects and often a single source
will contain internal ambiguities.
In May of 1974 the National Oceanographic Instrumentation Center (NOIC)
sponsored an interdisciplinary workshop on turbidity to identify the various
applications for turbidity data and to determine techniques for turbidity
measurement. The proceedings of that workshop were published and conclusions
and recommendations were made (Proceedings, NOIC ..», 1974). A complete
treatment of the topic of water turbidity is beyond the scope of this report.
The interested reader is referred to the aforementioned proceedings and to a
recent review paper (Pijanowski 1975) for a more complete discussion.
One recommendation of the NOIC workshop, which will be followed in this
report, was that turbidity should be defined as a qualitative and relative
appearance descriptor of water clarity. To illustrate this definition the
analogy was drawn between turbidity and "warmth" which is also a qualitative
and relative term. One does not measure warmth; one measures temperature.
Likewise one does not measure turbidity; one measures beam transmittance,
scattering coefficient, or some other quantitative parameter.
An attempt has been made to compile a composite and consistent set of
definitions of turbidity-related parameters from the three references
previously cited. Because of the ambiguous nature of the topic this attempt
is not completely successful. However, for purposes of this report,
terminology will be used according to the definitions given below.
Absolute Turbidity—the fractional decrease of incident
monochromatic light through the sample, integrating both
scattered and transmitted light.
10
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Apparent Color—Includes both the color due to substances In
solution (true color) and the color due to suspended matter
(turbidity).
Dissolved—filterable.
Filterable Residue—that portion of the total residue which
passes through a filter (glass fiber filter discs, without
organic binder, Reeve Angle Type 934-A 984-H, Gelman Type A,
or equivalent).
Fixed Residue—nonvolatile residue.
Jackson Candle Turbidity—an empirical measure of turbidity in
special apparatus. Based on the measurement of the depth of a
column of water sample that is just sufficient to extinguish
the image of a burning standard candle observed vertically
through the sample.
Nonfilterable Residue—that portion of the total residue
retained by a filter.
Nephelometric Turbidity—an empirical measure of turbidity based
on a measurement of the light-scattering characteristics
(Tyndall effect) of the particulate matter in the sample.
Nonsettleable Residue—that part of the total residue which
will not settle (floating or dissolved material).
Nonvolatile Residue—that part of the total residues remaining
after ignition for 1 hour at 550°C.
Particul ate Matter—that matter, exclusive of gasses, existing
in the nonliquid state which is dispersed in water to give a
heterogeneous mixture.
Settleable Residue—that part of the total residue which will
after sitting (or centrifuging to speed the process) settle to
the bottom of the sample containers measured volumetrically.
Suspended—nonfi 1 terabl e.
Total Residue—the sum of the homogeneous suspended and dis-
solved materials in a sample; evaporated and dried at 103°C to
105°C.
True Color—the color of water after the turbidity has been
removed. The recommended method for the removal of turbidity
is centrifugation.
11
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Turbidity—a qualitative descriptor of water clarity.
Volatile Residue—that part of the total residues lost after
ignition for one hour at 550°C.
METHODS OF MEASUREMENT
It is important to note that there are certain initial constraints on how
suspended sediment is to be measured. The U.S. EPA issued permits for turbid
discharges in natural waterways. To achieve maximum compatibility with
existing guidelines, it would be desirable if remote monitoring could measure
the same parameters specified in existing permits. Thus frequency of usage
within the scientific/legal community dealing with water quality is felt to be
an important criterion in deciding how sediment concentrations should be
measured for this project.
A partial tabulation of the parameters specified in existing permits has
been compiled by the Environmental Monitoring Systems Laboratory—Las Vegas
(USEPA, undated memorandum). This tabulation listed 165 water quality
parameters, of which 11 were thought to be closely related either directly or
indirectly to water turbidity. An example of an indirect relationship would
be that of certain dissolved solids which in themselves are colorless and
cause no turbidity, but which are nutrients stimulating algae growth which
results in water turbidity. Table 1 lists these turbidity-related parameters
in order of decreasing frequency of occurrence in existing permits.
TABLE 1. TURBIDITY-RELATED PARAMETERS USED IN
EPA PERMITS
Parameter Number EPA Permits
Nonfilterable Residue (105°C) 3954
Settleable Residue (volumetric) 675
Nonsettleable Residue 404
Nonfilterable Residue (180°C) 334
Filterable Residue (180°C) 278
Nephelometric Turbidity (NTU) 235
Total Residue (105°C) 56
Filterable Residue (105°C) 51
Color (Pt-Co Units) 25
Fixed Residue (550°C) 9
Nonfilterable, Volatile Residue 6
12
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Notice that in Table 1 a drying temperature is often specified. The three
drying temperatures most commonly used give the following results:
105°C—the sample retains mechanically occluded water and water
of crystallization. Organic loss is very slight if at all.
180°C~mechanically-occluded water is almost all gone, some
water of crystallization remains. Organic matter is reduced
but not completely destroyed.
550°C—mechanically occluded water, water of crystallization,
and organic matter are all gone.
The frequency-of-usage criterion clearly dictates the nonfilterable
residue dried at 105°C as the best parameter to relate to spectral reflectance
signatures. However, this parameter seems to be oriented toward point source
wastewater discharges because it includes both organic and inorganic
particulate matter. The nonpoint source water pollution, for which the remote
techniques are especially useful, would consist primarily of inorganics such
as silt, sand, and clay particles. This type of particulate matter would
probably best be represented by nonfilterable, fixed residue. The fixed
residue measurement, however, is virtually unused at this time. Furthermore,
the elevated drying temperature (550°C) results in decreased accuracy in the
laboratory measurement of this parameter. Thus, the choice between
nonfilterable residue (105°C) and nonfilterable, fixed residue (550°C) is not
obvious.
Fortunately, the water samples collected from Lake Mead contained
negligible amounts of organic particulate matter and the two measurements were
essentially equivalent. Thus, nonfilterable residue (105°C) has been selected
as the primary water parameter of interest for this initial phase of study.
Nine of the 11 parameters listed in Table 1 (settleable and nonsettleable
residues were omitted) were measured on the water samples collected at Lake
Mead. In the course of the spectral data analysis it was found that
nephelometric turbidity was a significant parameter. Nephelometric turbidity
and nonfilterable residue (105°C) are then the two water quality parameters
that have been used in the statistical analysis reported here. The other
seven are not included in the analysis but are available if needed for more
detailed analysis in the future.
The analysis of water samples was performed in the laboratories of the
Methods Development and Analytical Support Branch at the EPA's Environmental
Monitoring Systems Laboratory—Las Vegas (EMSL-LV). Measurements were
conducted according to standard methods as defined by the American Public
Health Association (1971). The reader is referred to this source for a
detailed discussion of laboratory methods.
13
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SECTION IV
PERIPHERAL EFFECTS
GENERAL DISCUSSION
The color of a water body, as observed from the air, Is dependent upon
phenomena that can be classified into four categories: illumination source,
atmosphere, surface reflection, volume reflection. Only volume effects are
indicative of water turbidity. Thus the volume spectral reflectance of the
water, pw(x), is the parameter which should be correlated with suspended
sediment concentration (nonfilterable residue). Source, atmospheric, and
surface effects are called peripheral effects because they mask the water
color resulting from volume reflectance.
Peripheral effects have been ignored by most previous investigators who
have usually worked with the surface albedo which is defined as the ratio of
the energy leaving the water to that falling on it (Jerlov 1968). The albedo,
therefore, contains the sum of the surface reflection plus the light
backscattered from the water volume. If the albedo is measured from some
altitude above the surface, the apparent albedo also contains light scattered
into the sensor aperture by the intervening atmosphere. Using the surface
albedo is a valid procedure for the typical "case study" approach where a
statistical algorithm relating the albedo to some water quality parameter is
derived from data collected the same day and under the same conditions as the
data to which the algorithm will be applied. In this case peripheral effects
have the same effect on all data and tend to cancel out in the statistical
analysis. However, in developing a general algorithm for application to
various'data sets taken under differing conditions, peripheral effects must be
removed, leaving the volume spectral reflectance which should be invariant
under differing environmental conditions.
In developing a technique for removal of peripheral effects, the long-
range objective of the project must be kept in mind. That objective is the
development of techniques for remote turbidity measurement which are
applicable to an airborne multispectral scanner. Therefore, any techniques
must be easily transferable from boat data to airborne data. A technique
similar to the Scene Color Standard (SCS) Technique (Piech and Walker 1971)
was chosen as the best method of correcting the spectrometer data collected
for this project, and also as being the most promising for use with airborne
data.
14
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The SCS technique originally had no provision for wind effects on the
optical properties of the surface. Also, the lens effect (see page 20) of the
surface was previously overlooked but has been added here. These changes
should improve the accuracy of peripheral effects removal.
The following is a summary of some of the features which have been
influential in the selection of this technique:
The technique can be used without ground truth if common
materials of known reflectance can be found in the imagery.
If ground truth is required or desired to improve accuracy,
only two spectral reflectance measurements are needed.
These measurements can usually be made days or weeks after
overflight.
The above feature means that one can avoid the traditional
shotgun approach to ground truth, i.e., gather as much data as
possible in the hope that one will have the one or two numbers
needed for data analysis. Data can be examined in detail
first, and a team then sent out to get only the specific
pieces of information that can be used.
Switching from boat to aircraft will require no change in the
data quantification procedure.
The transition from spectrometer to scanner will also be no
problem since many of the scan angle corrections have been
included in the derivation, and those ignored can easily be
added without impacting the basic analysis procedures.
Absolute calibration of the sensor is not required.
MATHEMATICAL DISCUSSION
The categorization of interfering color effects into illumination source,
atmospheric, and surface reflection is convenient for conceptual purposes,
because it facilitates an understanding of the physical processes involved in
color masking. However, it is difficult to measure and remove these groups of
effects from airborne data. The SCS technique is based on a grouping of
peripheral effects into three parameters: a, a1, and a. This grouping
simplifies the mathematics, and most importantly, it makes the solution of the
color masking problem practical.
15
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The parameters a, a', and B are functions of wavelength and must,
therefore, be evaluated for each spectral band sampled by the spectrometer.
For a given wavelength band, the energy reaching the sensor can be written
E = ap + a'p_ + g (2)
W d
The term apw is the energy resulting from reflection within the water with
volume reflectance pw. The energy coming from surface reflection of
skylight is o'ps where ps is the reflectance of air-water interface.
Correction for surface reflection of sunlight has not been included. Thus,
pw cannot be determined in the sun glitter portion of the imagery. Light
that has never reached the scene, but is scattered into the sensor by the air
column in the sensor field of view, is represented by the term 3. Equation
(2) gives a complete account of all of the factors influencing apparent water
color, and it is from this equation that volume spectral reflectance must be
obtained.
The parameter a is proportional to total irradiance, atmospheric
transmittance, and water surface transmittance. It varies with weather
conditions, sun angle, and many other factors which are individually unknown.
The philosophy behind the SCS technique is that, although the variables cannot
be measured individually, they can be lumped together as a single parameter,
a, and the cumulative effects given a numerical value. Likewise, a', which is
proportional to atmospheric transmittance and skylight irradiance, can be
evaluated as a cumulative effect influencing surface reflection. Atmospheric
scattering and total irradiance influences 8, which can also be evaluated by
the SCS technique.
Once numerical values have been assigned to o, a1, and e, Equation (2) can
be solved for pw. This is done in each spectral band, and the result is the
true volume spectral reflectance with color masking by peripheral effects
removed.
Evaluation of Beta
Let us assume that the voltage output of the sensor is proportional to
energy falling on the detector. This voltage is biased by some value, V0,
and thus,
V - kxE + V0 (3)
where kx is the calibration coefficient for wavelength \. within the scene
imaged by the sensor we must find the shadow of some opaque object falling on
a uniform reflecting surface as shown in Figure 1. We need not know pc,
the reflectance of the surface.
16
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SHADOWED SURFACE
OF REFLECTANCE PC
SUNLIT SURFACE
OF REFLECTANCE
Figure 1. Geometry of measurement points and definition
of variables used in removing peripheral effects.
17
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The voltage out of the sensor as it looks at the outer edge of the shadow
is
Ve = kA(ke<*'P(L + 3) + V0 (4)
and as the view is near the base of the object,
+ &) + V (5)
Solving Equations 4 and 5 simultaneously gives
b - kbVe - V0(ke - kb)]/kx(ke - kbj (6)
The constants ke and kb are functions of object size, object reflectance,
and sun angle. The object size and sun angle can be determined by
photogrammetric techniques if stereo photo coverage is obtained from the
sensor platform. The object reflectance, p0, could be estimated for common
materials, or an in situ reflectance measurement could be made to improve
accuracy. Either kg or kb are approximated by the equation
2 IT
where $ is the horizontal angle in radians subtended by the object width
<)> is the vertical angle subtended by the object height as viewed from
the shadow edge or object base respectively.
Note from Equation 7 that if p0 = 1, then ke = 1 and kb = 1, and
Equation 6 for B becomes undefined. Thus accuracy in & calculation is
improved with smaller p0 values. Narrow objects also are preferable to wide
ones since they maximize the quantity (ke - kb) thus improving accuracy in
B. In the optimum case where p0 would be nearly zero and the object very
narrow, ke =* 1 and kb =i .4. Beta in this idealized case would reduce to
0 = 2Vb - Ve - V0)/kx (8)
18
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Approximation of Alpha
Alpha is approximated by finding in the scene, a sunlit surface of known
reflectance, pc. The reflectance of common surfaces may be estimated, or
accuracy improved by measuring p-. In either case, the voltage output as
the sensor views the surface win be
Vc = MC.PC + 3) + V0 (9)
Therefore,
"approx " ^ c
This approximate a is used to calculate a1, and then o1 is used to convert the
approximate a to the exact value.
Evaluation of Alpha Prime
The first step in the calculation of a' is to measure V£, the output as
the sensor views the sunlit portion of the shadowed surface of reflectance
pc. This voltage is given by
vc = kxK + *) + vo
which can be solved for p.
; - V0 - kx3)/kxa (12)
This value for p^. is substituted into Equation 4 or 5 to give a1
Using Equation 4, the solution for a' becomes
(13)
19
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Correction of Approximate Alpha
The parameter o was determined from a solid surface of known reflectance.
In this case, all incident energy is available for reflection and all
reflected energy is propagated up into the atmosphere. However, in the volume
reflectance of water, not all energy incident on the surface enters the water
to be available for possible scattering. Likewise, not all back-scattered
energy enters the atmosphere since some will be reflected back into the volume
by the air-water interface. Transmittance of the water surface is a function
of incidence angle and surface roughness.
The volume scattering problem is further complicated by the fact that the
light entering the water undergoes a lens effect (Jerlov 1968) where light is
refracted at the interface because of the discontinuity in the index of
refraction. This refraction effect must be accounted for in relating the
irradiance of reflectance panels in the air to the energy flux density in the
water volume. The lens effect, like surface transmittance, is a function of
surface roughness.
These factors differentiating water scattering from solid surface
reflectance, which were ignored in the original SCS technique, have been
accounted for here by making a correction to aapprox- The correction factor
will include several surface transmittance and Tens effect calculations as
discussed in the following paragraphs.
Correction for Surface Transmittance of Sunlight
Since o is intended to be proportional to the incident eneryy density in
the water volume, estimates of a made from observing the irradiance of a
horizontal panel in the air must be reduced by reflection losses at the
surface. Fresnel's Equation for the reflectance of unpolarized light from a
plane air-water interface is
n
ps
where z is the sun zenith angle
j = sin'1 (sin z/1.33);
Thus, the first correction to oapprox is
0 = "approx (1 - PS(Z)) (15)
20
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Correction for Lens Effect on Sunlight
Having corrected for surface transmittance, o is now correct if irradiance
of an underwater horizontal panel were in question. However, a should be
proportional to underwater energy density, not underwater surface irraciiance.
Underwater energy density would irradiate an underwater horizontal panel with
efficiency equal to cos j. Thus, to determine energy density the a for unuer-
water surface irradiance is modified further by removing the cos j factor.
The total correction to aapprox for the direct sunlight case is then given by
« = "approx'1 - PS(Z»/COS J (16)
The name "lens effect" is used for the cos j term because j is a refraction
related parameter and the magnitude of this correction is a function of the
index of refraction.
The symbol T will be used to represent the total correction factor for
parallel rays of light incident on a flat water surface.
T = (1 - PS(Z))/COS j (17)
Figure 2 is a plot of T as a function of incidence angle. In this fiyure the
difference between the Fresnel transmittance curve and T is attributable to
the lens effect. Piech and Walker (1971) included Fresnel reflection
corrections in the SCS technique, but did not make any lens effect corrections
which could introduce errors of as much as 20 percent at larger zenith angles.
This error cannot be tolerated if volume spectral reflectance is to be
quantified with a variance of less than 0.05.
Correction for Wind Roughening of Water Surface
When the surface of a water body is roughened by wind, the sloped wave
faces alter the angle of incidence of sunlight. Also, sloped and curved
surfaces will influence the magnitude of the lens effect. This problem has
been handled by considering the rough surface to consist of a large number of
small facets (plane surfaces). Equation 17 can be used to calculate the a
correction factor for each facet, and these can be averaged to give a mean
correction factor for the rough surface.
The distribution of facet slopes has been shown to be a function of a
single variable, wind velocity (Cox and Munk 1956). Their experimental data
was best fit with the Gram-Charlier Series of fourth order Hermite polyno-
mials. This distribution can be approximated, with sufficient accuracy for
21
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§e
a
CO
6
*-
mJ
Uc,
UJ
ee
K
FRESNEL TRANSMITTANCE
.40
.20
30 SO 70
ANGLE OF INCIDENCE (deg)
Figure 2. Correction factor to be applied to approximate alpha for
sunlight on a flat water surface.
22
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purposes of this project, by a Gaussian distribution function. In general,
Cox and Munk found the distribution of upwind slope components to differ from
crosswind slope component distributions. However, the spectrometer was
mounted on the boat such that the field of view would normally include a
superposition of direct waves and waves reflected from the side of the boat.
In this mixture of waves traveling in different directions it has been assumed
that any asymmetry with respect to wind direction has been lost. The standard
deviations of the distributions of both upwind and crosswind slope components
are given by
,
au = oc = 0(0.003 + 0.00512W)] (18)
where W is the wind velocity in meters/second.
The probability of a facet having a slope with upwind and crosswind com-
ponents of u and c is
P(UiC) = —I— e^2/^ + c2/°c) (19)
This is a two-dimensional distribution function, but since it is symmetrical,
it can be represented by one-half a cross-section in any direction. Figure 3
shows the cross-section of the slope probability function for several wind
velocities.
If the a correction factor for each facet and the probability of
occurrence of any facet slope are known, it is possible to calculate the mean
correction factor for the entire roughened surface. This becomes a numerical
integration problem which is accomplished by stepping in small increments
through all possible facet slopes and summing each T weighted by P.J the
normalized probability of slope angle Yn-. Let z be the incidence angle of
sunlight on the ith facet.
N P1U-.l(z1)JcM,1 (2Q)
COS j^ COS Yn-
The cos Y-J term in the above equation is a correction term resulting from
the fact that a rough water surface has more area than a flat one.
23
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SURFACE SLOPE (deg)
Figure 3. Surface slope distribution function for several wind velocities.
-------
Figure 4 shows the mean a correction factor as a function of wind velocity
for several sun zenith angles. Note that wind roughening does not have a
drastic effect. For zenith angles less than 45° the correction factor
increases with increasing wind, but for angles laryer than 45° it decreases.
At 45° the a correction is independent of the presence of waves.
Correction of Surface Transmittance and Lens Effect for Skyliyht on a Flat
Water Surface
4T
1 3-
1 1-
9-
SKYLIGHT
10
15
WIND VELOCITY (m/s)
Figure 4. Mean o correction factors as a function of wind velocity for
several sun zenith angles and for skylight.
25
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In addition to direct sunlight, indirect sunlight scattered by the
atmosphere illuminates the earth's surface. This scattered sunlight, called
skylight, differs from direct sunlight in that it is incident upon the water
surface from all directions rather than being in parallel rays with a single
incidence angle. Alpha is proportional to the underwater energy density and,
therefore, contains a contribution from skylight as well as sunlight. That
portion of aappr:ox attributable to skylight must be corrected by a factor T'
which includesTresnel transmittance and lens effects for skylight.
The skylight case can be evaluated numerically by considering a large
number of point sources equally spaced about the sky. The contribution of the
k source to the surface illumination is
Ik = IQ cos zk (21)
where IQ is the illumination from a source directly overhead
zk is the zenith angle of the k source.
The correction for irradiance from the k source is given by Equation 17.
Summing the transmitted energy flux density from all k sources and dividing
this by the sum of the surface irradiance from all sources gives T'.
K
I [1 - ps(zk)]/cos jk cos zk
k=l
k=l
cos zk (22)
This expression would be correct if skylight were unpolarized and the sky were
of equal radiance at every point.
Unlike sunlight, which is unpolarized, light from a clear sky is partly
polarized. The degree of polarization is dependent on the part of the sky
under observation, the solar elevation, and the air turbidity (Sekera 1957).
Polarization can range from zero to over 90 percent. Clouds have a strung
depolarizing effect (Jerlov 1968). Therefore, the Fresnel reflectance used in
Equation 22 is not necessarily applicable to the skylight case. However, we
join with previous investigators, including the SCS technique developers, and
ignore the polarization of skylight.
In developing the SCS technique, Piech and Walker (1971) also assumed that
skylight was a uniform radiance distribution. Many other investigators have
done likewise, and under this assumption the skylight correction factor
calculated from Equation 22 is 1.115.
26
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As the sky becomes overcast the radiance, L, can be represented as a
function of incidence angle by a cardiodal distribution (Moon and Spencer
1942).
L(z) • L(ir/2) (1 + 2cos z) (23)
Neither the uniform nor cardiodal distributions are really representative of a
clear sky.
The clear sky radiance distribution (Jerlov 1968) shown in Figure 5 has a
maximum near the sun and a minimum on the antisolar side. Weighting factors,
W^, for each of the k sources included in the calculation were taken from
Figure 5. The transmittance is then given by
cos zk
(24)
cos zk
This equation gives a correction factor of 1.122 which is not appreciably
different from that calculated for uniform radiance. The distribution in
Figure 5 was for a 40° sun elevation, and as the sun elevation changes, the
skylight distribution also changes. For purposes of this project sun
elevation has not been included as a variable affecting skylight a correction
factors. The 40° sun elevation case is typical for our data and so the
distribution given in Figure 5 was used in all cases.
Correction for Skylight on a Wind-Roughened Surface
As was the case with sunlight, the o correction factor for skylight will
also be affected by the wind-induced roughening of the water surface. The
correction factor for this case can be numerically evaluated as before by
considering the rough surface to be made up of N facets. If the sky radiance
is approximated by K sources, the correction factor for the k source is given
by Equation 20. Summing the corrections of all k sources and normalizing by
the total surface irradiance from all sources gives the skylight a correction
factor for a wind-roughened surface.
27
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1.0 .9 .8
2.0
65
4
.55
SUN
oo
Figure 5. Radiance distribution for a clear sky (Jerlov, 1968)
-------
i-IN IN • i i «* » r\ i r\
T. = Jill Izl (25)
I wk cos zk
k=l K K
This equation has been evaluated as a function of wind velocity using the
radiance distribution shown in Figure 5. These results were included in
Figure 4. The skylight a correction factor model Equation 25 was not
evaluated for each data set because the calculations are very time consuming.
The skylight factor was taken rather from the piecewise linear relationship
shown in Figure 4.
, _ 1.122 + 0.0022H (W<5)
T " 1.133 + 0.0006(W - 5.0) (W>5)
By adding the lens effect and wind roughening the a correction factor for
skylight is substantially different from that used in the SCS technique. For
a typical case where W = 5 m/sec, a difference of 21 percent exists between
our value of 1.133 and Piech and Walker's (1971) value of 0.934. This
difference does not introduce a significant error into volume reflectance on
clear days where less than 10 percent of the total irradiance is from
skylight. However, on overcast days skylight accounts for nearly half of the
total irradiance and this inaccuracy in the SCS technique is significant.
Surface Transmittance for Upwelling Light
As upwelling light reflected from within the water volume encounters the
air-water interface another transmittance factor must be considered. The
surface reduces the amount of upwelling energy entering the atmosphere and
increases the irradiance of the water volume because of internal reflection.
With upwelling energy leaving the surface at angle 9, the observation
angle is reduced by the Fresnel reflectance, ps(9); because of refraction,
light leaving the surface at angle 8 will be incident on the water surface
from below an angle j where j = sin-1 (sine/1.33). If, as in the
downwelling case, one considers the water surface to consist of numerous
facets, the summation of transmittance over all facets yields the following
expression for the effective transmittance, T, of upwelling light through the
entire wind-roughened surface.
29
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N
cos j/ cos YI
(27)
P.. cos e
1=1 1
Light incident upon the water surface from below at angles greater than
48.6° is totally reflected back into the water volume. The upwelliny
scattered light can be considered diffuse to the first approximation, which
means that a considerable amount of upwelling energy is incident on the
surface at angles greater than 48.6°. Jerlov (1968) has evaluated the
internal reflectance of water for upwelling diffuse light to be 48 percent.
This internal reflection in effect adds to the irradiance of the water volume.
For typical cases where pw = 0.1 and the slanting paths of internally
reflected light are quite long, errors caused by ignoring internal reflection
are on the order of 2 percent. Internal reflection was ignored in the data
reduction procedures used here. It should be noted, however, that for high
particulate concentrations (> 250 mg/1) where Pw ^ 0.2 and mean free path
lengths are small, ignoring internal reflection could cause errors on the
order of 10 percent.
Summary of Approximate Alpha Correction
Equation 2 is the basic defining equation for removal of peripheral
effects. In that equation, a represents the light available for scattering in
the water volume just below the surface. Alpha was approximated by looking at
a standard calibration panel exposed to both sun and sky irradiance. The
direct sunlight component of oapprox is then
a = a - a1 (28)
asun Bapprox
There are basic differences between reflectance of a panel above the water
and scattering in an underwater volume. Thus the aapprox calculated from
the reflectance panels in Equation 10 is not exactly Correct for representing
energy available for scattering. The transmittance, reflectance, and lens
effect factors just discussed are employed to correct
-------
Evaluation of Skylight Reflectance
Reflected sunlight has been eliminated by avoiding observation angles
where this effect occurs. However, surface reflected skylight will be present
in any observation of a water body. The second term in Equation 2 represents
reflected skylight. For a flat water surface the skyliyht reflectance,
ps(e), is the Fresnel reflectance (Equation 14) evaluated at the observation
angle, e.
If the surface is roughened by wind, the surface reflectance can be
computed by averaging the individual reflectances of a larye number of facets
as was done in the a correction factor calculation.
N
I piPs(9i) cos e^cos YI
ps(e) = ^ (30)
I Pi COS 9./COS yi
Since only vertical observation data are included in the present analysis and
because the surface slope distributions (Figure 3) show no slopes yreater than
30°, any reflected skylight reaching the spectrometer was reflected at an
incidence angle of 30° or less. Fresnel reflectance is nearly constant U.Oi!
over the 0° to 30° range, thus, this value was used and the individual
reflectance of facets were not averaged. In dealing with other than vertical
observation angles in the future, Equation 3U will have to be evaluated.
Calculating Volume Spectral Reflectance
Combining Equations 1 and 2 gives an expression for voltage output by the
sensor when viewing water.
Vw = kAa>w + W9* + \* * Vo
Solving this equation for water reflectance results in the water volume
reflectance with peripheral effects removed.
(32)
For data taken from a boat, air-light is not a factor so the kx5 term has
been dropped. The constants o, a1, and VQ are, in general, functions of
wavelength. The volume spectral reflectance, pv/U), is obtained when each
31
-------
wavelength sampled by the spectrometer is evaluated in terms of these
constants and solved in Equation 31.
The parameter k^, the spectrometer sensitivity, cancels out when the
derived expressions for a, a1, and 3 are substituted into Equation 32. This
means that an absolute calibration of the spectrometer is not required. The
only requirement is that the calibration be constant over the duration of a
measurement sequence.
MAGNITUDE OF PERIPHERAL EFFECTS
Peripheral effects which mask the volume spectral reflectance of a water
body obviously exist, but the question arises as to the magnitude and
significance of these effects. What error could be expected if removal of
peripheral effects were ignored and multispectral turbidity estimates were
based on the albedo rather than volume reflectance' Is the accuracy of remote
turbidity measurements increased significantly over the SCS technique'3 Two
sample cases are presented here to indicate the typical magnitude of
peripheral effects, and to provide a comparison between the two correction
methods.
The sample chosen to represent a typical clear sky case was sample 24775-7
taken on 9/4/75 at the mouth of the Colorado River. The sun elevation for
this observation was 50.2° and there was no wind. A Muddy River sample,
32375-5, was chosen to represent a typical case with a thinly overcast sky.
Sun elevation in this case was 25.6° and a 1 m/s (3 mph) breeze was blowing
when this sample was collected on 11/19/75. Figure 6 shows a1fa which
represents the percentage of total underwater illumination which originates as
skylight for these two cases. As would be expected intuitively the amount of
skylight relative to direct sunlight is increased by the overcast which was
quite thin in this case. For a heavy cloud cover, skylight would probably
account for about 50 percent of the underwater energy density across the
entire spectrum.
Since surface reflected skylight is one of the peripheral effects in
question, it would be expected that the difference between the albedo and the
volume reflectance would be larger on overcast days. Fiyures 7 and 8 show the
albedo, SCS technique volume reflectance, and Equation 32 volume reflectance
for the overcast and clear skies respectively. As expected the peripheral
effects and the variation between methods is greater for the overcast sky than
for the clear sky. The difference between the albedo and Equation 32 ranges
from 20 percent to 30 percent in the visible part of the spectrum for the
overcast case and from 10 percent to 15 percent for the clear case. In most
places the SCS technique makes up less than one-half of this difference.
Thus, the difference between Equation 31 and the SCS technique is definitely
significant.
-------
SOT
50'
40'
M
-------
THIN OVERCAST
08
iu 06
.04
02
400
500
600
700
800
900
1000
WAVELENGTH (nm)
Figure 7. Comparison of surface albedo and calculated water volume
reflectances for a typical overcast sky.
34
-------
CLEAR
400
500
600
700
800
900
1000
WAVELENGTH (nm)
Figure 8. Comparison of surface albedo and calculated water volume
reflectances for a typical clear sky.
35
-------
SECTION V
INSTRUMENTATION
SPECTROMETER
Field measurements of water spectral radiance were made with a filter
wheel spectroradiometer which was constructed for this project at the EPA's
Environmental Monitoring Systems Laboratory, Las Vegas, Nevada. Detailed
documentation of the engineering design of this instrument has already oeen
written (Novotny 1975a, 1975b). Only a brief description of the major
features of the spectrometer will be included here.
Filter Wheel
Spectral discrimination was accomplished with a circular filter wheel
which is continuously variable from 343 to 690 nm and contained eight discrete
filter elements in the 703- to 984-nm range. A stepping motor moved the
filter wheel through the discrete filters and 12 positions on the continuously
variable portion. The Jet Propulsion Laboratory (JPL) of the California
Institute of Technology used a Gary 14 spectrophotometer equipped with an
absorption slide wire to measure center wavelength and pass-band at each of
the 20 filter positions. Table 2 contains the JPL measurement results.
Detector
The detector was a United Detector Technology, Inc., Model Pin 10DP. This
is a planar diffused, silicon photovoltaic detector that was operated in the
current mode. In this arrangement the detector can be considered a current
source that is directly proportional to the incident radiation over ID decades
of light intensity.
Preamp
Signal amplification was achieved by a current mode operational amplifier.
With Field Effect Transistor (FET) input and a 10-Mn feedback resistor, the
usable range of linearity was reduced to four or five decades. This
configuration presents an intrinsic problem of drift due to lack of chopper
stabilization. However, field procedures were developed with this in mind and
drift was not thought to be a significant problem.
36
-------
TABLE 2. JPL SUPPLIED FILTER DATA
Filter
Position
1
2
3
4
5
8
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Center
Wavelength (nm)
343
377
385
415
436
480
517
550
583
620
652
690
703
742
782
829
862
905
942
984
Half-Power
Pass-Band (nm)
18
19
14
12
13
15
15
14
13
16
15
16
18
21
21
24
20
19
21
21
Transmittance
0.36
0.29
0.28
0.30
0.29
0.28
0.26
0.27
0.25
0.26
0.27
0.29
0.68
0.53
0.58
0.36
0.40
0.47
0.48
0.34
Chart Recorder
The spectrometer data were recorded on an Astro-Med strip chart recorder
that had two analog data channels and an event marker. One analog channel
recorded the signal from the detector and the other a 10 pulse/revolution
wavelength marker signal. The event marker recorded the begin-of-scan point.
Power Supply
Initial field work was performed with the electronics powered by Ni-Cd or
lead-acid batteries. Battery failure was a frequent problem which was solved
by installing a a.c. to d.c. inverter to obtain 110 Va.c. from the 12 Vd.c.
boat battery. The 110 Va.c. drove a regulated power supply which supplied the
28 Vd.c. required by the spectrometer electronics.
37
-------
SPECTROMETER MOUNTING
The spectrometer was mounted above the cabin roof of a 22-foot cabin
cruiser as shown in Figure 9. The spectrometer head was affixed to a
periscope tube with a 45° mirror which folded the field-of-view by 90°
permitting vertical viewing of the water from a height of about 2.5 m. The
mounting platform could be rotated for the spectrometer to view the water at
angles up to 45° either side of the vertical. Laboratory experiments showed
the field-of-view to be 7 cm in diameter at the periscope aperture. A
half-angle divergence of 2.5° gave a field-of-view of about 25 cm at water
level.
The flat black panel on the side of the boat served a twofold purpose.
The first was to reduce the reflectance of sunlight from the side of the boat
into the water volume viewed by the spectrometer. The second function is
illustrated in Figure 10 which shows the lower portion of the panel folded
down into a horizontal position to hold standard reflectance panels. This
arrangement held the panels just a few centimeters above the water surface so
that they would receive the same amount of sunlight and skylight irradiance as
was incident on the water surface.
CALIBRATED REFLECTANCE STANDARDS
Since drift in the spectrometer electronics was thought probable, absolute
calibration of the spectrometer was not attempted. The alternative to
absolute calibration was to make relative measurements where backscattered
light from the water is compared to radiance of a surface of known
reflectance. Reflectance standards were, therefore, prepared for field use.
The construction and calibration of the field reflectance panels is discussed
below.
Construction
Two panels, one gray and one white, were used as reflectance standards.
These were constructed by spray painting two 0.6-m by 0.9 m pieces of aluminum
sheet metal. This gave fairly uniform reflectance surfaces and good
durability when properly handled. The panels were repainted whenever they
began to show wear which occurred seven times during the course of the
project. Panels were recalibrated after each repainting.
The paint used was Krylon spray paint manufactured by Borden, Inc. The
white panel was painted with Krylon Flat White Enamel, No. 1502, Federal Color
Standard 595 No. 37875. This titanium dioxide-pigmented paint is believed to
be of high quality and good diffuse reflectance since it has been considered
in the past as a coating for optical integrating spheres (Grum and Luckey
1968).
38
-------
CO
10
Figure 9. Spectrometer head, periscope, mounting platform, and reflectance panel holder installed on boat.
-------
Figure 10. Reflectance panel holder in use.
40
-------
The gray panel was painted with Krylon All-Purpose Gray, No. 1318. Like
the white, the gray panels seemed to be fairly uniform and very diffuse. The
nonuniformity of the panels has been measured and these results are presented
in the error analysis section.
Calibration
The calibration of the field reflectance standards is traceable to freshly
smoked magnesium oxide (MgO). Reflectance values for MgO were taken from two
literature sources: Grum and Luckey (1968), and Encyclopedia of Industrial
Chemical Analysis (1966). The NASA National Space Technology Laboratories at
Bay St. Louis, Mississippi, used a Gary 17 Spectrophotometer and Reflectance
Module to provide relative data for MgO compared to Kodak neutral test cards
which had nominal reflectances of 18 percent and 90 percent. The reflectance
values for MgO combined with the test cards/MgO relative data provided
calibration of the neutral test cards. These cards were then the working
standards for calibration of the painted panels.
The EPA spectrometer was brought into the laboratory to perform this
calibration procedure. The neutral test cards and the painted panels were
both viewed by the spectrometer under constant illumination conditions. The
ratios of spectrometer outputs for two cases combined with the previously
determined reflectance of the test cards resulted in assignment of values for
the spectral reflectance of the field standards. Figure 11 shows the
reflectance values for MgO and for typical test cards and painted panels.
41
-------
1.0
.8
2 KODAK IB^C
400 500 600 700 800
WAVELENGTH (nm)
900
1000
Figure 11. Typical reflectance values for MgO, Kodak neutral
test cards, and painted calibration panels.
42
-------
SECTION VI
ERROR ANALYSIS
INSTRUMENTAL UNCERTAINTIES
Uncertainties in Reflectance Measurement
Many variables affect-the water volume reflectance calculated from data
recorded by the spectrometer. Each of these variables has a degree of
uncertainty associated with It, and the uncertainties In each variable
contribute to an overall uncertainty In the calculated reflectance value. An
error analysis has been performed to estimate the uncertainties In volume
spectral reflectance which are attributable to instrumental sources.
Laboratory instruments for reflectance measurement generally consist of a
light source, detector, and reflectance standard for comparison with the
sample. Thus, the term instrument, as applied to field work, includes the
illumination source (the sun) and the painted calibration panels in addition
to the spectrometer which detects and records the reflected radiance.
The three types of data shown in Figure 12 are required to make a
reflectance measurement. The spectrometer output recorded while viewing the
calibration panel can be written as
VA = k^L + C (33)
where L is the radiance of the panel which has reflectance pc
k^ is the spectrometer sensitivity factor converting radiance to strip
chart deflection
C is the spectrometer offset in units of chart deflection.
If the water of reflectance pw is the target rather than the calibration
panel, then the spectrometer output would be
FB s (
43
-------
J
CHART
RECORDER
SPECTROMETER
6
J
CHART
RECORDER
SPECTROMETER
VPC
tar
CHART
RECORDER
SPECTROMETER
N^ SKY ILLUMINATION /
AALIBRATIOI
: WATER:
Figure 12. Experimental setup for measuring water reflectance.
-------
Covering the spectrometer aperture prevents all light from entering and gives
the output for the L = 0 case.
Vc = C (35)
Solving Equation 33 for pw and substituting terms from Equation 31 and
Equation 34 allows us to write an equation for pw in terms of V/\, Vg,
and V.
-------
XL
(37)
A complete derivation of the equations required for the error analysis is
too lengthy to include here, but the formulas given resulted from algebraic
manipulation of variances using the following formulas (tievington 1969).
x = au + bv: a2 =
x = ± auv:
x - ± au/v:
= au/lj2
= aj/u2
2abouv
(38)
- 20Jv/uv
The variance in water reflectance normalized by the reflectance value can be
shown to be
w _
V
(39)
where G = 1 if water is recorded on low gain
G = 2.64 if water is recorded on high gain.
Notice the pw on the right hand side of Equation 39 indicates that variance
in water reflectance is a function of the reflectance value. Accuracy values
must, therefore, be calculated at some specified turbidity/reflectance level.
The normalized variance in the calibration panel, ojL/Pc. can be
determined directly by making reflectance measurements on various spots on the
different panels used throughout the project. Six panels painted with Krylon
Gray Primer were used, and their reflectances were measured to give the mean
spectral reflectance and standard deviations shown in Figure 13.
The uncertainties er| L and or, are not as easily determined but the
routine field procedures did result in data suitable for making that
measurement. The spectrometer was equipped with a gain switch which added an
extra stage of amplification. Normally some of the data at each station were
taken on high gain and some on low gain. Since it wasn't known if the gain of
the additional stage was constant, the gain was measured at each station so
that gain changes could be accurately removed in the data reduction process.
The procedure for gain measurement is shown diagrammatically in Figure 14.
The signal at point A is the same as Equation 33 and the signal at point U is
46
-------
12 r
.10-
08
.06
.04
.02
.00
400
500
600
700
800
900
1000
WAVELENGTH (nm)
Figure 13. Spectral reflectance data for Krylon
Gray Primer calibration panels.
Gain is therefore calculated by
(40)
6 = (VD - VC)/(VX - Vc)
(41)
The uncertainty in the gain measurement can be expressed as a function of the
variances of the individual variables.
47
-------
SPECTROMETER
00
CHART
RECORDER
\
/
CHART
RECORDER
-©
SKY ILLUMINATION
/CALIBRATION!
PANEL \
™ \
Figure 14. Experimental setup for measuring gain of last amplification
stage of spectrometer electronics.
-------
°a •
ALA j
The variance in the gain values calculated from the field data shoulu
therefore give an indication of the cumulative effects of o? . ana at-
A
Data from 12 days was used to calculate gains at as many wavelengths as
possible (high gain signals frequently went off scale at some wavelengths
making gain calculation impossible). The mean value of the 145 calculations
of G was 2.64 and o| was determined to be 0.00899. The variance in the gain
for the same wavelength on different days was not appreciably larger than the
variance for different wavelengths on the same day. It is, therefore,
concluded that the gain was constant throughout the project and the overall
or value was all attributable to o2. , and ar.
KXL
Equation 42 can be rewritten substituting 2.64 for G.
(kxL)"2 |~13.94 of L + 15.94 ojl (43)
The variance in the gain was observed to be different at different wave-
lengths. Figure 15 shows as as a function of wavelength. The product
in Equation 43 is the strip chart deflection in centimeters when looking at
the gray calibration panel (low gain setting) under typical field conditions.
The average value of k\L calculated from the same data used in oetermininy
oQ is shown in Figure 16.
The values for OQ and k\L contained in these figures can be used in
Equation 43 to obtain a value for the weighted sum of aiLl. anu <*£•
However, we need to enter the values of these variables individually into
Equation 39 to compute the variance of the reflectance measurement. The
separation can be accomplished by realizing that Oc is the uncertainty in
strip chart offset, and as such, it is independent of signal level and is not
a function of wavelength. This offset uncertainty contains the inaccuracies
in reading the strip chart as well as possible errors from other sources.
Chart reading accuracies were estimated to be about ±0.02 cm. Therefore, ac
should be about 0.0004 cm2 as a minimum, and possibly larger if other factors
introduce significant errors into offsets. Figure 15 showed the smallest ay
value to be at 620 nm.
49
-------
06T
.05- •
04 •
.03' •
c«a
02 •
.01--
.00
400
500
600
700
800
900
1000
WAVELENGTH (nm)
Figure 15. Variance in gain measurements as a function of wavelenyth.
Evaluating Equation 42 at this wavelength gives a - 0.00011 cm2. A
negative variance, which is mathematical Iy2impossible, apparently results from
the fact that the 0.004 cm estimate for ac was too large. If CTQ is
reduced to 0.00031 cm2 Equation 42 gives a akxL value of zero- Th1s means
that &c accounts for all the variability in measuring G, or in other words,
the strip chart reading uncertainties are the only significant errors in
determining offsets. A OQ value of 0.00031 can, therefore, be assigned to
all wavelengths allowing Equation 42 to be solved for 0kxL« Figure 17
shows a|<
a function of wavelength.
50
-------
7-r
400
500
EDO
1000
WAVELENGTH (nm)
Figure 16. Average strip chart deflection as a function of
wavelength for data used in calculating
-------
.016 T
.014
.012
.Ola-
's .008 +
.008 •
.004-
.002
400
600
700
800
900
\
1000
WAVELENGTH (nm)
Figure 17. Variance in illumination and spectrometer electronics
as a function of wavelength.
52
-------
The last variable required for calculation of ajL is pw, the volume
reflectance of the water. In the analysis work described in Section IX
unweighted second-order polynomials were fitted to the nonfilterable residue-
volume reflectance relationships at each wavelength for silt and fine sand
particles. These polynomials were used to calculate the typical volume
spectral reflectance curves for sediment concentrations of 25 and 250 mg/1
plotted in Figure 18.
All information is now at hand for using Equation 38 to calculate the
total instrumental uncertainties in volume reflectance. This calculation was
performed for 25 and 250 mg/1 cases and the results are shown in Fiyure 19.
At 250 mg/1 the spectrometer would have been on low gain, and at 25 mg/1 it
would have been on high gain; so these gain settings were used in the
calculation.
Figure 19 shows the normalized variance in water volume spectral
reflectance to be less than 0.05 over the entire spectral range of the
instrument for concentrations of 25 mg/1 and above.
Uncertainties in Units of Suspended Sediment
If volume reflectance was linearly related to suspended sediment
concentration and if zero sediment corresponded to zero reflectance, then the
normalized variance in terms of suspended sediment would be equivalent to the
normalized variance in reflectance measurements. However, neither of these
conditions holds true so additional information and calculation is required to
relate instrumental uncertainties in reflectance to uncertainties in units of
nonfilterable residue (105°C).
Let reflectance sensitivity, Apw, be defined as the change in
reflectance resulting from a 1 mg/1 change in sediment concentration. In
other words, sensitivity is the slope of the reflectance-nonfilteraable
residue curve. The instrumental uncertainties in units of reflectance can be
converted to milligrams per liter using &pw as follows:
(44)
residue = w pw
Figure 20 shows reflectance sensitivity as a function of wavelength for
typical 25 and 250 mg/1 cases for silt and fine sand particles. Sensitivities
were calculated from polynomial fits to the Lake Mead data reported in Section
IX.
53
-------
SILT
FINE SAND
u
<
u
g/l
.10.
400
1000
WAVELENGTH (nm)
Figure 18. Typical volume spectral reflectance curves for water
containing suspended sediment concentrations of 25 and 250 my/1.
Data from Figure 20 were used with Equation 44 to calculate the
instrumental uncertainties in units of mg/l of nonfilterable residue shown in
Figures 21 and 22. These figures show the instrumental errors to be smallest
at the near infrared (IR) wavelengths. It should be kept in mind that these
results are unique to the instrument used here, and that for another sensor
system the spectral distribution of instrumental uncertainties could be
entirely different.
Comparison of Figure 21 with Figure 19 leads to a significant conclusion.
Figure 19 shows that the spectrometer is capable of o2 = 0.05 accuracy in
measuring the volume reflectance of typical water containing 25 my/1 of
54
-------
06 T
04
3.
-->.
02
SILT
FINE SANO
O =.05
250 mg/l
400 500 600 700
900
1000
WAVELENGTH (nm)
Figure 19. Normalized variance in volume spectral reflectance
resulting from instrumental uncertainties.
suspended sediment. Yet when instrumental uncertainties are expressed in
terms of uncertainty in residue values, Figure 21 shows that the instrument is
not capable of the desired accuracy over most of the visible portion of the
spectrum. Accuracy in reflectance measurement and accuracy in sediment
measurement can be drastically different, thus a given accuracy in the
measurement of some turbidity-related parameter will require an instrument of
considerably better accuracy.
Uncertainties in Units of Nephelometric Turbidity
In the course of this study nephelometric turbidity emerged as an
important parameter. Since this parameter became heavily used in the data
55
-------
.0012,
SILT
FINE SAND
.0010
.0008
.0006.
M
IU
01
.0004
.0002
400
900
1000
WAVELENGTH (nm)
Figure 20. Sensitivity of reflectance to changes in sediment
concentration as a function of wavelength.
analysis, it was thought useful to transform instrumental uncertainties into
NTUs. The same procedure was used for this calculation as was used in con-
verting to units of nonfilterable residue - 105°C. Calculations were per-
formed for turbidities of 15 and 150 NTU with the results shown in Figure 23.
In terms of normalized variances the instrumental uncertainties in residue
measurements at 25 ing/1 are about the same as the uncertainties in turoiuity
measurement at 15 NTU. However, the 150 NTU curve shows somewnat larger
uncertainties in the red portion of the spectrum than did the 250 mg/1 residue
curve.
56
-------
=• 10
OE
UJ
U
s
ee
h-
S
3136
.2304
1600
• 1024
0578
0256
0064
u
z
K
400
500
600
700
800
900
1000
WAVELENGTH (nm)
Figure 21. Instrumental uncertainties expressed in units of sediment
concentration for 25 mg/1 water.
CONCEPTUAL UNCERTAINTIES
Attention is now directed at a different class of errors which result from
lack of precision in concepts as opposed to instrumental uncertainties which
result from lack of precision in measuring instruments. For example,
turbidity in a water body is generally expected to be a function of depth.
This function was not measured in the field. The procedure was to sample both
ends of the function (surface and Secchi depth) arid averaye these values to
give a single value. It is conceptually incorrect to represent an unknown
function by the mean value of its end points unless the function is linear.
57
-------
140
120
100-
« 80f
LU
u
2
60.
40
2D.
250 mg/l
SILT
FINE SAND
ALL LAKE MEAD DATA
.3138
• .2304
• 1600
•0064
400
SOO
600
700
800
900
1000
WAVELENGTH (urn)
Figure 22. Instrumental uncertainties expressed in units of sediment
concentration for 250 mg/l water.
Thus, the ground-truth values are subject to a certain amount of uncertainty
because of this conceptual imprecision.
Another possible source of conceptual uncertainty in the ground-truth data
results from the choice of a filter with a 0.00045-nm pore size for separating
filterable from nonfilterable residues. This selection carries with it the
tacit assumption that all sediment particles in the water sample are larger
58
-------
10 <
5
i
s
60
40 >
IS NTU
ISO NTU
400 500 600 700
800
WAVELENGTH (nm)
T 1.000
.. 444
• m
400 SOD BOO 700 BOO 900 tOOO
WAVELENGTH (nm|
u
z
1600
. 0711
• 0178
900 1000
Figure 23. Instrumental uncertainties expressed in units of
nephelometric turbidity for 15 and 150 NTU water.
59
-------
than 0.00045 nm in diameter. Table 3 lists the diameters and settling times
of various classes of participates.
Part of the clay particle size range is smaller than the pore size of the
filter used in the laboratory analysis of water samples. Thus, if two samples
have the same amount of sediment but a different distribution of particle
sizes, the laboratory analysis could detect a different percentage of the
particles in each sample. The result would be a different nonfilterable
residue value for each when, in fact, the sediment concentrations were
identical.
TABLE 3. SIZE RANliES UF VARIUUS PARTICIPATES
Diameter (mm)
Order of Size
Time to Settle 1 Ft.
10 - 0.15
0.15 - 0.015
0.015 - 0.0015
0.001
0.002 - 0.0001
0.00001
Gravel
Course sand
Fine sand
Silt
Bacteria
Clay particles
Colloidal particles
0.3 sec.
0.3 - 38 sec.
38 sec. - 33 min.
33 min. - 55 hrs.
55 hrs.
230 days
63 years
Additional uncertainty results from procedures used for removal of
peripheral effects. Certain assumptions and approximations are made in
developing a method for removal of these effects (Section IV). These
approximations are probably valid on the average, but for any given sample
they may not be absolutely true.
The possible sources of conceptual uncertainty are numerous, but these
three examples, plus one other, are probably the most significant. Estimates
are given below for the typical magnitudes of these four sources of
uncertainty in the Lake Mead data.
Depth Distribution of Turbidity
This error source actually involves more than just the assumption that
turbidity, which is a function of depth, can be represented by the mean value
of samples taken at the surface and at the Secchi depth. Because water
attenuation is a function of wavelength, each wavelength of incident light can
penetrate to a different depth. The Secchi depth is representative of maximum
penetration for the visible wavelengths. However, penetration for the near-IR
wavelengths may be only a few centimeters. This means that unless the turoid-
ity is uniform with depth, each wavelength will be reflected from a volume
60
-------
with a different effective sediment concentration. Figure 24 shows the
estimated penetration depth as a function of wavelength assuming a typical
particulate reflectance and a 2 percent return to the surface. Errors are,
therefore, being introduced not only by representing functions with single
values, but also by ignoring the fact that the best value for representing the
function will change with wavelength.
To estimate the magnitude of this type of error, 70 surface-depth sample
pairs were examined and nonfilterable residue values at 105°C ranged from
10 to 64 mg/1. The mean value for each pair was calculated and the standard
deviation of the individual measurements about the means was found to be ±7.38
mg/1. A portion of this variability is due to instrumental uncertainty in the
laboratory measurement of nonfilterable residues. To determine the
contributions from laboratory instrumental uncertainties, 12 water samples
with residues in the same 10 to 64 mg/1 range were subjected to replicate
sample analysis. Samples were divided and each half treated as a separate
sample. The standard deviation between the values for each half and the mean
values for both halves was found to be ±3.39 mg/1, which is attributable to
only instrumental errors. Removing instrumental errors leaves a standard
deviation of ±6.5 mg/1, which must be attributed to the variability of residue
concentration with depth.
The mean residue value for the 70 surface-depth sample pairs was 25.3
mg/1. Thus, the conceptual uncertainty resulting from the depth variability
of turbidity expressed as a normalized variance is 0.067. This is larger than
the 0.05 variance requirement established by EPA.
It should be noted that the same problem arises with in situ instrumen-
tation. If sediment concentration varies with depth, measurements taken with
a sampling depth with the in situ sensor may not represent the sediment
concentration in that water body. Since this type of error is characteristic
of the turbidity measurement problem in general and not unique to the airborne
multispectral method, it probably should not be included in the estimates of
accuracy of the remote measurements. However, it must not be forgotten that
this estimated variability of ±6.5 mg/1 did exist within the upper 2 meters of
the Lake Mead test sites, and anytime ground truth is used to verify a remote
result this factor will enter in.
The same procedure was used to estimate the depth variability of
nephelometric turbidity. The result in this case was ±2.8 NTJ about a mean of
13.8 NTU for normalized variance of 0.041.
Pore Size of Filters for Extracting Nonfilterable Residues
In the laboratory analysis of water samples, a filtration process was used
to extract nonfilterable residue which presumably is the sediment in the
sample. The nonfilterable residue value will be an accurate measure of
sediment concentration only if the filter catches nearly all of the sediment
present. As previously mentioned, clay particles can be smaller than the
0.00045-mm pore size of the filters so that part of the sediment in the clay
particle-size range would not be detected by the sample analysis.
61
-------
ST
3--
o
?
•
t=
400
500
BOO
700
800
900
1000
WAVELENGTH (nm|
Figure 24. Maximum depth of water penetration by sunlight assuming
reflectance from a panel with a typical sediment spectral
reflectance and a two percent return to the surface.
Two reasons can be given in support of the fact that there was no
significant amount of small clay particles in the Lake Mead samples. The
first argument is based on the settling time given for clay particles in Table
3. It was observed in the field that stations which had sediment concentra-
tions of several hundred milligrams/liter and Secchi depths of only a few
centimeters on one day would be sediment free with Secchi depths of several
meters the next day. If clay particles take 230 days to settle 1 foot, the
sediment load on the first day could not have included significant amounts of
clay particles or the water would not have cleared within 24 hours.
The second argument against the presence of significant amounts of clay
particles comes from a statistical analysis of the laboratory data. If a
portion of the suspended sediment in the samples is clay particles, it would
62
-------
be expected that samples with higher sediment content would result in hiyher
filterable residue values as a result of the small sediment particles passed
by the filter. One would expect in this case to see statistical correlation
between filterable and nonfilterable residues.
Before analyzing residue data for this type of correlation it must be
noted that other factors could also cause correlation to exist. For example,
if sediment-bearing water from a river is emptying into a lake and the river
is of higher salinity than the lake, then dilution processes would cause both
the sediment concentration and the salinity (filterable residue) to decrease
with distance from the mouth of the river. One would then observe correlation
between filterable and nonfilterable residues but this would result from
dilution rather than filters passing a portion of the sediment. For this
reason data from the Colorado River and Las Vegas Wash test sites must be
excluded from the analysis since these sites contained inflows of water of
lower and higher salinity content respectively. Figure 25 shows a least-
squares linear fit to the filterable-nonfilterable residue relationships for
the Colorado River and Las Vegas Wash data. The large and opposite slopes of
these lines results from dilution of high and low salinity inflows with the
Lake Mead water.
Dilution was not thought to be a factor at the other three test sites.
The filterable-nonfilterable residue relationships in these cases should
indicate the amount of sediment passed through the filter. Forty-four samples
with nonfilterable residue values in the range 10 to 100 mg/1 were available
for analysis from the Muddy River, Virgin River, and Government Wash test
sites. A least-square fit to these data is shown by the middle line in Fiyure
25. This shows a slight decrease in filterable residues with increasing
nonfilterable residues. The negative slope to the line is not statistically
significant. If the number of samples used and the scatter in the data are
considered, the slope would have to exceed the dotted lines in Figure 25 to be
statistically significant at the 90 percent confidence level. Thus, it can be
concluded that within the accuracy limits of the Lake Mead data, there is no
correlation between filterable and nonfilterable residues. This in turn leads
to the conclusion that there was not a significant amount of clay particles
being passed through the filters.
For the Lake Mead data there is apparently no conceptual uncertainty
introduced by the choice of filter pore size. However, for other water bodies
this may not be the case and it should be kept in mind in future studies that
this type of uncertainty could be significant.
Removal of Peripheral Effects
A good test of the accuracy in removal of peripheral effects would be to
look at water of known constant volume reflectance under varying sular,
atmospheric, and surface conditions. Unfortunately, this is not easily done
in the field since the time required for a change in weather conditions is
usually sufficient to allow a possible change in water turbidity. In fact,
the suspended sediment at many sampling stations resulted from resuspension of
bottom deposits by wind and wave action. This observed correlation between
63
-------
1800T
o
in
1600-
1400-
1200-
1000"
600"
400
90% CONFIDENCE
INTERVAL
ano--
20 40 60 80 100
NONFILTERABLE RESIDUE - 105° (mg/l)
Figure 25. Least-squares linear fits to filterable and nonfilterable residue
values from the analysis of the Lake Mead water samples.
64
-------
weather and sediment concentration would preclude the general assumption that
water volume spectral reflectance remains constant under changing weather
conditions.
The assumption of uniform water would tend to be more valid in the open-
water areas of the lake. One open-water station, MV1 (see Figure 31), was
sampled under both clear and overcast sky conditions. Unfortunately, a few
days prior to the collection of the overcast sky data on November 14, 1975,
the lake apparently underwent an inversion. This changed the water color from
its blue-green summertime appearance, which it had when the clear sky data
were recorded on August 8, 1975, to a yellow-yreen color. The assumption of
uniform volume reflectance is, therefore, questionable even for this open-
water case. This is, however, the best test case we have, and although a
shift of the reflectance peak from blue-green to yellow-green is expected, the
magnitude of the reflectance might be expected to be about the same in both
cases. Table 4 gives a comparison of sky and water conditions on these two
days.
TABLE 4. SKY AND WATER CONDITION AT STATION MV1 ON 8/8/75 AND 11/14/75
Parameter 8/8/75 11/14/75
Cloud cover
Percent illumination®
652 nm
Clear
6%
Overcast
35%
resulting from skylight
Sun elevation
Wind velocity
Sea State
Secchi depth
Nonfilterable residue (
Turbidity
105°C)
70 deg.
1.0 m/sec.
2 cm
5 in
<5 mg/1
1.0 NTU
24 deg.
Calm
2 m
<5 mg/1
3.3 NTU
Data acquisition at station MV1 on November 14, 1975, was done under the
heaviest cloud cover encountered during the entire project. These two
examples probably represent the largest possible contrast in peripheral
effects within the Lake Mead data.
Figure 26 shows a different albedo for the overcast and clear sky cases
which were assumed to be of approximately equal water volume reflectance. The
albedo can be divided into a volume reflectance component and a peripheral
effects component according to the model developed in Section IV. Figure 26
shows the two components for each case. The peripheral effects component is
much larger on the overcast day, and the volume reflectances are about equal.
Both results are as expected, indicating that the procedure for removing
peripheral effects was fairly accurate in this case if the "assumption of equal
reflectance was valid.
65
-------
u
i
en
05 T
04- OVERCAST
03-
.02
.01-
ALBEDO
400
SOD
600
WAVELENGTH (nm)
700
02 T
LU
u
u 01 f
400
.03 T
02
01-
EFFECTS
PERIPHERAL
500 600
WAVELENGTH (nm)
700
400 500 600
WAVELENGTH (nm)
700
Figure 26. Albedos, peripheral effects, and volume reflectances of
a clear and an overcast day at station MV1.
-------
There is no sufficient data to assign a numerical value to the uncertainty
in removing peripheral effects, nor can it be claimed on the basis of one
sample that the uncertainty will always be relatively small. A quantitative
analysis of the errors associated with the removal of peripheral effects is a
subject which needs to be included in the next phase of the turbidity study.
Coincidence of Reflectance Data and Mater Samples
The water viewed by the spectrometer is not the same water that is put
into the sample bottle. Normally the water is homogeneous enouyh that this
fact is of no consequence. However, in some cases where the water is non-
uniform and moving, this problem can be significant.
Sampling stations L06 and C06 through Cll normally hau currents with
velocities up to 1.5 m/sec. Since the spectrometer required 30 seconds to
sample its entire spectral ranye, the data were from a 45 m stretch of river
rather than from a single point. Swirls and eddies associated with the water
movement made the sediment concentration quite variable. Thus, each
wavelength was in effect seeing a different sediment concentration and what
went into the sample bottle was different yet.
Wherever this moving water was a problem, sediment concentrations were
high and Secchi depths very small and both water samples were really surface
samples. An examination of the variability in these replicate surface samples
can give an estimate of the magnitude of the uncertainty associated with the
lack of coincidence of reflectance and ground truth data. Thirty-one sample
pairs from stations with currents were analyzed and found to have a standard
deviation of ±33.8 mg/1 about a mean value of 230 my/1. Expressed as a
normalized variance this uncertainty is 0.022.
The data coincidence uncertainty was also evaluated in units of
nephelometric turbidity. The same 31 samples had a mean value of 129 NTJ, a
standard deviation of ±14.8 NTU, and a normalized variance of 0.013.
LABORATORY ACCURACY
The laboratory analysis of water samples collected coincident with
spectral reflectance data provided the ground truth for derivation and
evaluation of multispectral turbidity algorithms. The laboratory procedures
for measuring the turbidity-related water parameters described in Section III
are subject to a certain amount of error which contributes to the overall
uncertainty in the statistical results obtained from the Lake Mead data.
Laboratory accuracies for the seven measurements were determined by
replicate sample analysis of 21 selected samples. These samples were divided
in half and each half treated as a separate sample. The difference between
results for the halves of the same sample is an indication of the accuracy of
the laboratory procedures. Color and turbidity measurements were not included
87
-------
in the replicate sample analysis. Accuracies for these parameters are taken
from method description (American Public Health Association, 1971). Table 5
gives the accuracies of the nine measured water parameters.
TABLE 5. UNCERTAINTIES IN LABORATORY ANALYSIS RESULTS
Parameter
Filterable Residue
(105°C)
Filterable Residue
(180°C)
Nonfilterable Residue
(105°C)
Nonfilterable Residue
(180°C)
Nonfilterable Residue
(550°C)
Nonfilterable, Volatile
Residue
Total Residue
(105°C)
Color
Turbidity
Mean
781 mg/1
747 mg/1
27.1 mg/1
24.4 mg/1
20.4 mg/1
4.4 mg/1
808 mg/1
20
5 NTU
25 NTU
70 NTU
250 NTU
Standard
Deviation
±9.3 mg/1
±13.3 mg/1
±4.3 mg/1
±5.7 mg/1
±8.2 mg/1
±1U.O mg/1
±10.3 mg/1
±5
±0.05 NTU
±0.5 NTU
±2.5 NTU
±5.0 NTU
Normalized
Variance
0.0001
0.0003
0.0252
0.0546
0.1616
5.1o53
0.0002
0.0625
0.0001
0.0004
0.0013
0.0001
Note the large variances associated with the nonfilterable residues
compared with the small variances associated with turbidity. This seems to
indicate the superiority of optical techniques over gravimetric techniques for
measuring the low sediment concentrations typical of natural water bodies.
Since the remote method is optical, it is possible that the accuracy of remote
techniques may exceed the accuracy of laboratory measurements made
gravimetrically.
58
-------
ERROR SUMMARY
Table 6 contains a summary of the error sources discussed in this section.
Since instrumental errors are a function of wavelength, total uncertainty will
vary slightly with wavelength. Table 6 contains data for the 652 nm (red) and
782 nm (near-IR) wavelengths only.
TABLE 6. SUMMARY OF UNCERTAINTIES IN THE LAKE MEAD DATA IN UNITS
OF SUSPENDED SEDIMENT
Type
Source
25 mg/1 Water 250 mg/1 Water
652 nrn 782 nm 652 nm 782 nm
Instrumental
Conceptual
Total
Spectrometer
Laboratory
Depth Distribution
Peripheral Effects
Filter Pore Size
Sample Coincidence
4.8
3.4
6.5
0.0
8.8
mg/1
2.1
3.4
6.5
0.0
7.6 -
mg/1
57.0
12.5
0.0
36.7
68.9
ing/1
28.0
12.5
....
0.0
36.7
47.8
mg/1
Table 7 is the error summary given in units of nephelometric turbidity.
TABLE 7. SUMMARY OF UNCERTAINTIES IN THE LAKE MEAD DATA IN UNITS
OF NEPHELOMETRIC TURBIDITY
Type
Source
15 NTd Water 150 NTU Water
652 nm 782 nm 652 nm 782 nm
Instrumental
Conceptual
Total
Spectrometer
Laboratory
Depth Distribution
Peripheral Effects
Filter Pore Size
Sample Coincidence
3.1
0.3
3.0
0.0
____
4.3 NTU
1.3
0.3
3.0
____
0.0
....
3.3 NTU
43
3.6
._._
0.0
17.2
46.6 NTU
16.5
3.6
-___
____
0.0
17.2
24.1 NTU
69
-------
If it is assumed that errors for sediment concentrations or turbidities
other than those specifically evaluated are represented by a linear inter-
polation between the evaluated points, then expected accuracies as a function
of ground truth value would be as shown in Fiyure 27. This figure would tend
to lead to the following conclusions.
Algorithms based on IR wavelengths will be more accurate than
those operating at visible wavelengths. This is a result of
the spectral response of the spectrometer used here and is not
an inherent property of water volume reflectance.
In the visible wavelength there is not a significant difference
in accuracy between measurements of nonfilterable residues and
nephelometric turbidities. However, in the near-IK wavelengths
nephelometric turbidity can be measured more accurately.
Visible algorithms are not expected to meet EPA's desired accu-
racy of a2 = 0.05. IR algorithms should achieve this accuracy
for high sediment concentrations. Nephelometric turbidity
measurements at IR wavelengths may be capable of 0.05 variances
down to the desired 25 mg/1 (=s 15 NTJ) threshold.
Although the desired accuracy cannot be met in every case, we
should not miss it by far. If the error analysis results are
verified by the performance of actual algorithms, accuracy
should be close enough to what was desired that remote
multispectral techniques will prove to be feasible for EPA
monitoring purposes.
70
-------
Ul
ec
1
LU
oe
NONFILTERABLE RESIDUE -105°C
NEPHELOMETRIC TURBIDITY
20<
10-
GROUND - TRUTH VALUE
Figure 27. Uncertainties in the Lake Mead data as a
function of residue and turbidity values.
300
71
-------
SECTION VII
DATA ACQUISITION
LAKE MEAD TEST SITES
The data base for the analysis work undertaken to determine feasibility of
remote techniques for monitoriny suspended sediment was acquired through field
operations as Lake Mead, Nevada-Arizona, from June 20, 1975, to January 8,
1976. Lake Mead is not a turbid water body and is, therefore, not an ideal
test site for water turbidity studies. It was selected because of its
proximity to the Las Vegas, Nevada, offices of project personnel. Although
the lake was not ideal, it proved to be an adequate test site.
Since an investigation of the transferability of signatures is a prime
objective of this study, five test sites within the lake were selected which
we hoped would have different sediment types. These sites are shown in Figure
28. The physical characteristics of each site are described below.
Colorado River Inflow
The Colorado River, spanned by Hoover Dam to form Lake Mead, carries a
considerable sediment load into the lake. The Glen Canyon Dam 483 kilometers
(300 miles) upstream from Lake Mead forms Lake Powell which collects all
sediment from the upper basin of the Colorado River watershed. Thus, the
sediment entering Lake Mead originates from bed and beach degradation in the
canyon areas below Glen Canyon Dam. The Grand Canyon gauging station 322
kilometers (200 miles) above Lake Mead measured an annual sediment load of
13.1 million metric tons in 1969, the last year for which data are available
(Laursen and Silverston 1976).
Sampling extended up to Columbine Falls in an area known as the Lower
Granite Gorge. At this point the river current was observed to be quite
variable ranging up to 1.5 m/sec. At times of high current, suspended
sediment concentration was greatly increased, probably because of resuspension
of particles which had settled during times of slack current. Sampling at
this site was conducted during the month of September and at this time the
river water was 18°C compared to reported lake water temperatures of 27°C.
Government Hash
There is no natural inflow at this test site except from very infrequent
flash-floods. Bottom sediments here were thought to consist of particles
72
-------
--4
OJ
SITE
MUDDY AND VIRGIN RIVERS
SITE 3
LAS VEGAS AND GOVERNMENT WASHES
Figure 28. Lake Mead test sites.
-------
resulting from bank erosion in the wash duriny flash-flood periods. Turbidity
at this site was the result of resuspension of bottom sediments. During the
summer months man-made agitation (swimming, water skiing, boatiny, etc.)
provided the resuspension mechanism. During the winter months wind and wave
action would occasionally generate considerable resuspension but generally the
water was very clear. We were forced to resort to using the prop wash of the
boat over shallow areas to artificially resuspend sediments in order to obtain
high turbidity data in the wintertime.
Las Vegas Wash
This wash receives a continual flow of wastewater from the Clark County
sewage treatment facilities. The inflow here is extremely turbid, presumably
as the result of bank erosion in the sand bed of the wash. The sediment was
observed to settle almost immediately upon entering the slack water of the
lake.
Because of its origin this inflow was thought to be rich in dissolved
matter, some of which would contribute to accelerated growth of algae and
phytoplankton. This site was sampled for this reason, in hope that the
question of chlorophyll interference could be investigated from data collected
here.
Muddy River
The Muddy River is a constant running stream originating from warm springs
about 40 kilometers (25 miles) above Lake Mead. Except in times of heavy
rains and flash-flooding, it probably carries little sediment. Extensive
agricultural activities are conducted over the entire length of this river
valley, and sediment and wastes resulting from agriculture undoubtedly enter
the river at times.
The mouth of the river was not accessible from the lake in a boat of the
size being used and so no current-suspended sediment was observed here.
Turbidity was quite variable from day to day, but no correlation was observed
between turbidity and any specific factor such as river inflow or wind
velocity.
Virgin River
Water flow in this river is seasonal. Snowmelt runoff from southwestern
Utah results in large flow-rates and substantial sediment loads in the
springtime. The July through November sampling period at this site
corresponded to periods of no significant inflow.
Although river flow did not bring suspended sediment to this site, wave
action over submerged mud flats near the mouth of the river did generate good
sediment concentrations when the conditions were right.
74
-------
The Virgin River, like the Muddy River, supports agriculture along its
banks for many miles above Lake Mead. Pollutants associated with agricultural
activities undoubtedly enter the lake from this river, but since flow had
ceased during our data acquisition, this is not thought to be a factor in this
study.
SAMPLING STATIONS
Specific sampling stations were selected at each site. These locations
are shown in Figures 29 through 31. No attempt was made to obtain equal
numbers of samples from each station. Stations with higher turbidity were
generally sampled more frequently than others. Forty samples were acquired
from each of the five sites for a total of 200 samples.
FIELD PROCEDURES
Each station sampling consisted of the recording of spectrometer data, the
collection of water samples, and atmospheric or sun conditions. Widely
varying conditions were encountered which required occasional adjustments in
field procedures. However, for the majority of samples the field procedures
were as described below.
Spectrometer Data
Once the boat was positioned and anchored with the spectrometer side
toward the sun, the acquisition of spectrometer data proceeded as follows,
The holder for the calibration panels was lowered into the hor-
izontal position and the gray panel was put in place. With the
spectrometer on the low gain setting, the sunlit gray panel was
used to adjust the strip chart gain so that maximum chart
deflection would be about 80 percent of full scale. The chart
recorder gain was not changed again at this station.
Two complete spectral scans of gray panel data were recorded:
one at the spectrometer high gain position and one at the low
gain position.
The gray calibration panel was replaced with the white one.
With the spectrometer on low gain and a shadow cast on the
white panel, one spectral scan is recorded. The shadow was
created by a hand-held device as shown in Figure 32.
After covering the aperture of the spectrometer to block all
light from entering, one scan was recorded at both the hiyh
gain and low gain position.
Calibration panels were removed and panel holder raised to
permit viewing of the water. Either the high or low
75
-------
Figure 29. Sampling stations at the Colorado River site.
76
-------
Figure 30. Sampling stations at the Las Vegas Wash and
Government Wash sites.
77
-------
V "° ° '''/ fa* not, AI
s-"\>v^ / c ^/"
-------
Figure 32. Casting a shadow on the calibration panel.
-------
spectrometer gain position was selected depending on water
turbidity. Five complete scans of data were recorded at verti-
cal viewing, 15° fore and aft, and 30° fore and aft.
Mater Samples
While the five spectral scans of the water were being recorded two water
samples were collected. One sample was from the surface and was collected by
dipping into the lake with a bucket. The second sample was taken at the
Secchi extinction depth using a Van Dorn sampler. The water samples were
stored on ice in 3.8-liter (1-gallon) containers until delivered to the EPA
Laboratory in Las Vegas.
Related Field Parameters
For each sample, the top half of the form shown in Figure 33 was completed
as a record of conditions at the time. Some of these parameters were
specifically needed to accomplish peripheral effects removal while others were
of general interest because of their possible effects on the data. Color
photographs of sky and water conditions were taken at most sampling stations.
DATA REDUCTION
Spectrometer data were recorded in the field on a strip chart recorder.
Manual reading of signal levels from the strip chart and keypunching of these
values was required to reduce the data to a computer compatible form.
Figure 34 shows the video channel signals for a typical data set. The
signal for the covered aperture case is not shown since it was perfectly flat
at 2.0 cm. These data were recorded at Las Vegas Wash, Station L06, on
December 17, 1975. The water samples collected here contained 212.5 mg/1 of
nonfilterable residue which gave a high return from the water. In this case
all data were recorded at the low gain setting. Deflection values in
centimeters were keypunched along with water sample analysis results and field
observations for input into the computer program VOLKEF, which calculates
volume spectral reflectance according to the method described in Section IV.
The computer output for the Figure 34 sample case is shown in Figure 35.
This report contains only this one computer-generated data tabulation as
an example. Tabulations of raw data for all 200 samples collected at Lake
Mead are too voluminous to include here. Computer printouts like that shown
in Figure 35 for all of the Lake Mead data have been delivered to the EPA
Technical Monitor as a separate volume.
The data reduction program, VOLREF, was written as part of this project
and was run on a CDC 6400 at the Department of Energy (DOE) computer facility.
This program has not been formally documented but the comment statements
contained within the program listing should provide adequate documentation for
purposes of this project. Appendix B is a listing of this program.
80
-------
MULTISPECTRAL TURBIDITY TECHNIQUES PROJECT
J. 0. 71.03 (ROAP 22AEB - task 7)
Field Data Sheet
FIELD OBSERVATIONS
Identification sample no. 351*7,5-
IS
time IQlG" PDT
Location general discription [.
grid coordinates
Conditions sun elevation ""X'l.'Z.
sun azimuth 1 IP 0
wind direction _^1'\<5
wind velocity -3, 0
water depth 0.V?
Photography sky photo no. —
oblique water photo no.
SI
SCS Standards sun /3
LABORATORY ANALYSIS REPORT
nonfilt residue (105) 2«J$
settleable residue
nonsettleable residue
nonfilt residue (180) aU5"
filt residue (180) ^ iflT
turbidity "7O
OA. '
N
W
deg
deg
.deg
m/s
m
mg/1
ml/1
mg/1
mg/1
mg/1
NTU
date /3l/ IT/ 7£~
observer (/,*( §
J^^s-t^ U) AAJL
station no. L0(y
depth St^iA^txgi. m
secchi depth d, It- m
sky conditions C^LLA>f
boat heading ^10 deg
sea state , fl / m
vert water photo no. '
shadow / 1/
total residue (105) "3N7 mg/1
filt residue (105) Sg^ mg/1
nonfilt, fixed residue 2."33 mg/1
color — Pt-Co units
nonfilt, vol residue 17, mg/1
REMARKS
Figure 33. Field observations form filled out at each sampling station.
81
-------
w-
-- _;_-
GRAY PANEL
-t_ri~"?hlr
•
SHADED WHITE PANEL
WATER
Figure 34. Spectrometer video outputs as recorded on strip
chart for sample 35175-1.
32
-------
ENVIRONMENTAL PROTECTION AGENCY - EMSL/LV
MULT I SPECTRAL TURBIDITY TECHNIQUES STUDY
SAMPLE NUMBER
DATE
T1MF (PDTI
SKY PHOTO NO.
VFPT. PHOTO NO.
OPL. PHOTO NO.
SfCCHl DEPTH
SFA STATE
LOOK AMGLF
81* T HEADING
?UN ELEVATION
SUN AZIMUTH
WIND DIRECTION
WIND VELOCITY
35175-1
IP/17/75
1015
1
2
.1 M
1.0 CM
0.0 DEG
210.0 DEG
27.2 DEG
lf.0.0 DEG
.n DEG
SITE
STATION
KEMARKS-
LAS VEGAS WASH
L06
2.15.
3.0 M/5
LABORATORY ANALYSIS REPORT
NONFILT RESIDUE (105)
FILT RESIDUF (105»
MONF1LT RESIDUE (1801
FILT RESIDUF. (180)
TURBIDITY
212.5 MG/L
28B9.0 MG/L
210.0 MG/L
2815.0 MG/L
60.0 NTU
TOTAL RESIDUE (105)
NONFILT, FIXED RESIDUE
COLOR (PT-CO TESTI
NONFILT. VOL RESIDUE
3102.0 MG/L
198.5 MG/L
1 1.5 MG/L
00
co
V
0
L
P
F
F
L
F
r
T
A
c
E
.20
.15
10
.05
..., , , , j , ,.
400 500 600 700
.-I 1.
800
--I--
900
— I
lono
(continued)
WAVELENGTH (Nil
Figure 35. Computer printout for the data shown in Figure 34.
-------
SAMP)
3517=5-1 CONTINUFU
FNGTH
VZ
VG
VW
ALFA
ALFAP
RV
CXI
-p.
1
?
4
«;
f,
7
ft
q
10
11
1?
n
14
m
i*
17
i °
10
20
343
377
415
436
4PO
517
550
5R3
620
652
690
703
742
7B2
H29
R62
90S
942
9R4
0.00
o.no
o.oo
.09
.98
.98
.98
.9fi
.98
.98
.3
3.39
3.59
3.60
3.45
6.16
<3.«.0
7.33
5.30
5.60
-0.00
-0.00
-0.00
?.56
3.06
3.?5
3.01
2.93
2.96
3.06
3.00
2.8<<
4.41
6.09
4.95
3.66
3.40
3.34
3.60
3.00
-0.00
-o.no
-0.00
2.15
3.01
3.17
3. 15
4.?5
4.13
4.?0
7. SB
6.*9
5.1 1
3.«2
3. no
2. A3
2.62
2.16
0.00
0.00
0.00
S.62
11.87
16.98
17.14
1A. 46
22.82
27.56
28.15
26.32
80.93
98.80
64.33
57.67
63.96
82.11
55.13
0.00
0.00
0.00
.07
.98
.24
.80
.69
.79
.99
.91
.62
4.56
7.71
5.57
3.15
2.77
2.76
3.37
2.12
0.00
0.00
0.00
2.64
3.12
4.62
5.80
7.35
8.04
8.09
8.21
8. 31
6.81
2.91
3.06
2.76
1.67
.93
.70
.25
Figure 35. (Continued)
-------
SECTION VIII
DATA DESCRIPTION
SUSPENDED SEDIMENT CONCENTRATIONS
Water with high concentrations of suspended sediment was not easily found
in Lake Mead. Figure 36 is a histogram of nonfilterable residue (105°C)
values in the 200 samples collected from the lake. The sediment loaas ranged
from 0.0 to 1137.0 mg/1 but the distribution is heavily weighted toward the
low concentration end. It would have been better to have a more uniform
distribution of samples over the entire range, but the data collected should
be adequate for the intended statistical analysis.
VARIABILITY OF SEDIMENT TYPES
Since an investigation of the transferability of algorithms between
sediment types is a major objective of this study, it is necessary to
determine if the data set does indeed contain different sediment types. Three
different comparisons have been made between data from the five sites. In all
comparisons the conclusion reached is that the Lake Mead data is representa-
tive of a large variety of sediment types and should, therefore, be well
suited for signature transferability study. The specific comparisons are
summarized below.
Visual Appearance
Sediment samples were dredged from the lake bottom with the buat anchor at
each of the five sites. Visually these samples all appear different. Color
tones range from gray for Las Vegas Wash, to yellow-brown for the Muddy River,
to dark brown for the Colorado River.
Spectral Reflectance
The silt samples all had higher reflectance when dry than when wet. The
samples were moistened to be more representative of what the sediment would
look like suspended in water, and the spectral reflectance of the moistened
samples was measured. Measurements were made in the laboratory usiny the
field spectrometer to give relative values with respect to Kodak gray cards
whose spectral reflectance was known.
35
-------
60r
50--I
40-
Ob
5
<
W)
30"
20-
10-
1000
1200
NONFILTERABLE RESIDUE (mg/l)
Figure 36. Histogram of nonfilterable residue (105°C)
values in the 200 Lake Mead samples.
Figure 37 shows the reflectance curves for the five moistened sediment
samples. These curves generally agree with the visual observations, i.e., the
gray Las Vegas Wash sample reflectance is flat in the visible range, the
darkest colored sample from the Colorado River shows the lowest spectral
reflectance, etc. Spectral reflectance curves indicate a diversity of
sediment types.
86
-------
.30 ••
.20 +
.10--
COLORADO RIVER
GOVERNMENT WASH
LAS VEGAS WASH
MUDDY RIVER
VIRGIN RIVER
400
500
600
700
800
900
1000
WAVELENGTH (nm)
Figure 37. Spectral reflectance curves for the moistened sediment samples.
37
-------
Scattering Properties
The optical properties of sediment in suspension were compared by relating
the laboratory measurements of nonfilterable residue (105°C) to nephelometric
turbidity which is a light-scattering measurement. These two parameters are
plotted in Figure 38 for all samples in the 50 to 500 mg/1 range. No well-
defined relationship is apparent in this figure. The uncertainty in
laboratory measurements is given by the bars in the center of the graph to
show that the scatter in data points cannot be accounted for by instrumental
uncertainties. The only conclusion which can be drawn from this graph is that
the sediments in the samples are widely varying in scattering properties.
Figure 38 also shows two turbidity vs. residue curves given by previous
investigators. Both curves are linear but drastically different in slope.
Rosgen (1975) states that the sediment in his study originated from stream
bank erosion and consisted of fine sand particles. Scherz and Van Domelen
(1975) identify the sediment for their curve as taconite rock flour which
consists of extremely fine particles, presumably in the clay particle range.
If the difference between the slopes of these lines is primarily the result of
particle size, they would seem to represent the extreme cases in the
nephelometric turbidity-nonfilterable residue (105°C) relationship. Une
probably will not find particles smaller than those encountered by Scherz and
Van Doinelen, and particles larger than those encountered by Rosgen would be
too large to remain in suspension. Since the Lake Mead data set contains
points in line with each of these curves and others covering the entire area
between the lines, it is concluded that, in terms of scattering properties,
the data contain sediment variability spanning the entire expected range.
However, the number of samples at the clay end of the range is very small
which is consistent with the earlier conclusion (page 64) that there was not a
significant amount of clay particles in the Lake Mead water samples.
COLOR INTERFERENCES
Water color can be the result of phenomena other than scattering by
sediment particles. Color effects from other sources will interfere with
estimates of suspended sediment concentration based on water color. The two
most common color interferences are thought to result from the presence of
tannic acid and small living organism in the water. The choice of sampling
sites at Lake Mead was made in the hope that these interfering effects would
be present in part of the data so that their significance could be evaluated.
The following paragraphs discuss the existence of these two effects in the
Lake Mead data.
Tannic Acid
The presence of tannic acid in natural water bodies is the result of the
decay of humic material. This compound absorbs blue light resulting in a
water color ranging from yellow to reddish-brown depending on the acia
concentration.
88
-------
SOOT
a
55
(SCHERZ AND VAN DOMELEN. 1975)
X
200-
100-
400
500
NONFILTERABLE RESIDUE-105'C
-------
The platinum-cobalt color test was included in the laboratory analysis of
water samples to detect the presence of tannic acid. However, stanuard
methods for this test require a maximum sample hold time of 24 hours, and
frequently the color test could not be made within this time. The color test
was performed on 70 of the 200 samples collected. Table 8 lists the number of
samples tested and the mean color values by site.
TABLE 8. PLATINUM-CUBALT CULUR AVERAGES BY SITE
Site
Colorado River
Government Mash
Las Vegas Wash
Muddy River
Virgin River
Number Tested
0
17
15
12
26
Average
Pt-Co Color
..
10
21
14
12
A value of 10 Pt-Co units is the detection threshold for this test. There
was, therefore, virtually no tannic acid color at four of the five sites. The
Las Vegas Wash site had some color but a value of 21 is not thought to be high
enough for tannic acid to be considered a significant source of color inter-
ference. Tannic acid color interference cannot, therefore, be investigated in
the present study.
Living Organisms
Living organisms in the near surface water result in light absorption by
chlorophyll, carotenoids, xanthophyll, and various photosynthetic pigments.
Figure 39 shows the absorption curve of a natural phytoplankton population.
This curve showing strong absorption in the blue and a weaker absorption in
the red is typical of chlorophyll-bearing marine organisms.
The water at the Las Vegas Wash and Government Wash sites was visually
observed to have a greener appearance than the water at the other three sites.
The greener water color is believed to result from a higher concentration of
chlorophyll-bearing organisms at these sites. This is to be expected since
this part of the lake undoubtedly receives nutrient enrichment from the Las
Vegas Wash inflow. Figure 40 shows statistical estimates of the volume
spectral reflectance for 0 NTU turbidity water from the Government Wash and
Las Vegas Wash sites compared to the same turbidity water at the other three
sites. Notice that the Las Vegas and Government Wash curve is more sharply
peaked in the green. Presumably this is the result of chlorophyll absorption
90
-------
v»
<
u
400
500
700
WAVELENGTH (nm)
Figure 39. Spectral absorption curve of a natural
phytoplankton population.
91
-------
20 NTU
u
z
U
kbi
«J
u»
LU
oe
CHLOROPHYLL
INTERFERENCE
FINE SAND
SILT
.02
400
500
600
700
800
900
1000
WAVELENGTH (nm)
Figure 40. Statistical estimates of volume spectral reflectance
for 0 and 20 NTU turbidity levels. Fine sand data are
predominantly from Government and Las Vegas Washes;
silt data are from the other three sites.
92
-------
in the blue and red, thus confirming the presence of higher chlorophyll
concentrations at these sites.
Spectral reflectance curves for a turbidity of 20 MTU are also shown in
Figure 40 for these two cases. With this turbidity the shapes of the curves
are almost identical and the chlorophyll absorption is not seen. It is
concluded that chlorophyll absorption is a relatively weak effect requiriny
long path lengths to produce noticeable results. Thus, particle scattering,
by reducing the mean path length of light through the water, reduces the
chlorophyll absorption effect. Particle scattering is apparently a much
stronger effect, predominating over chlorophyll absorption even with
relatively low sediment concentrations. Over the range of EPA interest, i.e.
greater than 25 mg/1 suspended solids, chlorophyll interference is not
believed to introduce significant errors in sediment measurements. This
statement, of course, would probably not be true if the water body were in a
condition of extreme algae bloom, but for typical chlorophyll concentrations
only very low turbidity data should be seriously affected.
93
-------
SECTION IX
DATA ANALYSIS
INTRODUCTION TO DATA ANALYSIS
Analysis of the volume reflectance and associated water sample data from
Lake Mead is the focal point of this study. The data acquisition, data
reduction, error analysis and other work discussed thus far is all supportive
of the data analysis work from which will come answers to the question of
feasibility of remote multispectral techniques for monitoring suspended
sediments. A brief general discussion outlining the scope and setting the
tone for the analysis task is presented here prior to the more detailed
analysis results.
A Statistical or an Analytical Approach
There are generally two possible means of seeking a solution to a problem
such as the interaction of incident light with a water body and its
constituents. With an analytical approach, all of the physical processes
involved are mathematically defined, resulting in a model which uniquely
describes volume reflectance in terms of measurable physical parameters. The
statistical analysis involves gathering a large volume of data, presumably
typical of all possible data, in an attempt to find statistical correlation
between parameters of interest. The statistical analysis can be conducted
apart from any attempt to answer why the correlation exists based on an
understanding of the physical processes. Once statistical relationships have
been found and defined in terms of confidence intervals, the problem has been
statistically solved.
At first glance the analytical solution normally seems the more desirable.
However, many problems are so complex that they are amenable only to a
statistical solution, and often a statistical solution is sufficient for some
application. Such is the case here. The volume reflectance-suspended
sediment relationship presents a very complex analytical problem. The
statistical approach is much more easily handled and, if properly formulated,
statistical analysis is sufficient for purposes of demonstrating feasibility.
Thus, the analysis reported here is of a statistical nature. Analytical
physical explanations for observed relationships are considered beyond the
scope of the present study. Feasibility and signature transferability will be
demonstrated on a statistical basis.
94
-------
Feasibility and Optimality
It is important to consider the difference between demonstrating
feasibility and establishing optimality of statistical techniques. The
problem of findiny optimum statistical algorithms is demonstrated by the data
shown in Figure 41. This figure shows six "best fit" curves for relating
volume reflectance at 652 nm to nonfilterable residue (105°C) for silt
particles in Lake Mead. These curves vary widely and yet each one is a "best
fit" according to some definition of "best".
Four of these curves are least-squares second order polynomial fits where
the curve is of the form
y = a + bx + ex2 (45)
The method of least-squares requires that we minimize X2 which is the measure
of the goodness of fit.
Ay
<
2
-2
= °
(y. - a - bx. - ex?)21 (46)
where Ay^ is the error in the fit for the i point
G.J is the weighting factor for the i point
The minimum value of x2 can be determined by setting the derivatives of x2
with respect to each of the coefficients equal to 0 and solving the resulting
simultaneous equations.
Within the framework of the least-squares polynomial technique the choice
must be made as to whether reflectance or suspended sediment is to be
considered the independent variable. A choice also exists concerning
appropriate weighting factors. The two weighting factor selections trieu here
were o? = y.,-, called statistical weighting, and a^ = 1, called
unweighted. The four possible combinations of independent variable and
weighting factors all give different curves in Figure 41 even though each was
calculated by the least-squares polynomial technique.
The piecewise linear fit was accomplished by dividing the data into three
groups representing three reflectance ranges. A linear least-squares fit was
applied to each group with a result quite different from the polynomial
curves.
95
-------
u
u
SILT
A=652 nm
RESIDUE INOEP - STATISTICAL
—- RESIDUE INOEP. - UNWEIGHTED
—> REFLECTANCE INDEP - STATISTICAL
- REFLECTANCE INOEP. - UNWEIGHTED
— P1ECEWISE LINEAR
EQ *HF=n (REFLECTANCE INOEP.)
100
NONFILTERABLE RESIDUE - 105° (mg/l)
Figure 41. Six "best fit" curves for volume reflectance
at 652 nm vs. nonfilterable residue (105°C) for
silt-sized particles in Lake Mead.
96
-------
The last curve, which is different from the previous five, in Figure 41
was calculated using a technique which was ultimately chosen for use in the
analysis work reported here. A derivation of this method appears in
subsequent discussion.
The best of these "best fits" should be taken as the optimum alyonthm for
predicting nonfilterable residue values oased on water volume reflectance at
652 nm. Best is determined statistical optimality and depends on the data
itself, the intended application of the results, and many other factors.
This analysis work does not include an investigation of statistical
optimality. Selection of a statistical technique was based on the data and
the investigator's previous experience. This method may or may not be
optimal, but algorithms need not be optimal in order to demonstrate
feasibility, which is the stated objective of this project. Optimality is
deferred to in subsequent phases of this study.
VERIFICATION OF THE PARTICLE SIZE HYPOTHESIS
Figure 38 showed a wide variation in the scattering properties of the Lake
Mead water samples as indicated by the scatter of points when nephelometnc
turbidity is plotted against nonfilterable residue. Results by other
investigators who were cited in the discussion of Figure 38 led to the
hypothesis that particle size is the primary factor determining the scattering
properties of suspended sediment.
Although it has just been stated that physical explanations of observed
relationships are not the objective of this study, particle size seems to be
of such importance that it is imperative that the above hypothesis be verified
if possible. The significance of the particle size parameter results from the
signature transferability question. If sediment color, composition, texture,
etc., are the dominant factors, then the possible variations are infinite and
the probability is small that algorithms designed for one site will apply to
data from another site. Extensive ground truth would, therefore, be required
and the desirability of remote multispectral monitoring would be greatly
reduced. However, if particle size is the primary scatteriny-related
parameter, there is a better possibility of signature transferability and
minimal ground truth requirements.
Division of the Data Set
If Rosgen's (1975) curve (Figure 38) is taken to be typical of fine sand
particles and Scherz and Van Domelen's (1975) curve is typical of clay
particles, it would seem reasonable to assume that silt-sized particles would
fall on a line between the other two. The 200 Lake Mead data samples were,
therefore, divided into three groups tentatively labeled fine sand, silt, and
clay depending upon where the nonfilterable resioue-nephelometric turbiuity
point fell with respect to the three lines shown in Figure 42.
97
-------
500
400-
E
o
300-
200-
100
CLAY
FINE SAND
100
200
300
400
500
NONFILTERABLE RESIDUE-105°C (mg/l)
Figure 42. Typical nonfilterable residue-nephelometric
turbidity relationships for various particle sizes.
98
-------
The results of the division are given in Table 9 which shows the number of
samples from each site that fell into each category. Notice that the
Colorado, Muddy, and Virgin River sites samples fall predominantly into the
silt category. Government and Las Vegas Wash samples are predominantly fine
sand. Of the 53 samples not falling in the predominant group for their site,
39 contained less than 10 mg/1 of nonfilterable residue (105°C). Samples this
clean are in the noise level of the laboratory analysis of nonfilterable
residues so their failure to agree is not significant. Only 14 samples with
meaningful suspended sediment concentrations failed to group with the rest of
the samples from their site.
TABLE 9. GROUPING OF SAMPLES BY SITE AND PARTICLE SIZE
Particle Size
Site Clay Silt Fine Sana
Colorado River
Government Wash
Las Vegas Wash
Muddy River
Virgin River
1
1
0
4
11
30
8
10
31
25
9
31
30
5
4
Total 17 104 79
The interesting thing about site groupings is that they have no apparent
relationship to sediment color. For example, available photography and the
sediment spectral reflectance curves (Figure 37) show that the Muddy and
Colorado River sites had the highest and lowest reflectances respectively, yet
they were grouped together. Visually the Government Wash sample looks most
like the Muddy or Virgin River sediment, yet in terms of scattering properties
it is associated with the gray colored Las Vegas Wash sample. Therefore,
particle size appears to be a more differentiating factor than sediment color.
Particle Size Measurements
Data reported by other investigators suggest the importance of particle
size, and division of the Lake Mead data set according to scattering
properties tended to support this hypothesis since grouping was not consistent
with sediment color. Yet the primary role of particle size had not definitely
been proven. It seemed that the particle size hypothesis would be proven only
by direct measurement of the size of the particles in the sediment samples
taken from the lake bottom at each site.
99
-------
The EPA laboratory in Las Vegas performed the analysis of Lake Mead water
samples but did not have the capability to perform this type of measurement.
Sediment samples were, therefore, sent to Battelle Laboratories in Columbus,
Ohio, where particle distribution were measured on a Coulter counter. The
particle size distribution data are shown in Figures 43 and 44.
Figure 43 shows size distributions from the Muddy, Colorado, and Virgin
River samples. These are seen to be quite similar and within the silt
particle size range just as had been inferred from the nonfilterable
residue-nephelometric turbidity plots. Figure 44 shows size distributions for
the two sites which were tentatively identified as fine sand. (The Las Vegas
Wash sample is not the same one that came from station L05, but is a sample
from station L06 which is closer to the mouth of the wash.) The Las Vegas
Wash particles do indeed fall in the fine-sand range; however, the Government
Wash sample does not. Several explanations for this could probably oe
offered. The most reasonable seems to be the fact that prop-wash resuspension
was frequently used here to create turbidity when the natural resuspension
mechanisms were not present. The prop wash would often create a hole up to a
half meter deep in the bottom of the lake, digging into much coarser deposits
than would be picked up by the anchor. Our sediment sample is, therefore,
possibly not representative of what was suspended in the water.
In spite of the anomalous behavior of the Government Wash sample, the data
from the other four samples have sufficiently verified the particle size
hypothesis. In summary, the investigation of the particle size question has
resulted in the following information.
Particle size is more important than sediment color in determin-
ing scattering properties.
The ratio of nonfilterable residue (105°C) to nephelometric
turbidity is a good indicator of particle size. This ratio
will typically have the values 3.1, 1.4, and 0.8 for fine
sand, silt, and clay respectively.
One of the more valuable pieces of ground truth data from a site
to be monitored would be several water samples which could be
analyzed to determine the nonfilterable residue-nephelometric
turbidity ratio for that site.
Because particle size rather than color is dominant, the
prospects look good for some degree of site-to-site signature
transferability.
POLYNOMIAL FITS TO RESIDUE/TURBIDITY VS. VOLUME REFLECTANCE
Volume Reflectance-Nonfilterable Residue
Before considering the multispectral problem it is informative to look at
single-wavelength relationships. A cursory examination of the data reveals
100
-------
100
e
LU
55 80
CJ
C9
I—
C9
LU
5
60
40
20
.5
MUDDY RIVER
COLORADO RIVER
VIRGIN RIVER
( SILT PARTICLE SIZE
) RANGE FROM TABLE V-1
I I I—I I I I
50
100
PARTICLE DIAMETER (M)
Figure 43. Particle size distribution for Muddy, Viryin,
and Colorado Kiver sediment samples.
-------
o
ro
100
g
LU
co 80
<
CJ
so-
UJ
oc
C9
ca
20
FINE SAND PARTICLE SIZE I
RANGE FROM TABLE V-1
LAS VEGAS WASH
GOVERNMENT WASH
.5
10
PARTICLE DIAMETER
50
100
Figure 44. Particle size distribution for Las Vegas and
Government Wash sediment samples.
-------
definite nonlinearity. The Fortran subroutine, POLFIT, given by Bevington
(1969) was, therefore, used to fit various least-squares polynomials to the
data. As has been previously demonstrated, the optimum method of fitting a
curve is not always obvious, so several orders of polynomials were considered.
The obvious nonlinearity in the data ruled out first-order (linear)
polynomials. Polynomials of third or higher orders seemed to be fitting
individual data points rather than representing actual reflectance properties.
Thus the choice of second-order polynomials seemed most appropriate.
Polynomials were calculated considering reflectance to be the independent
variable and also with nonfilterable residue as the independent variable.
Both unweighted and statistically weighted fits were investigated. A second-
order unweighted least-squares polynomial with nonfilterable residue as the
independent variable was chosen as the method of fitting single-wavelength
volume reflectance to nonfilterable residue (105°C) in Figures 45 through 48.
An equation of the form shown below was fit to each of the data sets grouped
by particle size.
PW = an + a (residue) + a (residue)2 (47)
w u i 2
Examination of the curves shown here for four selected wavelengths led to
the following conclusions.
Reflectance-nonfilterable residue relationships are strongly
influenced by particle size.
At visible wavelengths the sensitivity of reflectance to
incremental changes in nonfilterable residues decreases with
increasing residue values. A point is reached in the vicinity
of several hundred milligrams/liter where saturation occurs.
Above this point reflectance is insensitive to changes in
residue values.
Maximum sensitivity at low sediment concentrations occurs in the
red portion of the spectrum.
The near-IR wavelengths are nearly linear and do not show the
saturation that appears in the visible. These wavelengths,
therefore, have the greatest analytical range.
Since red wavelengths yield maximum sensitivity at low concen-
trations and near-IR wavelengths yield maximum sensitivity at
high concentrations, it becomes apparent that to optimize
accuracy over a large analytical range of suspended sediment
concentrations, a multispectral approach will be required.
103
-------
.15
.10
u
2
s
a
_i
o
.05
BLUE
X=480nm
CLAY
100
200
SILT
300
NONFILTERABLE RESIDUE-105°C (mg/l)
Figure 45. Volume reflectance at 480 nm as a function of
nonfilterable residue (105°C).
104
-------
15 T
10 •
u
z
u
OS-
SILT
GREEN
X=550nm
100
200
300
NONFILTERABLE RESIDUE 105°C (mg/l)
Figure 46. Volume reflectance at 550 nm as a function
of nonfilterable residue (105°C).
105
-------
10- •
RED
X=S52nm
SILT
300
NONFILTERABLE RESIDUE-105° (mg/l)
Figure 47. Volume reflectance at 652 nm as a function
of nonfilterable residue (105°C).
Volume Reflectance-Nephelometric Turbidity
The same polynomial fitting procedure was used to supply curves for the
volume reflectance-nephelometric turbidity relationships. These curves are
shown in Figures 49 through 52.
The difference between the turbidity curves and the residue curves is
significant. The following conclusions have been drawn from these data.
A reflectance saturation occurs in the nephelometnc turbidity
relationships at visible wavelengths but not at near-IK
106
-------
ee
yj
s
100 200
NONFILTERABLE RESIDUE -HJ5°C (mg/l)
Figure 48. Volume reflectance at 782 nm as a function
of nonfilterable residue (105°C).
107
-------
IS
M 10
u
OS
BLUE
X=480nm
SILT
CLAY
SAND
•*•
100 200
NEPHELOMETRIC TURBIDITY (NTU)
300
Figure 49. Volume reflectance at 480 nm as a function
of nephelometric turbidity.
wavelengths. This result is the same as that observed with
nonfilterable residues.
There is much less variability in the turbidity curves resulting
from differences in particle size.
Since the turbidity-reflectance relationships are less sensitive
to changes in sediment type than are the nonfilterable resiuue-
reflectance relationships, nephelometric turbidity would appear
to be a parameter more amenable to remote monitoring than
nonfilterable residue.
108
-------
1ST
.10"
OS-'
SILT
CLAY
FINE SAND
GREEN
X=550nm
-I-
-H
100 200
NEPHELQMETRIC TURBIDITY (NTU)
300
Figure 50. Volume reflectance at 550 nm as a function
of nephelometric turbidity.
A STATISTICAL METHOD FOR OBTAINING MULTISPECTRAL QUADRATIC ALGORITHMS
The multispectral approach rather than single wavelength is preferable for
the single-wavelength polynomial curves discussed above. Further, it has been
shown that the parameters of interest are not linearly related to reflectance
in the visible portion of the spectrum. Thus we know that a nonlinear,
multivariate, statistical method will be required to obtain yood algorithms
for predicting residue/turbidity values from volume spectral reflectance. The
subroutine POLFIT, which was used to calculate the single-wavelenyth
polynomials, does not handle multivariate data. No other existing software
109
-------
30 T
u
z
u
LU
^
U.
IU
ee
u
£
SILT
RED
X=652nm
100 200
NEPHELOMETRIC TURBIDITY (NTU)
300
Figure 51. Volume reflectance at 652 nm as a function
of nephelometric turbidity.
was available which could be used for nonlinear, multivariate statistical
analysis. It was, therefore, necessary to develop this capability as part of
this study.
Two approaches to the nonlinear, multivariate problem were considered.
The first would be to linearize the parameter of interest in each coordinate
of measurement space, and then apply linear analysis to the transformed aata.
The second approach, and the one followed here, was to develop nonlinear
algorithms which operate directly on the raw volume reflectance data.
110
-------
•1ST
10-
05-
NEAR-IR
A.=78Znm
•I-
100 200
NEPHELOMETRIC TURBIDITY (NTU)
300
Figure 52. Volume reflectance at 782 run as a function
of nepleometric turbidity.
We need to make a transition now from the physical concept of reflectance
spectra to the abstract mathematical concept of multidimensional vector
spaces. If we consider K wavelengths simultaneously, the dimensionality of
the vector space will be 2K, and a spectrum can be represented by a row
vector, X, whose components are the first and second powers of the spectral
reflectance values.
x ,
2 2
,PSP ,p^.
. 1 2 2
(48)
111
-------
where p^ is the reflectance of k wavelength. Let V be another row vector
V = TV ,v ,v v .1 (49)
L 1 2 3 2KJ
called the prediction vector. The prediction, p, of some turbidity related
parameter will be given by
p = VXT (50)
(The superscript in the above equation denotes transposition.) The problem
can now be treated as linear in X although it is actually quadratic in terms
of reflectance. If g is the ground truth value of the residue/turbidity
parameter of interest, the error, e, in the. multispectral prediction is yiven
by
e = p - g • VXT - g (51)
We now consider a large number of data vectors which will serve as the
training data from which a statistical algorithm will be developed. The nth
vector in the training set, Xn, has ground truth value gn, and the error
in the statistical prediction of gn will be called en. The problem is to
find the vector V such that
y e2 = minimum (52)
n
where N is the total number of samples in the training set
The sum of the errors squared is given by
i*, • j«!vT - *i&\ * j^
The prediction vector which minimizes the sum of the squares of the errors is
found by setting aze^/aV =0. The property of partial derivatives
v (54)
3V " L W
112
-------
allows us to write
3V
• 0 (55)
If summations are replaced by averages nothiny is changed mathematically but
the notion is simplified allowing the desired V to be given by
vT = 7777 (56)
Vn Vn
Any multispectral algorithm obtained from Equation 56 is constrained to
assign the origin of the vector space to a residue/turbidity value of 0. This
is not a physically realistic constraint since the Lake Mead data show
sediment-free water can have reflectances of five percent or more at some
wavelengths. Unweighted second-order polynomials with residue/turbidity as
the independent variable, such as those shown previously in Figures 45 through
52, are felt to give the best estimate of volume reflectance for zero
suspended sediment. The zero sediment reflectance for the k wavelength, zk,
can be subtracted from p^, to give modified data vectors, X'.
Xn = [.PJ-V'.VZ^.Z^.... <57>
If we design a modified V1 based on Xn' training data, the result is a
statistical algorithm which minimizes Ee^ but which is constrained to a
proper zero point.
When applying these V algorithms to nontraininy-set data, z^'s must be
subtracted from each data vector. For production processiny this subtraction
adds computation time reducing the efficiency of the algorithm. Also, we must
keep track of zk values to be used with each algorithm. Rather than do this
it is advisable to transform V' back to a form that will be equivalent to V
but which can operate directly on the uncorrected reflectance data. Tne com-
ponents of the new prediction vector for this case can be shown to be given by
vk = vk - 2Vizk for k odd
(58)
v = v for k even
113
-------
and the statistical prediction is then given by
p = VXT + vn (59)
where
K
v, = I (vVz? - v^_lZJ (60)
This technique is developed for multispectral algorithms but for K = 1 the
technique reduces to a single-wavelength polynomial fit. Thus all alyorithms
reported in the remainder of this section, whether they are sinyle-wavelenyth
or multispectral, were obtained according to the method just described.
The Fortran program ALGOR was written to implement this technique on the
CDC 6400. This program took as input the cards put out by VQLKEF which
contained spectral reflectance and water sample analysis results. ALUUR will
calculate quadratic multispectral alyorithms to predict any of the water
sample parameters from any selected combination of wavelengths. Appendix B is
a listing of this program.
EVALUATION OF STATISTICAL ALGORITHMS
Detuning by Addition of Random Noise
The most desirable method of evaluating statistical prediction algorithms
is to obtain a set of data called a test set which does not include the
training set from which the algorithm was designed. Applying an alyoritnm to
the test set gives an independent check on accuracy. By collecting 200
samples at Lake Mead, it was hoped that there would be enough data to pruviae
for separate, statistically significant training and test sets. However, the
small number of samples with high sediment concentrations made it impossible
to divide the data in this manner and still maintain the statistical
significance of both sets at high concentrations. Thus, it is necessary to
evaluate accuracy by applying algorithms back to the traininy sets.
Accuracy evaluations based on the training set generally tend to yive
values which are too low unless the set is very large. This happens because
the algorithm is "fine-tuned" to the training set and operates on nuances
peculiar to the training set that are not representative of the data in
general. An algorithm fine-tuned to a training set in this manner will not do
nearly as well when applied to an independent test set.
Since the accuracy evaluations here must be done with the traininy set, it
is desirable to make a correction to prevent misleadinyly low accuracy
114
-------
estimates. One way to do this is to corrupt the training set data by addiny a
certain amount of random noise. This has the effect of preventing the
algorithm from being too finely tuned. It is not necessary to actually
generate and add random noise since the same effect can be achieved by simply
increasing the diagonal elements of the matrix xjx .
To demonstrate this random noise effect, the 40 Muddy River samples were
divided into two halves. A six-wavelength algorithm was designed from the
half consisting of the even numbered samples with varying amounts of random
noise added. These algorithms were applied to the half of the data containing
the odd numbered samples as well as back to the even numbered training set.
Accuracies for these two cases have been plotted in Figure 53 as a function of
noise added. It is seen here that without random noise the training set
evaluation of accuracy is very good and the test set is poor. As noise is
added, the two accuracy methods begin to converge and the training set
accuracy evaluation becomes more representative of what an independent test
set evaluation shows. Two percent random noise was, therefore, added to
"detune" all of the algorithms reported in the remainder of this section.
Method of Reporting Accuracies
When algorithms are applied to training set data, what is the best way to
express the resulting errors? Errors are associated with samples with
residue/turbidity values ranging from zero to several hundred. A simple root
mean square (rms) error calculation is not too meaningful because of the large
range. A 10 mg/1 error in a value of 200 mg/1 is small but a 10 mg/1 error in
a value of 5 mg/1 is large. It seems more desirable to express errors as a
function of ground truth values. It was decided to report algorithm
accuracies in this report by putting ground truth and absolute value of error
data into the subroutine POLFIT in order to fit unweighted second-order
polynomials. This procedure gives a least-squares fit to the absolute value
of the errors. This is not necessarily identical to a standard deviation.
Since the error analysis results were expressed in standard deviations, the
error analysis is not expected to correspond numerically with least-squares
fits to absolute values. However, even though the two error expressions may
not be numerically equivalent, they should correspond in principle. For
example, if the error analysis showed errors for the IR wavelengths to be 50
percent smaller than those in the visible, the algorithm error evaluation for
these two cases should show approximately the same 50 percent difference.
SINGLE CHANNEL ALGORITHMS FOR VERIFICATION OF ERROR ANALYSIS RESULTS
The analysis of errors in the 200 Lake Mead samples was summarized by
Figure 27 which showed expected errors at red (652 nm) and near-IR (782 nm)
wavelengths. An important analysis task was to actually design algorithms to
predict nonfilterable residues and nephelometric turbidities from volume
reflectances at these two wavelengths. If the algorithms agree with the error
analysis results, it would tend to verify both the error analysis procedures
and also the statistical methods used in designing algorithms.
115
-------
25-r
20--
TRAINING SET
TEST SET
\
I
i
t
15- \
i
t
i
10- •
e
&
co
i
i
t
i
4
10
RANDOM NOISE (%)
Figure 53. Effects of random noise addition on training set
and test set accuracy evaluations.
116
-------
Separate algorithms were designed for silt and fine sand particle sizes,
but the errors for the two cases were combined in calculating the polynomial
fit to the absolute value of the errors. Table 10 contains the coefficients
for these single-wavelength algorithms.
TABLE 10. SINGLE-WAVELENGTH ALGORITHMS
Wavelength
652
652
782
782
652
652
782
782
Particle Size
Silt
Fine Sand
Silt
Fine Sand
Silt
Fine Sand
Silt
Fine Sand
Parameter
NTU
NTU
NTU
NTU
mg/1
mg/1
mg/1
mg/1
- PARTICLE SIZE KNOWN
V0
3.0
-8.8
0.0
0.0
-0.1
-28.0
0.0
0.0
vl
-291.0
772.1
1070
1692
-195.7
2493
1519
5316
V2
6826
-880.4
4453
-4806
8142
-4910
5343
-19305
These algorithms were applied to the Lake Mead data polynomials fit to the
absolute value of the errors with the result shown in Figure 54. Comparison
of Figures 54 and 27 shows a strong resemblance between the error analysis
results and the actual performance of the single-wavelength algorithms. Note
the following specific points of comparison.
The error analysis predicted about 55 percent larger errors for
the red wavelength than for the near-IR wavelength at ground
truth values of 200. Actual algorithms for red data had 65
percent larger errors than did the near-IR algorithms.
The error analysis predicted that in the near-IR turbidity pre-
diction errors would be 26 percent smaller than residue errors
at ground truth values of 200. Actual algorithms resulted in
25 percent smaller errors for turbidity.
The error analysis results contained a crossover at a yround
truth value of 50 between the red NTU and mg/1 curves. The
actual algorithms have this same crossover.
This type of agreement seems to establish the validity of both the error
analysis and the statistical algorithms.
In comparing these two figures notice that although the principal features
are similar, the magnitudes of the errors differ by about 30 percent. This is
not surprising since numerical differences could occur for the following
reasons.
117
-------
V)
40
20 >
100 200
GROUND TRUTH VALUE
Figure 54. Uncertainties in remote measurements based on
red or near-IR volume reflectance.
118
-------
One figure shows standard deviations; the other fiyure shows a
least-squares fit to the absolute value of the errors.
The error analysis did not include variability of the sediment
types which would contribute to the measured errors of actual
algorithms.
Random noise has been added in the design of the algorithms to
degrade their accuracy.
Another interesting feature of Figure 54 is the upward curvature of the
curve representing errors in nonfilterable residue predictions based upon the
red wavelength. This apparently results from saturations in the visible
wavelengths which leaves reflectance insensitive to changes in sediment
concentration above about 200 mg/1 (see Fiyure 54).
MULTISPECTRAL ALGORITHMS
The data analysis reported thus far has shown that volume reflectance at
visible wavelengths gives the best sensitivity to sediment changes at low
concentrations, but saturation occurs above about 200 mg/1. The near-IR
reflectance does not saturate but lacks sensitivity at low concentrations.
Thus to optimize both analytical range and sensitivity a multispectral
approach has been suggested. The program ALGOR was, therefore, used to
generate and evaluate 2, 6, and 10-wavelength multispectral quadratic
algorithms for prediction of nephelometric turbidity and nonfilterable residue
(105°C).
The data set was divided into clay, silt, and fine sand subsets as
previously described, and algorithms were generated for the silt and fine sand
cases. (The clay subset was not used because its 17 samples were not enough
to be statistically significant.) The algorithms were applied back to the
training sets to evaluate accuracy, but the errors for the silt and fine sand
cases were combined before performing the error fit calculation. Thus
accuracies reported here are representative of what would be expected if the
particle size is known for a monitoring site.
Tables 11 through 14 contain the coefficients of the multispectral
algorithms. The least-squares fits to the absolute values of the algorithm
errors are shown in Figures 55 and 56 for the nonfilterable residue and
nephelometric turbidity algorithms respectively. Also shown in these figures
for sake of comparison are the near-IR single-wavelength algorithm results
from Figure 54. The determination of which wavelengths were to be used in the
multispectral algorithms resulted from a rather arbitrary selection by the
investigator. Selection was not made according to any specific mathematical
criteria.
Notice that at low turbidities the expected improvement of the two-
wavelength algorithm over the near-IR algorithm is not present. This is a
characteristic of the data set and not a general result. The reason for this
can be seen from the error analysis (Figures 21 and 23) which show that the
119
-------
TABLE 11. MULTISPECTRAL ALGORITHM COEFFICIENTS*
FINE SAND - NONFILTERABLE RESIDUE (105°C)
Wavelength
(nm)
415
436
480
517
550-
583
620
652
690
703
742
782
829
862
905
942
984
vo
2X 6X
Algorithm Algorithm
-434.0/964.6
54Z.9/-8396
1327/-13051 1001/-4030
1207/-10269
4208/6204 2516/9475
1338/8828
-13.53 -16.40
IDA
Algorithm
95.99/-6S29
-240.3/16128
279.0/-9770
163.9/-4333
384.7/-189.8
654.3/-9407
862.S/-3442
2401/-226.8
1837/10584
-734.8/40652
-14.67
* Coefficients in each column are given in the format first-order
coefficient/second-order coefficient.
120
-------
TABLE 12. MULTISPECTRAL ALGORITHM COEFFICIENTS*
SILT - NONFILTERABLE RESIDUE (105°C)
Wavelength
(nm)
415
436
480
517
550
583
620
652
690
703
742
782
829
862
905
942
984
vo
2X 6A
Algorithm Algorithm
-141.9/730.4
458.4/-4580
354.7/-2058 263.47-547.4
290.6/-517.3
1496/6089 1129/6922
978.7/7342
-7.26 -16.54
10X
Algorithm
31.06/743.5
-213.9/5251
25. 98/- 1804
438.6/-4S36
219.8/-2638
314.2/715.3
228.4/-303.6
899.3/5491
542.0/226.9
1583/-11175
-18.01
* Coefficients in each column are given in the format first-order
coefficient/second-order coefficient.
121
-------
TABLE 13. MULTISPECTRAL ALliURITHM COEFFICIENTS*
FINE SAND - NEPHELOMETRIC TURBIDITY
Wavelength 2x
(nm) Algorithm
415
436
480
517
550
583
620
652 450.6/-3480
690
703
742
782 1179.6/2873
829
862
905
942
984
v0 -4.76
6X
Algorithm
-253.9/2905
221.5/-2820
286.4/-1339
383.2/-227S
724.0/5039
279.1/-1237
-5.05
10X
Algorithm
84.06/-3316
-89.67/3536
-40.80/-756.7
74.66/-1404
134.7/175.7
220.2/-2344
260.8/-1129
656.6/-928.1
368.2/-1307
339.8/33043
-4.07
* Coefficients in each column are given in the format first-order
coefficient/second-order coefficient.
122
-------
TABLE 14. MULTISPECTRAL ALGORITHM COEFFICIENTS*
SILT - NEPHELOMETRIC TURBIDITY
Wavelength
(nm)
415
436
480
517
550
583
620
652
690
703
742
782
829
862
905
942
984
vo
2X 6A
Algorithm Algorithm
-35.38/1075
299.9/-3919
138.4/-179.8 144.1/1006
174.8/300.9
822.0/5338 602.1/4162
399.5/-1354
-3.43 -11.77
10\
Algorithm
11.17/83.96
106.9/-1073
-198.5/-2090
281.1/-4179
115.6/123.7
174.2/-258.6
134.6/-51.81
614.9/5113
330.9/2003
418.2/-6144
-9.49
* Coefficients in each column are given in the format first-order
coefficient/second-order coefficient.
123
-------
f
K
K
20
NONFILTERABLE RESIDUE-105'C (mg/l)
Figure 55, Accuracies of multispectral algorithms for
predicting nonfilterable residue (105°C).
124
-------
10
NEPHELOMETRIC TURBIDITY (NTU)
Figure 56. Accuracies of multispectral algorithms for
predicting nephelometric turbidity.
125
-------
red wavelength, which is supposed to be the source of the accuracy
improvement, has rather large instrumental uncertainties. With an improved
spectrometer, more of the expected advantage of the two-wavelength algorithm
would be realized.
Study of the multispectral results leads to the following conclusions.
As the number of wavelengths is increased the accuracy improve-
ment is not dramatic.
Since spectral reflectance curves of the sediment samples
(Figure 37) were lacking any spectral fine structure, the
improvement resulting from added wavelengths is thought to be
the result of a -\/R reduction of random noise rather than the
result of better resolution of sediment signatures.
Sensor and data processing costs both go up rapidly with
increasing numbers of wavelengths. A trade-off between cost
and accuracy is, therefore, involved in deciding how many
wavelengths to use. It is expected that the best choice will
generally be in the range of two to four wavelengths.
Accuracy improvements resulting from more wavelengths will
probably not be great enough to justify the additional costs.
Nephelometric turbidity can be predicted from volume spectral
reflectance with more accuracy than nonfilterable residue
(105°C). For example, Figure 55 shows the 10-wavelength
prediction of a nonfilterable residue of 250 mg/1 has an
uncertainty of ±50.4 mg/1 for a variance of 0.041. The same
sample, if it consisted of silt-sized particles, would have a
nephelometric turbidity of 180 NTU. According to Figure 56 a
10-wavelength prediction of this value would have an
uncertainty of ±28 NTU for a variance of 0.025.
Even with a multispectral system it is not expected that an
accuracy of o2 = 0.05 will be possible all the way down to
25 mg/1. However, one should be able to come quite close to
achieving EPA's desired accuracy.
SIGNATURE TRANSFERABILITY
The single-wavelength and multispectral algorithms have demonstrated that
volume reflectance can be related to suspended sediment concentration with
accuracies approaching EPA's requirements. Thus part of the feasibility
question has been answered. Signature transferability is the other basic
issue to be addressed in order to completely demonstrate feasibility. Is each
monitoring site or sediment type a unique case, or is there some commonality
between sites and sediment types which would permit multispectral monitoring
without extensive ground truth9
126
-------
Thus far the analysis results have indicated that the factor of common-
ality for nonfilterable residue is particle size, and that nephelometric
turbidity-volume reflectance signatures may be transferable without any a
priori knowledge. An additional analysis task was undertaken to further
substantiate these conclusions. Algorithms designed from silt data were
applied to fine sand data with the intent that the accuracy of these
misapplied algorithms would be an indicator of signature transferability.
Only samples with nonfilterable residue (105°C) values in the range 0 to
50 mg/1 were used in this step. The higher concentration ranges were ignored
because the relatively few samples there raised some question as to
statistical significance. The silt subset contained 86 samples in the 0- to
50-mg/l range which were used as the training set for six-wavelength
algorithms for nonfilterable residue and nephelometric turbidity. Tables 15
and 16 contain the coefficients of these algorithms. These two algorithms
were applied back to the silt training set to estimate their accuracy which is
shown in Figure 57.
The fine sand subset contained 55 samples in the 0- to 50-mg/l range to
which the algorithms of Tables 15 and 16 were also applied. The accuracy of
the silt algorithms misapplied to the fine sand data is also shown in Figure
57. Notice that misapplying algorithms, in the nonfilterable residue case
resulted in large errors. Therefore, it is further demonstrated that
signature transferability in this parameter will not be possible unless
particle size is known. However, misapplication of the nephelometric
turbidity algorithm results in virtually no increase in errors. Thus
nephelometric turbidity exhibits a good probability of signature transfer.
For purposes of remote monitoring nephelometric turbidity would, therefore,
have to be considered a more desirable indicator of suspended sediment.
UNIVERSAL NEPHELOMETRIC TURBIDITY ALGORITHMS
It has been concluded that if suspended sediment is expressed in units of
nephelometric turbidity, volume reflectance signatures are invariant between
sediment types. Therefore, the final analysis step would be to combine clay,
silt, and fine sand subsets and design nephelometric turbidity algorithms
which would presumably be of universal applicability regardless of sediment
type.
Three universal algorithms have been developed. Two are single-wavelength
algorithms operating on volume reflectance at the red (652 nm) and near-IR
(782 nm) wavelengths. The third is a two-wavelength algorithm operating on
both of these wavelengths. These wavelengths were selected because they
roughly correspond to bands obtainable by densitometric analysis of color-
infrared photography, and they also correspond to LANDSAT bands 5 and 6. Thus
other investigators using these types of sensors might find these algorithms
of interest, and if volume reflectance can be derived from their data, these
investigators may provide data of value in verifying the conclusions that have
led to these algorithms.
127
-------
Table 17 contains the coefficients of the universal nephelometric
turbidity algorithms and Figure 58 shows their expected accuracies.
TABLE 15. MULTISPECTRAL ALGORITHM - NONFILTERABLE
RESIDUE (0 TO 50 mg/1 SILT)
Wavelength
(nm)
517
583
652
703
782
862
vo
First-Order Coefficient
-47.91
11.74
132.6
287.6
938.8
1059
-4.53
Second-Order Coefficient
471.3
-437.1
-196.8
-1104
-15307
-11564
TABLE 16. MULTISPECTRAL ALGORITHM - NEPHELOMETRIC
TURBIDITY (0 TO 40 NTU SILT)
Wavelength
(nm)
517
583
652
703
782
'862
First-Order Coefficient
-13.36
-7.43
86.54
213.0
858.6
620.5
Second-Order Coefficient
-17.59
-63.56
-677.6
-787.1
-257.7
-262.77
-3.05
128
-------
ST
SILT APPLIED
TO SAND
SILT APPLIED TO SILT
NEPHELOMETRIC TURBIDITY
10
20
30
40
o
te.
oe
20 T
10-
NONFILTERABLE
RESIDUE-105°C
10
SILT APPLIED TO SILT
20
30
40
50
GROUND TRUTH VALUE
Figure 57. Comparison between accuracies of correct
and misapplied six-wavelength algorithms.
129
-------
TABLE 17. UNIVERSAL NEPHELOMETRIC TURBIDITY ALGORITHMS
Wavelength First-Order Second-Order
Type (nm) v0 Coefficient Coefficient
Single-wavelength 652 -4.38 33.96 5352
Single-wavelength 782 0.0 1181 4062
Two-wavelength 652 233.7 -1384
130
-------
50
100
ISO
250
NEPHELOMETRIC TURBIDITY (MTU)
Figure 58. Expected accuracy of universal nephelometric
turbidity algorithms.
131
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SECTION X
REFERENCES
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Blanchard, B. J., and R. W. Learner, 1973. American Water Resources
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Klooster, S., and J. Scherz, 1974. "Water Quality in Photographic Analysis",
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Lillesand, T., 1973. "Use of Aerial Photography to Quantitatively Estimate
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Novotny, J., 1975b. "Job Order 30.02 - Spectrometer Development and
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Pionke, H., and B. Blanchard, 1975. "The Remote Sensing of Suspended
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Pijanowski, B., 1975. "The Meaning and Measurement of Turbidity",
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133
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Scherz, J., and J. Van Dome1 en, 1975. "Water Quality Indicators Obtainable
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134
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APPENDIX A
METRIC CONVERSION TABLE
Non-metric Unit
Multiply by
Metric Unit
feet (ft)
gallon (gal)
miles (mi)
0.3048
3.8
1.609
meters (m)
liters (1)
kilometers (km)
135
-------
APPENDIX B
VOLREF
PROGRAM LISTING
136
-------
\/Ol_RF.F (INPUT, OUTPUT.TAPE5=INPUT,TAP£*=OUTPUT. PUNCH)
lJ~rir,OAM T/VKH.S AS INPUT PUNCHED CAHOS CONTAINING SPECTROMETER
ON STWIP CHAPTS IN THE FIFLD AND CALCULATES WATER VOLUME SPECTRAL
C -yFFI rCTANCE. THF. PERIPHERAL EFFFCTS MASKING TRUE VflLUMF REFLECTANCE A*E
C ofOVEO 4Y THE SCS TECHNIQUE DEVFLOPKD RY PIECH AND WALKER (197Z)
C
C' »OOOO1 «044«4»a44>->6»{»OI>0i)el>e4>-{>O ({fO^O^-Oit^ttO-AHOO-OO-dOOOC^^-tt^^O^XXO^vOdtXIOOSUOOOO
C
c T"IS P»OGPAM !<; INTEMOED FOR USE WITH THE EMA E^SL/LV SPECTWOM£TER
C *'HICH SAMPLFS 20 WAVELENGTHS. THUS. DIMENSIONS OF ARRAYS AHE SET
C accn"DIi"GLY.
C
"> I -IF MS I ON ALFA (20) .ALFflP(20> ,LAMHOA(?0) ,R(20» 14) tSl TE (2)
(M iFN^ION VZ(20) .VGI20) ,PAR(H) .COM (8) ,VE (20) ,VW (?0) . VES (?0)
UT'FNSION LAflELI?) .OATA(&) .A(29t7) ,ASTOH(29) »VWS(20) «VGS(20)
INTEGER CDL>3L«A. BLANK. ASTOR
OATA NCH/20/
OATA BLANK/i i/
C
C EMTE' VALUES OF REFLECTANCE STANDARDS
r
c NO. i FLAT WHITE ENAMFL - PPANO UNKNOWN
c
>)ATA (R(I.l) tl=l«20) /O. 7. n. 7 t 0. 7,0.7.0. 7 t 0.705.0.71 t 0.72. 0.72, 0.7
1 ?, 0. 72 . 0. 7T, 0.73. 0.72.0. 72.0. 7. 0.6B.O. 65. 0.*>5.0.*i35/
C
C MO. ? ZY^OLYTF SPEFD-E-NAMfL G"AY METAL PRIMER (Oa?7)
C
OATA (Rll.2) .1=1. 201/0. 23.0. 23.0. 23.0. ?3.0.?3. 0.23. 0.23, 0.227.0.22
1 1 .0.21 3- 0.205. 0.192. 0.189. 0.1 7«,0. 163«0. 154.0. 145.0. 13,0. 125. 0.1 25
2/
C
C NO. 3 KPYLON GRAY PRIMER (NO. 2 KECOATED)
C
DATA (RIT.3) .1 = 1 .20)/.04..nS6..09<»..ll..062..0SQ,.05Q'.05<»,.OS7..0S(S,.05<>..05*.0^7..0<>5/
C
c NO. <. KP.YLON FLAT WHITE ENAMEL INO.I RECOATEDI
c
PATA (RII.4) ,1=1.?0) /O. 7,0. 7, n. 7. 0.7. 0.7. 0.72. 0.74, 0.745. 0.73, 0.7
1 1 5.0. 71 .0.71 .0. ?(>«;, 0.7Q5. 0.705, 0.7, 0.69, 0.6^.0. 65.0.635/
C
C JO. 3 a*'0 NO. 4 LOST OVERBOAPO
C
C NO. ^ KCYLON FLAT WHITE ENAMEL (NEW AL SHFFT - SOME AL SHOWING THROUGH PAIN
C
C NO. fr KOYLON GRAY PW1MER (OVER PREVIOUS FLAT SLACK)
C
nft T A (R (I,M , I = l,?0)/.04,.05'S..094,.l ,.097..085..076..07,.066».062
l..nf...0^5..053,.OS2,.0?4,.05«.047,.045«.043*.04?/
C
C NO. 7 KPYLON GRAY PRIMER (NO. * kECOATED)
C
,I = l«20>/.04,.OS6,.094,.107..10^..092,.083«.07f...072,.
137
-------
c
c
c
c
c
c
r
c
r
c
c
c
NO
If. M . .niS7..ri/3'3,.064,.o5f«..Oc>9..0*',.057..052..049..046/
a *.OSfi..094«. 1069.1 02 t.n<)3.. 001 9.07*9. 073 1
1 . 060 « . 0*7 , . ofeS , . 064 . . Oft t . 0*3 • . 0* 1 , . 06 « . 056 * . 053 1 . 053/
12 ZYNOLYTE SPEED-E-IJA^FL FLAT WHITE (0377) JOVEP. NO. io>
13 KPYLON r,e8..68/
rftVELFNGThS IN NANOMtTEWS WHICH THE SPECTOQMETES SAMPLES
DATA LA»HOA/343»377,385.<»15.<»36«4ao«517.550.583,620»652»690»703»7<»
AXES AND LAPELS FOR SPECTRAL PLOTS
.00 I — •/.A<2*,2>/«-- 1-
OATA A(?6*1)X*
1 '/
OATA A(27,U/«
10
20
DATA A(?9,l)/«
400 »/.A<27.2)/«
700
1000'/
2 «/.A(2997)/i
r«ATA A(J,l)/t
t/
.15-
DATA CAPO RECOGNITION LARELS
I
I
.10 -
.05 -
— T —•/9AC2697)/"—I 1
500 »/9A(2793)/« 60
80Q >/,A(27.6)/* 90
«/,A(2993)/' WAVE
•/,A(2996)/»-
I •»/»A(6.1)/'V .20 - •
I •/,
I '/,
I •/•
V.AdO. I
'/.A.(14,1)/«E
•/
•IATA LAHEL/'IO
1TE* '-'LAB
DO 3007 1=1,20
9(1.51=9(1,4)
P(I.10)=H(I.<»)
u(I.1?)=R(I,4)
•••COVCPEO
•,'END
»,'SUN
','SHADOW
138
-------
r C,FTIIJ "&INT AWOAY *IH I'jFOR'.'AriON MOT FNTEWFO VIA DATA STATEMENTS
C
)u ?i 1=1. s
?1 MI.1)=A(2«1)
'10 ?? I=??.2S
?? A0 ?3 1 = 1.7
4(Q.l ) -at?. 1)
a ( 1?«1) =4(^.1
« 2)
00 IS 1=1 .29
15 4SrCP(I )=*(!. 1 )
C
c KEGTM ^FADING HATA CAWOS
c
?000 4£40(5.100) COLftL« ALPHA, PATA
100 '•(P»'Ar(?Ain,6F10.0)
c
c IF CARO LA^FL READS 'F.NO' TERMINATE PROCESSING
c
IFICDLdL.EO.LAHELI?) ) GO TO 777
r
C IF C^RO LA4FL PE40S "WATER" «£AO WATER DATA AND PHOCESS
C
IF
-------
r IF Cftwo | «|1PL =?EAf)S 'SHAOOy,! P£4D >?ATA FOP »F.FLFCTANCE STANDARD SHADED
C si INI iG'-n THFN r,u HACK ANO K?K»O ANOTHER CAPO
r
10 lf'(rnL:>L.FrO.LA*ELf4) ) f.O TO 11
r-0 TO 12
11 "JEAfMS.lOD VE
)
r,0 TO .?000
C
C IF CAR') I.A3FL ^EAOS 'LA3« UF.AD IN LABORATORY ANALYSIS RESULTS Tn£N GO
c -AC< Af-in ^FAO ANOTHF.P CAPO
C
12 IF(Cni.rfL.f;O.LA-«FL(6) 1 00 TO 13
r,0 TO 14
13 3FAPI5.101) PAR
'*0 TO 2000
r
C IF CSPO LA9FL »?EADS MO* PF.AO IN SAMPLE IDENTIFICATION AND OTHFR
c -FLATEH INFORMATION AND THEN GO HACK AND RFAO ANOTHER CAPO
c
14 lF(CnL^L.EO.LARFL(H ) GO TO *
GO TO ?000
4 H OEG/UH WIND VELO
PAH(l) .PAP (7) ,PAW(8) ,PAR(9)
10R FO**yAT(?7H LA-^O^ATOBY ANALYSIS REPORT//1 OX . ?1HNONF ILT RESIDUE (105
l)«X.Ffr.l»5H Mr,/L,?OX.19HTOTAL RESIDUE « 105) • 10X.F6. 1 *5H MG/L/10X.1
140
-------
(iri5)>llX.F*.].5H Mf,/L.?OX,27HNONFILT. FIXED "ESIOU
.FS.l .5n Mfi/L)
is, ing) PAR (6) .PAhiiQ) .HAP (5) .PARII 1) .°AR(6)
NFiLT ^FSIOUF. < i«oi .OX.FS.I «SH Mr,/L,?ox.i8HCOLOR (
1UT-C'> TFST) .12X,F«;.l,Sx /IflX.mHKILT RFSIOHE ( ISO) . 1 1 X,F*,. l ,5H MG
?/L«?0<.?nHMQNFILT. VOL ^F.S IOUE « 1 OX.F 5. 1 tSH »«G/L /I OX ,9HTURf*I DI TY,2
TlX.FS.l.^H MTU)
r
C ^EL/»NG=SI-WINniR
nELANG=AflS(OELANG)
IF (OELANG.GT. 180.0) OEL ANG=360.0-OELANG
CALL SU^TRM (W.DELANG.PHI * TPANS1 »2>
C
C CALCULATE TWSMITTANCE OF WIND ROUGHENED SURFACE FOR UPWELLING LIGHT
C tT ANGLE OF OBSERVATION
C
IF(OFLANG.r,T.l0 ?n 1 = 1.20
C
£ CONVERT SHADE DATA RECOWV.n 0'J HIGH REFLECTANCE STANDARD TO WHAT IT WOULD
C -JE^N If THE LOW REFLECTANCE STANDARD HAD BEEN USED INSTEAD
C
->ATIO=3< I .'vlHEFSNI /W( T .NREFSH1
VE(I)=KATIO«(VE(I)-V7(I) )
r
c CALCULATE APPROXIMATE ALPHA
r
4LFA (I) = (vr,(I I-VZ(I) )/W(I
c
c CALCULATE AL°HA PRIME
141
-------
"(, I I )=-/M M-V7I I)
IF (Vf.(I) .LT.n.Ofll J G<> TO 30
r,0 TO 31
ftLFAPd>=n.O
A|.FAd)=TOANS?«l (TK'ANSlMLFAd) ) •( ( SK YTPN-T°ANS1 ) » ALF AP ( I ) ) )
IFIALFAd) .LT.O.nOl) GO 10 32
C r&LC'lL*!1-"
r
3? vw(J)=0.0
ALF* in =0.0
iJHF: SPF.CTUA|.
) /ALFA
?<* •'•«)( i i=o.n
c
C I nan Pf-.f'LFCTANCK; VAi.uFS INTO PLOT
C
CALL °LTARY (V^fA)
c
C -3IMT OUT PI OT OF SPECTRUM
C
wPIT? (ft. 11 1 )
111 ro-M4T ,PAR(9)
3 ro-jTTMUE
C
C PiJ'JC" ')UT DATA ON
C
121
c "BINT TABULATION OF ALL °AW OATA AND INTERMEDIATE JESULTS
c
rO&"AT(A10.9F7.1 J
113 FO^VAT ( 1 SHI SAMPLE NiJMrtFP .A10.10H CONT INUFD///)
i-'PITFCii, IK.)
vw( I ) =ww ( I j »ion.o
»'RITF(6.11S) I .LAMSOAI I) .VZ(I) ,VGS(I) .VESd)
1 I ) . vw ( I )
I 15 KOD(iATdX.I2.I6.<«X.F10.?.6X.F10.?t6X.F10.2fAX.F10.2.6X.F10.2.6X.Fl
,ALFA(I) , ALF API
5 CONTINUE
142
-------
c
C I--OAV 'i(J(-CTJA| UATA F-QM P|.OT ai-'
f
•iO 1* 1-1.?*
)<, a ( I .1 ) =&STOw< I)
C
C '-in h'-CK aNO al-:ftn IN ^OWf 06Ta
c
on ro ?ooo
r
c
C ..'CITE ^POCL^SING TERMJNATFD "
C
777 JPITElh.110)
110 t'O-'MATItSHltNO CAPO FNCO'JNTPhiKO - PPOCESSINfi
143
-------
SUiiPOUTlNE auRTRN(w,OF.LANGiPHl,TRANS.UORD)
C
£ 3 o « e« o<
C
C THIS SUKrtOUflNE CALCULATES Int TKANSMl1TANCE OF THE AIR-WATEK INTEHF
C GIVEM *1ND VELOCITY AND LOOK ANGLE WITH RESPECT TO THE HORIZON AND w
C DIRECTION
C
C
C IS THE WIND VELOCITY IN M/bEC - SUPPLIED BY CALLING PROGRAM
C
C -JELANG IS THE HORIZONTAL ANGLE IN DEGREES BETWEEN SUN AZIMUTH AN'
C POINTING UPwlND - SuPPLltD BY THE CALLING PROGRAM
C
C PHI IS THE SUN ELEVATION IN UEGREtS ABOVE THt HORIZON - SUPPLIED
C CALLING PRObRAM
C
C TRANS IS THE CALCULATED SURFACE TKANSMlTTANCE - RETURNED TO THE
C CALLING PROGRAM
C
C UORD IS A FLAG INDICATING WHETHER CALCULATION IS FOR UPWELLING
C (UOPD=1) OR DOWNWELLING (UORU=2) LIGHT
C
INTEGER UORO
OELANG=DELANG/57.29578
PHl=PHI/b7.2V578
XEN1TH=1.5707963-PHI
C
C CALCULATE CROSS- AND UPWINO INCREMENTS TO ADD TO ANGLES TO ACCOUNT F
C NONPERPENOICULAK INCIDENCE
C
X=COS(DELANO)/TAN(PHI)
DAN&U=ATAN(A)
X=SIN(DELANO)/TAN(PHI)
UANGC=ATAN(A)
C
C CALCULATE VALUES FOR SIGU AND SIGC
C
SIGU=((0.003*(0.00512»W))/Z.U>««0.5
bIGC=SIGU
C
C
C LOOP ON ETA (UPtfINO 'STANDARDIZED1 SLOPE COMPONENT)
C
F.TA=-3.2
PSUM=0.0
bUV=0.0
DO 1 J=1.31
tTA=ETA*0.2
Xl=-3.2
r
C CALCULATE UPWlNU COMPONENT OF TOTAL SLOPE (WIND » SUN EFFECTS)
C
Y=ETA«SIGU
144
-------
ANGU=ATAN(Y)
UN EFFECTS)
C
SLOPE=((bLU»SLU)*(SLC«SLC))««0.5
C
C OBTAIN REFLECTANCE FOR THIS SLOPE
C
THETA=ATAN(SLOPE)
CALL ROES(THETAfREF)
C
C SUM REFLECTANCES WEIGHTED BY THE PROBAdlLlTY OF EACH TIMES THE COSINE
C OF THE INCIDENCE ANGLE TIMES THE AREA
C
SINJ=SIN(THETAI/1.3333
XJ=ASIN(SINJ)
IF(UORO.EQ.l) XsCOS(XJ)
IFIUORD.E0.2) X=COS(THETA)/COS(XJ)
SUM=SUM* ( (1.0-REF)«A»P«AK£A)
IF(UORD.EO.l) PSUM=PSUM»(P«CUS(THtTA)«AHEA)
C
C ADD OTHER HALF OF PROBABILITY FUNCTION
C
3 ANGC=ANGC-OANGC
ANGC=-ANGC»DANGC
IF(ANGU.GT.1.5707963.OR.ANGU.LT.-1.5707963) GU TO 4
145
-------
IF
SLOPE=< ) X=COS
SUM=SUM» «1.0-HEF)»X»P«AHILA)
C
C SUM PROBABILITIES SINCE QISlKlrlU I ION FUNCTION IS UNNORMAL I ZtU
C
1F(UORO.E.Q.1 ) PSUM = HSUM« ( H«CUS ( THiTA ) «AH£A)
2 CONTINUE
C
C BECAUSE OF OOUHLING FOrt SYMMETHY. THE ABOVE LOOP 010 NOT INCLUDE THE
C CASE. CALCULATE VALUES FOrt THIS CASE AND ADD TO SUMS
C
CALL PrtOB (0.0,ETA,M,H,SIGU,S1GC>
1F(ANGU. 01.1.5707963. OR. ANGU.LT. -1.5707963) GO TO 1
SLC=TAN(UANuC)
bLOPE=( (SLU«SLU) • (SLC'SLC) )*«0.5
THETA=ATAN
IF(UORO.EQ.l) X=COS(XJ)
IF(UORO.tQ.2) X=COS(TMETA)/CUS(XJ)
SUM=SUM« ( (1.0-REF)«X»P«AHEA)
IF (UORO.EO. 1 ) PSUMaPSUM* (P«COS (THETA) «AREA)
1 IFIUORO.E0.2) PSUM=PSUM»P
C
C CALCULATE FACTOK TO NORMALIZE PROBABILITY OISTRIbUTION FUNCTION
C
XNORM=1.0/PSUM
IF (UORO.EO. 2) XNORM=XNORM/COMZEN1TH)
C
C NORMALIZE SUM OF THE REFLECTANCES
C
SUM=SUM4XNORM
C
C CALCULATE SURFACE TRANSMI T TANCE
C
TRANS=SUM
UELANG=OtLANG857. 29578
METUHN
END
146
-------
c
C '>'.:>< .« ,lw««040'>4-0i}«4ri»4f<>il"ao<»e»«l»»a««»««« •»«»»«<»«« » Ofc «« fl » O «« O O O O »«««»<
c
C TnlS S JP "OUT I ME LOADS CFFLFCTAisjrE" VALUES INTO T*E APPROPRIATE LOCATIONS IN
r iv fiJWAY TO HE MINTED TO KO-M THf PLOT OF SPFCTKAL REFLECTANCE.
C c-ipjFS 4°F '•'NTr'rtF.n AT 10 MM INTERVALS WITH LINEAR INTERPOLATION SUPPLYING
c T^K VAI nt-'S wHKiJi: ACTUAL MEASUREMENTS DO NOT Exi«;r. VALUES BELOW o.o
C fcMP> \HnvF H'?-* A^E Tt^UNCATFO.
C
C
C VW IS THE A-)
PVwC^JsViKtS) •( (VW(A)-VW(S) )/*.0)
) =VW(5) * ( ( Vw(6)-Vw(5) ) /2.0)
)=Vto(5) *( (VW(6)-VW(5) )/ 1.133)
ilsVWtfe) »( (VM(7)-VVi(6) JM.O)
i ni =vw«hi * ( (vwm-vw(6) >/2.0)
! 1 )=VW(b» »( (vwt7)-VW(ft) )./ 1.333)
KV"(1?)=\/W(7)
FVW<13)=VW(7)»((VW(8)-VW<7))/3.0)
147
-------
c
c
c
Vv.1 (
>n=.)=vwnj
i(17)Ttfw(n)
i ( 19) =Vhl (V)
i=VW(9)
(VW(9)-VW(d)
<((2?)=VW(10)
3)=VW(10)*i
.5)
!si
(VW(ini-vw(9J J/4.01
'1.J33)
1/1.5)
i=VW(H)*( (\/W(12i-VW(ll} 1/1.331)
FVW(29)=\/W(12)
I=VW(13)
i=VW(13)«
'=VW(13)»
=VW(13)«
KVM3M=\
i=VW(U)«
.(37)=Vi*(14) «
l=VW(15)
i=Vto(15)«
FVW(«*0)=VW(15)*
=VW(15)«
=VW(16)
=VW(16»*
=VW(16)»
=VW(17)
=VW(171*
=VW(17I*
=VW(17I*
=VW(17)«
(VVK14)
(VW(14J.
(VW(lS)-
VW(13) 1/4.0)
vw(13) )/2.0)
vw(i3) )/ 1.333)
VW(14) )/4.0)
VW(14) )/2.0)
VW(14) j/1.333)
(VW(16)-Vw
(VW(16)-VW(15) 1/1.667)
(VnM lfe)-V'W
=VW(18)
=VW(lo)
=VW(19)
=VW(19I
=VW(19)
(VW(17)-VW(16))/3.0)
7)-\/W(16) 1/1.5)
Vto(17))/1.667)
VW(17))/1.25)
(VW(|8)-VW(17) 1/2.5)
(VWU81-VWU7) )/?.5)
(VW(18)
(VW(18)
(VW(19)-VW<1*))/3.0)
ViV(19) )/4.Q)
VW(19) J/2.0)
V«((19) 1/1.133)
(Vtt(?0)
(VW«?0)
(VW«20)
F.XDANntD SEFLECTftNCE ARPAY INTO PPINT A«RAY
00 S 1=1 «5R
x=(FVrt(I)«100.0)*0.5
IF (IVW.f,T.?5) IVW = ?5
IF (IVW.LT.O) IVW=0
IS=IS*1
148
-------
IF i is.GT.inj
IF (IDX.tQ.P'j) r,Q TO
S ' O'JT
"KT
* NP>
IS)
149
-------
HI '(•'llJFINF SKY l*.S«YTf.N.SKYKEF)
0<' J, •"«•« ^ Jfc - >>«0 J44 300 »{<_ u" V404-4IOO40 .1 tt fc » » « 4 « « «> 0 4 O •> 33O444 > v 4 O -i 4 fa O O 4 4 4 4 4 O
C THIS SLil>^i"iiirir4F CALCULfllFS TH£ TRANSMISSION OF LIGHT aCPOSS THF MP-WATE*
C 1NTFJF6CK A« A FUNCTION OF -VINO VELOCITY. THF. °EFl_F.CT ANCF OF
C ^KYI. IG-IT IS ALSO CALCULATED
C
C
C •< IS -vl»'0 VfLUCITY IM Ml:TtDS/SFCOND SUPPLIEO BY THE CALLING
r
C SKYT«N IS TMF SKYLIGHT T = AMS'iI SS I ON FACTOR "ETUONED TO THE CALLING PR
C
C SK.1PK.F IS TriE SKYLIGHT REFLECTANCE HEUlPNED TO THE CALLING PPOGflAM
C
T. 0.0001) T,0 TO 1
r,0 TO ?.
\ SKY^EF=0.0?66
IF (w.CiT.0.5) SKYPFF = 0.02
? |F(H.f,T.S.O) SKYHN=].m*<0.0006«(W-5.0)
IF(V.LE.S.O)
150
-------
r
r e e ;• t a
r
C THJ<; SUH^OUTINF CAI.CUI.ATF.S THF «F.FI.FCTANCF. OF THE SIP-WATFP
C ^3 UNHPLftm^FO LIGHT USING FHFS.'jF|. *S FOLIATION 4MD flSSUMlNG M = 1.333
C
r -A • • •> tt
C
C THtia IS THE ANGLE OF INCUIFMCF. IN RADIANS MKA^UWEO WITH PKS"FCT TO THI
C SURFACE NORMAL - SUP^LIFll ^Y THE CAILING PROGRAM
C
c WEF is THF CALCULATFO «;UJFACF: REFLECTANCE - AETUPNED TO CALLING PROGRA*
r
"E4L NJ
IF(THF.TA.LT. 0.017<.S31) GO TO 1
. 3.133
J=ASIN(SJ)
IPJ=I*J
IMJ=I-J
SSIPJ=STN(IPJ)»SIN(IPJ)
SSIMJ=SIN(IMJ)»SIN(IMJ)
TSI"J=TAN(IPj)«TAN(IOj)
0.5»( (SSIMJ/SSIPJ)*(TSIMJ/TSIPJ)
GO TO 777
777
151
-------
(XJ.FTA.w.PtSIfill.SIGC)
c
C O 5 O . Ir 1. C >OO^3Ci/<, ^OIO '.',«'(', iiiffC^-UOOft «.«w ••»
c
C THIS r»l»HPOUlPJE C AI.CULATFS THE PROBABILITY OF OCCURANCE OF A GIVEN SEA
C SLOPE «IHKN "INT VELOCITY IS KNOWM. THE CALCULATION IS BASEO ON A
C PoOH-iRlLlTr OISTi*IHUTION TtlMCTION
C THIS A^PC-OftCH IS ^ASEO ON TH£ WOKK OF COX AND
C
C
C XI AND rTA AWE THE 'STflNOAWOI/FO' C»OSS- ANH UPWIND SLOPE COMPONENTS
C SUPPLIEO 9Y THE CALLING PBOGPAM
C
C v, IS THE •< I NO VFLOCITY IN M/SEC - SUPPLIED «Y THE CALLING PROGPAM
C
C ° I? THE CALCULATED PWOP4RILITY (UNNOR-ALIZ^D) - RETURNED TO THE
C r ALL ING P"1G3AM
r
C CAlCULATEO FROM WIND VELOCITY AND RETURNFD TQ THE CALLING PROGRAM
C
C
C CALCULATE THE SLOPE STANDARD DEVIATIONS FOR CROSS- AND UPWIND DIRECTIONS
C
=( (0.n03»(0.005i;>«W)l/Z.O)«»0.5
C
C CALCULATE TH£ INDIVIDUAL TERMS IN THE PROBABILITY DISTRIBUTION FUNCTION
C
A=n.l5915/(SIGU»SIGC)
-=-0.5«< (XI»XI)*
-------
APPENDIX C
ALGOR
PROGRAM LISTING
i5o
-------
Al GU* (INPUT. OUTPUT, TAPF.5= INPUT. TAPE* = OUT PUT, PUNCH)
c
C J o o i ,o.>«"}*i>««<»<»o»*o#u.to., n,«*n» •<>'.>4<'>oi>4'.>«eooa«ctto-«<>o«««oea««4»4a904oooeo0
C
C THIS PPOC.RA" TAKtS 45 INPUT PUNCHED CAHOS OUTPUT BY VOLR£F WHICH
C CONTAIN -ATF.P VOLUME wF.FLFC T ANCE AND WATER SAMPLE ANALYSIS DATA.
C FROM THIS DATA MULTJbPECTRAL OUAOWATIC ALGORITHM'S ARE CALCULATED TO
C- PREDICT ANY OF THE SAMPLE ANALYSIS PARAMETERS FROM SELECTED WAVELENGTHS
C
C THIS PROGRAM IS INTENDED FOR USE WITH DATA GENERATED BY THE EPA EMSL/LV
C SPfCTPOMF.TE* WHICH SAMPLES 20 WAVELENGTHS. THUS DIMENSIONS OF ARRAYS ARE
C SET ACCORDINGLY
C
C THE MAXIMUM TRAINING SET SIZE IS 200
C
lOURLE PRECISION COV
DIMENSION COV (57 .57) , PHI (40) , I USE (40) .DATA (40, 200 ) ,V(M) ,COM(8)
DIMENSION VP(40)
OIMfNSION GT(200,9) ,ZTUR(20)
OATA ENO/'ENO •/
XNS=0.0
C
C »EAD IN PARAMETERS FOR THIS PUN
C
OEAO(5«96> NCtXNOISE.IPAR.IPUNCH
96 FQRMATU10.F10. 0.2110)
HfEAD(5,95) (lUSE(I) ,1 = 1 ,<»0,2)
95 FORMAT 4RITE(6.120) SAMPNO
120 FORMAT(IX.AIO)
^EADCS.100) (OATA(N.I) ,N=1.40«2)
100 FORMAT (lOFft.O)
C
c SUBTRACT ZEHO TURBIDITY REFLECTANCE VALUES AND SQUARE DATA
154
-------
I -0
DO 1 J=l .40.2
')ATA(j,I)=nATA(J,I)-ZTUP»DATA(M,I) )
00 4 L=l »NC
ANnnn NOISE BY EXPANDING DIAGONAL ELEMENTS
c
x=1.0*XNOISE
no <*04 n = i,<»o
404 covdi,in=cov(iitii)»x
c
C INVENT X TRANSPOSE X MATRIX
c
CALL MATINV(COV,NC,OET)
C
C CALCULATE COEFFICIENTS V PRIME
C
DO ft 1=1 -NC
00 6 J=1«NC
6 VP(I)=VP
301 FORMAT114H1WEIGHT VECTOR//)
155
-------
F(6tll2> V
112 KO^MATiablS.S/)
•'Rim 6*11 3)
113 -0»MATUHl)
C
c A^OI Y ALGORITHM ro TKAINING SET DATA
c
wWl IE (ft. 102)
10? FORMAT {,?5H TRAINING SET rtEPOHT CAKD//1 OX . 1 2KJROUNO FHUTH. 1 OX . 1RHHE
1 viOTF ^E 4SUREMENT 1 1 3
rRHTOT=0.0
no 10 I=I.NS
o=0.0
no 11 J=I»NC
L=IUSE(J)
f:RR=P-GT(I.IPARJ
C
C WRITE AND PUNCH TRAINING SET EWROR DATA
C
uRITE<6.110) GTUiIPARl.PtERR
110 e-OHMAT(12X,K7.2tl7X,F7.2i!7X.F7.2)
IF
-------
sijr-POUTINF MATlNVUPPAY.NORnLR.DET)
riOUHLE PHEC1SION AKPAY.AMAX.SAVE'»A.R.C
•tli-.F'-JSION ARRAY (57,57) .IK(S7).JK(57)
10 ')ET=1.0
11 -10 100 K=1.NOROER
C
c FIND L'^GEST ELEMENT APP.AY IN REST OF MATRIX
c
AMAX=0.0
21 no 30 i=K.NOK»neR
DO 30 J=K,NOROER
4=DARS(AMAX)
H=APPAY(I.J)
C=DAHS(B)
?3 IF(A-C) 24.24,30
2<, AMAX = ARPAY(I.J)
IK(K)=I
JK(K)=J
30 CONTINUE
C
c INTERCHANGE ROWS AND COLUMNS TO PUT AMAX IN ARRAYK,K)
c
31 IF(AMAX) fcl.32»<»l
32 n£T=0.0
r,0 TO 140
41 I=IK(K)
JF(I-K) 21.51,43
43 00 50 J=1.NORDER
SAVE=ARRAY(K,J)
4RRAY(K,J)=ARRAY(I,J)
50 4RRAY(I.J)=-SAVE
51 J=JK(K)
IF(J-K) 21.61,53
53 00 60 I=1.NOROER
SAVP=AR«AY(I,K)
ARPAY(I.K)=ARRAY(I,J)
60 ARRAYd.J): -SAVE
C
c ACCUMULATE ELEMENTS OF INVERSE MATRIX
c
61 00 70 I=1,NORDER
IF(I-K) 63,70,63
63 4RSAY(I.K)= -ARRAY(I,K)/AMAX
70 CONTINUE
71 00 80 I=liNOROER
•^0 80 J=1.NORDER
IF(I-K) 74,a0.74
74 IF(J-K) 75,80,75
75 4RWAY(I•J)=ARRAY(I,J)*ARRAY(I,K)«ARRAY(K,J)
80 CONTINUE
81 00 00 Jsl.NOROER
TF(J-K) 83,90,83
83 ARRAY(K,J)=ARRAY(K.J)/AMAX
00 CONTINUE
ARRAY(K.K)=1.0/AMAX
100 DET=OET«AMAX
157
-------
C ^ESTnWc GrfOKtflNG OF
C
'>0 130 L = l ,MOROER
J=IK(K)
TK(J-K) 111,111,105
105 10 110 I=1,NOROEP
( I .K J =-AHRAY ( I , J)
110 4«*
-------
TECHNICAL REPORT DATA
(Please read Inunctions on the reverse before completing)
REPORT NO
EPA-600/4-80-019
3 RECIPIENT'S ACCESSIOf*NO
TITLE AND SUBTITLE
MULTISPECTRAL TECHNIQUES FOR REMOTE MONITORING
OF SEDIMENT IN WATER: A feasibility investigation
5 REPORT DATE
March 1980
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
Ronald J. Holyer
8. PERFORMING ORGANIZATION REPORT NO
PERFORMING ORGANIZATION NAME AND ADDRESS
Lockheed Electronics Company, Inc.
4220 S. Maryland Parkway
Suite 120
Las Vegas, Nevada 89109
10. PROGRAM ELEMENT NO.
1HU620
11. CONTRACT/GRANT NO.
2 SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency—Las Vegas, NV
)ffice of Research and Development
Environmental Monitoring Systems Laboratory
Las Vegas, Nevada 89114
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/07
5. SUPPLEMENTARY NOTES
NTIS-Only distribution
6. ABSTRACT
A data acquisition and analysis program has been undertaken to demonstrate the
feasibility of remote multispectral techniques for monitoring suspended sediment
concentrations in natural water bodies. Two hundred surface albedo measurements (400
:o 1,000 nanometers) were made at Lake Mead with coincident water sampling for
laboratory analysis. Water volume spectral reflectance was calculated from the
recorded surface albedo, and volume reflectance-suspended sediment relationships were
investigated. Statistical analysis has shown that quantitative estimates of
nonfilterable residue (105°C) and nephelometric turbidity can be made from volume
spectral reflectance data with sufficient accuracy to make the rnultispectral technique
feasible for sediment
monitoring.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b IDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Croup
remote sensing
turbidity
spectroscopy
suspended sediment
water quality
Lake Mead
multispectral
techniques
08 H
13 B
14 B
2U F
3. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19 SECURITY CLASS (Tna Report I
UNCLASSIFIED
21 NO Or PAGES
174
20 SECURITY CLASS (This page I
UNCLASSIFIED
22 PRICE
EPA Form 2220-1 (9-73)
-------
INSTRUCTIONS
1. REPORT NUMBER
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2. LEAVE BLANK
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4. TITLE AND SUBTITLE
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type or otherwise subordinate it to main title. When a report is prepared in more than one volume, repeat the primary title, add volume
number and include subtitle for the specific title.
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approval, date of preparation, etc.].
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zation.
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IS. SUPPLEMENTARY NOTES
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To be published in, Supersedes, Supplements, etc.
16. ABSTRACT
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significant bibliography or literature survey, mention it here.
17. KEY WORDS AND DOCUMENT ANALYSIS
(a) DESCRIPTORS - Select from the Thesaurus of Engineering and Scientific Terms the proper authorized terms that identify the major
concept of the research and are sufficiently specific and precise to be used as index entries for cataloging.
(b) IDENTIFIERS AND OPEN-ENDED TERMS - Use identifiers for project names, code names, equipment designators, etc. Use open-
ended terms written in descriptor form for those subjects for which no descriptor exists.
(c) COSATI FIELD GROUP - Field and group assignments are to be taken from the 1965 COSATI Subject Category List. Since the ma-
jority of documents are multidisciplinary in nature, the Primary Field/Group assignment(s) will be specific discipline, area of human
endeavor, or type of physical object. The application(s) will be cross-referenced with secondary Field/Group assignments that will follow
the primary posting(s).
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EPA Form 2220-1 (9-73) (Ravune)
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