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Thesis/Dissertation Collections
8-1-1997
Synthetic image generation of factory stack and
water cooling tower plumes
S. Didi Kuo
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Recommended Citation
SYNTHETIC IMAGE
GENERATION OF FACTORY
STACK AND
WATER COOLING
TOWER PLUMES
by
S. Didi Kuo
Captain, USAF
B.S. United States Air Force Academy (1988)
A dissertation submitted in partial fulfillment
of the requirements for the degree of Ph.D.
in the Chester F. Carlson Center for Imaging
Science in the College of Science of the
Rochester Institute of Technology
August 1997
Signature of the Author
_
Accepted by
Harry E. Rhody
CHESTER F. CARLSON
CENTER FOR IMAGING SCIENCE
COLLEGE OF SCIENCE
ROCHESTER INSTITUTE OF TECHNOLOGY
ROCHESTER, NEW YORK
CERTIFICATE OF APPROVAL
Ph.D. DEGREE DISSERTATION
The Ph.D. Degree Dissertation of S. Didi Kuo
has been examined and approved by the
dissertation committee as satisfactory for the
dissertation requirement for the
Ph.D. degree in Imaging Science
Dr. John Schott, Dissertation Advisor
Dr. Roger Easton
Dr. Hsien Lee
Dr. Michael Kotlarchyk
DISSERTATION RELEASE PERMISSION
ROCHESTER INSTITUTE OF TECHNOLOGY
COLLEGE OF SCIENCE
CHESTER F. CARLSON CENTER FOR IMAGING SCIENCE
Title of Thesis:
Synthetic Image Generation of Factory Stack and Water
Cooling Tower Plumes
I, S. Didi Kuo, hereby grant permission to the Wallace Memorial Library of R.I.T. to
reproduce my thesis
in
whole or
in
part. Any reproduction will not be for commercial use
or profit.
Signature:
_
SYNTHETIC IMAGE
GENERATION
OF
FACTORY
STACK
AND WATER
COOLING
TOWER PLUMES
by
S. Didi Kuo
Submitted
to the
Center for
Imaging
Science
in
the
College
of
Science
in
partial
fulfillment
of
the
requirements
for
the
Ph.D. Degree
at
the
Rochester Institute
of
Technology
ABSTRACT
Remote sensing
ofcooling
tower
andfactory
stack plumesmay
provide uniqueinformation
onthe
constituents of
the
plume.Potential
information
ofthe
power generatedby
the
plant orthe
chemical composition ofthe
factory
productsmay
be
gatheredfrom
thermal
emission and absorptionin
the
infrared
band,
orfrom
scattering
oflight
in
the
visibleband.
A
new modelfor
generating
syntheticimages
of plumeshas been developed
using
DIRSIG,
aradiometrically
based
ray-tracing
code.Existing
modelsthat
determine
the
characteristics ofthe
plume(constituents,
concentration,
particulatesizing,
andtemperature)
are usedto
constructthe
plumein DIRSIG.
The
effectsof scatteredlight
using Mie
theory
and radiativetransfer,
as well asthermal
self-emission andabsorption
from
withinthe plume,
aremodeledfor different
regions ofthe
plume.Both
single andmultiplescattering
methods are available.The ray-tracing
accountsfor
radiancefrom
the plume,
atmosphere,
andbackground.
'Synthetic
generatedimages
ofacooling
tower plume,
composed of waterdroplets,
and afactory
stack
plume,
composed of methylchloride,
are producedfor
visible,
MWIR,
andLWIR
bands. Images
ofthe
plumefrom different
sensor platforms are also produced.Observations
aremade onthe
interaction
between
the
plume andits
background
and possible effectsfor
remotesensing.Images
of gas plumesusing
a
hyperspectral
sensor areillustrated.
Several sensitivity
studies aredone
to
demonstrate
the
effects of changesin
plume characteristics onthe
resulting image.
Inverse
algorithmsthat
determine
the
plumeeffluent concentration are
tested
onthe
plumeimages.
A
validationis done
onthe
gas plume modelusing
experimentaldata
collected on aSF6
plume.Results
showthe
integrated
plume modelto
be in
good agreement withthe
actualdata from five
to
onehundred
metersfrom
the
stackexit.The scattering
modelsaretested
againstMODTRAN. The
validity
andlimitations
ofthese
models arediscussed
as a result ofthese tests.
Finally
two
atmosphericscattering
Acknowledgments
I
wishto thank
my advisor,
John
Schott,
for his
help
and guidance.His
suggestionfor
this
researchtopic,
and continueddirection,
enabled meto
successfully
completemy dissertation.
I
am also gratefulto
my
committee:Roger
Easton,
Hsien
Lee,
andMichael
Kotlarchyk.
They
each offered me advicefrom
their
areas of expertisethat
helped improve
the
quality
ofmy
dissertation.
I
am appreciative ofthe
supportfrom Scott
Brown
andRolando
Raqueno.
I
could neverhave
finished
if
notfor
their
help
withthe
countlesshours
ofdebugging
code.There
were also several others outside ofRIT
that
gave assistanceto
me.Bill
Powers,
Lance
O'Steen,
andJack Fansalow
provided me withthe
necessary
plume modelsI
needed.Jim
Godfrey
andhis
organizationgave me experimentaldata
for
validation ofmy
work.Thanks
alsoto
Gus
Braun
for
the
color science adviceandWendy
Abbott
for
Dedication
I
wishto
dedicate
this
researchto
my
family,
especially
my
motherandfather.
I
could nothave
gottenthis
far
withoutthe
encouragementfrom my
parentsin
the
pursuit ofknowledge.
I
also wantto
thank the
friends I've
made overthe three
years whilehere in Rochester.
The
friendship
they
provided gave me awelcome
break
from
the
long
stretches ofstudying
anddoing
research,
and madelife
enjoyableup
here in
the
northerntundra.
Most
ofallI
wantto thank
God for His
grace which enabled meto
completemy
work.Only
He
can makethe
real rainbows and sunsetsthat
awe andinspire
us.They
surely
are a sign ofHis
TABLE OF
CONTENTS
LIST
OF FIGURES
X
LIST
OF
TABLES
XIV
1.
INTRODUCTION
1
2.
THEORY
3
2.1 Consideration
for
Remote Sensing
of
Plumes
3
2.1.1
Factory
Stack Plumes
3
2.1.2
Cooling
Tower Plumes
5
23.
Plume Modeling
6
2.2.IJPL Plume
Model
6
2.2.2
LANL Plume Model
7
23 Interaction
of
Light
with the
Plume
8
2.3.1 Gas Absorption
8
2.3.2
Scattering
10
2.3.3 Extinction
14
2.3.4 Thermal Self-Emission
75
2.3.5
Radiative Transfer
16
2.4 Governing
Equations
forRemote Sensing
of
Plumes
20
2.4.1 Solar
andSelf-emissive
Radiation Incident
onthe
Plume
1
21
2.4.2 Radiationfrom
the
Plume
23
2.4.3
Upward
Looking
Sensor
25
2.4.4
Downward
Looking
Sensor
26
3. MODELING
AND ALGORITHM DEVELOPMENT
28
3.2
LANL Plume Model
28
3.2.1
Running
the
LANL
Plume Model
29
3.2.2
Building
the
LANL
ACAD
Model
30
3.3 JPL
Plume Model
32
3.3.1
Running
the
JPL Plume Model
32
3.4 Plume Model Translator
38
3.5 DIRSIG
42
3.5.1
Initializing
DIRSIG
42
3.5.2
Ray-tracing
through
Plume Regions
44
3.5.3 Multiple
Scattering
45
3.5.4 Integrated JPL Plume Model
47
3.5.5 Other Special Cases
48
4.
RESULTS
49
4.1 Gas Plumes
49
4.1.1 JPL
ACAD Model
49
4.1.2 Integrated JPL
Model
54
4.2
Scattering Plumes
62
4.2.1
Homogenous
(Water
Droplet)
Plume
62
4.2.2 LANL
Cooling
Tower
Plume
78
5.1 Validation
ofGas Plume Model
82
5.1.1 Experimental
Description
82
5.1.2 Creation
of
the
DIRSIG Background
Scene
84
5.1.3 Validation ofACAD JPL Model.
86
5.1.4 Validation ofIntegrated JPL Model
91
5.2 Scattering Validation
withMODTRAN
98
5.2.1
MODTRAN.
!
99
5.2.2 Results
100
53
The Rainbow
104
5.3.1
Theory
104
5.3.2
Procedure
106
5.3.3 Results
108
5.4 Sunset
with
Red Clouds
1 13
6. CONCLUSIONS AND
RECOMMENDATIONS
119
6.1
Summary
119
6.2
Conclusions
119
APPENDIX A: MIE
SCATTERING
THEORY
124
APPENDIX
B:
IMPORTANCE
OF
MULTIPLE
SCATTERING IN
PLUMES
..130APPENDIX C: PARTICLE SIZE
DISTRIBUTION
135
APPENDIX
D:
TWO-STREAM
APPROXIMATION
FOR RADIATIVE
TRANSFER
IN
WATER CLOUDS
140
APPENDIX E
:
TESTING INVERSE ALGORITHMS ON
PLUME IMAGES
....144APPENDIX F: CREATING
A
COLOR
IMAGE IN DIRSIG
150
APPENDIX G: ADDING ADDITIONAL GASES
TO THE
GAS
DATABASE
...151APPENDIX H:
DIRSIG
PLUME FILE FORMATS
152
APPENDIX I:
NTS VALIDATION
FILES
158
LIST OF FIGURES
Figure 2-1. Angular
Scattering
Distribution for
aWater droplet in
the
Visible
Wavelength
13
Figure 2-2. Angular
Scattering
Distribution for
aWater Droplet
in
the
MWIR
.13
Figure
2-3.
Source Terms for Radiative Transfer
18
Figure
2-4. Flux Streams for Two-Stream Approximation
18
Figure 2-5. Atmospheric
Transmission,
Solar
Irradiance,
andThermal
Self Emission
21
Figure 2-6. Sources
ofRadiation
ontothe
Plume
22
Figure 2-7.
Scattering
withinthe
Plume
23
Figure
2-8. Upward
Looking
Sensor
26
Figure
2-9.
Downward
Looking
Sensor
27
Figure 3-1. Process
Flow
in
Building
Plume
Scene
28
Figure 3-2.
I/O Flow
for BuildLANL
31
Figure
3-3. ACAD LANL Plume Model
31
Figure 3-4. Scene Coordinates for JPL Plume
Model
34
Figure 3-5.
I/O Flow
for BuildJPL
35
Figure 3-6.
Side
View
ofSingle Slice in
ACAD
Model
36
Figure
3-7. ACAD JPL
Plume
Model
withThree
Regions
37
Figure 3-8.
ACAD
JPL
"Wander"Plume Model
37
Figure 3-9. Flowchart
for
PMT
Code
39
Figure
3-10.
Ray Tracing
Through Rectangular Plume Model
44
Figure 3-11. Multiple
Scattering
Sources
for
Downward
Looking
Sensor
.'.46
Figure
3-12.
Multiple
Scattering
Sources
for
Upward
Looking
Sensor
47
Figure
4-1.
Hyperspectral images
ofCH3C1
plumefrom
an airborne sensor at3.33
um(a)
and10
urn(b)
and a groundbased
sensorat3.33
um(c)
and10
um(d)
50
Figure
4-2. JPL
"wander"plumefilled
with waterdroplets
(left,
visibleband)
and methyl chloride(right,
3.33 um)
52
Figure
4-3. 10
urnImages
ofCH3C1
withVariable Concentration
53
Figure
4-4. 10
umImages
ofCH3C1
withVariable Temperature
53
Figure 4-8. Integrated JPL
modelimages from
anairbornesensor at3.33
um(a)
and10
um(b)
and a ground
based
sensor at3.33
um(c)
and10
um(d)
55
Figure
4-9.
Downwind Characteristics
ofIntegrated Plume Model
56
Figure 4-10. Reduced Gas Release Rate Images
at3.33
um(a)
and10
um(b)
andContrast
Ratio
(c)
57
Figure 4-11.
Decreased Plume Temperature Images
at3.33
um(a)
and10
um(b)
andContrast
Ratio
(c)
58
Figure
4-12.
Lowered Atmospheric
Stability
Images
at3.33
um(a)
and10
um(b)
andContrast Ratio (c)59
Figure 4-13. Absorbance Curves for Methyl Chloride
(CH3C1)
in
MWIR
(a)
andLWIR
(b)
60
Figure
4-14. Plume Images
atDesignated
Spectral
Bands
61
Figure
4-15.
Integrated JPL Model
withTime
Varying
Meterological
Conditions
62
Figure 4-16.
Maximum Optical Depth for Four Plume
Number
Densities
63
Figure 4-17. Visible Images
ofPlume
atNoon
withVarying
Number
Density
64
Figure 4-18. Optical
andRadiometric Properties
for
Noon
Plumes
65
Figure
4-19.
Visible
Images
ofPlume
atNoon
Using
Single
Scattering
Model
66
Figure 4-20.
Optical
andRadiometric Properties
for Noon
Plumes
Using
Single
Scattering
Model
67
Figure
4-21. Visible
Images
ofPlumeat8:00 A.M.
68
Figure
4-22. Optical
andRadiometric Properties
for 8:00
A.M.
Plumes
69
Figure 4-23.
Visible Images
ofPlume
at8:00 A.M.
Using
Single
Scattering
Model
70
Figure
4-24.
Optical
andRadiometric Properties
for 8:00
A.M.
Plumes
Using
Single
Scattering
Model
....71
Figure
4-25. Visible Images
ofPlume
at11:00 A.M.
for
Upward
Looking
Sensor
72
Figure
4-26.
Optical
andRadiometric Properties
for
1 1
:00A.M.
Plumes
for Upward
Looking
Sensor
73
Figure
4-27.
Visible
Images
ofPlume
at1 1
:00A.M.
for
Upward
Looking
Sensor
Using
Single
Scattering
Model
74
Figure 4-28. Optical
andRadiometric Properties
for
1 1
:00A.M. Plumes
for
Upward
Looking
Sensor;
Using
Single
Scattering
Model
.... _ ~74
Figure
4-29.
Visible Images
ofPlume
at8:00 AM.
for
Upward
Looking
Sensor
75
Figure
4-30. Optical
andRadiometric Properties
for 8:00
A.M. Plumes
for
Upward
Looking
Sensor
76
Figure 4-31. Visible Images
ofPlume
at1
1
:00A.M.
for
Upward
Looking
Sensor
Using
Single
Scattering
Model
77
Figure
4-32. Optical
andRadiometric Properties
for
8:00 A.M.
Plumes for
Upward
Looking
Sensor
Using
Single
Scattering
Model
77
Figure
4-33. LANL Plume Properties
79
Figure
4-34.
Visible, MWIR,
andLWIR Images
ofthe
LANL
plume model80
Figure
4-35. Optical Properties
ofLANL Plume
80
Figure
5-1. Absorbance Curve
for
SF6at
10
ppm-m83
Figure
5-3.
SF6
Plume Images from Band
1
(left)
and2
(right)
ofTI
ILRS-RS18c
84
Figure 5-4. DIRSIG Scene
ofNTS Background
85
Figure 5-5. Overhead
andSide View
ofACAD
Plume Model
(Band
1)
87
Figure 5-6. ACAD Plume Model in Band 1
(left)
andBand 2
(right)
using NTS
Look Angles
87
Figure
5-7.
Downwind Radiance Profile in Band
1
88
Figure 5-8. Downwind Radiance Profile in Band 2
88
Figure 5-9.
Cross-sectional Radiance Profile
ofPlume
7
Meters Downwind in Band
1
89
Figure 5-10.
Cross-sectional Radiance Profile
ofPlume7
Meters
Downwind
in Band 2
..89
Figure
5-11.
Cross-sectional Radiance Profile
ofPlume100
Meters
Downwind
in Band 1
90
Figure 5-12. Cross-sectional Radiance Profile
ofPlume
100
Meters Downwind
in Band 2
90
Figure 5-13. Overhead
andSide
View
ofIntegrated JPL Plume
Model
91
Figure 5-14.
Measured Plume Temperature Downwind from Stack
92
Figure 5-15. DIRSIG Plume Temperature
92
Figure 5-16. DIRSIG Column
Density
Downwind
from Stack
93
Figure
5-17.
Column
Density
Profile
at100
Meters Downwind
ofStack
94
Figure
5-18.
Integrated Plume Model in
Band 1
(left)
andBand 2
(right)
using NTS Look Angles
94
Figure 5-19. Downwind Radiance
Profile
in
Band 1
95
Figure 5-20.
Downwind Radiance
Profile
in
Band
2
95
Figure
5-21.
Cross-sectional
Radiance Profile
ofPlume 7
Meters
Downwind
in
Band 1
96
Figure
5-22.
Cross-sectional
Radiance Profile
ofPlume 7 Meters Downwind in
Band
2
96
Figure 5-23.
Cross-sectional Radiance
Profile
ofPlume
100 Meters Downwind
in
Band 1
97
Figure 5-24.
Cross-sectional
Radiance Profile
ofPlume 100 Meters Downwind
in
Band
2
97
Figure
5-25.
Geometries
usedfor
Scattering
Validation
,100
Figure
5-26.
DIRSIG-MODTRAN Contrast
for
Downward-looking
Noon Case
101
Figure 5-27.
DIRSIG-MODTRAN
Contrast for
Downward-looking
8:00 A.M. Case
102
Figure 5-28. DIRSIG-MODTRAN
Contrast for
Upward-looking
Noon
Case
103
Figure
5-29.
DIRSIG-MODTRAN Contrast
for
Upward-looking
8:00
A.M.
Case
103
Figure
5-30. Angular
Scattering
Coefficient
for
aWater Droplet
at450
nm __106
Figure
5-31.
Geometry
Used
to
Create
Rainbow
Scene
107
Figure
5-32. Rainbow
with20
um meandroplet
size and associated sizedistribution
and angularscattering
coefficient charts109
Figure
5-33. Rainbow
with100
um meandroplet
size and associated sizedistribution
andangularscattering
coefficientcharts110
Figure
5-34. Rainbow
with200
um meandroplet
size and associated sizedistribution
andangularFigure 5-35. Full DIRSIG Rainbow
112
Figure 5-36. Actual
andDIRSIG
(1815)
Sunset Images
114
Figure
5-37.
Actual
andDIRSIG
(1830)
Sunset Images
115
Figure 5-38. DIRSIG
(1840)
Sunset Image
116
Figure
5-39. Solar Irradiance
onClouds
atThree Sunset Times
117
Figure 5-40. Radiance from Center
andFringe
ofCloud
118
Figure
A-l.
Geometry
ofIncident
andScattered Fields
124
Figure
B-l. Plume Layer Model Constructed for MODTRAN3
131
Figure B-2. Average Spectral Single
Scattering
Albedo
ofPlume
132
Figure B-3.
Spectral Transmission for Different Plume Models
133
Figure B-4. Spectral Ratio
ofMultiple
to
Single
Scattering
for Plume
Models
134
Figure B-5. Spectral Ratio
ofScattered
to
Total Radiance for Plume Models
134
Figure C-l.
LANL Modified Gamma Size Distribution
136
Figure C-2. MODTRAN Modified Gamma Size Distribution
136
Figure C-3. MODTRAN Lognormal Size Distribution
137
Figure C-4. Effects
ofVariance in
Size
Distribution
onExtinction
Efficiency
139
Figure D-l.
Two-Stream
Approximation using
Plane
Parallel
Layer
140
Figure E-l.
Estimating
Plume
Depth
.145
Figure E-2. LWIR
andMWIR Images
ofSingle
Region JPL ACAD Plume
146
Figure E-3. Estimated VMR
Image
andValues
ofPlume
in
LWIR
(a)
andMWIR
(b)
147
Figure E-4. Estimated
VMR
Image
andValues
ofPlume
in
LWIR
(a)
andMWIR
(b)
for
Plume
at
Ambient Temperature
148
Figure E-5.
LWIR
andMWIR Images
ofSingle Region JPL ACAD
Plume
148
Figure
E-6.
Estimated
VMR Image
andValues
ofPlume in LWIR
(a)
andMWIR
(b)
from
an
Airborne Sensor
149
LIST OF TABLES
Table 3-1. Input Parameters for LANL Plume Model
29
Table 3-2. Input Parameters for JPL Plume Model
33
Table 3-3. Plume
Debug
Images
for ACAD Models
43
Table 3-4. Plume
Debug
Images for Integrated JPL Model
44
Table
4-1
.Methyl Chloride Plume Properties
50
Table
4-2. Radiometric Values Plume Images
51
Table 4-3. Initial Plume Characteristics
55
Table 4-4. Optical Properties
ofHomogenous Plume
63
Table 4-5. Properties
ofLANL
Plume
78
Table 4-6.
Optical
Properties
of6
umWater Droplet
79
Table
5-1.
Emissivity
andRadiance
Values for NTS
Scene
85
Table 5-2.
Region Description
ofACAD
Plume Model
86
Table 5-3.
Primary
andSecondary
Rainbow Angles
Using
Geometrical Optics
105
Table 5-4.
Primary
andSecondary
Rainbow Angles
Using
Mie
Scattering
Theory.
106
Table 5-5. Cloud Characteristics
113
1.
Introduction
Remote sensing
offactory
stack andcooling
tower
plumeshas
the
potentialto
revealinformation
about
the
constituents ofthe
plumes.The intelligence
community,
nuclear proliferationmonitors, the
Environmental Protection
Agency
(EPA),
andthe
Department
ofEnergy
(DOE)
have looked
atgathering
information from
observations
of plumes.In
the
case offactory
stacks,
determination
ofthe
species andconcentrationof
the
plume canhelp
revealthe
chemical componentsofthe
factory
products.For
plumesfrom cooling towers,
the
temperature
and waterdroplet
characteristicsmay
indicate
the
output power ofthe
station.
Ideally,
observationofthe
plume shouldbe done
by
a sensorlocated
nextto the
factory
or powerstation;
however,
this
is
notalwayspossible.Airborne
and satellite remotesensing
would provide coverage notonly
ofinaccessible
areas,
but
over wide areas at regularintervals.
Both
passive and active remotesensing
of plumes arecurrently
being
investigated.
While
active methods(i.e.,
laser
remotesensing)
canprovide more accurate
determination
ofthe
concentration ofeffluentsin
the plume,
they
canonly
provideinformation
at certainwavelengths.In addition,
active platformshave limited
coverageand are expensiveto
produce and maintain.
Passive
sensorsonexisting
platforms can provideinformation
on plumes over a widespectral
band,
andmuitispectralimage fusion
canbe
usedto
yield additionalinformation.
Coverage
also wouldbe
more widespread and reliable.Synthetic
image
generation(SIG)
will aidin
the
investigation
of plumephenomenology
andin
the
understanding
of remotesensing
of plumes.SIG is
the
process ofusing
first
principlesfrom
radiometry
to
simulatean
image
as seenby
a particular sensor.SIG
providesthe
ability
to
modelimages
under avariety
ofconditions
(wavelength,
sensorplatform,
sceneconditions,
etc.).These
syntheticimages
canthen
be
usedto
predict sensor performance under various
conditions,
and provide away
to test
remotesensing
algorithms.Synthetic
plumeimagery
can reveal notonly
how
a plume willlook
to
asensor,
but
alsohow
it
willinteract
with
the
background
andsurrounding
atmosphere.A variety
ofplumeimages
canbe
generatedusing
different
sources,
meteorologicalconditions,
viewing
conditions,
and wavelengths.Algorithms
designed
to
determine
effluent concentration canbe
tested
onthese
images
to
determine
their
accuracy
and robustness.The
radiancereaching
the
sensorfrom
the
plume originatesfrom
several sources.Direct
sunlightand
diffuse
skylightare scatteredfrom
the
plume.The
type
ofscattering
(Mie
orRayleigh)
depends
onthe
spectral
band
and particulate size.The
intensity
ofscattering
depends
onthe
concentrations andparticle sizedistribution.
Multiple scattering
will occur withinthe
plumeif
the
opticaldepth is large.
Thermal
selfemission and absorption
by
the
plume willbe
apparentin
the
MWIR (3-5 urn)
andLWIR (8-12
um)
regions.
The
amount of self-emissiondepends
onthe
emissivity
andtemperature
ofthe
plume.The
transmission
ofthe
plume willbe
dependent
onthe
spectralabsorbance ofthe
particulate.The
generation of syntheticimages
of plumes must accountfor
all ofthese
factors
to
produce ahas
this
ability
(Schott,
1993).
It
is
currently
employedby
the
Center for
Imaging
Science
atthe
Rochester
Institute
ofTechnology
for simulating images for
various remotesensing
platforms.DIRSIG
is
aray-tracing
codethat
incorporates MODTRAN
to
produce aradiometrically
accurateimage
atthe
sensorof a scenebuilt
by
the
user.The
objective ofthis
researchis
to
develop
aradiometrically
accurate methodfor
producing
synthetic
images
of plumes.This
method needsto
accountfor
the
maininteractions
ofthe
plume withits
environment.
Existing
modelsfor
cooling
tower
andfactory
stack plumes are usedto
providethe
plumegeometry
andcharacteristics(constituents,
concentration,
particulatesizing,
andtemperature).
The
plumes are representedeitherexternally
by
AutoCAD
(ACAD)
models orinternally
withinDIRSIG.
The
effectsofscattering, self-emission,
and absorptionfrom
the
plume areincorporated in
DIRSIG
ona pixel-by-pixelbasis.
Atmospheric
radiativetransfer
theory
is
usedto
accountfor
multiplescattering
withinthe
plume.Different
spectralgasdatabases
areincluded
in
orderto
model avariety
of gas plumes.A secondary
objective ofthis
researchis
to
demonstrate how
this
methodology
canbe
usedto
understand remote
sensing
of plumes.SIG
scenes of plumes are generatedfor both
ground-based andairborne sensorsat a
variety
of wavelengths.Special
emphasisis
givento the
useofhyperspectral
sensorsin
the
detection
of gas plumes.Sensitivity
studies aredone
onthe
plume-background contrastbased
onchanges
in
the
plume characteristics.Finally,
abrief demonstration
is
shownin
the
appendix ofhow inverse
algorithmsthat
determine
plume concentrations are used withDIRSIG
plumes.The
final
objectiveis
to
validatethe
modelsdeveloped
in
this
research.This
is
done
with actualexperimental
data
whereavailable,
or against other validated computer models.A
validation ofthe
DIRISG
gas plume model used experimental
data
collected of aSF6
plume atthe
Nevada
Test Site.
The scattering
plume model
is
comparedto
results obtainedfrom
MODTRAN.
Two
atmosphericscattering
effectssimulated
by
DIRSIG
are also presented as a result ofthis
research. .This
dissertation
is
divided
into
six chapters and nine appendices.Chapter 2
coversthe
theory
neededfor
modeling
plumesin
DIRSIG.
This
includes
the
physics andradiometry
of plumes andthe
governing
equationsfor
remote sensing.Chapter
3
describes
the
algorithms usedto
createthe
plume modelsand
how
they
areimplemented
in
DIRSIG.
It
is
intended
to
be
a user's manualfor future
users ofthe
DIRSIG
plume code.Chapter 4
gives various results and examples of plumeimages.
Both
gas andscattering
plumesare shownusing different
sensorplatforms and plume parameters.Chapter 5
presentsthe
validation results againstthe
NTS
plumes andMODTRAN
code.Also
the
DIRSIG
images
of atmosphericscattering
are shownin
this
chapter as a qualitative validation ofthe
code.Conclusions
andrecommendations of
this
research are givenChapter
6.
The
appendices give additionaltheoretical
background
onMie
scattering,
radiativetransfer,
particle sizedistribution,
andinverse
algorithms.Code
and2.
Theory
This
chapterdiscusses
the
theory behind modeling
plumesin DIRSIG. It
coversthe
basic
physicsand
radiometry
ofhow
the
plumeinteracts
withits
environment.The interaction
oflight
and matterin
the
form
ofscattering, absorption,
and radiativetransfer
is
emphasized.While
there
is
abrief discussion
ofhow
plumes aremodeled,
this
chapterdoes
not coverthe
dynamics
oftheir
plumes evolution.Other
research
has been done in
this
area andreferencesare givento them.
The governing
equationsfor
remotesensing
ofthe
plume arecoveredfor both
ground-basedand airborne sensors.2.1
Consideration
for
Remote
Sensing
of
Plumes
2.1.1
Factory
Stack
Plumes
Release
of various chemical effluentsby
afactory
into
the
atmosphere can reveal materialsthat
are
being
used orproducedby
the
factory. Common
emissionsfrom
power plantsinclude
CO,
C02, NO,
N02, N20, S02, HC1,
CHt,
NH3,
H20,
andNCHO. Sulfur
hexafluoride
(SF6)
is commonly
used as a plumetracer
gasdue
to
its large
absorbance cross-section.These
particulatestypically
have diameters
under0.1
um
(Blumenthal,
1981).
The
exceptionis
N02
(White,
1981)
which canhave diameters
around0.6
um andis
the
dominant
absorberin
the
visible region.The local
humidity
level
can cause anincrease
in
particulatesize
due
to
condensation of water vapor ontothe
nuclei(Hanel,
1972).
Normally,
there
is
very
little
scattering
unlessflyash
and sulfates are presentin large
amounts(which
may
occurin
modemfossil fuel
power plantsnot under emission control).
Typical
temperatures
atthe
stack exit of an oilburning
plant are around495
K(Selby,
1978).
A
comprehensivestudy
offactory
stackemissions,
including
computercodeto
simulatethem,
wasdone
by
the
EPA
between
1979
and1981
(Seigneur,
1985). The
plumes oftwo
coal-burning
power plants anda copper smelter were measuredby
four
teleradiometers
atdownwind distances
from 17
to
34
km.
The
data
was comparedto the
PLUEVUEII
code which used radiativetransfer
equations with angular
multi-scattering
terms
to
find
the
radiancereaching
the
sensor whenlooking
at a plume(Seigneur,
1984). In
the
visible region(400-650
nm), the
program predictedthe
plume/sky
radiance ratio over a range ofviewing
angles.The
data
collectedfrom
these
experimentsmay
be
usefulfor
validation,
but
most ofthe
measurementsaretaken too
far downwind
from
the
stack exit.A
series of chemical gases were released under controlled conditions atthe
Nevada Test Site
(NTS)
in
1994
(Westberg,
1996).
These
plumes were monitored overthe
first 500
mby
severalinstruments
including
a multi-spectral sensor.The
images
producedwere calibratedradiometrically
using
The chemistry
withinthe
plumecanbe
very
complex.Some
gasesthat
emergefrom
the
stack areconverted
to
particulates asthey
interact
withthe
atmosphere.For
example sulfurdioxide
will changeinto
sulfate,
and nitrogendioxide
to
nitrate.The
rate of conversiondepends
strongly
onthe
atmosphericconditions.
The
temperature
ofthe
plume alsodrops
asthe
cooler ambient airis
entrainedinto it. The
rateof entrainment
depends
onthe
turbulence
andlocation
ofthe
boundary
layer
ofthe
lower
atmosphere.All
of
these
effectsincrease
the
difficulty
ofaccurately
modeling
the
mixture of gases and particulates andtheir
concentration
downstream
ofthe
stack.From
animaging
perspective,
the
amountof sunlight scatteredfrom
afactory
plumetowards
the
sensorwill
depend
onthe
type
ofparticulate,
its
concentration,
andits
sizedistribution function. Most
gasplumes scatter
weakly
due
to the
small particulate size.The
type
ofscattering
willgenerally
be
ofthe
Rayleigh
type.
If
a sufficient concentrationof waterdroplets
are presentin
the
plumethey
willbe
the
dominant
source of scattering.An
exceptionis
when sulfates andflyash
are presentin
the
plume.These
particles
have diameters
of0.5
um andlarger
and causeMie scattering
of visiblelight
(White,
1981).
The
detection
and quantification of gasesin
the
plumeby
remotesensing
presents some unique problems.Many
variables areinvolved in
the
formation
ofthe
plumethat
makethe
inverse
problem ofcharacterization
difficult.
Both
active(LIDAR)
and passivetechniques
have been investigated
anddeveloped.
One
ofthe
most successful methods usesFourier Transform Infrared
Spectroscopy
(FTIR).
Much
workhas been done in
this
area ofdetection
and quantification of moleculesin
plumes(Haus,
1994).
Signal processing
techniques
are usedto
matchthe
spectrum withknown
gas signaturesthat
may
existin
the
plume.A
plume analysis code was writtenfor
FTIR
sensors and usedto
determine
contrastSNR
for
asensor on a satellite and airborne platform against
different
temperature
plumes(Hilgeman,
1996).
The
types
ofgases,
andtheir
mixing
ratios,
canthen
be
usedto
determine
the
productsofthe
factory.
While
FTIR
can provide spectraldata,
it does
not provideany
spatialdata.
However
withthe
new generation ofhyperspectral
imaging
sensors, the
potentialnow existsto
extractboth
spectral and spatialinformation from
remotely
sensedimages
ofthe
plume.Spatial information
wouldhelp
givethe
physicaldimension
ofthe
plume as well as provide
mixing
ratiosofthe
gasesas afunction
of position withinthe
plume.In
additionsimultaneous measurements of
background
signature canbe
usedto
improve
the
SNR
ofthe
plumesignature.
Work
is
currently
being
done
withthe
Thermal Infrared
Imaging
Spectrometer
(TIRIS)
for
plumedetection
(Gat,
1997).
This is
a pushbroom system which operatesfrom 7.5
-14.0
umin
64
spectralbands.
Spectral
resolutionis
10
cm"1
at
10
um.The
amount ofgas releasedby
afactory
stackis
usually
measured asa release rate(lbs/hour
ormolar
density [moles/m3]
=release rate
rams/sec]
(2-1
)
(stack
area[m2]
stackvelocity
[m/s]
molecular weight[gms/mole])
The
volumemixing
ratio(VMR
measuredin
parts per million)
ofthe
speciesis found
by dividing
the
molardensity by
the
normal volume of a perfectgas adjustedfor
the
ambienttemperature
and pressure(.00224
nrVmole atSTP). Once
the
molardensity
for
each speciesis
found,
the
molar ratio ofthe
different
speciesis defined
asmolar
ratk>A/B
= molardensity
ofA /molardensity
ofB.
(2-2)
A
hyperspectral image has
the
potentialto
yieldthe
VMR
of each species(and
hence
the
molarmixing
ratio)
on a pixel-by-pixelbasis (see
Appendix
E).
2.1.2
Cooling
Tower Plumes
There is
considerableinterest in
monitoring
the
power generatedby
both
nuclear andfossil-fuel
power plants.In
the
former
case,
non-proliferationtreaties
requiredetection
ofthe
possible production of materialfor
nuclear weapons.The
power generatedis
relatedto the
wasteheat
released as athermal
plumefrom
the
cooling
tower
which containsheated
ambient airas well as vaporizedcooling
water.The
radiative properties ofthe
plumemay
be
detected
andmeasuredby
remote sensors.The
plumetemperature
and waterdroplet
content willdetermine
the
amount ofemittedthermal
radiation.Studies
ofcooling
tower
plumeshave
been
done
by
Argonnes National
Lab
(Carhart, 1981),
DOE
(O'Steen, 1995),
andLos Alamos
National Lab
(Powers,
1995).
There
aretwo
main sources of waterdroplets in
cooling
tower
plumes(Sauvageot,
1989).
The
circulation water ofthe
condensersis
cooledby
evaporation andthermic transfer to the
airand carriedaway
by
the
naturalor mechanicaldraft
ofthe tower.
When
this
water vapormixes withthe
colder ambientair,
recondensation occurs on small atmospheric nuclei present and waterdroplets
areformed.
This
first
type
ofdroplet is
called"recondensation"
droplets
andgenerally
have diameters
smallerthan
20
um.The
exhaustemerging
from
the tower
also contains small amounts of salts usedto
prevent algae growth onthe
side ofthe tower.
These
saltsform larger
nucleifor
condensation andthe
resulting
waterdroplets
have
sizesfrom
20
to
100
um.This
secondtype
ofdroplets
are calleddrift
droplets.
It
wasfound
that the
number of recondensationdroplets
wereten times
greaterthan the
drift
droplets.
Thus,
whilethe
sizedistribution
ofthe
cooling
tower
plumeis
bimodal,
the
effects ofthe
larger
drift droplets
canbe ignored due
to their
relatively
small number.bands,
radiancefrom
the
plume willbe
dominated
by
thermal
self emission.However,
scattering
from
water
droplets
will alsobe
considered.At
visiblewavelengths,
scattering from
waterdroplets
and other plume constituentsis
the
main source ofradiancedetected
atthe
sensor.The
emissivity
ofthe
plumedepends
onthe
liquid
watercontent,
whichin
turn
depends
onthe
sizedistribution
ofthe
waterdroplets.
Droplet
sizedistribution
will also affectthe
scattering, absorption,
andthermal
self-emissionfrom
the
plume.
2.2
Plume
Modeling
Modeling
plumesis
avery
complex processthat
involves hydrodynamic
andturbulence
flow
theory.
Since
the
aim ofthis
researchis
to
modelthe
images
of plumes and notthe
plumesthemselves,
only
abrief description
of plumemodeling
willbe
given.The
two
plume modelsdescribed
willbe
those
used
in DIRSIG.
2.2.1
JPL Plume Model
The first
plume modelis designed
to
model gas plumes releasedfrom
afactory
stack.It
wasoriginally
developed
by
the
EPA
(Haugan, 1975),
andhas been
modifiedby
Kaman
Corp
andthe
Jet
Propulsion Lab (henceforth
calledthe
JPL
model).It
is
currently
being
maintainedby
RSA Systems. The
JPL
modelis
aGaussian
plume modelbased
onthe
Brigg's
equationfor
plumedynamics
(Bennett, 1992,
Halitsky,
1989).
For
a neutralatmosphere, the
Brigg
equationis
commonly
usedto
givethe
plumecenterline
height.
It
assumes abuoyant
rise ofthe
plume.The
plume entrains ambient air at a rate proportionalto
its
velocity
and cross-sectional area relativeto the
surrounding
areaFor
aneutrally
buoyant
effluent, the
plumeheight is:
h
=h+3
rjn ^
m
+
3
.1/3
(2-3)
where
h0
is
the
stackheight,
r0
is
the
stackradius,
xthe
downwind
distance,
and mthe
emissionvelocity
ratio,
defined
asthe
vertical emissionvelocity
divided
by
the
wind velocity.A
Gaussian distribution
ofthe
concentration of gases or aerosols
from
the
plume centerlineis
assumedofthe
form:
c
=Q
2
no
ycrzjUexp
y
.2
^
2C7,
exp
2cr.2(
+
exp
{z
+
h)
2\lot
(2-4)
where x
is
the
downwind
distance,
y
is
the
lateral distance from
the centerline,
zis
the
verticaldistance
from
the
ground,
Q
is
the
sourceintensity
(mass
released per unittime),
uis
the
meanwindspeed,
h
the
plumeThe dilution factor
at aparticular position withinthe
plume canfound
by dividing
the
originalstackconcentration
C0=Q/nr02w
by
C:
D
=2
a
a.
Cm0
wr2m
exp
y
2a,
exp
2a2.
2\
f
+
exp
J
\
(z
+
h)
2a22\
(2-5)
where w
is
the
vertical emissionvelocity
and m=w/u.It
should
be
notedthat the
Gaussian
modelin
the
lateral direction holds for
allstability
conditions,
whilethe
verticaldistribution
only
holds for
stable andneutralatmospheric conditions.
The JPL
model calculatesthe
initial
conditions atthe
stack exitfor
several parametersincluding
plume
temperature
andVMR.
The dilution factor is
then
calculateddownwind
atany
point withinthe
plumeusing
eqn.2-5.
The
parameters ofthe
plume atthat
point arethen
determined
by
multiplying
the
dilution factors
withthe
initial
parametersatthe
stack exit.The
JPL
modelis designed for
factory
stackplumes
containing
multiple species.Inputs
to the
codeinclude
gastype
and releaserate,
stackgeometry,
and meteorologicalconditions(including
time-varying
conditions).The
outputs aredownwind
location,
plume centerlineheight,
and plumecharacteristics(dilution,
temperature,
and volumemixing
ratio(VMR)).
Chapter 3
gives adetailed description
ofthe
JPL
code andits
outputs.2.2.2 LANL Plume Model
The
second plume model usedin DIRSIG
wasoriginally
developed
by
Argonnes National
Lab
andUniversity
ofIllinois
(ANL/UI)
and modifiedby
Los
Alamos
National Labs
(henceforth
to
be
referredto
asthe
LANL
model).It
is designed
to
simulatecooling
tower
plumes and uses anintegral
approachin
whichdispersion
and plumerise
take
place simultaneously.A
set of coupledordinary
nonlinear differential
equations are solved
to
yield plumetrajectory
and properties.The
model conservesfluxes
of physical plumeproperties,
whilerepresenting
the
dilution
ofthe
plumeby
entrainment ofthe
surrounding
ambient air.The differential
equations are representedby
the
conservation ofmass,
horizontal
and verticalmomentum, enthalpy,
andtotal
water.This
modeltreats the
cross section ofthe
plume as a whole and solvesthe
governing
equationsusing
the
local
valuesfor
the
windspeed,
direction,
andtemperature
gradient.Thus
the
plumeis
cylindricalin
shape andits
properties are uniformalong
a cross-section perpendicularto the
plume axis.Also
the
increase in
waterdroplet
sizedue
to
condensationis
tracked
using
classic cloud models(Liou,
1992).
The
initial
plumetemperature
anddroplet
numberdensity
is
specifiedby
the
user.The initial
numberdensity
is
determined
asN,
=PaWl
where
pa is
the
density
of waterin
ambient air.W/ is
the
massliquid
watermixing
ratio, /?/
is
the
density
ofliquid
water,
and ris
the
initial droplet
radius.W/
describes
the
amount ofinitial liquid
waterin
the
plume.The
droplet
radius willhave
a sizedistribution
asdescribed in
appendixC.
The
outputs ofthe
code are plumeradius,
temperature,
waterdroplet
size,
andnumberdensity
as afunction
ofdistance downwind
from
the tower.
The
numberdensity
downwind is
determined
as:N
=Nr
'A7^
^oJ
(2-7)
where
N0
andAT0
arethe
initial
(stack)
numberdensity
andtemperature contrast,
andAT
is
the temperature
contrast at
the
downwind
point.This
determination
ofthe
numberdensity
is
a change addedby
the
authorbased
onthe
dilution factor
usedin
the
JPL
plume model.It
was not part ofthe
original code whichdid
notexpressly
accountfor dilution
effects.A detailed description
ofthe
LANL
modelis found in Carhart
(1991)
and
Powers (1995).
2.3 Interaction
of
Light
with
the
Plume
This
sectiondescribes
aspects ofscattering,
absorption,
and emissiontheory
asthey
pertainto
modeling
syntheticimagery
of plumes.Multiple libraries have been
written onthese
subjects.For
the
area ofscattering theory,
the
classicis
by
Van de Hulst
(1959).
However,
a more readable and updatedform
canbe found in
Bohren (1980).
The
sameholds
true
for
radiativetransfer,
whereChandrasekhar
(1960)
is
the
classic,
but
Liou
(1980)
andGoody
(1989)
present an updated version.Detailed derivations for Mie
scattering
and radiativetransfer
areincluded in
Appendices A
andD.
2.3.1
Gas Absorption
?The
different
speciesin
a gas plume absorblight
at variouswavelengths,
depending
onthe
electronic, vibrational,
and rotationalbands. The field
ofspectroscopy specifically
considershow
gases canbe identified
by
their
absorption"fingerprints."
Since modeling
of gas plumes requiresknowledge
ofthe
absorption
spectrum,
this
section willbriefly
touch
onthis
process.For
a more complete coverage ofthis
topic
andhow
it
relatesto
remotesensing
the
readeris
referredto texts
by
Stephens
(1994),
Goody
(1989)
and
the
Handbook
ofGeophysics
andthe
Space Environment (1985).
There
arethree
main propertiesthat
describe
absorptionby
gas molecules:the
central position ofthe
line in
the spectrum, the
strengthofthe
line,
andthe
shape or profile ofthe
line.
In
the
visibleregion electronictransitions
in
individual
atomsand molecules absorbthe
impinging
electromagneticwave.These
electronic
transitions
arerelatively
quick (10"15(10"
seconds)
andthus
smallertransition
energies.In
the
far infrared (>20
um)
and microwaveregion,
rotational
transitions
arethe
dominant
absorption processes.Vibrational
transitions
occurin
polarmoleculesand
the
transition
states aregovernedby
quantum mechanics.Rotational
transitions
depend
onthe
geometrical configuration ofthe
moleculesandorientationofthe
moment ofinertia.
Gases
found in
plumes can
be
characterized aslinear
(such
asC02, N20),
symmetrictop (NH3,
CH3C1),
sphericalsymmetric
top
(CH,),
andasymmetrictop
(water
vapor).The
type
of configurationdetermines
the
location
of
the
absorption spectra.The
actual absorptionline
shapeis determined
by
severalfactors.
The
first is
naturalbroadening
whichresults
in
aband
oftransition
levels due
to
quantummechanical effects.This
is
a minorfactor in
gasplumes since
frequent
collisionsbetween
moleculesshortenthe
naturallifetime in
the
excited state.These
collision contribute
to
pressurebroadening
ofthe
line
shape.The resulting
shapeis described
by
aLorentzian
function
andthe
half-width is determined
by
the
atmospheric pressure andtemperature.
The
Doppler
effectalsobroadens
the
absorptionline. This
profileis described
by
aMaxwellian distribution
andagain
depends
on atmospheric pressure andtemperature.
The importance
of pressure vs.Doppler
broadening
is
expressed as aratio,
^o10"12-^
(2-8)
<*l
P
where
aD
andaL
arethe
half-widths
ofthe
Doppler
andLorentzian
profiles, v0
is
the
centerfrequency
(in
Hz),
andp is
the
pressurein
mbars.In
the
LWIR
at10
umat a pressure of1000
mbars, this
ratiois 0.03
indicating
that
pressurebroadening
is
the
mainfactor
in
determining
line
shape.The
absorption coefficientkabs(v)
is defined
as,
kabs(v)
=S-f(v-v0)[mi]
p-9)
where
S
is
the
strengthfactor
ofthe
absorbing
line (based
onthe transition
probability)
and/is
the
line
shape
function
centered on v0.The
transmission through
a gas plumeis found
using
the
Beer-Lambert
law
(also
known
asthe
Bouguer
law)
dE
=kextEdz
[W/m2],
(2-10)
where
E
is
the
irradiance, kext
is
the
extinctioncoefficient,
anddz
a unit pathlength
(the
implicit
dependence
on wavelengthhas been
omitted).When scattering
is
negligible(as
in
the
case of gasplumes),
then the
extinction andscattering
coefficientarethe
same.The
exponentialform for
ahomogeneous
medium
is
E
=E0e'K":
The
term
k,.*
zis
referredto
asthe
opticalthickness
or opticaldepth,
t'.The
transmission
is
the
ratio ofirradiance
outto
irradiance
in:
E
( vr
= =exp(-kMz)
=exp(-r')
.(2-12)
Databases for
gases often measuretransmittance
in
terms
ofabsorbance^
= -logI0r.(2-13)
The
absorbanceis
measuredfor
a gas at a particulartemperature
and columndensity. The
columndensity
is
the
VMR
ofthe
gas multipliedby
the
pathlength
ofthe
gas andis
expressed as ppm-m.For
a plume with aknown VMR
andtemperature,
kabs
is derived from
the
absorbance of a givendatabase
through
log10(e)-CDDB-TDB
Kbs
=,
m::Tp
Z
.(2-H)
where
ADB, CDDB,
andTDB
arethe absorbance,
columndensity,
andtemperature
from
the
gasdatabase.
VMRP
andTP
arethe
volumemixing
ratio andtemperature
ofthe
particular gas speciesin
the
plume.If
there
are multiple gasspecies, then the total
absorption coefficient ofthe
plumeis
the
sum ofthe
individual
coefficients.
If
the
columndensity
ofthe
plumeis
given, then the
opticaldepth
ofthe
plume canbe
found
from:
r'
=
CDP TP ADB
(2-15)
log10()-CDDB-TDB
where
CDP
is
the
columndensity
ofthe
plume.2.3.2
Scattering
A
plume scattersboth
sunlightand skylight.The
amount anddirection
ofscattering
depends
onthe
type
ofparticle,
its
numberdensity,
andthe
sizedistribution.
Since
no active sources areconsidered,
the
incoming
light
is
assumedto
be broad band
and unpolarized.Mie
theory
rigorously
describes scattering
of electromagnetic radiation
from
spherical particles(and
severalother shapes).Rayleigh scattering
canbe
treated
as an approximation ofMie
scattering
for
particlesthat
are small comparedto the
wavelength oflight.
Implicit
in
the
scattering
consideredhere
is
the
assumptionthat
the
wavelengthis
not changedby
the
scattering: no
Raman
ornonlinear
effects are considered.Also,
the
scatteredlight
is
incoherent,
that
is,
there
are no phase effectsbetween
the
light
scatteredfrom
multiple particles.Multiple scattering
canhave
sphere,
whichmay
be
the
caseif large
aerosol nuclei undergo condensation andhas
an outer shell composed of water.Also,
scattering from ice
crystalsin
cirrus clouds canbe
modeledusing
cylindricalparticles.
Algorithms
for Mie scattering from
coatedspheresandcylindersarefound in
Appendix
B
andC
inBohren(1983).
The
generalformulation is
to
startfrom Maxwell's
equationswith a spherical scattererthat
has
adifferent index
ofrefractionfrom
the
surrounding
medium.An
electromagneticfield is
generatedinside
the
sphere and ascattered
field
willbe induced
outsidethe
sphere.Boundary
conditionsareimposed
sothat
the tangential
componentsofthe
electric and magneticfields
arecontinuous acrossthe
interface
between
media.A scattering
matrixin
terms
ofthe
Stokes
parametersfor
the
incident
and scatteredlight
is
expressedas:Qs
u,
2..2k'r
S,
SuYO
'21
u
41 122 '32 '42'23
'33
'43
'24'34
w
Q,
(2-16)
where
I, Q,
U,
andV
arethe
Stokes
parameters,
k
the wavevector,
and rthe
distance
to the
detector.
The
elements ofthe
amplitudescattering
(Sn, Si2,
...)depend
onthe
scattering
angle.This
scattering
matrixis
alsoknown
as aMueller
matrix.For
a sphericalparticle, only the
diagonal
terms
andSi2, S2],
S34,
andS43
are not zerodue
to the
symmetry.Since
the
Stokes
parameters oflight
scatteredby
a collection ofrandomly
separated particlesis
the
sumofthe
Stokes
parameters ofthe
individual
particles,
the
scattering
matrixfor
a collection ofthese
particlesis
the
sum ofthe
individual
scattering
matrices.This
assumesthat
the
scattering
is independent
among
the
particles with no phaserelationship between
them.
For
unpolarizedsunlight, the
relationshipsfor
the
Stokes
parameters reduceto
E
=1
22
klr
SlA
Qs
=
l
klr
2jS,-,E,
1J12-^/u=v=o
(2-17)
Note
the
notationfor irradiance has been
changedfrom I
to
E
[w/m
]
for
consistency
withthe
DIRSIG
notation.
Several
terms
encounteredin
scattering
theory
are relevantto
scattering
in
a plume.The first is
the
particle size parameter:2mi
a
where
a
is
the
radius ofthe
particle andn0 is
the
mediumindex
of refraction.For
small valuesofX,
the
Rayleigh
scattering
approximation canbe
used.For larger
valuesofx,
geometrical optics approximations canbe
used(such
asthe case oftherainbow,
seeChapter
5).
The scattering
cross sectionC^
is defined
asthe
amount ofenergy
scattered acrossthe
surface area ofthe
particleby
the
incident irradiance. For
asphere, this
is
expressed asCsca
=TT
Z
(2
+
!Xk
f
+
\K
f
)
[m2],
(2-19)
K
n=lwhere
a,,
andbn
arescattering
coefficientsthat
depend
onthe
relativeindex
of refraction ratio ofthe
sphereto
the surrounding
medium expressedthrough the
Riccati-Bessel
andHankel
functions.
The
convergence ofthe
seriesis
roughly
proportionalto
the
size parameter.Thus for larger
particles,
lengthy
computation(and longer
computerrun-times)
willbe
neededto
find
the
cross-section.The
extinction cross-sectionis
similarly
determined
as:Cm
=if
I(2
+
l)Re{an+Z>}
[m2],
(2-20)
k
n=\The differential
scattering
cross sectiondCa*
/dW
is
the
energy
scattered perunittime
into
a unit solidangleabout
the
scattering
angle9
and azimuthal angle (j).The irradiance
ofthe
scatteredlight is
relatedto
the
incident irradiance
through the
differential scattering
cross section:dC
dilr
where r
is
the
distance
to the
detector.
For
unpolarizedlight,
the
differential scattering
cross sectionis
expressed as:
f^f
=^-
[m2/sr],
(2-22)
The
angularscattering
coefficient(3(8)
is
the
amountoflight
scatteredinto
the
direction 9
perunit solid angle per unitlength
ofthe
scattering
medium.It
is
defined
as/?(0)
=N^^[m-'sr1],
(2-23)
dCi
where
N is
the
numberdensity
ofthe
medium.1
dCsca
p=~c~~dir-
(2-24)
sea ""**'
The
asymmetry
parameterg
is
the
average cosineofthe
scattering
angle andis defined
asg
=(cos#)= \pcos6dCi.
(2-25)
4*When
the
scattering
is
isotropic,
g
is
zero.If scattering is in
the
forward direction
g
is
positive(with g
equalto
onefor
total
forward
scattering).Backscatter
causesg
to
be
negative,
withg
=-1
for
total
back
scattering.The scattering
efficiency
is
the
scattering
cross sectiondivided
by
the
particle cross-sectional area.For
aspherethis
is
^=%L=
%-(2"26)
(j
na
The
scattering
diagrams for
a spherical waterdroplet
as afunction
ofthe
incident
wavelengthare shownin
Figure
2-1
andFigure 2-2.
The
plot was generatedby
aMie scattering
codedescribed
in Appendix A.
Notice
that
whenthe
size ofthe
particle and wavelength ofincident
light
areapproximately
equal,
almostall of
the
scattering
is in
the
forward
direction,
whichis
consideredMie
scattering.Particle
Type: Water
Droplet
Index
of refraction:1.33
Incident
wavelength: .6328micronsDroplet
radius:.525micronsAsymmetry
parameter(g)
=0.828
Figure 2-1.
Angular
Scattering
Distribution
for
aWater droplet in
the
Visible Wavelength
Particle
Type: Water Droplet
Incident
wavelength:5.0
micronsIndex
of refraction:1.321
+.0126iDroplet
radius:.525micronsAsymme