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Microwave effects of gaseous sulfur dioxide (SO(2)) in the atmosphere of Venus and Earth

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Microwave Effects
of Gaseous Sulfur Dioxide (SO2)
in the Atmospheres of Venus and Earth
A Thesis
Presented to
The Academic Faculty
By
Shady H. Suleiman
In P artial Fulfillment
of th e Requirem ents for th e Degree of
Doctor of Philosophy in Electrical Engineering
G eorgia In stitu te o f Technology
May 1997
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UMI Number: 9735914
UMI Microform 9735914
Copyright 1997, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
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Ann Arbor, MI 48103
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Microwave Effects
of Gaseous Sulfur Dioxide (SO2)
in the Atmospheres of Venus and Earth
Approved:
r .P a u l'G . Steffes. Chairf S a n
Dr. Wavmbnd R. Scott
D ate approved by C hairm an Z J?
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To
my parents Hasan and Insaf
my brothers Jiab, Ism ail, Sam er, and Fadi
my sister Feda
and my wife V iana
for their love, patience, and support
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Acknowledgements
I would like to express my sincere appreciation to my advisor, Professor Paul G.
Steffes for his continuous support, patience, encouragem ent, a n d guidance during th e
course of this research. I would also like to th a n k my thesis com m ittee m em bers:
Professors Albin J. Gasiewski, W aymond R. S co tt, Andrew F. Peterson, and R obert
G. R oper for their useful suggestions and careful exam ination o f this docum ent.
1 would also like to acknowledge the support of the N atio n al Radio A stronomy
Observatory (N R A O ), especially Dr. Bryan J. B u tler for his collaboration and useful
discussions during th e conduct of th e VLA observation of Venus. N R A O is a facility of
th e N ational Science Foundation operated under cooperative agreem ent by Associated
Universities, Inc.
I would also like to thank my family and friends for th e ir encouregem ent and
support during my entire career at Georgia Tech: my loving p aren ts, Hasan and
Insaf; my wonderful wife, Viana, my dear brothers; Jiab , Ismail, S am er, Fadi, and m y
lovely young sister, Feda; my friends; M ohamed-Slim Alouini, D ave DeBoer, M arc
Kolodner, and Scott Borgsmiller for m aking m y g rad u ate studies a n d work enjoyable.
Finally, I would like to acknowledge the sponsorship of th e N atio n al Aeronautics
and Space A dm inistration Planetary Atmospheres Program u n d er g ran ts NAGW-533
and NAG5-4190.
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ii
Contents
A cknow ledgem ents
i
C ontents
ii
List o f Tables
v ii
List o f Figures
v iii
Sum m ary
x iv
1
IN T R O D U C T IO N
1
2
LABO RATO RY M EA SU R EM EN TS OF TH E MICROWAVE A B ­
SO R PT IO N A N D R E FR A C TIO N OF GASEOUS SO*
2.1
2.2
7
Microwave Absorption of Gaseous SO 2 ......................................................
7
2.1.1
T heoretical Background
...................................................................
7
2.1.2
E xperim ental A pproach
...................................................................
9
2.1.3
E xperim ental A p p a r a t u s ...................................................................
11
2.1.4
E xperim ental P r o c e d u r e ...................................................................
14
2.1.5
E xperim ental U n c e r t a i n t i e s ............................................................
15
2.1.6
E xperim ental R esu lts and I n te r p r e ta tio n ....................................
19
M odeling of th e Microwave Absorption of SO 2 ........................................
33
2.2.1
Overview of the S pectral Line Shape T h e o r y ..............................
33
2.2.2
M odeling R e s u l t s ................................................................................
37
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2.3
3
Microwave Refraction of Gaseous SO 2
42
IN TER PR ETA TIO N OF T H E M AGELLAN RA DIO OCCULTATION E X PE R IM E N T S AT V E N U S
4
50
3.1
Overview of R adio O ccultation E x p e r im e n ts ...........................................
-50
3.2
Interpretation of the A bsorptivity P r o f i l e s ..............................................
53
3.3
Interpretation of the R efractivity P r o file s ..................................................
63
M ODELING O F THE M ICROW AVE A N D M ILLIM ETER-W AVE
EM ISSION O F V E N U S
65
4.1
In tro d u c tio n ........................................................................................................
65
4.2
Theoretical Background
................................................................................
66
4.3
Param eters of th e R adiativ e Transfer M o d e l ............................................
72
4.4
4.3.1
T em perature-P ressure P r o f ile s ..........................................................
72
4.3.2
O pacity F o rm alism s..............................................................................
72
4.3.3
A bundance P r o f ile s ..............................................................................
75
Disk-Averaged Modeling R e s u lts ...................................................................
79
5 D U A L-FR EQ U EN C Y OBSERVATION OF V E N U S USIN G TH E
' VLA'
88
5.1
In tro d u c tio n ........................................................................................................
88
5.2
P r o c e d u r e ............................................................................................................
89
5.3
Calibration and D ata P ro c e ssin g ..................................................................
94
5.4
Results and In terp retatio n s
97
.........................................................................
6 LIM ITS OF T H E EFFEC TS OF S 0 2 ON IN SA R IM AG IN G OF
TER R ESTR IA L VO LCANO ES
115
6 .1
In tro d u c tio n ..............................................
115
6.2
Overview of INSAR T h e o r y .........................................................................
116
6.3
Effects of S 0 2 R efractivity on INSAR Imaging of Terrestrial Volcanoes 119
iii
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7 SU M M ARY A N D CONCLUSIONS
122
7.1
Uniqueness of W o rk ...........................................................................................
122
7.2
P u b lic a tio n s ........................................................................................................
124
7.3
Suggestions for Future W o r k ..........................................................................
127
A ppendix A PR O PO SA L TO OBSERVE V E N U S U SIN G TH E V LA 128
A .l VLA O bserving Application
..........................................................................
129
A .2 Scientific J u s tif ic a tio n .......................................................................................
131
Bibliography
135
VITA
144
iv
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V
List of Tables
1 .1
Venus and E arth: A Comparison of Physical C h aracteristics..................
*2.1 S pectrum Analyzer Instru m en t U ncertainty a t R esonant Frequencies.
3
16
2.2 M easured Microwave Absorption of Gaseous SO 2 in a C O 2 Atm osphere
at 295 K for Various Pressures and Frequencies..........................................
22
2.3 M easured Microwave A bsorption of Gaseous SO 2 in a C O 2 Atm osphere
at 365 K for Various Pressures and Frequencies..........................................
2.4
M easured Microwave Absorption of Gaseous SO 2 in a C O 2 A tm osphere
at 435 K for Various Pressures and Frequencies..........................................
2.5
23
M easured Microwave A bsorption of Gaseous SO 2 in a C O 2 A tm osphere
at 505 K for Various Pressures and Frequencies..........................................
2.6
23
24
Goodness of Fit Function ( \ 2) using th e New Ben-Reuven (BR), VanVleck and Weisskopf (V V W ), Janssen and Poynter (J P ), Gross (G R),
and Steffes and Eshlem an (SE) Formalisms.................................................
25
2.7
Values of P aram eters used in th e Developed Ben-Reuven Formalism.
43
2 .8
M easured Microwave R efraction of Gaseous SO 2 in a C O 2 A tm osphere
at 295 K for Various Pressures, and Frequencies.........................................
2.9
47
M easured Microwave R efraction of Gaseous SO 2 in a C O 2 A tm osphere
a t 365 K for Various Pressures, and Frequencies.........................................
48
2.10 M easured Microwave R efraction of Gaseous SO 2 in a C O 2 Atm osphere
at 435 K for Various Pressures, and Frequencies.........................................
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48
2.11 Measured Microwave Refraction of Gaseous SO 2 in a C 0 2 A tm osphere
at 505 K for Various Pressures, and Frequencies........................................
3.1
49
R efractivity of Gaseous S 0 2 in the Venus A tm osphere Based on our
Laboratory M easurem ents of th e S 0 2 D ensity Normalized R efractivity.
Also Shown is Resulting U ncertainty in Inferred T em perature Due to
S 0 2 R efractivity....................................................................................................
4.1
64
Measured Disk-Averaged Brightness T em peratures of Venus for Vari­
ous Frequencies as Compared to the R esults from th e New R adiative
Transfer Model using (1) Uniform S 0 2 A bundance of 75 p p m Below
48 km (T d i) and (2) the ISAV - 1 S 0 2 A bundance Profile (T d 2 )-
• • •
83
5.1
Positions of Venus and C alibrators during O bservation on 04/05/1996.
95
5.2
C haracteristics of Venus during Observation on 04/05/1996...................
95
5.3
Measured R esidual Brightness Tem peratures of Venus from N adir to
th e Equatorial Lim b.................................................................................................109
5.4
C om puted R esidual Brightness T em peratures of Venus from N adir to
th e Equatorial Limb using th e IS AVI S 0 2 A bundance Profile and the
M ariner 10 H 2 S 0 4 Abundance Profile................................................................. 109
5.5
Com puted R esidual Brightness T em peratures of Venus from N adir to
th e Equatorial Limb using a Uniform S 0 2 A bundance Profile of 75
ppm Below th e Main Cloud Layer and using th e M ariner 10 H 2 S 0 4
A bundance Profile.................................................................................................... 110
5.6
Measured R esidual Brightness T em peratures o f Venus from N adir to
th e Polar Lim bs.........................................................................................................I l l
5.7
Com puted R esidual Brightness Tem peratures of Venus from N adir to
th e Polar Limbs using the S 0 2 and H 2 S 0 4 A bundance Profiles Inferred
from the M agellan Spacecraft R adio O ccultation E xperim ents for O rbit
3212..........................................................................................................................
vi
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112
5.8
C om puted Residual Brightness Tem peratures o f Venus from N adir to
th e Polar Limbs using the SO 2 and H 2 SO 4 A bundance Profiles Inferred
from the Magellan Spacecraft Radio O ccultation E xperim ents for O rbit
321 3..........................................................................................................................
5.9
112
C om puted Residual Brightness T em peratures of Venus from N adir to
th e Polar Limbs using the SO 2 and H 2 SO 4 A bundance Profiles Inferred
from th e M agellan Spacecraft R adio O ccultation E xperim ents for O rbit
321 4 ..........................................................................................................................
6 .1
113
C haracteristics of an Airborne INSAR System used for th e Topo­
graphic M apping of Terrestrial Regions (Zebker an d G oldstein, 1986)
[85]............................................................................................................................
vii
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121
viii
List of Figures
2 .1
Block diagram o f the experim ental setu p used to m easure th e te m p e r­
a tu re dependence of th e microwave absorption of gaseous SO 2 under
sim ulated conditions for the Venus atm osphere..........................................
2.2
12
M easured ab sorptivity (normalized by num ber mixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of tem perature at 4 a tm for
a frequency of 2.25 GHz. The abscissa of the d ata points was shifted
from the actu a l tem p eratu re value for clarity. The
1 -a
error in th e
tem p eratu re m easurem ent is ± 2 K .................................................................
2.3
26
M easured absorptivity (normalized by num ber mixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of tem perature at 4-a tm for
a frequency o f 8.5 GHz. The abscissa of the d a ta points was shifted
from the a c tu a l tem p eratu re value for clarity. The
tem p eratu re m easurem ent is
2.4
±2
1 -a
error in th e
K.................................................................
27
M easured ab so rp tiv ity (normalized by num ber mixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of tem perature at 4 a tm for
a frequency of 21.7 GHz. T he abscissa of the d a ta points was shifted
from the actu a l tem p eratu re value for clarity. The l-a error in th e
tem p eratu re m easurem ent is ± 2 K.................................................................
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28
2.5
M easured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of te m p e ratu re at
2
a tm for
a frequency of 8.5 GHz. The abscissa of the d a ta points was shifted
from the actu al tem peratu re value for clarity. T h e T o error in th e
tem perature m easurem ent is ± 2 K ................................................................
2 .6
29
M easured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a CO 2 atm osphere as a function of frequency a t 4 atm for 295 K.
T he abscissa o f the d a ta points was shifted from th e actual frequency
value for clarity .....................................................................................................
30
2.7 Measured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a CO 2 atm osphere as a function of frequency a t 4 atm for 505 K .
T he abscissa o f the d a ta points was shifted from th e actual frequency
value for clarity.....................................................................................................
2.8
31
Measured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of pressure a t 296 K for a
frequency of 94.1 GHz (Fahd and StefFes, 1992) [6 ]. T he abscissa o f
th e d ata points was shifted from th e actu al tem p eratu re value for clarity. 32
2.9
Gaseous SO 2 line center intensities for frequencies below 750 GHz o b ­
tain ed from th e Poynter and P ick ett catalog (P oynter and P ick ett,
1985) [30]................................................................................................................
3.1
T h e Magellan spacecraft as it conducts a radio occultation experim ent
o f th e Venus atm osphere (StefFes et al., 1994) [44]....................................
3.2
39
51
T otal and residual S-band absorptivity profiles in th e Venus a tm o ­
sphere inferred from th e Magellan spacecraft radio occultation experi­
m ents for orbit 3213 (latitude is 67° n o rth ). The associated stan d ard
deviations are also shown...................................................................................
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55
3.3
Total an d residual X-band absorptivity profiles in th e Venus atm o­
sphere inferred from th e M agellan spacecraft radio occultation experi­
m ents for orbit 3213 (latitu d e is 67° north). The associated standard
deviations are also shown...................................................................................
3.4
55
Gaseous SO 2 abundance profile in th e Venus atm osphere inferred from
th e M agellan spacecraft radio occultation experim ents by using th e Sand X -band absorptivity profiles for orbit 3212 (latitu d e is 67° north).
3.5
Gaseous H 2 S 0
4
60
abundance profile in the Venus atm osphere inferred
from th e M agellan spacecraft radio occultation experim ents by using
the S- and X -band absorptivity profiles for orbit 3212 (la titu d e is 67°
north). Also shown is the gaseous H 2 S 0 4 saturation abundance profile.
3.6
60
Gaseous SO 2 abundance profile in th e Venus atm osphere inferred from
the M agellan spacecraft radio occultation experim ents by using th e Sand X -band absorptivity profiles for orbit 3213 (latitu d e is 67° north).
3.7
61
Gaseous H 2 S 0 4 abundance profile in the Venus atm osphere inferred
from th e M agellan spacecraft radio occultation experim ents by using
the S- and X -band absorptivity profiles for orbit 3213 (la titu d e is 67°
north). Also shown is the gaseous H 2 SO,, saturation abundance profile.
3.8
61
Gaseous SO 2 abundance profile in th e Venus atm osphere inferred from
the M agellan spacecraft radio occultation experim ent by using th e Sand X -band absorptivity profiles for orbit 3214 (latitude is 67° north).
3.9
Gaseous H 2 S 0
4
62
abundance profile in the Venus atm osphere inferred
from th e M agellan spacecraft radio occultation experim ent by using
the S- a n d X -band absorptivity profiles for orbit 3214 (la titu d e is 67°
north). Also shown is the gaseous H 2 S 0
4.1
4
saturation abundance profile.
62
G eom etry of Venus and its atm osphere used in th e disk-averaged ra­
diative tran sfer m odel.........................................................................................
x
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67
4.2
Geometry of Venus and its atm osphere used in th e look-angle radiative
transfer model.......................................................................................................
4.3
68
Tem perature as a function of altitu d e in th e Venus atm osphere ob­
tained using the Pioneer-Venus sounder a n d north probes (Seiff et a l,
1980) [53]................................................................................................................
4.4
73
Pressure as a function of a ltitu d e in th e Venus atm osphere obtained
using the Pioneer-Venus sounder and n o rth probes (Seiff et al., 1980)
[53]...........................................................................................................................
4.5
73
Abundance profile for gaseous H 2 SO 4 in th e Venus atm osphere derived
from the equatorial M ariner 10 radio o ccultation experim ents (Kolodner and StefFes, 1997) [2 ]....................................................................................
4.6
77
Abundance profile for gaseous SO 2 in th e Venus atm osphere obtained
from the ISA V -l/V EG A - 1 ultraviolet sp ectro m eter (B ertaux et a l,
1996) [1]......................................................................................'...........................
4.7
78
C om puted disk-averaged brightness tem p eratu res of Venus as a func­
tion of frequency for various vertical ab u n d an ce profiles of gaseous SO 2 .
Also shown in this figure are th e m easured centim eter and m illimeterwavelength disk-averaged brightness te m p e ratu res of Venus...................
4.8
84
Disk-averaged atm ospheric weighting functions of the Venus atm o­
sphere as a function of a ltitu d e a t frequencies of 8.42, 14.94, 22.46,
and 86.1 GHz. T he constituents of th e Venus atm osphere used in the
m odel are C 0 2, N 2 , H2SO4, H 2O, CO , O C S , and SO2, where uniform
abundance of 75 ppm below 48 km is used for SO 2 ...................................
4.9
85
Disk-averaged atm ospheric weighting functions of the Venus atm o ­
sphere as a function of a ltitu d e a t frequencies of 8.42, 14.94, 22.46,
and
8 6 .1
GHz. The constituents of th e Venus atm osphere used in th e
model are CO2, N2', H2SO4, H 2O, CO, O C S, and SO2, where th e ISAV1
vertical abundance profile is used for SO 2 .................................................
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86
4.10 Difference in th e disk-averaged brightness tem p eratu re as a function
of frequency betw een a Venus atm osphere with only C O 2 , N 2 , H 2 SO 4 ,
H 2 O, CO, and OCS and a Venus atm osphere with C O 2 , N 2 , H 2 SO 4 ,
H 2 O, CO, O C S, and SO 2 , w here three different vertical abundance
profiles are used for SO 2 ...........................................................................
5.1
87
Diagram of a tw o element interferom eter with the interferom eter base­
line coordinate system (u,v) and th e radio source coordinate system
(x,v) (Napier et al., 1983) [71].................................................................
91
5.2
O rientation of Venus in th e sky during observation as viewed from E arth. 96
5.3
Real part of th e observed visibility d ata at 14.94 GHz. Also shown is
a best fit which was obtained using a lim b-darkened disk model. . . .
5.4
Real part of th e observed visibility d a ta at 22.46 GHz. Also shown is
a best fit which was obtained using a lim b-darkened disk model.
5.5
. .
99
Measured brightness tem p eratu re m ap of Venus at 14.94 GHz. Note
th a t the brightness tem p eratu re at center of the m ap is 604.2 K. . . .
5.6
98
101
Measured brightness tem p eratu re m ap of Venus a t 22.46 GHz. Note
th a t the brightness tem p eratu re at center of the m ap is 541.6 K. . . .
102
5.7 Residual brightness tem p eratu re contour map of Venus at 14.94
GHz.
104
5.8 Residual brightness tem p eratu re contour map of Venus at 22.46
GHz.
105
5.9 Gray scale brightness tem p eratu re m ap of Venus a t 14.94 GHz.
. . . 106
5.10 Gray scale brightness tem p eratu re m ap of Venus a t 22.46 GHz.
. . . 107
6 .1
Diagram of a typical airborne INSAR system with th e imaging geom­
e try shown (Z ebker and G oldstein, 1986) [85].............................................
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117
Summary
T he microwave effects of gaseous sulfur dioxide (S O 2 ) in th e atm ospheres of Venus
and E arth have been investigated. New higher accuracy laboratory m easurem ents of
th e microwave absorbing and refracting properties of gaseous SO 2 u n d er sim ulated
Venus conditions have been conducted at frequencies (wavelengths) of 2.25 GHz (13.3
cm ). 8.5 GHz (3.5 cm ), and 21.7 GHz (1.4 cm). B ased on these m easurem ents, a new
em pirical microwave opacity m odel using the Ben Reuven spectral line sh ap e theory
has been derived. This new Opacity m odel provides a m ore accurate characterization
of gaseous SO 2 opacity in th e Venus atm osphere as com pared to previous models.
A new radiative transfer model (RTM ) for Venus which includes th e new opacity
model for gaseous SO 2 has also been developed. This new RTM provides a more
accurate interpretation of the microwave and m illim eter-w ave emission spectrum of
Venus. Specifically, it has been shown th a t a uniform SO 2 disk-averaged abundance
of 75 ppm below th e base of th e m ain cloud layer provides an excellent fit to the
m ost current disk-averaged brightness tem p eratu re m easurem ents at microwave and
millimeter-wave frequencies. F urtherm ore, a new uniform u pper limit of 150 ppm on
th e disk-averaged abundance of gaseous SO 2 below th e base of the m ain cloud layer
has been derived. T h e new laborato ry m easurem ents of the microwave absorbing and
refracting properties of gaseous S 0 2 have been also applied to the interp retatio n of
th e S-band (2.3 GHz) and X -band (8.4 GHz) absorptivity and refractivity profiles of
th e Venus atm osphere which were obtained from th e 1991 Magellan spacecraft radio
occultation experim ents. In additio n , th e SO 2 microwave refractivity m easurem ents
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have been used to investigate th e effects o f SO 2 on the airborne interferom etric syn­
thetic aperture radar (INSA R) imaging o f terrestrial volcanoes. Another im portant
part of this research has been th e conduct of a microwave observation of Venus using
th e Very Large Array (VLA) a t frequencies (wavelengths) o f 14.94 GHz (2 cm ) and
22.46 GHz (1.3 cm ), which has resulted in two high spatial resolution continuum emis­
sion m aps of Venus. Based on the new microw’ave opacity m easurem ents of gaseous
SO 2 and th e new’ radiative transfer m odel, these VLA emission maps have been used
to detect potential spatial variations in th e abundances and distribution of gaseous
SO 2 and gaseous H 2 SO 4 across the disk o f Venus. It has been concluded th a t in the
equatorial and m id-latitudinal regions of Venus, the SO 2 abundance profile derived
from the ISAV -1 ultraviolet spectroscopy experim ent (B ertaux et al., 1996) [1 ] and the
H 2 SO 4 abundance profile derived from th e M ariner 10 radio occultation experim ents
(Kolodner and Steffes, 1997) [2] are representative of the atm ospheric conditions. Ad­
ditionally. in the polar regions, larger abundances of both gaseous SO 2 and gaseous
H 2 SO 4 are indicated, as represented by th e H 2 S 0 4 abundance profiles derived from the
Magellan spacecraft radio occultation experim ents (Kolodner and Steffes, 1997) [2]
and by th e SO 2 abundance profiles derived in th is work (i.e., as per M agellan SO 2
abundance profiles above 37 km , and 150 ppm below’ 37 km ).
xiv
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1
CHAPTER 1
INTRODUCTION
Active and passive microwave rem ote sensing techniques have been extensively used
in studying and im aging th e two sister planets Venus and Earth. Venus, th e closest
planet to E arth , exhibits m any physical characteristics which are much like E arth
(see Table
1 . 1 ).
This has prom pted scientists to rem otely explore and investigate its
surface and atm osphere, which could also be critical to understanding th e processes
th a t shape th e E arth environm ent. Unlike th e terrestrial atm osphere, th e principal
constituent of the Venus atm osphere is gaseous carbon dioxide (C O 2 ) (O yam a et al.,
1980) [3]. It comprises 96.5% of th e atm osphere, and gaseous nitrogen (N 2 ) about
3.5%. O ther trace constituents are sulfur dioxide (SO 2 ), sulfuric acid vapor (H 2 SO 4 ),
carbon monoxide (C O ), carbonyl sulfide (O C S), and w ater vapor (H 2 O). Moreover, a
dense cloud layer which consists of liquid H 2 SO 4 particles is also present (Knollenberg
and H unten. 1980) [4]. T he prim ary sources of th e microwave opacity in the Venus
atm osphere are CO 2 , H 2 SO 4 vapor, and gaseous SO 2 . This thesis concentrates on the
microwave properties of gaseous SO 2 and th e ir effects in the atm ospheres of Venus
and E arth.
It is well known th a t gaseous SO 2 is a significant absorber in th e Venus atm o­
sphere at microwave and m illim eter-wave frequencies (Steffes and Eshlem an, 1981,
Fahd and Steffes, 1992) [5, 6 ]. It is also considered one of the m ost im portant gases
released by volcanoes into th e terrestrial atm osphere which could signal volcanic ac­
tivity (Malinconico, 1979, Friend et al., 1982) [7, 8 ]. Two different rem ote sensing
techniques used to study the atm osphere of Venus axe spacecraft radio occultation
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
experim ents and E arth-based radio astronom ical observations. From spacecraft radio
o ccultation experim ents, one can infer vertical profiles of atm ospheric refractivity,
absorptivity, tem perature, and pressure. W ith Earth-based radio astronom ical obser­
vations, one measures th e natural radio emission from th e p la n et and its atm o sp h ere
which is often expressed as th e brightness tem p eratu re. O ne rem o te sensing tech n iq u e
th a t is used for topographic m apping of surfaces is radar interferom etry. O f specific
in terest is th e m apping of volcanoes on Earth using airborne interferom etric sy n th etic
a p e rtu re radars (INSA R). Several terrestrial volcanoes have been imaged u sin g IN ­
SAR to study their topography and the topographic change due to new eru p tio n s
(Zebker et a/., 1994, M ouginis-M ark, 199-5) [9, 10]. Since SO 2 is one of th e m ajo r
gases released by volcanoes into th e Earth atm osphere, it m ay introduce significant
phase errors (i.e., increasing th e p a th length betw een the SO 2 source and th e IN SA R )
in th e reflected signal which could degrade th e quality of th e im age. Thus, to b e tte r
in te rp re t d a ta obtained from spacecraft radio occultation experim ents, E arth -b ased
radio astronom ical observations, and INSAR im aging of terrestrial volcanoes, th e
microwave properties o f gaseous SO 2 must be known.
T h e objective of th is research has been threefold. The first objective has been to
conduct laboratory m easurem ents of the microwave absorbing and refracting p ro p e r­
ties o f gaseous SO 2 . T h e second objective has been to apply these m easurem ents to
the in terpretation of d a ta obtained from E arth-based radio astronom ical observations
of Venus, spacecraft radio occultation experim ents of Venus, and INSAR im aging of
terrestrial volcanoes. T h e th ird objective has been to conduct a microwave obser­
vation o f Venus using th e W ry Large Array (V LA) in order to obtain high sp atial
resolution m aps of continuum emission at wavelengths of 1.3 cm and 2 cm. B ased on
our m easurem ents of th e microwave properties of gaseous SO 2 , these VLA em ission
m aps have been used to detect potential spatial variations in th e abundances and
d istribution of gaseous S O 2 across th e disk of Venus.
T h e problem of characterizing the microwave absorbing properties of gaseous
2
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Table
1 .1 :
Venus and E arth: A Comparison of Physical C haracteristics.
P aram eter,
Venus,
E a rth
Equatorial D iam eter
6052 km
6378 km
Relative Mass
0.815
1
Density
5.269 g /cm 3
5.517 g /c m 3
D istance from Sun
108 xlO 6 km
150x lO 6 km
R otation Period
243 E arth Days
1
R otation T ype
R etrograde
D irect
Atm ospheric Composition
C 0 2, n 2
n 2,
Surface Pressure
90 atm
1
Surface T em perature
733 Kelvin
300 K elvin
E a rth Day
0 2
a tm
3
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SO 2 under sim ulated conditions for th e Venus atm osphere has been addressed be­
fore. Laboratory m easurem ents have been conducted to characterize the microwave
and millimeter-wave opacity of gaseous SO 2 under Venus-like conditions. Steffes and
Eshleman [5] concluded th a t a t pressures from 1 to 5 atm ospheres (atm ) and a t tem ­
peratures from 297 to 355 K elvin (K) th a t th e absorption coefficient of gaseous SO2
in a CO 2 atm osphere at 2.257 GHz and 8.342 GHz had a
/ 2
frequency dependence
and was approxim ately 50% larger than th a t com puted from th e Van Vleck-Weisskopf
(VVW ) line shape theory. However, th e ir prelim inary m easurem ents did not account
for th e effects of “dielectric loading” in th e resonator used for th e experim ent (for a
description of dielectric loading, see Section 2.1.2.), nor were the effects of gaseous
SO 2 self-broadening considered. Subsequently, Fahd and Steffes (1992) [6 ] conducted
absorptivity m easurem ents of gaseous SO 2 in a CO 2 atm osphere at room tem pera­
ture (296 K) which partially accounted for th e effects of dielectric loading for the
following frequencies (wavelengths): 2.24 G H z (13.4 cm ), 21.7 GHz (1.4 cm ), and
94.1 GHz (0.32 cm). These m easurem ents showed th a t th e absorption coefficient of
gaseous SO 2 in a CO 2 atm osphere is in agreem ent w ith th e V V W line shape theory
at 21.7 GHz and 94.1 GHz b u t not at 2.24 G H z. In addition, th e results showed th at
the f 2 frequency dependence of the opacity of gaseous SO 2 is not uniformly valid for
all frequencies below 100 GHz and pressures above 1 a tm . Although some prelim i­
nary laboratory m easurem ents of th e opacity of gaseous SO 2 in a CO 2 atm osphere
in th e tem perature range from 297 to 355 K were m ade a t 2.257 GHz a n d 8.342
GHz (Steffes and Eshlem an, 1981) [5], no m easurem ents of th e tem p eratu re depen­
dence of gaseous SO 2 opacity were m ade for higher frequencies or tem p eratu res. As
a result, high-accuracy laboratory m easurem ents of th e te m p e ratu re dependence of
th e opacity from gaseous SO 2 in a C O 2 atm osphere a t characteristic tem p eratu res
of th e Venus atm osphere are of significance for the in terp retatio n of radio absorp­
tiv ity data obtained from spacecraft radio occultation experim ents and E arth-based
radio astronomical observations. The high-accuracy opacity m easurem ents have been
4
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achieved by m atch in g th e refractive indices of the lossy and lossless (non-absorbing)
gases used in th e experim ent. Thus, th e effects of dielectric loading on the quality
factor of th e resonator have been rem oved. The m easurem ents have been conducted
a t tem p eratures from 290 to 505 K an d a t pressures from 1 to 4 a tm for th e following
frequencies (w avelengths): 2.25 GHz (13.3 cm), 8.5 GHz (3.5 cm ), and 21.7 G H z
(1.4 cm). B ased on these m easurem ents, a new opacity model for gaseous SO 2 using
th e Ben-Reuven (B R ) spectral line sh ap e theory has been developed. T his new B R
model provides a m ore accurate characterization of gaseous SO 2 microwave opacity
in the Venus atm osphere as compared to other formalisms. It is also consistent w ith
the m illim eter-w avelength laboratory m easurem ents of gaseous SO 2 absorptivity th a t
were conducted by Fahd and Steffes (F ahd and Steffes, 1992) [6 ]. T h e new SO 2 opac­
ity formalism has been incorporated in to a newly developed rad iativ e transfer m odel
to explain th e microwave and millimeter-wave emission spectrum o f Venus and to
set an upper lim it on th e disk-averaged abundance of gaseous SO 2 below the base
of the main cloud layer. Furtherm ore, th e new B R model has been applied to th e
interpretation o f th e S-band (2.3 GHz) and X-band (8.4 GHz) ab so rp tiv ity profiles o f
th e Venus atm osphere which were ob tain ed from th e 1991 Magellan spacecraft radio
occultation experim ents (Jenkins et al., 1994) [1 1 ]. In addition, th e new BR m odel
has been used in a newly developed rad iativ e transfer model to in te rp re t th e
1 .3
cm
and 2 cm em ission m aps which have resulted from VLA observations of Venus (see
C hapter 5).
Another im p o rta n t quantity which has been m easured in conjunction with th e
opacity m easurem ents of gaseous SO 2 is its microwave refraction. T h e refractivity
of gaseous SO 2 , which has not been reported elsewhere in the lite ra tu re , has been
m easured at th e sam e tem peratures, pressures, and frequencies used for m easuring
its opacity. T his m easurem ent has been useful in determ ining th e contribution o f
gaseous SO 2 refractivity to the vertical refractivity profiles of the Venus atm osphere
which were inferred from th e 1991 M agellan spacecraft radio occultation experim ents
5
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(Jenkins e/ a/., 1994) [1 1 ]. A nother application for th e m easurem ent of gaseous SO 2
microwave refractivity has been in investigating th e effects of SO 2 on INSAR im aging
of terrestrial volcanoes.
The rem ainder of this thesis is divided into th e following chapters: In C h a p te r
2,
th e methodology and the results of th e laboratory m easurem ents of the microwave
absorption and refraction of gaseous SO 2 are presented. In ad d itio n , the developm ent
of a new microwave opacity model for gaseous SO 2 th a t uses th e Ben-Reuven sp ectral
line shape theory is discussed. In C hapter 3, th e new SO 2 opacity formalism an d
the SO 2 refractivity m easurem ents are applied to th e in terp retatio n of the S-band
and X-band absorptivity and refractivity profiles of the Venus atm osphere which
were obtained from the 1991 Magellan spacecraft radio occultation experim ents. In
C hapter 4. a new radiative transfer m odel (R TM ) th a t includes th e new form alism
for gaseous SO 2 opacity as well as o th er d a ta relevant to th e surface of Venus an d
its atm osphere is described. Furtherm ore, th e application of th is new RTM to recen t
disk-averaged observations of the microwave and millimeter-wave emission of Venus is
presented. In C h ap ter 5, the conduct of a dual-frequency observation of Venus using
the VLA is discussed. In addition, th e application of the new emission model to th e
interpretation of th e VLA emission m aps of Venus is described. In C hapter
6,
th e
effects of SO 2 microwave refractivity on INSAR im aging of te rrestrial volcanoes are
presented. Finally, th e summary and conclusions of this thesis which focus on th e
unique contributions of this work are given in C h ap ter 7.
6
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CHAPTER 2
LABORATORY MEASUREMENTS OF
THE MICROWAVE ABSORPTION
AND REFRACTION OF GASEOUS SO?
2.1
2.1.1
M icrowave A bsorption o f Gaseous SO 2
Theoretical Background
In a source-free, linear, isotropic, homogeneous, a n d lossy gaseous m edium , th e scalar
Helmholtz equation is written as
V V + 1’V = 0
(2.1)
where V’ denotes th e electric or m agnetic field a n d k is th e complex wave num ber
expressed as
k = P-ja
(2 . 2 )
where 0 is known as the phase co n stan t (in rad ian s per u n it length) and a is th e
absorption coefficient (in Nepers p e r u n it length) o r atten u atio n constant (also known
as th e absorptivity), which is defined as the power loss per unit length. For a uniform
plane wave propagating in the -ff-d irectio n in a lossy gas. th e electric and magnetic
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fields are given by
E( z ) = E 0e ' jkz = E oe~az€ -j0:
(2.3)
(2.4)
where E 0, H 0 are th e am plitudes of th e electric and magnetic fields, respectively.
Thus, in a lossy gas, the electric field am p litu d e of th e uniform p lan e wave
is a tte n u ate d in th e direction of propagation according to e~a:. If th e lossy gas is
characterized by th e complex p erm ittiv ity c = 3 — je " and the real perm eability fi,
then a and 3 are related to e, fi, and th e frequency o f propagation w as follows (R am o
d al.. 1965) [12]
(2.5)
3 = (JL>
( 2 .6 )
and therefore, the ratio of a to 3 yields
a
3
(2.7)
\
For a relatively low loss gas, th e ra tio e"/c# (which is known as th e “loss ta n g e n t” )
is much less than unity, and hence by using the Taylor expansion, Equation 2.7 reduces
to
( 2 .8 )
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Since th e phase constant /? = 2 i r / \ , where A is th e wavelength of th e propagating
wave, then the absorption coefficient becomes
where Qg = d / c" is the quality factor of the low loss gas. Thus, to m easure a at
.wavelength A, Q g should be know n. In the next section, the experim ental approach
used to m easure Q g and subsequently a is explained.
2.1.2
Experimental Approach
In general, Qg for a relatively low loss gaseous m ix tu re can be m easured by introducing
th e gaseous m ix tu re to a cavity resonator and observing its effect on th e resonant
properties of th e cavity (Townes and Schawlow, 1955) [13].
W ith th e absorbing
gaseous m ixture present, the observed quality factor of the cavity resonator, which is
defined as the average stored electrom agnetic energy divided by the energy dissipated
per radian change in phase, is reduced due to th e increase in losses. T he m easured
quality factor of th e gas-filled o r “loaded” resonator can be w ritten as (M atthaei et
a/., 1980) [14]
=
&
+
( 2 ' 1 0 )
where Q m is the m easured quality factor of the gas-filled or loaded cavity resonator,
Qc is the quality factor of the ev acu ated cavity w ith no coupling losses, and Qe\ , Q e2
are th e external quality factors d u e to coupling from th e input and o u tp u t ports of
th e cavity resonator, respectively.
In Equation 2.10, Qm is d ire c tly measured, since it can be expressed as Q =
/ r / A / , where f r is the cavity. reso n an t frequency and A / is its half-power b a n d ­
w idth. The term Q c is controlled by losses due to im perfectly conducting walls in th e
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cavity, as well as losses through ap ertu res opened in th e cavity resonator such as m ode
suppression slots. T h e term Qg accounts for losses in th e absorbing gaseous m ixture,
while Qei a n d Q e2 represent losses due to coupling from the input an d o u tp u t p o rts
of the resonator, respectively. Assum ing th a t the coupling ports are identical, th e n
Qe 1 = Qe2 = Qe- F urtherm ore, note th a t Qe is related to Q m and th e m easured tra n s­
missivity (t m) through a resonator a t resonance by th e following equation (M atthaei
et a/., 1980) [14]
0, = X
’
(2' U )
where tm is given by
tm =
1 0 ~s/1°,
(2 . 1 2 )
and 5 (in dB ) is th e insertion loss of th e cavity at its resonant frequency, which can
be directly m easured. Substituting
1
2 .1 1
into
yields
2 .1 0
_ (l/Q c) + (l/Q ,)
Qm~1 - y fe
,9 1 „.
'
(2,13)
To find Q g. one su b tracts th e m easured quality factor of a gas-filled o r loaded res­
onator ( Qmi ) from th e m easured quality factor of a gas-em pty or unloaded resonator
(<?mu)> which gives (D eB oer and Steffes, 1994) [15]
QS ~
1 ~ y/tmi
1 ~ y/^wii
Qm,
Qmu
( o- \ a \
’
{
]
where tml is th e m easured transm issivity of the loaded (gas-filled) reso n ato r and tmu
is th e m easured transm issivity of th e unloaded (evacuated) resonator.
Consequently, th e absorption coefficient for a relatively low loss gaseous m ixture
10
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can be directly determ ined from th e following expression:
w ith A in km and a in N epers/km . Note th a t
(or k m -1 )=
8 .6 8 6
1
N eper/km = 2 optical d ep th s/k m
d B /k m . where th e third notation is used in th is thesis to avoid any
am biguities.
It should be noted th a t the above expression for the absorption coefficient as­
sumes th a t the cav ity ’s contribution to the overall measured Q is not dependent on
the refractive (i.e., nonabsorptive) properties of th e gas. However, this is no t usually
the case because th e real part of th e dielectric constant of th e lossy gaseous m ixture
will a lte r the dielectric properties o f th e resonator and cause coupling variations from
the input and o u tp u t ports of th e resonator; an effect com m only referred to as “di­
electric loading” (Spilker, 1993) [16]. To remove the effects of dielectric loading, a
lossless (nonabsorbing) gas should b e used to m easure the unloaded term s Q mu and
t mu, such that th e shifts in the reso n an t frequency for th e lossy and lossless gases
relative to vacuum are equal (i.e., identical refractive indices). Note th a t when a
lossless gas is used, th e above expression for th e absorption coefficient is still valid,
since 1 JQg = 0 for th e nonabsorbing gas as well as for vacuum .
2.1.3
Experimental Apparatus
The experim ental setu p used to m easure the tem perature dependence of th e m i­
crowave absorptivity of gaseous SO 2 in a CO 2 atm osphere u n d er sim ulated Venus con­
ditions is similar to th a t previously used by DeBoer and Steffes (1994, 1995) [15, 17]
with m inor modifications. Figure 2.1 illustrates th e m easurem ent system, which con­
sists of a microwave subsystem , a Venus atmospheric sim ulator subsystem , and a d ata
acquisition subsystem.
T he microwave subsystem consists of two circular cylindrical cavity resonators.
11
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PC
Vfecutsn
Gauge
Display Pressure
Digital
Temperature
Controller
Regulator
CO, gas
Regulator
Cold
Bath
Figure 2 . 1 : Block diagram of th e experim ental setup used to m easure th e tem perature
dependence of the microwave absorption of gaseous SO 2 under sim u lated conditions
for the Venus atm osphere.
12
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One cavity resonator is designed to operate in th e frequency range
th e o th e r in th e range 8-27 GHz.
1 .3-8.5
G H z and
Each cavity has in p u t and output p o rts with
adjustable couplers used to couple energy into and out of th e resonators. In addition,
each cavity resonator incorporates two gaps to suppress th e degenerate TM /m„ modes
which have low-quality factors (Q ’s).
The in p u t port o f each cavity resonator is
connected to a microwave sweep oscillator. T h e oscillator consists of a m ain fram e
with a replaceable backward wave oscillator (BW O ) m odule. For the purposes of this
experim ent, three BWO m odules are used: th e first m odule operates in th e 2-4 GHz
range (S band), th e second m odule operates in th e 8-12 G H z range (X b an d ), while
the th ird m odule operates in th e 18-26 GHz range (K band). T h e output term inals of
the S and X band BWO m odules are fed to S and X band isolators, respectively, while
the o u tp u t term inal of th e K band BWO m odule is fed to a 10-dB atte n u ato r. Note
th a t th e a tte n u ato r and th e isolators are used to minimize any reflected signal from
the cavity resonator to th e sweep oscillator. Moreover, the isolators perm it essentially
u n atten u ated transm ission from th e sweep oscillator to th e cavity resonators. The
o u tp u t of each of the S and X band isolators is connected to th e input port o f th e 1.38.5 GHz resonator via a flexible coaxial cable, whereas the o u tp u t of th e a tte n u a to r is
connected to the input port of th e 8-27 GHz resonator via a three-spline rigid coaxial
cable. A high-resolution sp ectru m analyzer (H P 8562B) is th en used to m easure the
signal from the output po rts of th e two resonators.
T h e Venus atm ospheric sim ulator subsystem consists of a stainless steel pressure
vessel which contains th e tw o cavity resonators. This containm ent vessel, w hich can
w ithstand pressures up to
8
a tm , is placed inside a digitally controlled te m p e ratu re
cham ber th a t is capable of reaching tem p eratu res up to 600 K. Two therm ocouples
which are suspended w ithin th e pressure vessel are used to m onitor th e te m p e ratu re
of th e introduced gas. One therm ocouple is connected to a digital v o ltm eter, while
the o th er is connected to a digital tem p eratu re controller. B o th th e CO 2 gas cylinder
and th e SO 2 /C O 2 gaseous m ix tu re cylinder are connected to th e pressure vessel via
13
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a network of 3/8-inch stainless-steel tubing. In addition, regulators and valves are
included in th e tubing netw ork so th a t p arts of the m easurem ent system m ay be
isolated to detect gas leaks an d to ensure safety. A vacuum pum p th a t is capable of
achieving 3 to rr or less is used to evacuate th e pressure vessel before ad m ittin g the
gas. The vacuum statu s is m onitored via a digital therm ocouple vacuum gauge, which
can m easure pressures in th e range
1
to 800 torr. For higher pressure m easurem ents,
an analog positive pressure gauge which is able to m easure pressures in the range
0
to 7.8 atm is used, w ith ± 0 .1 3 a tm accuracy throughout its usable range.
The final subsystem is responsible for d a ta acquisition. T his subsystem consists
of a personal com puter loaded w ith a software package th a t is used to interface with
the HP 8562B spectrum analyzer via a general purpose interface bus (G PIB) (DeBoer
and Steffes. 1995) [17]. The softw are package reads, processes, and fits th e spectrum
data points. Then th e resonant frequency, half-power b andw idth, and am plitude at
the resonant frequency are found. T he spectrum m easurem ent is repeated several
tim es, and averages and variances are also com puted by th e software.
2.1.4
Experimental Procedure
T he first step in th e m easurem ent process is to heat the e n tire system for sufficient
tim e (approxim ately
12
hours) so th a t therm al equilibrium is achieved at th e desired
experim ental tem perature. T h en th e pressure vessel is evacuated, and the cavity
resonant frequency, th e half-power bandw idth, and the a m p litu d e at th e resonant
frequency are m easured for th re e different resonances: 2.25 G H z (13.3 cm ), 8.5 GHz
(3.5 cm), and 21.7 GHz (1.4 cm ).
N ote th a t a t 295 K th e quality factor of th e
evacuated resonator ranges betw een 70000-73000 at 2.25 G H z, 126000-128000 a t
8 .5
GHz, and 15000-15600 at 21.7 G H z. A prem ixed analyzed SO 2 /C O 2 gaseous m ix­
ture is then introduced slowiv in to th e pressure vessel until th e required pressure is
reached. As th e SO 2 /C O 2 gaseous m ix tu re is adm itted, changes in the resonant fre­
quency are observed. Thus, careful tracking of the desired resonance is im portant.
14
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since other resonances are present. Once th e resonant frequency stabilizes, th e sam e
m easurem ents performed for th e evacuated resonator are repeated for the gas-filled or
loaded resonator and, consequently, Qmi is determ ined. The pressure is then reduced
by venting, and subsequent m easurem ents a re likewise conducted at lower pressures
in order to determ ine the absorption coefficient of the SO 2 /C O 2 gaseous m ix tu re
at those pressures. After com pleting the required m easurem ents with the SO 2 /C O 2
gaseous m ixture, a vacuum is draw n in the pressure vessel, and th e quality factor of
each of the evacuated resonators is again m easured to ensure its consistency. N ext,
gaseous CO 2 is introduced into th e pressure vessel such th a t th e refractive indices
of the SO 2 /C O 2 gaseous m ixture and gaseous C O 2 are identical. The m easurem ent
procedure is then repeated, and Q mu is determ ined. Note th a t by measuring Q mu
with gaseous C O 2 rather than w ith a vacuum , th e effects of dielectric loading are
removed. Also note that the sm all absorptivity due to the pure C O 2 gas is well below
the detection sensitivity of th e m easurem ent system ; thus it serves as a “lossless*
reference (Ho et ah, 1966) [18]. T h e last step in th e experim ental procedure is to
m easure the am plitude of the tra n sm itte d signal directly from th e microwave sweep
oscillator to th e spectrum analyzer, which in tu rn , is used to determ ine the insertion
loss of each cavity resonator at its resonant frequency. Consequently, tm\ and t mu are
determ ined. N ote th at tmi and tmu range betw een 0.001 to 0.003 a t *2.25 GHz,
8 .0
GHz, and 21.7 GHz.
2.1.5
Experimental Uncertainties
Laboratory m easurem ents of th e microwave opacity from gaseous SO 2 in a CO 2 a t­
m osphere are sub ject to two classes of uncertainties. The first class is due to in stru ­
m ental errors which are caused by th e lim ited accuracy of th e equipm ent used to
m easure the resonant frequency, half-power bandw idth, transm issivity, mixing ratio
of th e gaseous m ixture, pressure, tem p eratu re, and resonance asym m etry. Table 2.1
shows the standard deviations of th e resonant frequency {<r/r,a) and the half-power
15
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Table 2.1: Spectrum A nalyzer Instrum ent U n certain ty a t R esonant Frequencies.
R esonant Frequency,
Vjr.c'
<7&f,0
(GHz)
(K H z)
(KHz)
2.25
25
0.240
8.5
95
0.800
21.7
372
4.820
bandw idth m easurem ents (<Ta /,0) due to the sp ectru m analyzer accuracy a t 2.25 GHz,
S.5 GHz, and 21.7 GHz (H ew lett-Packard C orporation, 1989) [19]. U ncertainties in
th e transm issivity m easurem ent have been neglected, since the worst case variations
in the expression
1
— \/i have been less than
1 %.
In the case of th e uncertainty in
th e mixing ratio of the gaseous m ixture, a cu sto m prem ixed, constituent-analyzed
SO 2 /C O 2 gaseous m ixture from Matheson G as C om pany has been used with ± 2 %
uncertainty in the stated com ponent mixing ra tio . For pressure m easurem ent, th e
analog pressure gauge has a ± 0 .1 3 atm uncertainty. In the case of tem p eratu re m ea­
surem ent. the digital te m p e ratu re controller h as ±0.25% of th e in p u t tem perature
span, which corresponds to ± 2 K. Another effect known as “resonance asym m etry"
m ay produce errors, since coupling from other resonances may d isto rt th e measured
bandw idth of th e resonance being m onitored. T h e asym m etry figure of merit A&j
defined as
A±f =
- . /*] x
1 0 o%,
(2.16)
Jh ~ Jl
where fh is the higher frequency a t half-power transm issivity and /) is the lower
frequency at half-power transm issivity is m onitored and recorded throughout th e
experim ents. Note that for a perfectly sym m etric resonance. .4 ^ / = 0%. However.
16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
th e m easured resonances are not perfectly symmm etric. W ith th e SO 2 /C O 2 gaseous
m ixture present in th e cavity resonator, th e absolute asym m etry has been about
5% at 2.25 GHz, 11-18% at 8.5 GHz, and
6 - 1 2 %.
1-
a t 21.7 GHz. Even w ith CO 2 gas
present, the corresponding resonance asym m etries are approxim ately equal to the
values obtained as w ith th e SO 2 /C O 2 present in the cavity. This im plies th a t th e
phenom enon of resonance asym m etry is not induced by the introduction of th e lossy
gaseous m ixture to th e cavity. Thus th e resonance asym m etry is m ost likely due
to th e im pedance m ism atch at th e probe-to-cable interface, which is a function of
frequency. However, since the effects of dielectric loading in these experim ents have
been removed (i.e., im pedance m ism atch effects have been also rem oved), the im pact
of resonance asym m etry on absorptivity measurem ents is generally negligible.
The other im p o rtan t class of uncertainties results from th e random electrical
noise in the system . This noise is caused by the large insertion loss of th e cavities
(due to m inim al coupling), which is necessary to m aintain high-quality factors. The
two quantities th at are influenced by th e electrical noise are th e resonant frequency
and th e half-power bandw idth. For repeated measurements, where
20
d a ta points
have been recorded per frequency, pressure, and tem perature, it has been found th a t
th e resonant frequency can be m easured very accurately (variance <0.01% ). However,
th e bandw idth m easurem ents are significantly affected by the random noise, which in
tu rn , influences th e m easured quality factor. Assuming Gaussian statistics, the total
standard deviation in th e
20
bandw idth m easurem ents (<Ta/,) taken for each m easured
absorption coefficient is obtained by m ultiplying the sample stan d ard deviation in
th e bandw idth (o'a /.) w ith a scale factor called the confidence interval, which is
norm alized to th e square root of th e num ber of repeated m easurem ents (Kreyszig,
1983) [20]. For th e 20 bandw idth m easurem ents, a 3.55 confidence interval has been
used, which corresponds to a 0.999 confidence level. Thus th e variance of th e repeated
17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bandw idth m easurem ents is calculated using
2 _ (3.55)2
A/t ~
20
A f‘
(2.17)
where
> )2
t=i
(2 -18)
where N =20 is th e total num ber of repeated half-power b andw idth m easurem ents,
A /, are the individual bandw idth m easurem ents, and < A / > is th e mean o f th e 20
bandw idth m easurem ents w hich is given by
< A /> = ^ E A / i
jV «=i
(2.19)
T he overall one-sigma e rro r (<r) in the m easured absorption coefficient ( a ) is de­
term ined by incorporating th e individual uncertainties into a “w orst case” u n certain ty
expression given by (DeBoer and Steffes, 1994) [15]
o
________________ ______________ ___
a = — — y/{< T l > + <
17
> -2 <
r ur,
>)
d B /k m
(2.20)
where
^ v2 v
<1»>
^
I”1 p
< r -r ,>
and K{ = l —
( —2
__
-
£ 7
1 _2
I ^Jrta
y * * f .a + CTa / , +
(
2
I
q T +
1 ^frta
1
^
o
.’------ )
, ^ /r io ^ A /ia ^
-
f n n, \
[2.21)
/ n nn\
(2 -2*>
tmi is the m easured transm issivity, and i = u, I denotes an unloaded
and loaded resonator, respectively. Note th at th e worst case uncertainty expression
accounts for th e correlation betw een th e errors in half-power bandw idth and resonant
frequency m easurem ents for b o th the loaded and unloaded resonators.
18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.1.6
Experimental Results and Interpretation
High accuracy laboratory m easurem ents of th e tem p eratu re dependence of th e mi­
crowave absorption from gaseous SO 2 in a C O 2 atm osphere have been conducted at
tem peratures from 290 to 505 K and at pressures from
1
to 4 a tm for th e following
frequencies (wavelengths): 2.25 GHz (13.3 cm ), 8.5 GHz (3.5 cm ), and 21.7 GHz (1.4
cm ). Tables 2.2. 2.3, 2.4, and 2.5 show th e results of these absorptivity measurem ents
with th e one-sigma uncertainty a t 295, 365, 435, and 505 K, respectively. For com­
parison purposes, these tables also show the calculated absorptivity of th e SO 2 /C O 2
gaseous m ixture using th e developed Ben-Reuven (BR) spectral line shape model,
which is discussed in th e next section. In ad d itio n , the value o f \B R i which is a
m easure of the goodness of the fitting function (of th e developed B R form alism ) with
respect to th e results of the absorptivity m easurem ents, is also shown in th e tables
(note th a t a smaller value of \ B
2 R im plies a b e tte r fit). For com parison purposes,
Table 2.6 gives the
\ 2
values obtained using th e new BR m odel, th e V V W model
(Van-Vleck and Weisskopf, 1945) [2 1 ], th e Gross (G R ) model (G ross, 1955) [22], the
Janssen and Poynter (J P ) m ultiplicative expression (Janssen and P oynter, 1981) [23],
and th e Steffes and Eshleman (SE) m ultiplicative expression (Steffes and Eshleman,
1981)- [5]. A -brief description of th e B R , V V W , G R , spectral line shape models is
provided in the next section. The J P and SE absorption coefficient expressions can
be expressed as
q jp = 16.02 x 106q f 2P 122T - 31
a SE = 25 x l O V
2 ^ 1'20? 1 - 3 1
d B /k m
dB /km
(2.23)
(2.24)
where q is th e SO 2 num ber mixing ratio, f is th e frequency in GHz, p is th e pressure
in a tm , and T is the tem perature in K.
Table 2.6 also gives the total of th e
\ 2
values for each form alism , which shows
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
th a t the new BR form alism has th e sm allest \ 2 to ta l. Thus the new BR model pro­
vides a b e tte r overall fit to the m easured microwave absorption of gaseous SO 2 in a
CO 2 atm osphere. Figures 2 .2 , 2.3, an d 2.4 show th e m easured absorptivity (norm al­
ized to num ber m ixing ratio) as a function of te m p eratu re at 4 a tm for frequencies
2.25 GHz, 8.5 G Hz, and 21.7 GHz, respectively. Also shown in th ese figures are th e
calculated absorptivities using th e developed BR, V V W , GR, JP , and SE models.
Note from these figures th a t the developed BR form alism provides a more accurate
characterization of th e microwave absorption of gaseous SO 2 in a C O 2 environm ent
as compared to th e o th er formalisms. Figure 2.5 presents the m easured norm alized
absorptivity
els
a function of tem p eratu re at 2 atm for a frequency of 8.5 GHz. From
this figure, it is clear th a t the developed BR model provides an excellent fit to the
measured d a ta even at low pressures.
O ther models are also shown in th e figure
for comparison. Figures 2.6 and 2.7 show the m easured absorptivity (norm alized to
num ber m ixing ratio) as a function of frequency at 4 a tm for 295 K and 505 K, re­
spectively. Again, one can see th a t th e developed BR formalism results in a b e tte r fit
to th e measured d ata as compared to o th er models for both the highest and lowest
tem peratures. However, it can be noticed from Figure 2.3 th a t one pair of m easured
absorptivities is inconsistent (error bars do not overlap). This inconsistency a t 435
Kelvin is likely due to errors in th e tem p eratu re m easurem ent which m ight have been
caused by th e im proper closure of th e valve inside th e tem p eratu re cham ber. Fig­
ure
2 .8
shows th e results of the gaseous SO 2 absorptivity experim ent conducted by
Fahd and Steffes (1992) [6 ] at a frequency of 94.1 GHz, pressures of
1
and
2
a tm , and
a t a tem p eratu re of 296 K. Also shown in this figure are th e calculated absorptivities
•
using the developed B R, VVW, G R , JP , and SE m odels. Note from this figure th a t
th e developed B R m odel provides an excellent fit to th e m easured m illim eter-w ave ab­
sorptivity d a ta as well as th e VVW and th e J P models. Thus, the new B R form alism
can also be applied to the interpretation of absorptivity d a ta in th e millim eter-wave
regim e of the electrom agnetic spectrum .
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
O verall, this new BR form alism provides a substantial im provem ent over previ­
ous m odels when com pared to our microwave absorptivity m easurem ents. Thus, it
will provide a m ore accurate interpretation of th e Venus d a ta o b tain ed from spacecraft
radio occultation experim ents and from E arth-based radio astronom ical observations.
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.2: Measured Microwave A bsorption of Gaseous SO 2 in a CO 2 A tm osphere
295 K for Various Pressures and Frequencies.
B a te
A p ril 28, 1994
M ay 16. 1994
J u n e 8, 1994
P re * # u re
F re q u e n c y
M ix in g R atio
M e a s u re d 0
C a lc u la te d 0
n tm
GHz
%
d B /k m
d B /k m
4 06
223
8.30
0 .7 4 3 ± 0 .0 3 7
0 .6 8 8
2 .2 3 6
4 06
8.5
8.30
10 205 ± 0 .138
9 .7 1 7
12.493
4 06
21 7
830
6 3 .8 9 9 ± 2.207
61 91 6
0.808
3 04
2 25
8.30
0 .4 5 2 ± 0 038
0 490
1.040
3.04
8 5
8.30
6 .9 3 1 ± 0 .1 6 2
6 .8 7 5
0 .1 2 2
*B R
3.04
217
8.30
4 9 .0 6 2 ± 2.870
4 3 .5 7 5
3 .6 5 5
2 .0 2
225
<30
0 .3 9 7 ± 0 .0 3 6
0 .3 0 7
5 .5 6 7
0 .6 1 9 '
2-02
8 .5
8.30
4 1 1 3 ± 0.154
4 .2 5 2
2.0 2
21 .7
8.30
2 8 603 ± 2-447
2 6 .9 9 0
0.434
4 .0 6
2 25
8.30
0 .6 1 3 ± 0 .0 3 7
0 .6 6 8
4 .0 1 0
4 .0 6
8 .5
8.30
1 0.004 ± 0.134
9 .7 1 7
4.611
4 .0 6
21-7
8.30
6 0 .9 8 1 ± 2.216
6 1 .9 1 6
0 .1 7 8
3 38
2 25
8.30
0 .5 4 1 ± 0 .0 3 7
0 .5 5 5
0 .1 3 7
3 .3 8
8.5
8.30
7 .8 4 9 ± 0 .146
7.601
0 .1 0 6
3 .3 8
217
8.30
5 2 941 ± 2.933
4 9 .5 1 3
1.366
2 .3 6
2 25
8.30
0 .2 8 2 ± 0 .037
0 .3 6 7
5.214
2 .3 6
8.5
8.30
4 .8 6 0 ± 0 .136
5 .0 9 7
2.930
2 .3 6
217
8.30
3 6 3 2 8 ± 2 .766
32 2 9 7
2.306
1.68
225
830
0 .1 4 2 ± 0.041
0 .2 4 9
6.621
1.68
8.5
8.30
3 .4 7 6 i : 0 .1 3 7
3 .4 4 5
0.051
1 68
21 7
8.30
2 1 3 8 9 ± 2.612
21.924
0 .0 4 2
4 .0 6
2-25
8.30
0 .6 1 6 ± 0 .0 3 7
0 .6 6 6
3 .7 4 5
3 .3 8
2-23
830
0 .5 0 2 ± 0 .0 3 6
0 .5 5 5
2.134
3 .04
225
8.30
0 .4 6 1 ± 0 .0 3 6
0 .4 9 0
0 .6 4 0
2 .3 6
2-25
8.30
0 .3 2 5 ± 0 .0 3 7
0 .3 6 7
1.244
2 .0 2
2-25
8.30
0 .2 1 6 ± 0 .0 3 6
0 .3 0 7
5 .656
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.3: M easured Microwave Absorption of Gaseous SO 2 in a C O j A tm osphere at
365 K for Various Pressures and Frequencies.
D a te
J u n e 24. 1994
P re * « u re
F req u en cy
M ixing R a tio
M e a s u re d 0
C a lc u la te d 0
u rn
GHz
%
d B /k m
d B /k m
*br
4 .0 6
2.26
830
0 .3 4 8 ± 0 .0 4 6
0 381
4 .0 6
6.6
6 30
5 .6 1 5 ± 0 .2 3 6
5.36
1.191
4 06
21 .7
8.30
29 346 ± 3 .1 5 7
33 93
2.1 0 4
3 04
2.2 6
8-30
0 .3 1 9 ± 0.0 4 8
0.274
0936
3.0 4
85
630
3 .7 9 0 ± 0 187
3.616
0 .0 1 9
0524
3.04
21.7
8.30
17.471 ± 2.974
24 091
4 .9 5 6
2 .0 2
2.26
8.30
0 .1 1 6 ± 0 .0 5 9
0.173
0.9 2 2
0 .9 5 5
2 .0 2
6.6
8.30
2 .2 2 6 ± 0.164
2 .389
2 .0 2
21.7
6.30
7 .2 7 5 ± 2 .9 2 0
16.137
7.2 4 9
A u g 1. 1994
4 .0 6
2.26
8.97
0 .3 4 2 ± 0.0 6 6
0.411
1 .1 0 7
4 .0 6
6 .6
8.97
6.674 ± 0 .2 9 7
5 .7 8 6
0.144
J u ly 31, 1994
4 06
2 1.7
8.97
32.3 0 4 ± 3 .060
3 6 .6 7 2
2037
A u g .1.1994
3.0 4
2-26
8.97
0 .2 5 3 ± 0.0 7 8
0 .2 9 6
0 .2 9 9
3 04
6.5
8.97
3 974 ± 0 230
4.121
0 .4 1 5
J u ly 31. 1994
3 04
21.7
8 .97
23 896 ± 4 441
2 6 .0 4 2
0.234
A u g . 1. 1994
2 .0 2
8.5
8.97
2 299 ± 0 .207
2 .5 8 0
1 .847
J u ly 31. 1994
202
21.7
8.97
1 3 .747 ± 2.853
16.359
0 .8 3 6
Table 2.4: M easured Microwave Absorption of Gaseous SO 2 in a CO 2 A tm osphere at
435 K for Various Pressures and Frequencies.
D a te
A u g 4. 1994
v3
*BR
P re * * u re
F re q u e n c y
M ixing R a tio
M easu red Q
C a lc u la te d a
a tm
GHz
*
d B /k m
( d B /k m )
4.0 6
2 .25
8.97
0 .2 2 3 ± 0 .0 7 8
0 .254
0 .1 5 3
4.06
8.5
897
2 .6 0 6 ± 0.231
3 .5 5 5
10.477
A u g 21, 2994
4.0 6
2 1 .7
8-97
2 7 .9 6 9 ± 6.528
2 2 .4 5 5
1.0 0 2
A u g 4. 1994
3.04
2.25
8-97
0 .1 4 0 ± 0 .0 6 2
0 .184
0.494
304
8.5
897
2 .2 2 6 ± 0 .230
2.5 4 6
1.929
3-04
2 1 .7
8.97
1 6 .7 6 0 i
5.853
16.071
0 .2 1 7
0 .6 3 7
A u g .2 1 . 1994
2-02
2.25
8.97
0 .0 5 3 ± 0 .0 7 9
0-116
A u g .4 . 1994
2 .0 2
6.6
8.97
1 .4 9 0 ± 0 .2 3 6
1612
0 .2 6 7
A u g .21. 1994
2 .0 2
21.7
8.97
1 1 .3 4 7 ± 6 .723
10.2 1 6
0 .0 2 6
4 .0 6
2.25
8.97
0 .2 8 9 ± 0 .0 6 5
0 .254
0 .2 9 0
4 .0 6
8.6
8.97
3 .2 7 7 ± 0 1 5 5
3 .5 5 5
3 .2 2 6
406
21.7
8.97
3 3 .2 4 6 ± 6.224
22 455
3 .006
2 .2 5
8.97
0 .2 4 9 ± 0 .0 6 9
0.184
0 .546
8.5
8.97
2.531 ± 0 .1 6 2
2.5 4 6
0.007
S e p t .22. 1994
A u g .2 1 , 1994
304
304
•
S e p t .22. 1994
3-04
21.7
8.97
2 0 .5 8 0 ± 6 .252
16071
0.5 2 0
A u g .2 1 . 1994
2-02
6 5
8.97
1 .1 6 2 ± 0.144
1.612
9.7 8 2
S e p t 22. 1994
2 02
21 7
8 97
15.201 ± 4 948
10.216
1.015
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.5: Measured Microwave A bsorption of Gaseous SO 2 in a CO 2 A tm osphere at
505 K for Various Pressures and Frequencies.
D a te
O c t.25. 1994
P re » * u re
F re q u e n c y
M ix in g R a tio
» t Ti
GHz
%
d B /k m
d B /k m
oe
2.25
a 66
0.252 ± 0 1 4 5
0 .1 6 3
0.377
a .5
2.436 ± 0 1 7 3
2.274
0 .663
11.905 ± 3 .4 2 6
14 33 6
0.503
0 075 ± 0 091
0 .1 1 8
0 .223
4
D ec 31. 1994
4 06
21.7
O c t.25. 1994
3 04
2.25
3 04
S.5
866
866
8.66
8 66
S e p t 23, 1994
304
21.7
8 .9 7
4 06
2 02
2.25
2 .0 2
8 5
8-66
8.66
S e p t 23. 1994
202
21.7
6 .9 7
O c t.26. 1994
4-06
2 25
4 06
8-5
J t n l . 1995
4 06
21.7
O c t 26. 1994
304
a5
O c t 25. 1994
866
866
866
866
M e tz u r e d
q
C a lc u la te d a
*BR
1.578 ± 0 .1 6 3
1.636
0.126
13.230 ± 7 .7 0 3
1 0 .700
0.106
0.058 ± 0 .0 9 9
0 .0 7 5
0 .030
1.153 ± 0 .1 5 0
1.046
0 .513
7.731 ± 7 .9 9 5
6 .8 6 9
P 01 2
0.188 ± 0 1 0 0
0 .1 6 3
0.062
2.488 ± 0 170
2.274
1.593
11.496 ± 2 .5 2 0
1 4.336
1.270
1.685 ± 0 . 1 7 3
1636
0.082
S e p t.24. 1994
3-04
21 7
6 .9 7
11.095 ± 6 .9 6 2
10.70
0.003
O c t 26. 1994
2 02
2 26
6 .6 6
0 .046 ± 0 .0 7 0
0-075
0.169
2.0 2
as
8.66
1.036 ± 0 1 6 0
1046
0.004
S e p t 24. 1994
2 02
21.7
8 97
5.856 ± 6 53 2
6 869
0.024
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.6: Goodness of F it Function ( \ 2) using th e New Ben-Reuven (B R ), VanVleck and Weisskopf (V V W ), Janssen an d P oynter (J P ), Gross (G R), and Steffes
and Eshlem an (SE) Form alism s.
2 236
.2
W VU’
16-262
4 396
X o*
20 1 8 951
190.260
*% R
0.41&
12 493
152 883
118 805
1936 638
3099.089
0.608
11.333
31 652
75.861
570 018
1
\ 3/ p
.2
.3
180 273
1.584
7 .3 2 0
66 4 1 7
0 .2 3 4
0.024
1.858
3218
24 617
1.84 7
0 .0 8 8
5.641
19.887
95618
25584
1 040
0538
10-801
4 6 5 .2 1 4
130 502
0 .8 3 8
0 .5 1 6
2.423
3 .4 5 7
0.122
28 407
63-945
4 5 0 .2 5 3
1242-184
0 .1 6 3
0.001
0 .2 9 9
3 0 .9 1 2
5 502
3 655
8-853
2 522
4 .5 2 8
134-869
1 0 .477
2 .4 4 6
18.328
116-546
167.841
5-567
11-807
1.506
7 0 .2 5 7
14 677
1.002
1.572
0 .3 4 5
0 .0 0 0
3151
0.819
3 349
32-949
92 965
555 227
0 .494
o .u o
0 .574
23-114
5 645
0-434
1 358
2-621
2.161
79.707
1 .929
0 .101
3 .6 7 7
2 7 .6 5 5
6 6 .2 7 5
4-010
0 .2 8 6
31-297
1 2 5 4 .4 8 9
298.987
0 .2 1 7
0 .3 4 9
0 .0 5 8
0.004
1.828
4-611
126 333
161.696
2 1 9 0 .9 3 6
34 5 9 356
0 .6 3 7
0 .3 8 6
0-581
5.996
2 .4 0 6
0 178
4 137
47.780
99 644
628 602
0 .2 6 7
0 .0 0 0
0 304
3 .5 1 5
18-671
0 .0 2 6
0 .0 4 3
0014
0003
0-556
0 137
2 794
9.668
641 444
157.676
0.106
44 773
104 648
8 7 3 -6 4 5
1933 678
0 .2 9 0
3 .072
0 123
32-092
3 .2 6 8
1 366
6 070
7 593
14-075
191886
3 .2 2 8
0 .4 8 5
1 1 .2 4 2
170.580
265.004
5 214
0 903
14 555
269 561
100-600
3 .006
3 .8 3 5
1 .866
0 716
0 536
2 930
5 .026
73.115
250 909
1048.206
0 .5 4 8
0 .9 9 6
0 .4 9 3
4.490
0.181
2 306
4 628
1.040
0 983
75.922
0 00 7
1 .612
0 .5 6 6
24 747
7 4 .246
6 821
3 .2 9 3
11.274
1 0 0 .2 5 2
51.006
0 .5 2 0
0 .7 0 2
0 .261
0.052
0 .9 6 2
0.051
5.969
14.085
36 348
39 6 511
9 .7 8 2
5 .2 8 3
1 0 .1 3 6
2 8 .6 6 0
8 7 .6 7 6
0 .0 5 5
0.011
3125
2-6 6 6
53.169
1 .0 1 5
1.127
0 .8 8 0
0.504
0 .363
30 549
12 4 9 73
296.666
0 .3 7 7
0-569
0 .3 8 8
1.144
0.001
2*134
0 406
. IS 312
734 826
195.802
0 .8 8 3
5 .2 0 3
0 .5 4 9
2 1.549
3 9 .6 7 2
0.640
1 104
10.187
5 0 5 -578
138 744
0503
0 .2 3 8
0 .8 3 7
2.578
1 0 .436
1.244
0 047
7.007
2 3 2 -5 6 7
78 706
0 .2 2 3
0 .0 9 8
0 .1 7 8
4.641
1.191
5 656
1 695
12.327
172-133
73.429
0126
0 .2 8 6
0 .0 7 2
11.050
31435
0.524
0 .1 4 5
2 75]
2 1 3 -917
42.579
0 108
0144
0 08 8
0 .0 0 9
0-217
1 191
14.303
3 454
13 9 .5 3 8
238.710
0 030
0-0 0 7
0 .0 1 3
0.914
0 .2 4 6
2.104
0 425
10 226
2 0 .2 6 5
95.665
0 .5 1 3
1-366
1.265
0.168
6 .1 5 6
0936
2 963
0-219
5 5 .6 3 2
8.204
0 .0 1 2
0 016
0 .0 1 8
0 .0 0 0
0 .1 0 3
0 019
4 .2 2 9
6-105
73-237
215.264
0 .0 6 2
0 .2 0 5
0 .0 6 9
4.600
0-350
4 956
3-127
11-857
16125
71.294
1-593
6 .9 0 2
1.123
19.529
3 7 .2 7 4
0-922
0 .3 4 2
1.197
20 3 4 9
7.718
1.270
0.681
1 .9 8 0
5.506
2 0 .7 6 7
0.955
0-076
4-651
20598
116.726
0 .0 8 2
1 .2 6 5
0 .1 3 6
6.303
21721
7-249
6-322
o
‘i
o
*#
0.042
8 745
12-511
41444
0 .0 0 3
0 .0 1 3
0 001
0.041
0 .6 7 6
1-107
0-056
3-114
1 34.051
29463
0 .1 6 9
0 .0 8 2
0 .1 0 5
2.302
0 .7 4 9
0-144
3 .5 5 7
8 514
133 4 7 0
211-391
0 .004
0 .1 2 9
0.101
1.255
9 .3 7 2
2-037
0-2 9 7 .
11.376
2 3 -7 3 7
115-007
0.024
0 .0 1 8
0 .0 1 5
0.065
0-463
0.299
0 .0 0 3
0 782
3 8 .1 7 7
9-600
134
518
14293
17610
T o itl
976
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J
Measured data
NewBR model
WW model
GR model
JP model
model
250
300
350
400
450
500
550
Temperature (K)
Figure 2.2: M easured absorptivity (normalized by num ber m ixing ratio ) of gaseous
SO 2 in a CO 2 atm osphere as a function of tem p eratu re a t 4 a tm for a frequency of
2.25 GHz. The abscissa of the d a ta points was shifted from th e actu al tem p eratu re
value for clarity. T he 1 -a error in th e tem perature m easurem ent is ± 2 K.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Measured data
■— New BR model
- - W W model
GR model
•••• JP model
—
model
210“
300
350
400
450
500
550
Temperature (K)
Figure 2.3: Measured absorptivity (norm alized by num ber m ixing ratio) of gaseous
SO 2 in a CO 2 atm osphere as a function o f tem p eratu re a t 4 a tm for a frequency of
8.5 GHz. T he abscissa of th e d ata points was shifted from th e actual tem p eratu re
value for clarity. The l-<r error in the te m p e ratu re m easurem ent is ± 2 K.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J
Measured data
New BR model
- - - WWmodel
GR model
• JP model
-+SE model
250
300
350
400
450
500
550
.Temperature (K)
Figure 2.4: M easured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a CO 2 atm osphere as a function of tem p eratu re a t 4 a tm for a frequency of
21.7 GHz. T he abscissa of the d a ta points was shifted from th e actual tem p eratu re
value for clarity. T h e 1 -rr error in th e tem perature m easurem ent is ± 2 K.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Measured data
NewBR model
WW model
GR model
400
Temperature (K)
Figure 2.5: M easured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of tem p eratu re a t
2
a tm for a frequency of
8.5 GHz. T he abscissa of th e d a ta points was shifted from th e actu al tem perature
value for clarity. T he l-o- error in th e tem perature m easurem ent is ± 2 K.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
10
E
£
* 10 ”
>
Z.
o
J
Measured data
--------------
New BR model
--------------VVW model
-------------
GR model
.................
JP model
h------------- y SE model
| 102
10
10
10
-t
10
10
Frequency (GH2)
F igure 2.6: Measured absorptivity (norm alized by num ber m ixing ratio) of gaseous
SO 2 in a CO 2 atm osphere as a function o f frequency a t 4 a tm for 295 K. The abscissa
of th e d a ta points was shifted from th e actual frequency value for clarity.
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
J
-------------10
I to3
Measured data
New BR model
--------------WW model
-------------- GR model
h------------- 1-
JP model
SE model
SwI*
>
aW
9
I 10
<
■o
«N
10
10
j. L
10
10
10
10
Frequency (GHz)
Figure 2.7: M easured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of frequency a t 4 a tm for 505 K. The abscissa
of the d a ta points was shifted from th e actual frequency value for clarity.
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J
Measured data
New BR model
WW model
GR model
JP model
i
^
SE model
12
1.4
Pressure (atm)
Figure
2 .8 :
M easured absorptivity (normalized by num ber m ixing ratio) of gaseous
SO 2 in a C O 2 atm osphere as a function of pressure at 296 K for a frequency o f 94.1
GHz (Fahd and Steffes, 1992) [6 ]. The abscissa of the d ata p oints was shifted from
the actual tem perature value for clarity.
32
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2.2
M odeling o f th e M icrowave A bsorption o f S 0 2
2.2.1
Overview o f the Spectral Line Shape Theory
It is well known th a t th e phenom enon of absorbing electrom agnetic waves by a t­
m ospheric gases becomes significant a t centim eter and m illim eter wavelengths. To
characterize the absorption as a function of frequency, one needs to know the m ixture
of gases, pressure, and the tem p eratu re of the environm ent (De P a te r and M itchell.
1993) [24]. General spectral line shape models for predicting the absorption of gases
were developed based on th e classical and quantum theory of radiation. These models
include th e Lorentz (Lorentz, 1915) [25], Van Vleck-Weisskopf (Van-Vleck and Weisskopf. 1945) [21], Gross (Gross, 1955) [22], Ben-Reuven (Ben-Reuven, 1966) [34],
and th e Voigt line shapes (M itchell and Zemansky, 1934) [28]. T hese spectral line
shape models are of great im portance because they can be incorporated into radiative
transfer models to infer abundance profiles for th e potential absorbers in the Venus
atm osphere, or can be. applied to opacity profiles obtained from radio occultation
experim ents.
T he spectral line shape theory for a collision- or pressure-broadened gaseous
system was first form ulated by Lorentz (Lorentz, 1915) [25] who considered the energy
transfer from an incident electric field to a molecule represented by a one-dimensional
linear harm onic oscillator. In his theoretical derivation, the initial conditions for the
equation of motion were determ ined assum ing th a t th e molecule undergoing a collision
does not interact w ith th e incident electric field, whose period was assumed to be
very short as com pared to the tim e between collisions. Therefore, Lorentz assumed
that molecules after collision are redistributed in accordance w ith th e Boltzm ann
law appropriate to th e field-free H am iltonian. Furtherm ore, Lorentz assumed th a t
the m olecular collisions are strong, th u s, the phase of th e oscillation is interrupted
and has no relation to the phase before the im pact. For rotational transitions, this
means th a t the orientation of the molecule after collision is arb itrary w ith respect to
33
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the direction of the incident field. Based on these assum ptions, Lorentz derived th e
absorption coefficient a and th e refractive index n which can be w ritten as (Van-Vleck
and Weisskopf, 1945) [21]
q
=
2irNe2
C " ) [
i t --------------me
[(^ -uJ0)2 + ( l / r ) 2 (u> +
t,2
-
1=
m(u.’2 - u ; 2) [
1
2
t
2 [(u >
+
Ur
u ) o ) 2
2
—u?0)2 + ( l / r ) 2]
(2.25)
+ ( l /r ) 2
~
r 2[(u> +
uj0
)2
+ ( l /r ) 2]
(2.26)
where A’ is th e num ber of molecules per unit volume, e is th e electron charge, m is th e
mass, c is th e speed of light, u; is the angular frequency of th e incident electric field,
im'0
is th e resonant angular frequency u.’0, and r is th e m ean tim e between collisions.
For the quantum m echanical system , th e quantum th eo ry of dispersion (H eitler,
1944) [26] shows that e2/ m is replaced by
87 r 2 i'ol/utj l 2 / 3
h, and u 0 by 2 ti /0, where
v0 = ( 1 1 ', — Wj ) / h is th e resonant frequency associated w ith a transition between
states i and j , fitJ is th e dipole m om ent for th e sam e tran sitio n , W{ and Wj are
energies associated w ith states i and j respectively, a n d h is th e Planck constant.
W ith su b stitution and sum m ation over the various possible transitions, th e absorption
coefficient for hu0 ^ i k T becom es (Van-Vleck and W eisskopf, 1945) [21]
_ ( 8ir3v N \ h £ , E j 1Mij
v )e ~ W}lkT
°
\ 6hc ) k T
'£ j e - wi / kT
where k is th e B oltzm ann constant, and
(2.27)
is th e Lorentz spectral line shape
which is given by
/i(*M 'o,7) = “7T
7
\ v o ~~ v ) 2 + ( l ) 2
(t/0 +
(2.28)
I/)2 + ( 7 ) 2
where v = «;/27r is th e frequency of the incident wave, and
7
=
1/ 2 jtt
half-width at half-maximum.
34
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is the line
For the L orentz spectral line shape, when u0
v, the absorption coefficient
becomes zero, w hich is in disagreem ent with th e Debye form ula for nonresonant ab­
sorption (Debye. 1929 and Van-Vleck and Weisskopf, 1945) [27, 21]. T he Debye
absorption coefficient is expressed as
AirNfi2 im2t
Q “ 3c k T 1 + uj2t 2
(
J
Note also th a t th e refractive index n 2 — 1 does not reduce to zero at high fre­
quencies. Thus, th e K ram ers-K ronig Equations (G orter and Kronig, 1936) [29] w hich
govern the relation betw een dispersion and absorption are not satisfied.
To resolve th e contradiction betw een the Debye and Lorentz absorption m odels.
Van Yleck and W eisskopf (Van-Vleck and Weisskopf. 1945) [21] derived an in teg rated
spectral line theory. T his was done by modifying th e assum ptions in the Lorentz
theory.
Van Vleck and Weisskopf assumed th a t the molecules after collision are
redistributed in accordance with th e Boltzm ann law appropriate to th e instantaneous
H am iltonian a fte r collision which includes the influence of the incident electric field
on th e oscillator, w hereas. Lorentz neglected it. Thus, the absorption coefficient and
th e refractive index were modified and can be w ritten as
Q =
„2 _ J
ft
1
JL/r
2r.Ve2
me
\w 0
-------------
. ix N e 2
/
o
©
(u>-u>0)2 -h ( l/r )2
[1 _
m(u>2-u;2)L
+
A
_or/
1/ T
(u? + u}0)2 + ( l / r ) 2
+ j(u > /u '°J
>0 ) 2
2ZSLLZ-2}ZLU
, + _2
\o
.
/i
/ _\oi
r2[(u; —“>o)2 + ( l/r ) 2]
•
- j(w /u;0)2
o
r2[(w+ u;0)2 + ( l /r ) 2]
(2.30)
1
(2.31)
The quantum m echanical ad ap tatio n still results in the absorption coefficient
given by Equation 2.27, bu t with th e following VVW spectral line shape
/vvw (*', v0.7 ) =
( : --------~ 2 ------ 2 + -'f--------^ 2 ------ 7 )
* vo \ ( i / 0 - t / ) + 7 2
{v0 + v) + 7 2/
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2.32)
N ote th a t when i/0 <C v, the absorption coefficient according to th e VVW spec­
tral line shape theory reduces to th e Debye formula for nonresonant absorption. As a
result, th e discrepancy between the Lorentz and Debye theories is resolved by using
the V V W spectral line shape theory. Also note th a t th e K ram ers-K ronig relationship
between dispersion and absorption is satisfied when using th e VVW theory.
A nother im portant spectral line shape theory for a collision- or pressure- broad­
ened gaseous system was developed by Gross (Gross, 1955) [22]. In his theory, Gross
assumed th a t th e duration of a collision is short com pared to th e resonant period.
This implies th a t th e m olecular position is unaltered by an instantaneous collision.
Furtherm ore, Gross assum ed that th e molecular velocities after collision are redis­
trib u ted according to a Maxwellian distribution. Based on these assum ptions, Gross
solved th e governing kinetic equation of the behavior of th e system of oscillators and
arrived a t the following spectral line shape
(l3 3 )
Besides the collision- or pressure-broadened gaseous system , th ere are situations,
where m ore than one agent for broadening th e spectral line shape of a gas is present.
For exam ple, experim ents conducted to determ ine th e lifetim e of the resonant sta te of
an absorption line are perform ed under conditions in which only n atu ral and Doppler
broadening are present (M itchell and Zemansky, 1934) [28]. To in te rp re t such ex­
perim ents, it is necessary to have a spectral line shape formula representing these
broadening mechanism s. This formula was first introduced by Voigt (M itchell and
Zemansky, 1934) [28].
T he last spectral line shape theory was developed by Ben-Reuven for a collisionor pressure-broadened gaseous system (Ben-Reuven, 1966) [34]. This theory is com­
prehensive in term s of incorporating th e effects of pressure-broadening, shifting, and
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
merging (interference) of d istinct resonance lines and even reduces to the V V W and
the G R spectral line shape theories under certain conditions (see next section). This
theory has been im plem ented in this thesis for th e developm ent of a model th a t repre­
sents th e microwave absorption of SO 2 /C O 2 gaseous m ixture u n d er Venus sim ulated
conditions. In th e n ex t section, the modeling results and th e Ben-Reuven spectral
line shape theory a re presented.
2.2.2
Modeling Results
An essential part of this research has been to develop a m odel th a t predicts the
absorption of gaseous SO 2 in a C O 2 atm osphere as a continuous function of frequency,
tem perature, pressure, and m ixing ratio. Previously, it was shown th a t th e opacity of
gaseous SO 2 under Venus-like conditions can be m odeled by using th e VVW line shape
theory at wavelengths shortw ard of 2 cm (Fahd and Steffes. 1992) [6 ]. However, for
wavelengths greater th a n 2 cm . th e measured SO 2 opacity was ab o u t 50% larger than
that com puted via th e V V W formalism and was modeled with a best-fit m ultiplicative
expression (Steffes a n d E shlem an. 1981, Fahd and Steffes, 1992) [5, 6 ]. Based on our
high-accuracy laboratory m easurem ents of th e microwave absorption from gaseous
SO 2 rn a CO 2 atm osphere, a new opacity m odel for gaseous SO 2 th a t uses th e BR
spectral line shape theory has been developed. This new BR m odel provides a more
accurate characterization of gaseous SO 2 microwave opacity in th e Venus atm osphere
as com pared to o th e r form alism s. In general, th e absorption m odel can be w ritten
for a single SO 2 ro ta tio n a l resonant line as
O = Omax^’7./*b»pe(^ ^o, •••)
Cm
where a max is the abso rp tio n at the line center in cm -1,
,
7
(2.34)
is th e linewidth in MHz,
/shape is th e spectral line shape function in M H z-1 , v is th e frequency of in terest in
MHz, and i/ 0 is the line center frequency in MHz.
37
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Now, th e absorption at the line center Qm*x for each line of gaseous SO 2 is
calculated using th e following expression (P oynter and P ick ett, 1985) [30]
= 102.4 6 ^ - 7 ( 7; ) ^ y ^ e - ^ c / W d / r - i / T o )
cm - i ?
(2 35)
where Psot is the partial pressure of gaseous SO 2 in torr, I is th e line center intensity
in nm 2 MHz, T 0 is th e reference tem p eratu re (T 0 = 300 K ), Ei is the lower state
energy in cm -1, k is B oltzm ann's constant = 1.38 x 10" 23 J / K , h is Planck’s constant
= 6.63 x 10- 3 4 J.s, and c is the speed of light in free space = 3 x 1010 cm /s.
Note th a t th e total absorption coefficient a t a p articu lar frequency is obtained
by sum m ing over all of the individual SO 2 line center intensities up to 750 GHz (1587
resonant lines) which are obtained from th e P o y n ter and P ick ett catalog (P o y n ter and
Pickett, 1985) [30]. Figure 2.9 shows th e SO 2 line center intensities as a function of
frequency. Only 49 lines are below 30 GHz, w ith peak intensities th a t are less than
4.-5 x 10~ 6 nm 2 MHz. Thus, the SO 2 microwave absorption is dom inated by th e line
centers th a t are above 30 GHz.
For th e spectral line shape function /*hape« a BR line shape expression has been
used in modeling th e microwave absorption from gaseous SO 2 in a CO 2 atm osphere.
This expression takes into account th e effect of pressure-broadening, shifting, m erging
(interference) of distinct resonance lines, and is applicable to centim eter wavelength
absorption even at pressures where th e linew idth is com parable to the resonant fre­
quency.
W hen a molecule in a gas absorbs a photon, spectral tra n sitio n between tw o en­
ergy levels of th e molecule is induced. As a result of collisions w ith other molecules,
th e photon absorbed is eventually dissipated to o th er degrees of freedom of th e gas
which results in shifting, broadening, and m erging of the absorbing molecule reso­
nance lines. In developing his spectral line shape, Ben-Reuven expressed th e effect
of collisions by introducing a tim e-independent non-H erm itian (or complex) pertu r-
38
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0
100
200
300
400
500
Frequency (GHz)
600
700
800
Figure 2.9: Gaseous SO 2 line center intensities for frequencies below 750 GHz obtained
from th e Poynter a n d Pickett catalog (P oynter and P ick ett, 1985) [30].
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bation to the resonance frequencies o f th e system (Baranger, 1958) [31, 32]. In gen­
eral. th e pertu rb atio n is a com plicated function of the photon frequency and th e
gas density. However, Ben-Reuven introduced several assum ptions which simplified
the perturbation and eventually th e derivation of th e spectral line shape. T he first
assum ption is th e im pact approxim ation assum ption which essentially assumes th a t
the average collision is weak. As a result, the change in th e wave function of th e
absorbing molecule is sm all and th e duration of th e transient effects of collisions is
negligibly short.
T hus, th e p ertu rb atio n is independent of frequency over a wide
range (B aranger, 1958) [31, 32, 33]. T h e second assum ption is th e binary collision
assum ption which states th a t the absorbing molecule interacts w ith one p ertu rb in g
molecule at a tim e as long the gas density is low. This implies th a t the p ertu rb atio n
is proportional to th e gas density, and th a t the correlations betw een different ab ­
sorbing molecules are negligible (Ben-Reuven, 1966 and Janssen, 1993) [34 , 35]. T h e
final assum ption is th a t th e gas sam ple is treated as a conservative system in th erm al
equilibrium , and radiation fields are weak enough to avoid satu ratio n (Karplus and
Schwinger, 1948) [36].
Based on these assum ptions Ben-Reuven derived the following spectral line shape
,c s
- ( v \ 2 { 7 ~ Q i / 2 + (7 + OtC^o + b )7 + 7 2 — C2]
/BR i M / o O - ^ ) = -
jt
[ — )
\ v 0 J
— f - : — ;------ T7T2
[v2
- (i/0 -(- b
y
-
Y
2 T ro h " 7
■+• C2]2 +
'a
4 i/2Y
—
WTT_,
M H z 1.
(2.36)
where th e linewidth
7
, th e coupling elem ent
and th e frequency shift element
6
for
an SO 2 /C O 2 gaseous m ixture can be expressed as
7 = (7 so2/ c o 2 )-Pc o 2
+ ( 7 so 2/ so 2) / ,so 2
MHz,
(2.37)
C = (Cso2 /cOj)-Pco 2
+ (Cso2 /so 2 )-Pso2
MHz,
(2.38)
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6 = f>so2Pso2
MHz,
(2.39)
where 7 so 2/c o 2 is th e foreign gas ( C 0 2) broadened linew idth p aram eter in M H z /to rr,
7 so 2 /so 2
is th e self-broadened linew idth param eter in M H z/to rr, £so2 /c o 2 is the foreign
(CO 2 ) gas coupling p aram eter in M H z/torr, £so2 /so 2 is th e self-coupling p a ra m ete r
in M H z/torr, 6 so 2 is th e frequency shift param eter in M H z/to rr. P co 2 is the p artial
pressure of gaseous C 0 2 in lo ir, n is th e tem perature dependence of th e linew idth, and
m is the tem perature dependence of the coupling elem ent. N ote th a t when £ =
6
= 0,
then th e BR spectral line shape reduces to the VVW line shape and when £ =
7
an d
6
= 0, then the BR spectral line shape reduces to the GR line shape.
From th e above discussion, it is evident th at seven param eters for the BR spec­
tral line shape function are needed in order to fit the absorptivity m easurem ents.
These param eters are
7 so 2 /c o 2, 7 so 2 /so2* Cso2 /co 2-
Cso2 /so 2, ^so2, n, and m. How-
ever, ')so 2 /c o 2 was m easured in th e laboratory for one resonant line a t 24.08 G H z,
and for th a t line it is 7.2 M H z/to rr (K rishnaji and C handra, 1963) [37]. F u rth er­
more, Kolbe et al. (1976) [38] used a self-broadened linew idth param eter 7 so 2 /so 2 of
16 M H z/torr as an average value of the measured linew idth param eters which range
from 13 to 19 M H z/torr. These values of 7.2 M H z/torr and 16 M H z/to rr for 7 so 2 /c o 2
and *)so2 /so 2. respectively, are thus assumed for all S 0 2 resonant lines, although it is
likely th at
7 so 2 /c o 2
and
7 so 2 /so 2
vary from line to line. To determ ine th e rest of th e
param eters, the goodness of fit function
\ 2
(Bevington, 1969) [39] has been globally
m inim ized to fit all of th e absorptivity m easurem ents. N ote th a t th e goodness of fit
function x 2 can be w ritten as
(2.40)
where a mi is th e m easured absorption coefficient, a Cl is th e calculated absorption
coefficient. crt is th e uncertainty in th e m easured absorption coefficient, and k is th e
num ber of m easured absorption coefficients.
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Now. global m inim ization is achieved by introducing a set of values for th e
param eters ( s o ^ c o ^ Cso2 /soj- <$so2> «, and m and com puting th e goodness o f fit
function
\ 2
for all absorptivity m easurem ents until
\ 2
converges to a minimum. N ote
th a t at the beginning of the search for the com bination of o p tim al values for the
above param eters, all values were varied including those for n and m. However,
during the initial search it was found th a t varying n and m betw een their theoretical
lim its (0.5 and
1
) had a slight im pact on th e quality of fit.
Therefore, n an d m
were set equal and th e search was continued u n til th e goodness o f fit function
\ 2
was
minimized. However, it is im portan t to em phasize th a t th e absorptivity calculated
by th e developed BR formalism is nearly insensitive to th e p aram eters r? and m.
For example, settin g n and m to 0.5, which is th e lower lim it of th e tem p eratu re
dependence of th e linew idth. results in only about 3.2% change in the absorption
coefficient at 2.25 GHz. 8.5 GHz. and 21.7 GHz for the highest pressure of 4 a tm ,
and the highest tem p eratu re of 505 K. Even for th e upper lim it o f 1 , the absorption
coefficient changes by only about 1.3%. Hence n and m are n o t th e key param eters
in the fitting procedure. This procedure has been repeated for m ore than 75 sets
of values, until convergence was achieved. Table 2.7 shows th e v alu es’of param eters
for th e developed BR formalism th a t yield the best fit for all microwave absorptivity
m easurem ents of th e gaseous SO 2 /C O 2 m ixture.
2.3
M icrowave R efraction o f G aseous SO 2
Although th e p rim ary objective of our laboratory m easurem ents has been th e de­
term ination of th e microwave opacity of gaseous SO 2 in a CO 2 environm ent u n d er
Venus-like conditions, th e microwave refractivity of the SO 2 /C O 2 gaseous m ix tu re
has been also m easured. This m easurem ent has been applied to th e interpretation
of the refractivity profiles of the Venus atm osphere obtained from th e 1991 M agellan
spacecraft radio occultation experim ents (Jenkins et a/., 1994) [11]. Furtherm ore, this
42
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Table 2.7: Values of Param eters used in th e Developed Ben-Reuven Formalism.
P aram eter
Value
7so 2/c o 2
7.2 M H z/torr
7S02/SO2
16 M H z/torr
Cso2/c o 2
1.3 M H z/torr
Cso2/so 2
1 .6
M H z/torr
fe o 2
2.9 M H z/torr
n = m
0.85
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SO 2 refractivity m easurem ent has been im portant in understanding th e microwave
effects of SO 2 on INSAR imaging o f terrestrial volcanoes. The refractivity of gaseous
SO 2 which has not been reported elsew here in the lite ra tu re , has been m easured a t
th e sam e frequencies, tem p eratu res, and pressures, used for measuring its opacity.
Recall that th e refractive index, n, of a gas is defined as the ratio of the velocity
of th e electrom agnetic wave in vacuum , c, to its velocity in the gas, vg. W hen using
a microwave resonator, n is sim ply th e ratio of the m easured resonant frequency of
th e evacuated resonator, / re, to th e m easured resonant frequency of th e gas-filled
resonator f rg. Thus, n is written as (T yler and Howard, 1969) [40]
(2.41)
x9
Jr g
and since n is very close to one, a general quantity known as the refractivity, N, is
defined as (Tyler and Howard, 1969) [40]
N = (n ~
1
) x
106
=
x I0 6
(2.42)
Jrg
which is often expressed in term s o f density normalized refractivity, A’p, given by
..
N
NRT
Ap = ~ = —
/n
(2-43)
where p is the m olecular num ber d en sity in molecules p e r cm3, R is th e ideal gas
constant = 1.36 x 10" 22 atm -cm 3 /K /m o le c u le , T is th e tem perature in K , and P is
the pressure in atm .
M easurem ents of th e microwave refractivity of th e SO 2 /C O 2 gaseous m ixture
have been performed using the sam e experim ental ap p aratu s and procedure described
in Sections 2.1.3 and 2.1.4. By m easuring th e change in th e resonant frequency of
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a given resonance relative to vacuum , th e refractivity o f the SO 2 /C O 2 gaseous m ix ­
tu re has been determ ined under th e sam e conditions used for m easuring its opacity.
T he refractivity of pure gaseous C 0 2 has been also m easured a t somewhat higher
pressures than those used for th e SO 2 /C O 2 gaseous m ixture. This is required for re ­
m oving the effects of dielectric loading in the resonator being used in th e experim ent,
and thus resulted in more accurate opacity m easurem ents of the SO 2 /C O 2 gaseous
m ixture. The refractivity of pure gaseous SO 2 can be found from th e refractivity of
th e SO 2 /C O 2 gaseous m ixture by using the following equation
N so, = A 's c /c o , - Noo, , c ° ^ ° i/C° ’
(2.44)
where A’so 2 is th e derived refractivity of pure gaseous SO 2 , Arso 2 /c o 2 is the m e a ­
sured refractivity of th e SO 2/C O 2 gaseous m ixture a t pressure Pso 2 /c o 2 4 N co 2 is th e
m easured refractivity of pure gaseous CO 2 at pressure Pqo2>and qco 2 is the n u m ­
ber mixing ratio of gaseous CO.2 in the SO 2 /C O 2 gaseous m ixture. N ote th at b o th
A ’s o 2/ c o 2
and A'co2 have been m easured at the sam e tem perature.
T he uncertainties in the refractivity m easurem ents are due to instrum ental and
random electrical noise errors in th e system . The instrum ental errors are caused by’
th e lim ited accuracy of the equipm ent used to m easure th e resonant frequency, m ixing
ra tio of the gaseous m ixture, pressure, and tem perature (see Section 2.1.5). The ra n ­
dom electrical noise influences th e m easurem ent of th e resonant frequency, especially
at th e highest frequency of 21.7 GHz, and is included in the one-sigm a uncertainty
of th e refractivity m easurem ent for all frequencies. Tables 2.8, 2.9, 2.10, and
2 .1 1
present the results of th e microwave refractivity m easurem ents of gaseous SO 2 w ith
th e associated one-sigma uncertainty a t 295, 365, 435, and 505 K, respectively. In
these tables, column 7 gives the m easured density norm alized refractivity for pure
gaseous SO 2 , NPS0j, where psor is th e SO 2 num ber m ixing ratio. From these tables
one can observe, as expected, th a t th e measured refractivites Nso 2/c o 2 and Nso 2 are
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
directly proportional to pressure and inversely proportional to tem perature. Also,
note that th e norm alized refractivity, NPS0j generally decreases as the tem p eratu re
increases. In addition, note th a t th e m easured refractivites a re not frequency d ep en ­
dent. A lthough, th e m easured refractivities of gaseous C 0 2 have not been rep o rted
in Tables 2 .8 -2 .ii. our results have been consistent w ith th e results of T yler and
Howard (1969) [40], and Essen and Froome (Essen and Froom e, 1951) [41] at am bient
conditions. T h e applications of these SO 2 refractivity m easurem ents are discussed in
C hapters 3 and
6
.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.8: M easured Microwave Refraction of G aseous SO 2 in a C 0 2 Atmosphere
295 K for Various Pressures, and Frequencies.
D a te
A p ril 2 8 , 1994
M a y 16. 1994
J u n e 8, ]994
pso 3/c o 3
F re q u e n c y
<*so3
(a tm )
(G H z )
%
**SO j / C O j
Nsoa
4.06
2.25
8 .3 0
3051.466 ± 1 5 .7 5 2
1 3 34.049 ± 1 6 1 0 2
4 06
8.5
4.06
21.7
8 .3 0
3053.467 ± 1 5 .6 2 0
1337.411 ± 1 8 .1 7 9
1.592 ± 0 .0 2 2
8 .3 0
3034.565 ± 2 4 .4 9 6
1324.451 ± 2 8 1 3 6
1.576 ± 0.034
3.04
3.04
2.25
8 .3 0
2306.956 ± 1 5 .7 3 5
1 0 2 6 .3 3 6 ± 18 0 0 6
1.632 ± 0.029
8.5
8 .3 0
2307.650 ± 1 5 .7 9 9
1 0 2 6.675 ± 1 8 .0 7 6
1.632 ± 0.029
x I Q * 16
1.586 ± 0.022
3 04
21 7
8 .3 0
2296 451 ± 2 4 .3 9 9
1 0 2 5.245 ± 27 9 1 0
1.630 ± 0.044
2.0 2
2.25
8 .3 0
1487.825 ± 1 5 .7 1 6
6 5 0 .5 9 7 ± 1 7 .9 2 2
1 .5 5 7 ± 0.043
2 02
6.5
8 .3 0
1488.001 ± 1 5 .7 8 3
6 5 0 .6 5 2 ± 1 7 .9 9 7
1.557 ± 0.043
2 02
21 7
8 .3 0
1489.539 ± 2 4 .3 7 4
6 6 0 .6 2 2 ± 2 7 .7 8 9
1.581 ± 0.067
4 .0 6
2.25
8 30
3087 008 ± 1 5 .7 5 3
1344 652 ± 18 0 5 9
1 .600 ± 0 021
4.06
8 5
8 .3 0
3086.998 ± 1 5 .6 2 3
1 3 4 3 .0 2 6 ± 1 8 .1 3 7
1.599 ± 0.Q22
406
21.7
6 .3 0
3076.105 ± 2 4 .4 7 1
1366.024 ± 2 8 .1 1 3
1.626
3-38
2.25
6 .3 0
2556.369 ± 1 5 .7 4 0
1 1 1 7 .4 2 2 ± 1 6 1 3 2
1 .598 ± 0.026
3 .38
8.5
8 .3 0
2553.799 ± 1 5 .8 0 6
1 1 1 6 .3 5 3 ± 1 8 .2 0 7
1.596 ± 0.026
3 38
21 7
8 .3 0
2546.156 ± 2 4 .4 9 5
1 1 2 2.738 ± 2 8 .2 2 4
1.605 ± 0 040
2 36
2.25
6 .3 0
1772.513 ± 1 5 .7 2 3
762.744 ± 1 8.031
1.603 p m 0.037
±
0.034
2 36
8 5
8 .3 0
1770.114 ± 1 5 .7 8 8
7 7 9 .3 4 2 ± 1 8 .1 0 3
1.596 ± 0.037
236
21.7
8 .3 0
1775.875 ± 2 4 -4 3 2
6 0 9.221 ± 2 7 .6 9 6
1-657 ± 0.057
1.66
2.25
8 .3 0
1269.781 ± 1 5 .7 1 2
5 7 2 .9 3 6 ± 1 7 .9 8 0
1.646 ± 0.052
1.68
8 5
6 .3 0
1269.467 ± 1 5 .7 7 4
5 7 2 .6 2 2 ± 1 8 .0 5 3
1-648 ± 0.052
1.691 p m 0.060
1.68
21.7
6 .5 0
1267.731 ± 2 4 .4 2 0
5 8 7 .8 7 1 ± 2 7 .9 4 5
4-06
2.25
6 .3 0
3 051.493 ± 1 5 .7 5 4
1 3 2 3.924 ± 1 6 .1 0 4
1.576 ± 0.022
3.38
2.25
8 .3 0
2511.971 ± 1 5 .7 4 2
1 0 9 3.394 ± 1 6 .0 7 8
1.563 ± 0.026
3.04
2.25
6 .3 0
2257.937 ± 1 5 .7 3 5
9 6 9 .9 2 4 ± 1 8 .0 6 4
1.574 ± 0.029
2 .3 6
2.25
6 .3 0
1763.611 ± 1 5.731
7 7 4 .0 7 9 i
1 8 .0 3 7
1.565 ± 0.037
2 .0 2
2.25
8 .3 0
1474.516 ± 1 5 .7 1 9
6 4 0 .2 6 3 ± 1 8 .1 0 0
1.532 ± 0.043
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.9: M easured Microwave Refraction of G aseous SO 2 in a C O 2 Atmosphere at
365 K for Various Pressures, a n d Frequencies.
D*te
J u n e 2 4 . 1994
pso 3/c o 3
F req u en cy
<iso3
(GH»)
%
Nso 3/ c o 3
**so3
n *so3
x 1 0 “ 1G
4 06
2 .2 5
8 .3 0
2 2 2 4 .9 0 3 ± 1 5 .6 2 6
8 7 1 .2 3 5 ± 18.497
4-06
6 .5
6 .3 0
2224.511 ± 1 6 .1 6 4
668.351 ± 18.604
1.279 ± 0.028
406
2 1 .7
6 30
2 2 3 6 .3 1 5 ± 2 4 .6 2 3
6 6 9 .2 3 8 ± 28.751
1 .310 ± 0.042
304
*
1.263 ± 0.027
2 25
6 .3 0
1672.169 ± 1 5 .9 6 9
679.771 ± 18.555
1 .337 ± 0.037
304
6.5
6 .3 0
1653.249 ± 1 5 6 0 3
6 5 2 .9 4 2 ± 18.503
1 264 ± 0.036
304
21 .7
8 .3 0
1699.416 ± 2 4 .5 0 6
7 0 4 .6 5 9 ± 2 8 .527
1.366 ± 0.056
2.02
2.2 5
6 .3 0
1064.617 ± 1 7 3 7 9
4 3 6 .5 9 9 ± 19.677
1.292 ± 0.056
202
S.5
6 .3 0
1055.791 ± 1 5 8 2 9
3 9 7 .8 0 9 ± 18.670
1.178 ± 0.055
202
21 .7
6 .3 0
1112.272 ± 24 46 3
4 6 0 .6 3 6 ± 26.314
1.364 ± 0.084
4 06
225
6 97
22 4 4.292 ± 15 879
67 9 119 ± 2 0 .673
1.196 ± 0 026
4 06
85
8 .9 7
2264 35 9 ± 1 8 .1 2 1
94 1.604 ± 2 0 .5 0 1
1 .283 ± 0.026
Ju ly 31. 1994
4 06
2 1.7
8 .9 7
2361.545 ± 2 4 .8 8 3
10 9 9.377 ± 4 5.128
1.496 ± 0.062
A ug
1. 1994
304
225
8 .9 7
1716.747 ± 1 6 .9 2 1
7 3 0.075 ± 19.948
1.329 ± 0 036
3.04
8.5
8 .9 7
1692 201 ± 1 5 .9 5 7
715.614 ± 18.472
2.302 ± 0.034
Ju ly 31. 1994
3.04
21.7
8 .9 7
1704-166 ± 2 5 .0 9 6
736.565 ± 30.125
1.344 ± 0 055
Aug
1. 1994
1. 1994
2 02
8.5
897
1098.12 ± 1 5 .9 6 2
462 428 ± 18 463
1 .2 6 7 ± 0.051
Ju ly 31. 1994
2 02
21 .7
897
1144.741 ± 2 5 .1 9 1
5 1 6 .6 6 5 ± 30.356
1.415 ± 0 083
Aug
Table 2.10: M easured Microwave Refraction of G aseous SO 2 in a C O 2 Atmosphere
at 435 K for Various Pressures, and Frequencies.
D tte
A ug 4. 1994
p s o 3/ c o 3
F re q u e n c y
9SO a
( * im )
(G H a l
95
4.0 6
2 .25
**S03 / C © 3
N so a
6 97
1764 01 2 ± 2 2 .6 5 9
60 6 157 ± 27.008
0 .9 8 4 ± 0 044
x 1 0 - 16
4.06
6 .5
8 .9 7
1713.032 ± 2 0 .4 6 5
5 2 2 .5 6 8 ± 23.630
0 849 ± 0 .038
21, 1994
4.0 6
21 7
8 .9 7
1590.432 ± 3 0 1 6 3
5 2 6 .3 6 5 ± 34.691
0 .8 5 5 ± 0 .056
A ug 4, 1994
3.04
2 .25
8 .9 7
1331.013 ± 2 1 .9 5 6
4 8 5 .6 0 6 ± 24.797
1 .0 5 3 ± 0.054
3.04
8.5
8 .9 7
1343.147 ± 2 0 .0 8 1
4 9 4 .7 9 7 ± 24.212
1 .0 7 3 ± 0.053
3.04
21.7
8 .9 7
1391.316 ± 2 7 .0 1 7
5 9 3 .2 1 5 ± 30.626
1.287 ± 0.066
202
2.25
8 .9 7
760.803 ± 3 2 .7 0 2
2 2 7 .2 7 0 ± 35.517
0 .7 4 2 ± 0.116
A ug
A ug 21. 1994
A ug. 4, 1994
2.02
6.5
8 .9 7
931.116 ± 2 5 .8 3 6
3 7 5 .3 9 6 ± 28.052
1.225 ± 0.092
A ug. 21. 1994
2.02
2 1 .7
8 .9 7
850.026 ± 2 7 .7 5 5
3 5 5 .4 2 1 ± 32.169
1 .1 6 0 ± 0.105
4.06
2.2 5
8 .9 7
1652.003 ± 1 6 .5 7 3
5 6 7 .3 2 9 ± 20.021
0.921 ± 0.033
4 .0 6
6.5
8 .9 7
1683.730 ± 2 8 .0 9 4
5 4 5 .7 4 6 ± 30.823
0 .8 8 6 ± 0.050
Sep. 22, 1994
4 .06
21 .7
8 .9 7
1812.624 ± 2 5 .4 0 9
6 9 0 .9 7 9 ± 32.016
1 .122 ± 0 052
A ug. 21. 1994
3.04
2.2 5
8 .9 7
1335.475 ± 1 7 .2 3 7
5 4 5 .2 1 4 ± 20.160
1.183 ± 0 044
3.04
8 5
6 .9 7
1246.666 ± 2 1 .8 3 0
4 0 9 .5 1 6 ± 28.019
0 .8 8 8 ± 0.061
S ep
22. 1994
3.04
217
8 .9 7
1354.302 ± 2 4 .7 2 6
505-570 ± 30 950
1 .0 9 7 ± 0 .067
A ug
21. 1994
2-02
6 5
8 .9 7
777.033 ± 1 7 .5 5 6
2 4 8 .6 7 3 ± 20 676
0 812 ± 0 .068
S ep
22. 1994
2 02
21.7
6 .9 7
673.104 ± 2 4 .5 9 5
3 0 7 .0 4 6 ± 29 807
1.002 ± 0 .097
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.11: M easured Microwave Refraction of Gaseous SO2 in a CO 2 Atm osphere
at 505 K for Various Pressures, and Frequencies.
D a te
O ct
25. 1994
P £ 0 3/C 0 3
F req u en cy
qso3
(a tm )
(GH*>
%
4 .0 6
2 26
6.66
1446 754 ± 1 6 .6 9 5
523.742 £ 20 4 6 0
1.023 £ 0.040
4 06
8.6
6.66
1450.784 £ 1 7 .8 6 7
510.676 £ 20 6 9 6
0.9 9 6 £ 0.040
0-969 £ 0.062
Nso 3/c o 3
N SO?
n pso
3
x 10~u
D ec
31. 1994
4 .0 6
21 7
8 .66
1485.783 £ 2 4 .6 6 1
506.536 £ 3 1 .7 5 7
O ct
25. 1994
3 04
225
8 66
1075.823 £ J 6 .1 7 9
386 694 £ 19.076
1-014 £ 0 .050
3.04
6.5
666
1063.163 £ 1 6 .1 3 7
409.062 £ 18.912
1.067 £ 0 .049
23. 1994
3.04
21.7
6 .97
1105 3 2 9 £ 2 4 .6 3 9
393.075 £ 3 1 .7 6 2
0 .990 £ 0 .080
O c t. 25. 1994
2 02
225
8 .66
699-347 £ 1 5 .6 3 4
233.448 £ 18.640
0 .9 1 6 £ 0.074
2 02
8.6
6 .66
700-263 £ 1 5 .6 3 5
256.438 £ 18-758
1.015 £ 0.074
2 .0 2
21.7
8 .97
689-161 £ 3 0 .9 6 4
207.729 £ 3 5 .6 9 7
0 .7 8 7 £ 0.135
S ep
S ep
23. 1994
O ct
26. 1994
4 .0 6
2.25
6 .66
1404-596 £ 1 6 .5 6 6
511.575 £ 2 1 .2 5 0
0 .9 9 9 £ 0 .0 4 2
4 06
6.5
S-6G
1440 467 £ 1 6 .6 0 0
506.951 £ 2 0 .0 4 9
0.994 £ 0 .039
Jan
1. 1996
4 .0 6
21 7
866
1499 556 £ 2 6 .0 5 3
549.005 £ 3 5 .5 7 0
1.072 £ 0 .070
O ct
26. 1994
3 04
6-5
6 .6 6
1056.110 £ 15 921
3 69.935 £ 19 075
0.-965 £ 0 .050
S ep
24. 1994
3 .04
21 7
897
1166 0 4 9 £ 3 1 .2 0 6
4 51.690 £ 35.351
1.136 £ 0.069
O ct
26. 1994
2 .0 2
2 25
666
6 7 7 .5 5 6 £ 15 901
227.607 £ 19.238
0.8 9 3 £ 0.076
2 .0 2
85
6 .6 6
666 490 £ 1 5 .6 2 8
2 27.322 £ 18.6 0 7
0 .8 9 2 £ 0.074
S ep . 24. 1994
2 02
21 7
8 .9 7
6 9 7 .8 7 6 £ 2 5-193
260.156 £ 3 2 .0 3 9
Q.986 £ 0.121
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
CHAPTER 3
INTERPRETATION OF THE
MAGELLAN RADIO OCCULTATION
EXPERIMENTS AT VENUS
3.1
Overview o f Radio O ccultation E xperim ents
The radio occultation technique is a powerful active rem ote sensing technique used
to investigate and acquire fundam ental inform ation about th e atm ospheres of planets
(Fjeldbo et al., 1971, Eshlem an, 1973, Steffes et al., 1994, Jenkins et al., 1994) [42,
43. 44, 11]. Using this technique, one can infer vertical profiles of atm ospheric refrac­
tivity, absorptivity, tem p eratu re, and pressure. In a radio occultation experim ent, a
spacecraft is used to tra n sm it a signal through th e atm osphere of the p lan et when
it passes behind the p la n e t’s limb as viewed from E arth (see Figure 3.1). Although
the spacecraft is occulted by the planet, th e tran sm itted signal still reaches a receiv­
ing statio n at E arth due to the effect o f refraction by the p la n e t’s atm osphere which
bends th e signal p ath tow ard Earth. T h e m easured quantities at the E a rth receiv­
ing sta tio n are the am p litu d e and frequency of th e received signal. T he m easured
frequency undergoes significant Doppler shift due to th e o rbital motion of th e space­
craft an d the ray bending in th e atm osphere. T he Doppler shift can be predicted and
must be accounted for before the radio occultation experim ent is conducted in order
to preprogram the E a rth station uplink tra n sm itte r and downlink receiver frequen-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SAR DATA
PLAYBACK
HIDE
TURN TO EARTH POINT
'■ " " - O /
DATA COLLECTION START
(TsO SEC, RAY ALTITUDE = 1252 KM)
BEGIN LIMB-TRACK-MANEUVER
(T = 305 SEC, RAY ALTITUDE = 352 KM)
TO EARTH
.r %
LOSS OF X-BAND SIGNAL
’ s 455 SEC, RAY ALTITUDE = 35.6 KM)
~ \
N
v W jp V V j j f RAY ALTITUPE r 3 3 .7 KM): \
e ^ l & r ^ i o s i o F S-BAND SIGNAL •
I M k L S K , RAVALTTTUDE= 33.8 KM) ...
J^Z-CRiTlCAL REFRACTION
__________________: ^
,
K
a r - « 5 8 2 8 6 f t ? r ^
y - -
-•'
ALTITUDE* * 2 .7 KM)
. . . .- I
Figure 3.1: The M agellan spacecraft as it conducts a radio occultation experim ent of
the Venus atm osphere (Steffes et al.. 1994) [44].
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
cies. N ote th a t in a two-way rad io occultation experim ent, such as was conducted
with M agellan, a reference signal is uplinked from th e E arth statio n to the spacecraft
in order to ensure stability of th e am plitude and frequency o f th e signal when it is
retransm itted by th e spacecraft. For the M agellan spacecraft, th e frequency o f th e
uplinked reference signal is
2 .1
G H z which th e spacecraft oscillator locks to and th e n
downlinks to th e E arth station tw o signals which are integer ratios of the received
frequency a t th e spacecraft, one a t a frequency of 2.3 GHz (S-band) and th e sec­
ond at a frequency of 8.4 GHz (X -band). From th e received frequency at the E a rth
station, th e location of the E a rth station relative to the p lan et, and the spacecraft
trajectory d ata at the tim e the signal was tra n sm itte d from th e spacecraft, th e ray
path param eters can be determ ined. These include the bending angle and th e ray
impact p aram eter which is defined as the distance from th e center of the planet to
the ray asym ptote of the path of th e bending signal. Subsequently, integral inversion
of the ray path param eters produces the vertical atm ospheric refractivity profiles.
Note th a t in the inversion process, a simplifying assum ption is m ade regarding th e
shape of th e atm osphere which for Venus is spherically sym m etric. If the bulk of
the atm ospheric constituents are known as is th e case for Venus, then the density
profiles can be determ ined directly from the refractivity profiles. Then assuming th a t
the atm osphere is in hydrostatic equilibrium , th e vertical pressure and tem p eratu re
profiles can be derived via integ ratin g the atm ospheric density profiles subject to th e
appropriate boundary conditions.
A fter determ ining the ray p a th param eters from the frequency d ata of th e re­
ceived signal, th e am plitude d a ta can be processed to infer th e vertical atm ospheric
absorptivity profiles. The m easured am plitude a t the E a rth statio n which is p ro ­
portional to th e intensity or pow er is reduced due to atm ospheric refractive effects,
atm ospheric absorption, and m ispointing of th e spacecraft an ten n a. To determ ine th e
atm ospheric absorption, the effect of antenna m ispointing on th e reduced-intensity
signal m u st be characterized and corrected. Furtherm ore, th e atm ospheric refractive
52
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effects which axe due to the changing index of refraction as a function of altitude
cause spreading of the transm itted b eam (also known as refractive defocusing) by the
spacecraft and thus, reduce th e intensity of the received signal at E arth . From the
occultation geometry and the ray p a th param eters, th e refractive defocusing effect
can be estim ated and subtracted from th e th e m easured intensity. Thus, th e rem ain­
ing intensity reduction (also known as th e excess a tten u atio n ) is due to atm ospheric
absorption. Subsequently, the vertical absorptivity profiles can be deduced from the
excess attenuation through integral inversion.
In th e next section, th e in terp retatio n of the absorptivity profiles obtained from
th e 1991 Magellan spacecraft radio occultation experim ents of the Venus atm osphere
is discussed.
3.2
Interpretation o f th e A bsorptivity Profiles
The new Ben-Reuven model for gaseous SO 2 microwave absorption has been applied
to the S-band (2.3 GHz or 13-cm) and X-band (8.4 GHz or 3.6-cm) absorptivity
profiles which were obtained from th e 1991 Magellan spacecraft radio occultation ex­
perim ents for orbits 3212. 3213, and 3214 (Jenkins et al., 1994) [1 1 ]. T hese profiles
were taken at a latitude of approxim ately 67° north. T h e objective has been to derive
accurate vertical abundance profiles for gaseous SO 2 in th e Venus atm osphere. As
was m entioned earlier, the microwave absorption in th e Venus atm osphere is prim ar­
ily due to CO 2 , gaseous H2SO4, and gaseous SO 2 . Since th e absorption due to CO 2
(pressure-broadened by CO 2 and N2) is well known (Ho et al., 1966, see also Section
4.3.2) [18], its contribution has been su b tracted from th e S- and X-band absorptivity
profiles for orbits 3212, 3213, and 3214. In th e subtraction process, the appropriate
pressure-tem perature profile obtained from th e Magellan spacecraft radio occultation
experim ents for each orbit has been used. In addition, uniform abundance distribu­
tions of 96.5% for CO 2 and 3.5% for N 2 have been used for all altitudes of th e Venus
53
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atm osphere (O yam a e t al., 1980) [3]. The rem aining absorption is prim arily due to
gaseous SO2 and gaseous H 2S 0 4. Figures 3.2 an d 3.3 show th e S- and X -band total
absorptivity profiles, respectively, w ith their associated standard deviations for orbit
3213. Also shown are the S- and X-band residual absorptivity profiles (i.e., those
w ith the C 0 2 opacity removed), respectively, w ith th e ir associated stan d a rd devia­
tions. Note from these figures th a t th e absorptivity above an altitude o f 50 km has
been truncated (also for orbits 3212 and 3214) since its presence is not statistically
significant at S- and X-bands due to the very low pressures (<0.95 a tm ) and the
atm ospheric turbulence at those altitudes. Also n o te th a t no absorptivity d a ta is
shown below an a ltitu d e of about 35 km (also for orbits 3212 and 3214) since critical
refraction occurs near th at altitud e. Figure 3.2 shows to tal absorptivities a t S-band
w ith peaks of 4.94 x
10-3
dB /km at 46.5 km, 5.17 x
10-3
d B /k m at 44 km , and 6.31 x
10~ 3 dB /km at 39 km . The corresponding S-band peak residual absorptivities with
th e ir percentages of th e total absorptivity are 4 .7 x
10-3
d B /k m (95.1%), 4 .9 x
10"3
d B /k m (94.8 %). and 5 .7 x 10“ 3 d B /k m (90.3%) d B /k m , respectively. Even at 35.5
km (pressure is about 5.17 a tm ), which is near th e lowest altitude probed by the
M agellan spacecraft radio occultation experim ents, th e S-band residual absorptivity
constitutes about 65.9%. of th e to ta l absorptivity. T hus, it can be seen th a t after
rem oving the contribution of CO 2 , a significant portion of th e total absorptivity at
S-band between 35 and 50 km is due to gaseous S 0 2 and gaseous H 2 S 0 4. Figure 3.3
show’s a peak to tal absorptivity a t X -band of 4 .0 6 x 10- 2 d B /k m at 38.5 km . The
corresponding X -band peak residual absorptivity is 3.2 x 10- 2 dB /km which is about
78.8% of the total absorptivity. A t 35.5 km, th e X -band to ta l absorptivity is 1.63 x
10~ 2 dB /km and th e corresponding residual ab so rp tiv ity is 0.4 x 10" 2 d B /k m which
is ab o u t 24.5% of th e total absorptivity. Again one can see th a t a significant portion
of th e total absorptivity at X -band between 35 an d 50 km is due to gaseous S 0 2
and gaseous H2 SO 4 . Note how?ever, th a t the contribution of C 0 2 to the X -band ab­
sorptivity is larger th an its contribution to the S-band absorptivity which is due to
•54
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55
SO
40
35
30.
8 -Sand Abaorpttvtty (dB/tem)
Figure 3.2: Total and residual S-band absorptivity profiles in th e Venus atm osphere
inferred from th e Magellan spacecraft radio occultation experim ents for orbit 3213
(latitude is 67° north). The associated stan d ard deviations are also shown.
65
60
40
35
30.
0.03
0.01
0.04
0.05
Figure 3.3: Total and residual X -band absorptivity profiles in th e Venus atm osphere
inferred from th e Magellan spacecraft radio occultation experim ents for orbit 3213
(latitude is 67° north). The associated stan d ard deviations a re also shown.
5-5
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the f
2
frequency dependence of th e microwave absorption of C O 2 . W ith regard to
orbits 3212 and 3214, total absorptivities have peaks between 4.5 x 10- 3 and
10" 3 d B /k m at S-band, and betw een 2.5 x
10~2
6 .0
x
an d 4.0 x 10“ 2 d B /k m at X-band
which are consistent w ith the peak absorptivities for orbit 3213. As for the residual
absorptivities, th e peaks are betw een 4.0x 10~ 3 an d 5 .5 x 10~ 3 d B /k m a t S-band,
and between 1.75x
10~2
and 3.25 x 10" 2 d B /k m a t X-band which are again consis­
te n t with th e peak residual absorptivities for orbit 3213. Furtherm ore, th e structural
features in th e S- and X-band absorptivity profiles for o rb it 3213 a re sim ilar to those
for orbit 3214, but not to those for o rb it 3212. T h e S- and X-band absorptivity pro­
files for orbit 3212 show an increase in the absorptivity as the a ltitu d e decreases from
50 km to th e 39-41 km region and then the abso rp tiv ity decreases as th e altitu d e
approaches 35 km. T hese structu ral variations in th e absorptivity profiles from orbit
3212 to orbit 3213 m ay be due to th e fact th a t th e Magellan spacecraft probed a
different region (due to a change in longitude) of th e Venus atm osphere. N ote th at
th e rotation period for the atm osphere of Venus is 5 days and th u s th e atm osphere
ro tated about 10° during each 3.26-hr orbit of the spacecraft.
Denoting th e S- and X-band residual absorptivities by
a f o 2+ H 2s o 4
^ d q so 2 +h2 so4>
respectively, these absorptivites can be expressed as a sum m ation o f th e individual
SO 2 and H 2 SO 4 absorptivites as
q Io 2 +h2so 4 = 9so 2 QnSo2 + 9h 2so 4 o^h 2 so 4
(3-1)
Qsb 2+H2 so 4 = 9so 2 Q&o2 + ?h 2so 4 o&
(3.2)
2S04
w here <?so2 and ?h 2so 4 are the abundances (mixing ratio s) of gaseous SO 2 and gaseous
H 2 SO 4 , respectively, and o fso 2 and a f H2SOl are th e abundance norm alized absorp­
tivities of gaseous
SO 2 and gaseous H 2 SO 4 , respectively. Note th at q ^ q 2 an d <*nS0 2
have been calculated by using the new Ben-Reuven m odel for gaseous SO 2 microwave
56
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absorption. Newly developed m ultiplicative expressions for the microwave absorption
o f gaseous H 2 SO 4 have been used to calculate
0^ 2
so 4 an<^ a nH2so 4 • These expressions
are w ritten as (K olodner and StefFes, 1997) [2]
/ eko\ 3.2±0.2
= 1 0 3 .5 8 7 ^ 356 ( — )
V T J
26GHz
d B /k m
(3.3)
/KKOn 3.0±0.2
= 443.570p1302 ( - = - )
V T J
8.39GHz
d B /k m
(3.4)
(v ~)
? / 2,
(j)
w here q is the abundance of gaseous H 2 SO 4 , P is the pressure in atm , and T is th e
tem perature in K elvin. Note th a t sm all frequency corrections given by (2.298/2.2 6 )1'21
and (8.426/8.39)1*21 have been applied to Equations 3.3 and 3.4, respectively, in o rd er
to m atch the M agellan frequencies (Kolodner and StefFes, 1997) [2].
The only rem aining unknowns in Equations 3.1 and 3.2 are qso 2 and ?h 2 so4Solving for these unkowns yields
s
q s o 2+ H 2S 04
,HiS0‘ = —
_
°nS02
V
~ p r “ Qs o 2+H2s o 4
;
QnHjSO, “ aK.*
°nH;SO,
nSO j
, SOl = a s o , 4-H,so, - W .s o X m s o ,
QnS02
( 3 -5)
(3
6)
The associated one-sigma s ta n d a rd deviation error in th e inferred gaseous S 02
and gaseous H2SO4 abundances den o ted by <r(7SOj and o ^ s o , , respectively, have been
estim ated using
(p^ v
-f ( - p a . ) a 2 x
<TtH2SOi ~
y
° 5 0 2 + H2 S 0 4
\ °\ n Sn O
S O2 j JJ
0 S O 2 + H ‘*2
2 SO
44
Jw
“
0S"
“
QnH2 S04 - ^ ^ QnH2S04
57
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/ n
*«»\
(3 -0
°nS0 2 ^
<TqS° 2
where a„s
and <rnx
“soj+HjSO, + (QnH2 S04) <^H2 so4
(3.8)
are th e stan d ard deviations in th e measured ab-
5O 2+ H 2S O 4
sorptivities at S- and X -bands, respectively.
Equations 3.5 through 3.S have been applied to th e S- and X -band absorptivity
profiles of the Venus atm osphere obtained from th e Magellan spacecraft radio occultation experim ents for orbits 3212, 3213, and 3214. Figures 3.4 an d 3.5 show th e
derived abundances of gaseous SO 2 and gaseous H 2 S 0 4, respectively, as a function
of altitu d e in the Venus atm osphere for orbit 3212. N ote from Figure 3.4 th a t th e
presence of gaseous S 0 2 is statistically significant between altitudes of 35 and 40 km .
Peak S 0 2 abundances of 130 ± 94 ppm and 143 ±
88
ppm ppm have been derived
at altitudes of 39 and 36.-5 km , respectively. T his significant presence of S 0 2 at these
altitudes is correlated with the decline in th e abundance opgaseous H 2 SO 4 as th e
altitu d e decreases from 40 to 35 km as shown in Figure 3.5. Note th a t between 35
and 40 km gaseous H 2 SO 4 therm ally decomposes u nder Venus atm ospheric conditions
(tem perature is between 408 and 445 K) into w ater vapor (H 2 0 ) an d sulfur trioxide
(SO 3 ). T he SO3 then reacts w ith carbon m onoxide (CO ) to form C 0 2 and S 0 2. T he
reaction C 0 -fS 0 3 peaks near 37 km (K rasnopolsky and Pollack, 1994) [45] which is
consistent with the altitudes at which gaseous S 0 2 peaks in th e Venus atm osphere
for orbit 3212 as seen from Figure 3.4. Above 40 km , th e abundance of gaseous S 0 2
is not pronounced and the microwave absorption is dom inated by th e th e presence of
H 2 SO 4 vapor. Note th a t th e H 2 SO 4 vapor abundance profile has a peak abundance of
4.9 ± 1 .2 ppm at 47 km which is near th e base o f th e m ain cloud layer in the Venus
at atm osphere. Above about 47 km , H 2 SO 4 vapor reaches satu ratio n (Knollenberg
and H unten, 1980) [4] and condensation begins which is noted from th e decrease in
gaseous H 2 SO 4 abundance as altitu d e increases from 47 to 50 km. For comparison
purposes, the saturation abundance profile for H 2 SO 4 vapor is also shown in Fig-
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ure 3.5 (Kolodner and Steffes, 1997) [2]. Note th a t th e derived abundances for H 2SO 4
vapor are slightly supersaturated betw een 47 and 50 km which m ay be p artially due
to th e uncertainties in th e expressions for the satu ratio n abundance of gaseous H 2 SO 4
(Kolodner and Steffes, 1997) [2]. Figures 3.6 and 3.7 present th e derived abundances
of gaseous SO2 and gaseous H 2 SO 4 , respectively, as a function of altitu d e in th e Venus
atm osphere for o rb it 3213. Unlike o rb it 3212, th e derived gaseous SO 2 abundance
profile for orbit 3213 shows a sharp peak of 399 ± 109 ppm a t 38.5 km and a sec­
ondary peak of 173 ± 106 at 41.5 km . This double-peak SO 2 abundance profile is
sim ilar to the SO 2
abundance profile obtained from th e ISAV - 1 ultraviolet spec­
troscopy experiment carried aboard th e Vega atm ospheric en try probes (B ertaux et
al., 1996, see also Section 4.3.3) [1] which shows a peak of 125 ppm a t 42.5 km and
a peak of 150 ppm a t 51.5 km. T h e derived abundance profile for gaseous H 2 SO 4
shows a peak abundance of 7.2 ± 0.8 at 46.5 km which is near th e base of th e main
cloud in the Venus atm osphere. A secondary peak of 3.3 ± 0.6 ppm at 39.5 km is
also present. Figures 3,8 and 3.9 present the derived abundances of gaseous SO 2 and
gaseous H 2 S 0 4, respectively, as a function of a ltitu d e in th e Venus atm osphere for
orbit 3214. Note th a t th e structural features in th e derived gaseous SO 2 and gaseous
H 2 SO 4 abundance profiles for orbit 3214 are sim ilar to those for o rb it 3213, but differ­
ent in th e peak levels of gaseous SO 2 abundance an d in th e existence of a secondary
peak for gaseous H 2 SO 4 . Figure 3.8 shows a sharp SO 2 abundance peak of 492 ±
87 ppm a t 39.5 km for orbit 3214 which is larger by 93 ppm from th e corresponding
peak for orbit 3213. A secondary SO 2 peak of
88
± 85 a t 42 km for orbit 3214 is
also shown in Figure 3.8 which is sm aller by 85 pp m from th e corresponding peak for
orbit 3213. Figure 3.9 shows a peak gaseous H 2 SO 4 abundance of 6.5 ±
1 .1
a t 46.5
km for orbit 3214 which is consistent w ith the gaseous H 2 SO 4 peak for orbit 3213.
However, note that th e gaseous H 2 SO 4 abundance profile for orbit 3214 does not have
a secondary peak as th e one for orbit 3213.
O ne common feature among o rb its 3212, 3213, and 3214 is the variation of
59
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59
“ o
SO
too
ISO
200
290
B « «m Suitor O ia la * AbunMnc* (ppm)
300
Figure 3.4: Gaseous SO 2 abundance profile in th e Venus atm osphere inferred from
the Magellan spacecraft radio occultation experim ents by using th e S- and X -band
absorptivity profiles for orbit 3212 (latitude is 67° north).
65
50
40
35
30
Figure 3.5: Gaseous H 2 S 0 4 abundance profile in th e Venus atm osphere inferred from
the M agellan spacecraft radio occultation experim ents by using the S- and X -band
absorptivity profiles for orbit 3212 (latitude is 67° north). Also shown is the gaseous
H 2 SO 4 saturation abundance profile.
60
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“ o
100
200
300
400
500
Sulfur O totM # A D undanc* (ppm)
500
Figure 3.6: Gaseous SO 2 abu n d an ce profile in th e Venus atm osphere inferred from
th e Magellan spacecraft radio occultation experim ents by using th e S- and X -band
absorptivity profiles for o rb it 3213 (latitude is 67° north).
55
50
40
35
30,
Sulfuric Add A bundance (ppm)
Figure 3.7: Gaseous H 2 SO 4 abu n d an ce profile in th e Venus atm osphere inferred from
th e Magellan spacecraft rad io occultation experim ents by using th e S- and X*band
absorptivity profiles for orbit 3213 (latitude is 67° n o rth ). Also shown is the gaseous
H 2 SO 4 saturation abundance profile.
61
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“ o
100
200
300
400
800
600
Q— 9Qu» Surfur Diowd* A p u n p an c* (ppm)
Figure 3.S: Gaseous S0_> abundance profile in the Venus atm osphere inferred from
the M agellan spacecraft radio occultation experim ent by using th e S- and X-band
absorptivity profiles for orbit 3214 (latitu d e is 67° north).
55
SO
40
35
30.
Figure 3.9: Gaseous H 2 SO 4 abundance profile in the Venus atm osphere inferred from
the M agellan spacecraft radio occultation experim ent by using th e S- and X-band
absorptivity profiles for orbit 3214 (latitu d e is 67° north). Also shown is th e gaseous
H2 SO 4 saturation abundance profile.
62
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gaseous SO 2 abundance between 35 and 50 km. A nother com m on feature is th e de­
crease in th e abundance of gaseous H2SO4 as th e a ltitu d e decreases from 38 to 35
km which is consistent w ith th e therm al decom position of gaseous H 2 SO 4 below 38
km in th e Venus atm osphere (von Zahn et a i, 1983) [46]. Furtherm ore, th e three
orbits show th a t the derived abundances for gaseous H2SO4 are slightly su p ersatu ­
rated betw een 47 and 50 km . On the o th e r hand, th e longitudinal variations (o rb it to
orbit) am ong the gaseous SO2 and gaseous H2SO4 vertical abundance profiles for the
three orbits are statistically significant a t some altitudes which indicate the presence
of local dynam ical m echanism s in the Venus atm osphere. N ote th a t latitudinal varia­
tions could also be deduced once the S- and X-band absorptivity profiles of th e Venus
atm osphere are obtained from the 1994 Magellan spacecraft radio occultation exper­
im ents at latitudes 62° south (S), 87° S, 49° north (N ), 74° N, and 82° N (Jenkins
et al.. 1994) [11]. Also note th a t S-band absorptivity profiles at latitu d e
88°
S of th e
Venus atm osphere were obtained from th e 1992 Magellan spacecraft radio occultation
experim ents for orbits 6369 and 6370. However, for operational reasons, the X -band
data was not reliable and therefore, th e above analysis can not be applied to infer
abundance profiles at this latitud e.
In th e next section, th e new laboratory m easurem ents of gaseous S 0 2 microwave
refractivity are applied to th e in terp retatio n of refractivity profiles obtained from th e
1991 M agellan spacecraft radio occultation experim ents.
3.3
Interpretation of th e R efractivity Profiles
The lab o rato ry m easurem ents of gaseous SO 2 microwave refractivity have been ap­
plied to the interpretation of th e Venus atm osphere refractivity profiles which were
obtained from th e 1991 M agellan spacecraft radio occultation experim ents for o rbits
3212, 3213. and 3214 (Jenkins et al.. 1994) [1 1 ]. The objective has been to exam ine
the potential contribution of gaseous SO 2 to these refractivity profiles. Table 3.1
63
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Table 3.1: R efractivity of Gaseous S 0 2 in th e Venus A tm osphere Based on our Lab­
oratory M easurem ents of th e S 0 2 D ensity Normalized Refractivity. Also Shown is
R esulting U ncertainty in Inferred T em perature Due to S 0 2 Refractivity.
A ltitu d e
P re ssu re
T e m p e r a tu r e
% C o n tr ib u tio n
A T
* tm
K
ppm
N* so a
x 10 “ '*
H sO j
km
36.6
4-7
434.6
231
1108
2.04
0.14
06
3213
3 8.5
3 .8
419 1
50 8
0.929
3.1S
0 .2 6
3214
3 9 .5
3.4
411.4
579
0.840
2 99
0 .2 7
O r b it
3212
K
1.1
11
shows th e peak S 0 2 abundances in the Venus atm osphere for th e three o rb its which
have been inferred from th e Magellan absorptivity profiles. Also shown is th e corre­
sponding refractivity of gaseous S 0 2 based on our laboratory m easurem ents of the
S 0 2 density normalized refractivity. In add itio n . Table 3.1 shows the p ercen t con­
trib u tio n of the S 0 2 refractivity to the to ta l refractivity inferred from th e M agellan
spacecraft radio occultation experim ents a t these altitudes. N ote th at even for these
elevated S 0 2 abundances, th e S 0 2 refractivity contribution is not significant. How­
ever, as shown in Table 3.1, its effect on th e accuracy of th e inferred te m p e ratu re is
non-trivial.
64
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65
CHAPTER 4
MODELING OF THE MICROWAVE
AND MILLIMETER-WAVE EMISSION
OF VENUS
4.1
Introduction
One of the most im p o rtan t aspects of th is research has been to model th e microwave
and millim eter-wave em ission spectrum from th e surface of Venus and its atm osphere.
This has been accom plished by solving th e radiative transfer equation. T h e radia­
tive transfer model (R TM ) computes th e brightness tem p eratu re of Venus given the
tem perature-pressure profile, the opacity formalisms for th e various atm ospheric con­
stitu en ts. and the vertical abundance profiles of the absorbing constituents.
The
developed RTM includes th e new BR m odel for gaseous SO 2 opacity as well as other
d ata relevant to th e surface of Venus an d its atm osphere. T his new m odel provides a
more accurate in te rp re ta tio n of the m icrowave and millimeter-wave emission spectrum
of Venus. The new RTM has been applied to th e recent disk-averaged observations of
the microwave and millim eter-wave em ission of Venus to infer an upper lim it on the
disk-averaged abundance of gaseous SO 2 below the m ain cloud layer. Furtherm ore,
the new emission m odel has been applied to th e interpretation of th e 1.3 cm and 2
cm em ission maps which resulted from th e VLA observation of Venus (see C hapter
5). In th e next section, th e theory used in developing th e radiative transfer model is
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explained.
4.2
T heoretical Background
The emission from th e surface of Venus and its atm osphere can be com puted using th e
radiative transfer equation (RTE). A ssum ing th a t radiation traverses an atm osphere
which is locally plane-parallel; th at is, an atm osphere which is stratified in planes
locally perpendicular to a given direction z measured upward from th e surface of
th e planet (generally valid for atm ospheres whose thickness is sm all compared w ith
its radius) and assum ing that the atm osphere is in local therm odynam ic equilibrium
(LTE). then th e R TE is given by (B uglia, 1986) [47]
B u( T , n ) = B A T ^ e - ^ +
• 'T to p
(4.1)
fl
where B„ is th e brightness which is defined as the power received p e r u n it area per
unit frequency p er u nit solid angle, v is the frequency, T is the physical tem p eratu re
at a given optical d epth, T surf is the surface brightness tem perature, r lop is th e optical
depth at the top of th e atm osphere which is defined to be zero,
is th e optical
depth at the surface of the planet, and // = cos 0, where 0 is known as th e viewing or
look angle which is defined as the angle between the line of sight em an atin g from a
particular point p and th e normal to th a t point (see Figures 4.1 and 4.2). Note th a t
th e optical depth r„ is defined as
/
2toP
a u(z')dz'
(4.2)
w here a„ is th e absorption coefficient of all atm ospheric constituents a t frequency u
and position z. For
a maxim um , and for
= 0; th at is, a t th e surface of th e planet, t„ = r surf which is
2
2
= ztop: that is. at th e top of th e atm osphere. r„ = rtop =
66
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0.
z
Line of sight
Normal to the
surface at p
Z « 0 ,’ xv - x surf .
*
Atmospheric
Layers
VENUS
Figure 4.1: Geometry of Venus and its atm osphere used in the disk-averaged radiative
transfer model.
In other words, as one ascends through th e atm osphere, z increases and the optical
depth decreases. This convention is being used since it provides m o re physical insight
into the problem of modeling th e emission from th e planet and its atm osphere as seen
by a.planetary observer.
The first term in E quation 4.1 represents th e brightness from th e surface a tte n u ­
ated by the intervening layers of th e atm osphere and th e second te rm is th e brightness
generated and attenuated by th e atm ospheric layers. Note th a t th e brightness from
th e surface is calculated given a surface brightness tem p eratu re Tsurf which is d e ter­
m ined using the expression (P etten g ill et al., 1992) [48]
Tgurf = eTphys + rT&y
(4.3)
where r is the surface reflectivity, T phys is th e physical te m p e ratu re of th e surface,
e is the surface emissivitv which is equal to
1 —r,
and T sky is th e sky tem p eratu re
which is determ ined from th e downwelling atm ospheric and cosmic background emis67
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Line of sight
Normal to p
to p
X
v
s u rf
VENUS
Atmospheric
Layers
Figure 4.2: Geometry of Venus and its atm osphere used in th e look-angle radiative
transfer model.
68
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sions which are th e n reflected by th e surface back to the atm osphere. Note th a t a
cosmic background tem perature of 2.7 k above the p la n et’s atm osphere is assum ed.
T he surface reflectivity r is calculated by averaging th e reflectivity for vertically an d
horizontally polarized electrom agnetic waves, r„ and r/,, respectively, which are given
by (Tsang et al., 1985) [49]
(4.4,
\ V*cos 6 ' + Tfay/ 1 - ^ S i n 2 0£i
(W
1
- ^
W\A - ?
sin2^ - f r cos6' \ 2
% s™26' ~
,
1,0 cos0£/
where 77, is the surface im pedance w hich is equal to
n 0/ t s, where \i0 is the perm e­
ability assuming a nonm agnetic surface which equals to 47r
x
10 - 7 H /m , es is th e
surface perm ittivity which is equal to 4.5e 0 for the Venus surface (Pettengill et al.,
1992) [48], where e0 = 8.85 x 10~ 12 F /m , and rja is the im pedance of the lowest
atm ospheric layer which is equal to yjfi0/e a, where e0 = n \e 0 and n a is the index
of refraction of th e lowest atm ospheric layer. The angle &e is the angle of emission
between the norm al to th e surface a n d th e line of sight which is equivalent to th e
look angle 6 shown in Figure 4.1. N o te th a t when com puting the emission as a func­
tion of the look angle 0 a t the top o f th e atm osphere (see Figure 4.2), th e angle of
emission 9t at th e surface is determ ined by ray-tracing in th e downward direction.
This is achieved by using Snell’s law along with th e knowledge of th e atm ospheric
index of refraction profile and the look angle 6 at the top of th e atm osphere. For th e
Venus atm osphere, th e index of refraction profile is obtained by using the appropriate
pressure-tem perature profiles, the d en sity normalized refractivities for gaseous CO 2
and N 2 (Essen and Froom e. 1951) [41], and by assuming uniform abundance d istri­
butions of 96.5% for C O 2 and 3.5% for N 2 a t all altitudes of the Venus atm osphere
(Oyama et al.. 1980) [3]. In addition to th e emission angle at th e surface, the ray
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tracing process produces an angle of emission for each atm ospheric layer which is used
in com puting the em ission from each layer. Note th a t for each look angle a t the top
of the atm osphere th ere is a unique ray path extending from the surface to th e top of
the atm osphere. Furtherm ore, it should b e emphasized th a t the effect of atm ospheric
refractivity on the com puted emission becomes most pronounced as one approaches
the planetary limb (M uhlem an tt a/,, 1979, and Good and Schloerb, 1983) [50, 51].
Note that as one views th e planet away from nadir (9 = 0), the slant p a th of ob­
servation encounters m ore atm ospheric structure, which results in more atm ospheric
refraction and absorption.
Equation 4.1 can be also w ritten in term s of an im portant q u an tity known as
the weighting function. T h e weighting function gives the altitu d es a t which th e atm o­
sphere contributes m ost to the calculated brightness. H ere, two weighting functions
are defined, one is the surface weighting function denoted by W/ *urf(/i), and th e other
is the atm ospheric w eighting function denoted by W * tmos[ z , f i ) . Thus, E quation 4.1
can be rew ritten as (B uglia. 1986) [47]
£ „ (t» =
b a n u rfiw rv)
+ Jo
a,cr(j) ) w r ” (*,#o</»
(4.6)
where
^ * 'urf(/J) = exp ( - f
\
” q„( 2 )— )
I1 /
«-(>') j )
u r n * . / - ) = <*p
(4.7)
^
(4.8)
Now, the brightness can be calculated by using the well-known Planck’s radiation
law which is expressed as (C handrasekhar, 1946) [52]
B (T)-2huZ! c2
" ( ) exp(hv/kT) —1
70
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/4<n
( 9)
where h is Planck's constant (6 .6 3 x l0 -34 J-sec), c is the speed of light (2.998x10®
m /sec), and k is B oltzm ann’s constant (1.38 x lO - 2 3 J/K ). T h en , B„(T) has u n its of
Wm~ 2 Hz~ 1s r ''1. N ote th a t when h v <C k T which is valid in th e microwave region
of the electrom agnetic spectrum , the P lan ck ’s radiation law reduces to the RayleighJeans approxim ation given by
2kT
^
(4 . 1 0 )
where A is th e wavelength.
The observed brightness of a p lan et is often expressed in term s of a q u an tity
known as the brightness tem perature. T h e brightness tem p eratu re is defined as the
tem perature at which a blackbody would produce a brightness th a t is equivalent to
th at of the planet at a specific frequency. T he brightness tem p eratu re, 7 b , can be
found by inverting P lanck’s radiation law
Tb =
r.
(4.11)
which when using the Rayleigh-Jeans approxim ation becomes
T
B
M, - >.
2k
*
*
W hen integrating E quation 4.1 over all angles of emission, th e disk-averaged
brightness is obtained as follows (Buglia, 1986) [47]
B„(T d ) =
2
/ B 1/(7’surf ) e " J ^tL/xd// +
2
JO
where
Td
f f
JO J r top
B,/ {T{Tl))e~'Z'dT'l/dn
is the disk-averaged brightness tem p eratu re.
71
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(4.13)
4.3
Param eters o f th e R adiative Transfer M odel
The param eters of the radiative transfer m odel (RTM ) are th e tem perature-pressure
profiles, th e opacity form alism s for th e various atm ospheric constituents, and the
vertical abundance profiles of th e absorbing constituents.
4.3.1
Temperature-Pressure Profiles
The tem perature-pressure profiles for th e atm osphere of Venus th a t are employed
in th e developed RTM model have been obtained from th e d a ta collected using the
Pioneer-Venus sounder and north probes (Seiff et al., 1980) [53]. Figure 4.3 shows the
tem p eratu re as a function of a ltitu d e in th e Venus atm osphere from the Pioneer-Venus
sounder and north probes. Figure 4.4 shows th e pressure as a function of altitu de
in the Venus atm osphere from th e Pioneer-Venus sounder and north probes. Note
th a t the Pioneer-Venus sounder probe tem perature-pressure profile represents the
equatorial regions in the Venus atm osphere. Thus, it is used in the RTM for latitudes
th a t are between -45° and 45°. T he Pioneer-Venus north probe tem perature-pressure
profile represents the polar regions in the Venus atm osphere. Thus, it-is used in the
RTM for latitudes th at are between ±45° and ± 90°. In addition to th e pressure and
tem p eratu re profiles, a physical Venus surface tem perature of 733 K is used in the
RTM.
4.3.2
Opacity Formalisms
The opacities of severed m ajor absorbing constituents at microwave and m illim eterwave frequencies in th e Venus atm osphere are incorporated in th e developed RTM.
These are th e opacities of the gaseous CO2-N2 m ixture, gaseous SO2, and gaseous
H2SO4. O ther opacities of trace gaseous constituents are also included in th e model.
These include the opacities of gaseous carbon m onoxide (CO), gaseous carbonyl sulfide
(O C S ), and w ater vapor (H2O).
72
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|30
300
400
600
800
700
Figure 4.3: T em perature as a function of altitude in th e Venus atm osphere obtained
using th e Pioneer-Venus sounder and no rth probes (Seiff et al., 1980) [53].
100
Figure 4.4: Pressure as a function of altitu d e in th e Venus atm osphere obtained using
the Pioneer-Venus sounder and no rth probes (Seiff et al., 1980) [53].
73
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The first source of th e microwave and m illim eter-wave opacity in th e Venus
atm osphere is gaseous CO 2 . Although C O 2 is a non-polar molecule, collision-induced
absorption by gaseous C 0 2 (B arrett, 1961) [54] is th e dom inant source of centim eterand millimeter-wavelength absorption a t low altitu d es of th e Venus atm osphere. To
determ ine th e opacity from gaseous C O 2 , Ho et al. (1966) [18] derived an expression
based on laboratory m easurem ents of gaseous C O 2 -N 2 m ixtures.
This expression
is accurate within a few percent for tem p eratu res up to 500 K and for a range of
pressures relevant to the Venus atm osphere. T h eir CO 2 -N 2 opacity formalism which
is incorporated in the developed RTM is given by
acojt*') = 1.15 x 10® (q2cQj + 0.259c o 2?n 2 + 0 .0 0 5 4 ?^ ) v 2P 2T ~ h d B /K m
(4.14)
where v is th e frequency in GHz, q is th e num ber mixing ratio, P is the pressure in
atm . and T is tem perature in K.
Besides th e m ajor opacity contribution from gaseous C O 2 in the lower atm o­
sphere, gaseous SO2 and gaseous H 2 SO 4 co n trib u te significantly to the microwave
and millimeter-wave absorption within th e Venus atm osphere (Steffes and Eshlem an,
1981, Fahd and Steffes, 1992, Steffes, 1985, Fahd, 1992) [5 ,6 ,5 5 ,5 6 ]. In th e developed
RTM. the newly derived Ben Reuven form alism for gaseous SO 2 opacity is used (see
Chapter
2
). For gaseous H 2 SO 4 microwave opacity, a newly developed m ultiplicative
expression based on new’ laboratory m easurem ents (K olodner and Steffes, 1997) [2 ] is
employed in the RTM. T he expression is given by
/ e c q v 3.0± 0.2
q = 53.601 x qpl u f l ls
d B /k m
(4.15)
where q is th e abundance of gaseous H2SO4, P is th e pressure in a tm , f is the frequency
in GHz, and T is the tem perature in Kelvin.
Although not present in sufficient q u an tities to effect th e microwave emission
of Venus below 100 GHz. the opacities of gaseous CO, gaseous OCS, and gaseous
74
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H2 O are included in th e developed RTM . Their opacities are represented by VVW
formalisms w ith th e corresponding line center intensities obtained from th e P oynter
and P ickett catalog (P oynter and P ick ett, 1985) [30].
In addition to th e above constituents in th e Venus atm osphere, a dense cloud
layer which consists of liquid sulfuric acid particles is also present between altitu d es
of 48-50 km (K nollenberg and H unten, 1980) [4]. The effects of liquid H2 SO 4 on
the microwave an d millimeter-wave emission of Venus were investigated in detail
by Fahd and Steffes (Fahd, 1992, Fahd and Steffes, 1991) [56, 57]. It was shown
that th e reflection coefficient for liquid H2SO4 with 25 microns for droplet size and
50 m g /m 3 for cloud bulk density is m uch less than th e transm ission coefficient by a
factor of 5x 104 for frequencies below 240 GHz. Thus, th e H 2 SO 4 cloud layer is m ostly
transm issive and th e scattering by liquid H 2 S 0 4 is not significant to th e emission a t
microwave and m illim eter-w ave frequencies. In addition, it was shown th a t liquid
H2 SO 4 decreases th e brightness tem p eratu re of Venus by less th an
longer th an
1
1
K a t wavelengths
cm and by only 1-2 K for wavelengths in the 2-10 m m range. Thus, th e
variations in liquid H 2 SO 4 abundance are therefore not a m ajo r source of variations
in th e observed brightness tem perature of Venus. Therefore, th e effects of scattering
by liquid H 2 SO 4 are not included in our new RTM.
4.3.3
Abundance Profiles
The last im p o rtan t param eter of the RTM which m ust be specified is the vertical
abundance d istribution of th e absorbing constituents in th e atm osphere of Venus. The
principal constituent of th e Venus atm osphere is gaseous C O 2 (O yam a et a/., 1980) [3 ].
It com prises 96.5% (bv volume) of the atm osphere, and gaseous N 2 constitutes about
3.5%. In the developed RTM , these m ixing ratios for C O 2 and N 2 are used for all
altitudes of the atm osphere of Venus.
For gaseous H2SO4, a vertical abundance profile derived from th e equatorial
M ariner 10 radio occultation experim ents (Howard et al., 1974, Lipa and Tyler.
75
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1979) [58, 59] is used in th e new R TM . Figure 4.5 shows the gaseous H 2 SO 4 ver­
tical abundance profile in the Venus atm osphere which was derived by inverting the
equatorial M ariner
10
S-band (2.295 G H z) absorptivity profile (K olodner and Steffes,
1997) [2]. Note that below an a ltitu d e of 38 km, it is assum ed th a t gaseous H 2SO 4
dissociates (0 ppm ).
Above 48 km , th e abundance of gaseous H 2 SO 4 follows the
satu ratio n abundance (Kolodner and Steffes. 1997) [2]. Also used in th e RTM to in­
terp ret th e VLA emission maps of Venus (see C h ap ter 5) are th e polar vertical H2SO4
abundance profiles derived from th e 1991 Magellan radio occultation experim ents for
orbits 3212, 3213. and 3214 (Jenkins et al., 1994, also see C hapter 3 for th e derived
H2SO4 abundance profiles) [ll].
T he abundance profiles for gaseous CO, gaseous OCS, and gaseous H 2 O are
obtained from K rasnopolskv and Pollack (1994) [45], where
1
ppm for gaseous CO is
assum ed near the surface of Venus and increases to 30 ppm as the altitu d e increases,
28 ppm for gaseous OCS is assumed n ear the surface and decreases to zero as the
a ltitu d e increases, and 90 ppm for w ater vapor is assum ed between 0-35 km and
decreases to 3-5 ppm as th e altitude increases above 35 km.
Finally, several abundance profiles for gasoeus SO 2 are employed in th e devel­
oped RTM . Uniform m ixing ratios of 75 ppm and 150 ppm for gaseous S 0 2 are adopted
for altitudes below th e m ain cloud layer (i.e, < 48 k m ). Above the cloud layer, the
SO 2 abundance profile is assumed to decay exponentially with a scale height of
3 .3
km (N a et al., 1994) [60]. In addition, a recent equatorial SO 2 abundance profile
(non-uniform ) obtained from the ISAV-1 ultraviolet (U V ) spectrom eter on board the
e n try probe which was released by th e V EG A -1 spacecraft (B ertaux et al., 1996) [1 ]
is used in the developed RTM. This abundance profile is shown in Figure 4.6 and is
characterized by double peaks. The first peak has an SO 2 abundance of 125 ppm at
42.5 km and the second SO 2 peak has an abundance peak of 150 ppm a t 51.5 km.
It should be noted th a t at low altitudes (i.e, below 12 km ) in the Venus atm osphere,
th e SO 2 abundances from the equatorial ISAV-1 profile are not consistent with the
76
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55
Mariner 10 Abundance
— Saturation Abundance
50
E
JC
07 45
T—
3
Z3
5
40
3-s s
0
5
10
15
G aseous Sulfuric Acid Abundance
20
Figure 4.5: A bundance profile for gaseous H 2 SO 4 in th e Venus atm osphere derived
from th e equatorial M ariner 10 radio occultation experim ents (Kolodner and Steffes,
1997) [2].
11
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E40
50
100
150
Abundance of Gaseous Sulfur Dioxide (ppm)
Figure 4.6: Abundance profile for gaseous SO 2 in th e Venus atm osphere obtained
from the ISAV-1 /V E G A - 1 ultraviolet spectrom eter (B ertaux et al., 1996) [1].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S 0 2 abundances which have been derived from recent chemical equilibrium models
(Feglev tt al., 1997) [61]. The ISAV -1 profile shows S 0 2 abundances of 20-25 ppm a t
12 km and below, whereas th e recent therm ochem ical models report S 0 2 abundances
of 100-130 ppm at 12 km and below. In addition to the above profiles, th e polar S 0 2
abundance profiles derived from th e 1991 M agellan radio occultation experim ents for
orbits 3212, 3213, and 3214 (Jenkins et al., 1994, also see C h ap ter 3 for th e dervied
S 0 2 abundance profiles) [1 1 ] are used in the new RTM to in terp ret the recent VLA
emission m ap s of Venus (see C hapter 5).
4.4
D isk-A veraged M odeling R esults
The new RTM model has been applied to th e in terpretation of the microwave and
millimeter-wave emission spectrum of Venus. Table 4.1 shows results for m easure­
ments of th e microwave and millimeter-wave disk-averaged brightness tem p eratu res
of Venus. For comparison purposes, Table 4.1 also shows th e com puted disk-averaged
brightness tem peratures (T qi and T d 2 ) of Venus for two different gaseous S 0 2 ver­
tical abundance profiles. T he first profile has a uniform S 0 2 abundance of 75 ppm
below an a ltitu d e of 48 km . Above 48 km it is assum ed th a t SO 2 decays exponentially
with a scale height of 3.3 km (see Column 4 of Table 4.1 for th e RTM results). T he
second profile is the ISAV - 1 S 0 2 abundance profile (see Colum n 5 of Table 4.1 for the
RTM results). Note th a t th e new RTM with an S 0 2 uniform abundance of 75 ppm
provides a good agreem ent with th e m easured brightness tem p eratu res at m icrowave
and millimeter-wave frequencies except for th e X -band (8.42 GHz) observation. This
discrepancy a t X-band was also observed using th e RTM developed by M uhlem an
(M uhleman et al., 1979) [50]. Also note th a t th e new RTM w ith the ISAV - 1 S 0 2
abundance profile provides a good agreem ent w ith the m easured brightness te m ­
peratures a t microwave frequencies except for th e 8.42 GHz observation. However,
at millimeter-wave frequencies th e com puted disk-averaged brightness tem p eratu res
79
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w ith the ISAV - 1 SO 2 abundance profile do not agree well w ith the m easured bright­
ness tem peratures as compared w ith using th e uniform SO 2 abundance of 75 ppm
especially at th e
8 6 .1
GHz observation.
Figure 4.7 shows the microwave and m illim eter-w avelength observations of the
disk-averaged brightness tem peratu res of Venus. Also shown in this figure is th e com­
p u ted disk-averaged brightness tem p eratu res of Venus as a function of frequency for
uniform gaseous SO 2 abundance below 48 km of 75 ppm and 150 ppm. In addition,
this figure shows th e com puted disk-averaged brightness tem peratures of Venus using
th e ISAV-1 SO 2 abundance profile. Note th a t th e new RTM with an SO 2 uniform
abundance of 75 ppm provides an excellent fit to the m easured brightness tem pera­
tures at microwave and m illim eter-w ave frequencies except for the X-band (8.42 GHz)
observation. Also note th a t the new RTM w ith the ISAV -1 SO 2 abundance profile
provides an excellent fit to the m easured brightness tem p eratu res at microwave fre­
quencies except for th e 8.42 GHz observation. However, a t millimeter-wave frequen­
cies (above 30 G Hz) th e com puted disk-averaged brightness tem peratures w ith the
ISAV -1 SO 2 abundance profile do not provide a good fit to the m easured bright­
ness tem peratures as compared w ith using th e uniform SO 2 abundance of 75 ppm
especially at th e
8 6 .1
GHz observation.
Figures 4.8 and 4.9 show th e disk-averaged atm ospheric weighting functions of
Venus as a function of altitude at frequencies of 8.42,14.94, 22.46, and
8 6 .1
GHz. The
constituents of th e Venus atm osphere included in th e model are CO 2 , N 2 , H 2 SO 4 , H 2 0 ,
CO , OCS, and SO 2 . For Figure 4.8 uniform SO 2 abundance of 75 ppm below 48 km is
used and for Figure 4.8 th e ISAV - 1 SO 2 vertical abundance profile is used. N ote from
Figure 4.8 th a t a t 8.42, 14.94, 22.46, and
8 6 .1
GHz, th e disk-averaged atm ospheric
weighting functions peak at altitud es of 7.25, 18.25, 27.75, and 46.75 km, respectively.
W hen using th e ISAV - 1 S 0 2 .vertical abundance profile, Figure 4.9 shows th a t a t 8.42,
14.94, 22.46. and 86.1 GHz, the disk-averaged atm ospheric weighting functions peak
at altitudes of 6.75. 17.75. 27.75. an d 52.25 km , respectively. N ote th at below’ 38 km,
80
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the contribution to the weighting functions shown in Figures 4.8 and 4.9 is mostly
due to the absorption from CO2 and N2. Between 38 and 52 km, the contribution to
the weighting functions is mostly due to gaseous SO2 and gaseous H2SO4.
Figure 4.10 shows the difference in the disk-averaged brightness temperature as
a function of frequency between a Venus atmosphere with only CO2 , N2 , H2 SO4 , H2 O.
CO. and OCS and a Venus atmosphere with C 0 2, N2, H2 SO 4 . H2 0 , CO, OCS, and
SO2 . For gaseous S 0 2, three different vertical abundance profiles are used. The first
and the second profiles have uniform SO 2 abundances of 75 ppm and 150 ppm below
48 km. respectively. Above 48 km it is assumed that S 0 2 decays exponentially with
a scale height of 3.3 km. The third profile is the ISAV- 1 S 0 2 abundance profile. Note
from Figure 4.10 that the largest drop in the disk-averaged brightness temperature
due to the absorption from gaseous S 0 2 (assuming uniform abundances of 75 ppm
and 150 ppm below 48 km) occurs in the frequency range between 15 GHz and 26
GHz. For uniform abundances of 75 ppm and 150 ppm, the largest drop in the diskaveraged brightness temperatures are 13.7 K and 24.8 K, respectively. For the ISAV- 1
S 0 2 abundance profile, the largest drop in the disk-averaged brightness temperature
due to the absorption from gaseous S 0 2 occurs in the frequency range between 65 GHz
and 75 GHz with a peak of 32.2 K at 70 GHz. Thus, observations in the frequency
ranges between 15 GHz and 26 GHz and between 65 GHz and 75 GHz are most
sensitive to detecting gaseous S 0 2.
Another important result from the new emission model is the determination of a
new upper limit on the disk-averaged abundance of gaseous S 0 2 below the main cloud
layer. At 22.46 GHz which is one frequency in the K-band region that is most sensitive
to detecting gaseous S 0 2, the measured disk-averaged brightness temperature from
our VLA observation of Venus (see Table 4.1 and Chapter 5) is 499.1 ± 25 K. By
matching the computed emission from the new RTM to the
-1
a error bar of the
measured K-band emission, one obtains a new upper limit of 150 ppm on the diskaveraged abundance of gaseous S 0 2 below the main cloud layer (based on uniform
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
m ixing, also see Figure 4.7). This result is in agreem ent w ith recent infrared (IR )
E arth-based observations which showed an SO 2 abundance of 130 ± 40 ppm betw een
35 and 45 km (B ezard et al., 1993) [69]. Also th e new SO2 u p p er lim it of 150 p p m
compares well w ith previous spacecraft in situ m easurem ents. T h e Venera 11/12 gas
chrom atograph experim ents reported an SO 2 abundance of 130 ± 35 ppm at 42 km
and below (G elm an et al.. 1979) [70]. The Pioneer Venus gas chrom atograph reported
an SO 2 abundance of 185 ± 43 ppm at
22
km (O yam a et al., 1980) [3].
In th e next chapter, th e conduct of a dual-frequency observation of Venus using
the VLA and th e in terpretation of the resulting emission m aps using the new RTM
are discussed.
82
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T able 4.1: M easured Disk-Averaged Brightness Tem peratures of Venus for Various
Frequencies as C om pared to the R esults from th e New R adiative Transfer Model
using (1) Uniform SO 2 Abundance of 75 ppm Below 48 km ( T d i ) a n d (2) th e ISAV-1
SO 2 A bundance Profile (T d 2 )F req u en cy
W a v e le n g th
( GHz )
(cm)
M e& sured T
q
fK|
C o m p u te d T
qj
<K )
C o m p u te d T ^ a
R e f e re n c e
(K )
1.42
21.13
617 4 2 5 s
6105
6 10.1
B e rg e t t a t.. 1972 [62]
11
2 0 .00
636 4 20*
6 1 1 .2
6 1 0 .7
P e tte n g ill e t of., I9 6 0 [63].
2.91
10.31
620 4 30*
6 2 4 .5
623 3
V e iu k h n o v ik * y i, 1969 [64]-
$.0
6 00
652 4 30*
6 3 5 .2
634 0
B erg e e t of., 1972 [62].
0 42
3 .5 6
652 ± 15°
6 1 2 .6
6 13.4
S teffes e t of.. 1990 [65]
9 62
3 .1 2
600 4 35*
5 9 6 .4
599.4
B erg e t t a t., 1972 [62]
12-11
2 70
612 4 37*
5 7 9 .9
561.1
M c C u llo u g h . 1972 [6 6 ].
13 3
2 .2 6
561 4 19°
5 5 4 .3
555 3
S teffes e t a t 1990 [65].
14 94
2 00
5 6 5 -i ± 17*
5 3 7 .2
536 0
O u r V LA O b s e r v a tio n . 1996.
S teffes e t a t.. 1990 [65].
10.46
1.63
520 4 17°
5 0 6 .6
5 0 6 .0
2 2.26
1.35
507 4 2 2 °
4 60.1
4 7 6 .7
S teffes e t a t., 1990 [65]
2 2.46
1.34
499 1 4 25*
4 7 6 .6
475 3
O u r V L A O b s e r v a ti o n , 1996.
3 7 .50
0 .6 0
440 4 35*
4 2 1 .0
4 1 3 .5
V e tu k h n o v s k * y t t t a t., 19 6 3 [67].
66 1
0 .3 5
3 5 7 .5 4 13.1*
3 5 3 .5
3 3 6 .6
U lich t t a t., 19 6 0 [6 6 ].
83
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700
J
650
600
J
JT
Measured data
_________
75 ppm
_________
150 ppm
..................
ISAV- 1 profile
550
\\< >T
500
&450
1 400
350
300
100
Frequency (GHz)
Figure 4.7: C om puted disk-averaged brightness tem peratures of Venus as a function
of frequency for various vertical abundance profiles of gaseous SC>2 - Also shown
in this figure are th e m easured cen tim eter and m illim eter-w avelength disk-averaged
brightness te m p e ratu res of Venus.
84
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"E 40
JC
§30
8.42 GHz
14.94 GHz
22.46 GHz
86.1 GHz
0.005
0.01
0.015
0.02
0.025
0.03
Atmospheric Weighting Function
0.035
0.04
0.045
Figure 4.8: Disk-averaged atm ospheric weighting functions of the Venus atm osphere
as a function of a ltitu d e at frequencies of 8.42, 14.94, 22.46, and
8 6 .1
GHz. The
constituents of th e Venus atm osphere used in the m odel are CO 2 , N 2 , H 2 SO 4 , H 2 O,
CO, OCS, and SO 2 , w here uniform abundance of 75 p p m below 48 km is used for
S 0 2.
85
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*
8.42 GHz
14.94 GHz
22.46 GHz
86.1 GHz
0
0.005
0.01
0.015 0.02 0.025 0.03 0.035
Atmospheric Weighting Function
0.04
0.045
0.05
Figure 4.9: Disk-averaged atmospheric weighting functions of the Venus atmosphere
as a function of altitude at frequencies of 8.42, 14.94, 22.46, and
86.1
GHz. The
constituents of the Venus atmosphere used in the model are CO 2 , N2 , H2 SO4 , H 2 O,
CO, OCS, and SO 2 , where the ISAV- 1 vertical abundance profile is used for SO 2 .
86
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- * 75 ppm
150 ppm
ISAV-1 profile
100
Frequency (GHz)
Figure 4.10: Difference in the disk-averaged brightness te m p e ratu re as a function of
frequency betw een a Venus atm osphere w ith only C 0 2, N 2, H 2 S 0 4, H 2 0 , C O , and
OCS and a Venus atm osphere w ith C 0 2, N2, H 2 S 0 4, H 2 0 , C O , OCS, and S 0 2, where
three different vertical abundance profiles are used for S 0 2.
87
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88
CHAPTER 5
DUAL-FREQUENCY OBSERVATION
OF VENUS USING THE VLA
5.1
Introduction
On April 5, 1996, an observation of Venus a t 1.3 cm (22.46 GHz or K -band) and
2 cm (14.94 GHz or U -band) was conducted using the N ational Radio Astronom y
O bservatory Very Large A rray (NRAO-VLA) near Socorro, New Mexico. T he VLA
site which is located in th e Plains of San A gustin is especially suitable for conduct­
ing observations since th e surrounding m ountains provide an environm ent which is
relatively free from te rrestrial radio frequency interference. Furtherm ore, th e 7000foot elevation of the P lains of San Agustin arid th e dry clim ate tend to minimize
phase fluctuations associated with variations in atm ospheric w ater vapor (N apier et
a/., 1983) [71].
T he VLA is a state-of-the-art interferom eter and is th e m ost powerful synthesis
array in th e world which is capable of producing radio images; commonly referred to
as emission m aps or brightness distributions. T he angular resolution which can be
achieved w ith th e VLA is on th e order of a few ten th s of an arc-second (N apier et al.,
1983) [71]. T h e VLA consists of 27 antennas (NRAO, 1989) [72], each a n ten n a with
a diam eter of 25 meters (82 feet). The antennas can be pointed to any position in the
sky to an accuracy of
10
arc-sec and can be m oved independently in azim uth and in
elevation. T h e antennas a re arranged in a Y -shape with nine antennas on each arm of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
th e Y. There are four basic configurations for the VLA denoted D, C , B, and A. T h e
D-configuration is th e most com pact and the A-configuration is th e largest. Our VLA
observation of Venus was conducted when the VLA was in th e C-configuration. In
this configuration, th e separation betw een adjacent an ten n as is 73 m which results in
a separation of 3.4 km between th e farthest antennas in th e array (Perley, 1995) [73].
The objective of this observation was to obtain high spatial resolution continuum
emission m aps of Venus at w avelengths of 1.3 cm an d 2 cm. These emission m aps
are used to detect potential sp atial variations in th e vertical abundance distributions
of gaseous SO 2 and gaseous H 2 SO 4 across the disk of Venus. This has been achieved
by using a newly developed rad iativ e transfer model which incorporates the new Ben
Reuven model for the microw’ave absorption of gaseous SO 2 and th e new m ultiplicative
expressions for th e microwave absorption of gaseous H 2 SO 4 (Kolodner and Steffes,
1997) [2].
In order to observe Venus using th e VLA, a proposal was w ritten and subm itted
to NRAO. The proposal was reviewed by a panel of scientists and la te r accepted by
th e NRAO scheduling com m ittee. T he proposal which consists of th e VLA observing
application and a scientific justification is shown in A ppendix A. A description of th e
procedure for observing Venus using th e VLA is presented in the next section.
5.2
Procedure
To construct a synthesis image of a radio source using th e VLA, radio waves collected
by th e 27 elem ents of th e interferom eter are combined in pairs by devices known as th e
correlators (Thom pson, 1994) [74]. N ote th a t for a synthesis array of 27 antennas, a
to tal of 351 pairs can be formed. T h e correlator consists of a voltage m ultiplier circuit
followed by a tim e averaging (integ ratin g ) circuit. T h e o u tp u t of th e correlator, when
calibrated, is a m easure of th e am p litu d e and phase of th e visibility function for
th e specific baseline between th e antennas. The visibility is a complex quantity, th e
89
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m agnitude of which is often expressed in units of Janskys (Jy) where
1
J y = l x lO - 2 6
W m - 2 Hz-1 . The visibility quantities V» are related to th e brightness d istrib u tio n B„
of th e radio source by a two-dimensional Fourier transform as (see e.g., T hom pson et
a/., 1991) [75]
V ;( u ,v ) = r
I " B t/( x , y ) e 2^ ' ‘T+^ d x d y
(5.1)
J —oo «/-oo
where u and v represent th e interferom eter baselines m easured in th e east-w est and
north-south directions, respectively, and x and y denote th e coordinates of th e ra­
dio source brightness distribution as shown in Figure 5.1.
Note th a t B u( x , y ) =
A „ { x .y ) B l ( x ,y ) where A„ is th e primary beam or norm alized reception p a tte rn
(power p a tte rn ) of the individual interferom eter elem ents and B'„ is th e a c tu a l b rig h t­
ness distribution (Thom pson. 1994) [74]. A ssum ing that th e prim ary beam is identical
for each antenna in th e VLA and has a G aussian shape then A„(x, y) is calculated
using
A ^ x . y ) = A u{<t>) = e
J
(5.2)
= 2 \/ln2 . <p is t h e a n g u la r d is ta n c e f r o m t h e c e n te r o f t h e d is k o f t h e p la n e t ,
w here
a n d <?hpb\y is t h e h a lf-p o w e r b e a m w id t h or fu ll w id t h a t h a lf m a x im u m
(F W H M ) o f
t h e p r im a r y b e a m .
T he inverse Fourier transform of Equation
6 .1
gives
B„{x, y ) = [°°
Vy(u, v ) e - 2irj[ux+^ d u d v
J — OO J —00
N ote
in th e
(5.3)
however, th a t th e observed visibilities are m easured a t p a rtic u la r places
u-v plane. T hus, a sam pling function S { u ,v ) is introduced to rep resen t th e
discrete visibility m easurem ents in the u-v plane. The sam pling function S ( u , v ) is
90
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f|
\
Correl
•Q tor
Cr - '
V(U,Y)
Figure 5.1: Diagram of a two elem ent interferom eter with th e interferom eter baseline
coordinate system (u .v) and th e radio source coordin ate sy ste m (x .y ) (Napier d al..
19S3) [71].
91
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given by (Sram ek and Schwab, 1994) [76]
M
S (u . v) - ^ 2 W k6{u - u k, t» - Vk )
fc=i
(5.4)
where (u k, v k ) represents th e coordinates of th e u-v points a t which the visibilities
are m easured. M is the to ta l num ber of m easured visibilities, and W k is th e weight
assigned to each visibility point. There are th re e choices of w eighting schemes th a t
can be used to minimize th e noise on th e resulting emission m ap. These are natural,
uniform, and robust which is an adaptive com bination of both natural and uniform
(Sramek and Schwab. 1994)
[76]. In th e n atu ral weighting scheme, all m easured
visibilities are assigned th e sam e weight which results in th e m inim ization of th e
effects of therm al noise and thus gives the highest signal-to-noise ratio. In th e uniform
weighting scheme, equal weight is assigned to each m easured visibility point located
within a reactangular cell in th e uv plane. T his weight is com puted based on the
num ber of m easured visibilities within th e p a rticu lar uv cell. U niform weighting has
th e advantage of m inimizing the sidelobe levels. In th e observation of Venus using th e
VLA, an adaptive robust weighting was used to optim ize th e signal-to-noise ratio and
th e sidelobe levels. Inserting the sam pling function S(u,v) into Equation 6.2 results
in the following
B ? { x , y ) = [°° r
5 (u , v)V„(u, v)e~2ri{ux^ d u d v
(5.5)
J — OO j —00
which is w ritten in discrete form as
M
£ ? ( * ,y ) = £ W kK ( u k, v k )e~2^
k=\
where
+^
(5.6)
Bj?(x. y) is commonly referred to as th e “d irty ” brightness m ap which has
a basic apparent structure of the observed radio source except th a t the fine details
92
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are still distorted by th e sidelobes. As in Equation 6.5, the dirty image is sim ply
th e inverse discrete Fourier transform (D FT ) of th e visibility samples. N ote however
th a t th e inverse D F T is im plem ented after proper editing and calibration (see next
section) is applied to th e observed visibilities in order to recover the tru e visibilities.
Using th e convolution theorem for Fourier transform s which states th a t th e Fourier
transform of a product of functions is th e convolution of their Fourier transform s,
then Equation 6.4 can be few ritten 'as
B ? ( x , y ) = B u{ z , y ) * F { x , y )
(5.7)
where B „ (x ,y ) is th e tru e brightness m ap convolved w ith the point spread function
F(x.y): also known as th e “d irty ’' synthesized beam which can be expressed as
r
r
J'-O G J
S ( u , v ) e - 2*]{UI+Vv)dudv
(5.8)
— OC
To obtain the tru e m ap S „ (x ,y ) of the radio source a variety of deconvolution
techniques may be applied to th e convolution equation. For the VLA observation of
Venus, th e deconvolution was achieved using th e “CLEAN” algorithm (Cornwell and
B raun. 1994) [77] as p art of th e NRAO Astronom ical Im age Processing System (AIPS)
(NRAO, 1994) [78]. Basically, th e CLEAN algorithm decomposes th e dirty brightness
m ap into
determ ined
a num ber of point sources. For each point source, a clean com ponent is
by m ultiplying th e d irty synthesized beam with a scaling factor. The
clean com ponents axe th en subtracted from th e d irty brightness m ap at th e positions •
of th e point sources. T he residual d irty brightness m ap is stored and later added to the
clean brightness m ap. T h e clean brightness m ap is produced by convolving the clean
com ponents w ith a G aussian clean beam which has a half power beam w idth (H PB W )
equal to th e H PB W of th e dirty beam .
rectangular m atrix or “grid".
This clean brightness m ap is a regular,
Each grid point or “pixel” represents a particular
93
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spatial coordinate on th e radio source, and th e num ber associated w ith th e pixel is
the brightness in units of Jy per beam area, or Jy per square arc second, which can
then be converted into brightness tem p eratu re (in K elvins).
5.3
C alibration and D a ta P rocessing
T he objective of this observation was to develop well calibrated m aps o f th e 1.3 cm
and 2 cm continuum em ission of Venus. Following th e observation, th e recorded raw
visibilities were exam ined to identify and discard any corrupt data. T h e discrepant
visibility d a ta can result from a variety of sources which include m alfunctioning of an
antenna or a receiver system , bad w eather, d a ta recording errors, a n te n n a tracking
inaccuracies, incorrect observing param eters, and interference from radax and satel­
lites. In addition to editing, th e raw visibility d ata were calibrated in o rd e r to remove
the effects of tim e-variable atm ospheric phase changes, gain instabilities in th e array,
and phase offsets in th e an ten n a prim ary beam . T hree radio sources were selected for
calibration. These are th e prim ary calibrators 3C4S and 3C286, and th e secondary
calibrator 0403+260. T h e positions of th e calibrators are shown in T ab le 5.1. Ta­
ble 5.2 gives the characteristics of Venus during the VLA observation.
Figure 5.2
shows th e orientation of Venus in the sky during observation as viewed from E arth .
The secondary calibrator which was approxim ately a t th e sam e elevation in th e sky
as Venus was observed periodically (every 15 m inutes) to calibrate th e am plitudes
and phases of th e observed visibilities. T he secondary' calibrator was scanned for 1.5
m inutes a t each frequency (at 14.94 GHz and then a t 22.46 GHz). N ext, Venus was
observed a t 22.46 GHz. a n d then at 14.94 GHz. The scanning tim e of Venus a t each
frequency was
6
m inutes. T hen the secondary calibrator was again observed a t 14.94
GHz. and th en at 22.46 GHz. This sequence was repeated until the to ta l assigned
tim e for observation ( ~ 12 hours) was com pleted. As p a rt of th e above sequence, th e
two prim ary calibrators were each observed once in place of Venus at tw’o different
94
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Table 5.1: Positions of Venus and C alibrators during Observation on 04/05/1996.
A pparent R ight Ascension
A pparent Declination
(hr)
(degrees)
Venus
3.94
+24
3C286
13.52
+30.51
3C48
1.63
+33.16
0403+260
4.05
+26
Source
Table 5.2: C haracteristics of Venus during Observation on 04/05/1996.
A pparent R ight Ascension
3.94 hr
A pparent D eclination
+24°
Geocentric D istance
0.6718 AU
Apparent D iam eter
25 arc-seconds
Sub-earth L atitude
-4.6°
N orth Pole Position Angle
-12.4°
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EaTlb'
* * * * * *
■jfVetms
ibe
, 0 . 0 netvi^ oT1
r igate o -
96
tim es when th ey were at about th e sam e elevation as th e secondary calibrator in order
to fix the absolute flux scale. N ote th a t at each frequency change, the subreflector
of each a n ten n a in the array was ro tated so th a t th e focal po in t of the antenna was
positioned to eith er the 1.3 cm receiver or to th e 2 cm receiver, which can tak e as
much as 30 seconds.
Figures 5.3 and 5.4 show a p artial set of th e observed visibility d ata of Venus at
14.94 GHz and 22.46 GHz, respectively. Also shown in these figures is a best fit to th e
observed visibility d ata which was obtained using a limb-darkened disk model (B u tler
et al., 1997) [79]. The q u an tity 3 = R y /u 2 -f- u2, where R is th e radius of Venus in
radians, and y /u 2 + v 2 is th e projected baseline of each antenna p air in the VLA. N ote
th a t the fitting model gives a Venus to tal flux density V 0 (which corresponds to th e
visibility when 3 = 0) of 45.19 ± 1.36 Jy and 90.05 ± 4.5 Jy a t 14.94 GHz and 22.46
GHz. respectively. These to ta l flux densities were used to derive the disk-averaged
brightness tem peratures ( T d ) of Venus (565.8 ± 17 K at 14.94 GHz and 499.1 ± 25
K at 22.46 GHz) using, the relation (Gulkis, 1987) [80]
TTo _- jAj M
j j »-
t(5.9)
* Q)
where A is th e wavelength, k is th e B oltzm ann’s constant, and Q = x R 2/ D 2 is th e
solid angle of th e disk of Venus as viewed from E arth . (R is th e radius of Venus,
including its atm osphere, which equals 6120 km (M uhlem an et al., 1979) [50] and D
is th e geocentric distance (see T able 5.2)).
In th e next section, th e em ission m aps obtained from th e VLA observation of
Venus and th e ir interpretations axe discussed.
5.4
R esu lts and Interpretations
Two high spatial resolution continuum emission m aps for Venus were obtained a t 1.3
cm (22.46 GHz or K-band) and 2 cm (14.94 GHz or U-band). T he emission m aps are
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Figure 5.3: Real p a rt o f th e observed visibility d a ta at 14.94 G H z. Also shown
best fit which was ob tain ed using a lim b-darkened disk model.
98
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Figure 5.3: Real part of the observed visibility d ata at 14.94 GHz. Also shown is a
best fit which was obtained using a limb-darkened disk m odel.
9S
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i----------•---------- 1----------
1----------
1---------- ■
---------- 1---------- 1---------- 1---------- '---------- r
CO
c
(>!y)
o
o
Figure 5.4: Real part of th e observed visibility data at 22.46 GHz. Also shown is a
best fit which was obtained using a lim b-darkened disk m odel.
99
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512 x 512 pixels w ith an angular resolution of 0.2 x 0.2 arc-second. The disk of Venus
covers only 125 x 125 pixels with an effective angular diam eter of 25 arc-seconds. The
em ission maps display th e brightness tem p eratu re in units of Kelvins as a function
of Venus spatial coordinates in arc-seconds. Figures 5.5 and 5.6 show contour m aps
for th e measured brightness tem p eratu res of Venus a t U- and K -band, respectively.
T he m easured brightness tem peratures a t th e center pixel of th e emission m aps (at
nad ir or look angle 0 = 0) are 604.2 ± 0.95 K and 541.6 dk 1.21 K a t U- and K-band,
respectively. Knowledge of these rm s errors is useful in th e com parison of pixels on
th e im age. For exam ple, th e 1 -<t u n certain ty of th e differential brightness tem p eratu re
between the nadir pixel and one at th e limb of th e planet would be 1.3 K a t U-band
and 1.7 K at K-band. However, th e overall u n certain ty of th e value of all pixels is
subject to the uncertainty in the flux of th e reference calibrator sources, which adds
approxim ately 3% at U -band and 5% at K -band to th e uncertainty.
In order to detect potential spatial variations in th e vertical abundance distri­
butions of gaseous SO 2 and gaseous H 2 SO 4 from th e VLA emission m aps of Venus
at U- and K-band. th e contribution to th e m easured brightness tem peratures due
to gaseous CO 2 , N 2 , H 2 O, CO, and O CS have been su b tracted from these emission
m aps. Thus, the residual brightness tem p eratu res are prim arily due to gaseous S 0 2
and gaseous H 2 SO 4 . T h e brightness tem p eratu res due to gaseous C O 2 , N 2 , H 2 0 . CO,
and OCS in the Venus atm osphere have been com puted for each pixel on th e U- and
K -band emission m aps using the new rad iativ e transfer m odel (see C hapter 4). Before
su btracting the radiative transfer m odel m aps from th e VLA emission maps of Venus,
two additional steps have been applied to th e m odel results. F irst, a prim ary beam
correction was applied to th e model brightness tem p eratu res w here 178.4 and 118.7
arc-seconds have been used for the half-power beam w idths o f th e VLA individual
antenna prim ary beam a t U- and K -band, respectively. This correction reduces the
m odel brightness tem peratures by approxim ately 1.3% and 3% a t the limb of Venus
at U- and K-band. respectively, and decreases to zero a t th e center of the disk. The
100
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595
?
604
8
©
CO
I
o
W
CO
-5
-10
-10
5
0
arc-second
5
10
15
Figure 5.5: M easured brightness tem p eratu re m ap of Venus a t 14.94 G Hz. N ote th at
the brightness tem p eratu re at center of th e m ap is 604.2 K.
101
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541
-5
-10
-10
0
-5
5
10
15
arc-second
Figure 5.6: M easured brightness tem p eratu re m a p of Venus a t 22.46 GHz. N ote th a t
the brightness tem p eratu re at cen ter of the m ap is 541.6 K.
102
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second step has been to convolve or sm ear the model brightness tem p eratu re m ap
with a representation of the synthesized beam of th e VLA. In this way th e model will
most accurately m atch the observed m ap. For this purpose, two sm earing m atrices
have been generated. At U-band, th e smearing m atrix is 19 x 19 pixels and uses
a Gaussian synthesized beam with a half-power beam w idth of 1.45 arc-seconds. At
K -band, the sm earing m atrix is 15 x 15 pixels and uses a Gaussian synthesized beam
with a half-power beam w idth of 1.1 arc-seconds. Note th a t the sizes o f th e smearing
m atrices represent the Gaussian synthesized beam of the VLA a t U- and K-band
down to the -20 dB level. The two-dimensional convolution of th e m odel brightness
tem perature m aps with the smearing m atrices have been perform ed using th e M atlab
d ata processing software. The result of this process has been th e production of two
model brightness tem p eratu re maps th a t are com patible with th e VLA emission maps
at l T- and K-band.
Figures 5.7 an d 5.8 show contour m aps for the residual brightness tem peratures
of Venus at U- and K -band, respectively. Figures 5.9 and 5.10 show gray scale plots
for th e residual brightness tem peratures of Venus a t U- find K -band, respectively.
T he m ain features in these figures are th e significant polar limb darkening of 20-36
K a t latitudes above 60° and the equatorial limb darkening of 10-17 K. T he results
displayed in these figures are consistent with the results obtained by th e Pioneer
Venus O rbiter Infrared Radiom eter experim ent (Taylor el al., 1980) [81]. The peak
polar residual brightness tem peratures (i.e., m axim um darkening) are -33.6 K at Uband and -35.8 K a t K-band, both of which are located at th e south pole. The peak
equatorial residual brightness tem p eratu re is -14.4 K a t U-band which is located at
th e east limb and -17 K at K-band which is located a t th e west lim b. A relatively small
residual was d etected at th e nadir point (1.7 K at U-band and -2.3 K a t K-band).
T h e features shown in the residual brightness tem peratures m aps of Venus at
U- and K-band suggest the presence of either gaseous SO2 and gaseous H2SO4 in
the polar limbs of Venus. However, in th e equatorial and m id -latitu d in al zones th e
103
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-15
-10
-5
0
5
10
15
a rc -se c o n d
Figure 5.7: Residual b righ tn ess tem p eratu re contour m ap o f Venus at 14.94 G H z.
104
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■c
-3
-3
-9
-3
-5
-1 0
-5
0
5
10
15
arc -sec o n d
Figure o.S: Residual brightness tem p eratu re contour m ap o f Venus at 22.46 G H z.
lOo
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arc-second
arc-second
Figure 5.9: G ray scale brightness tem p eratu re m a p of Venus at 14.94 GHz.
106
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arc-second
arc-second
Figure 5.10: G ray scale brightness tem p eratu re m ap of Venus a t 22.46 GHz.
107
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abundances of gaseous SO 2 and gaseous H 2 SO 4 are lower. T he equatorial and polar
limb darkenings relative to the centers of the U- an d K-band emission m aps (i.e.,
relative to nadir where th e look angle is zero) can be in terp reted using various vertical
SO 2 and H 2 SO 4 abundance profiles.
T his referencing to nadir is essential to the
interpretation of the VLA emission m ap s in order to elim inate effect of th e errors in
the m easured brightness tem peratures which are introduced by the u n certain ty in the
absolute flux scale. Note th a t these erro rs are approxim ately 3% at U-band (about 17
K) and 5% at K-band (about 25 K) w hich are on th e order of the residual brightness
tem peratures present on th e VLA em ission maps.
Table 5.3 shows the measured residual brightness tem peratures (A T b m ) of Venus
from nadir to the equatorial limb at U- and K-band. In this table, column 3 gives the
mean residual brightness tem peratures for the east an d west equatorial lim bs. Note
that the equatorial limb of Venus consists of all pixels w ith look angles g reater than
75°. T he total num ber of these pixels for the east an d west limbs is 44. Table 5.4
shows th e com puted residual brightness tem peratures ( A T b c ) of Venus a t th e limb
relative to nadir. T he com puted residual brightness tem p eratu res have been obtained
by using th e equatorial ISAVl SO2 abundance profile (B ertaux et al.i 1996) [1] and
the equatorial M ariner
10
H2SO4 abundance profile (K olodner and Steffes, 1997) [2 ]
(see C hapter 4) at the nadir pixel and a t all pixels in th e equatorial lim b region.
Note th a t th e com puted and m easured equatorial lim b darkening relative to nadir
are consistent at K-band.
At U -band, th e com puted darkening relative to nadir
is higher th an the measured peak darkening by ab o u t
6
K. Table 5.5 shows th e
com puted residual brightness tem p eratu res ( A T b c ) o f Venus at the lim b relative to
nadir assum ing a uniform SO 2 abundance profile of 75 ppm below th e m ain cloud
layer (i.e., below 48 km) and th e eq u ato rial M ariner 10 H2SO4 abundance profile.
Note th a t th e com puted and m easured equatorial lim b darkening relative to nadir
are consistent at U-band. At K -band, th e com puted darkening relative to nadir is
lower than th e measured mean darkening by about 5 K.
108
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Table 5.3: M easured Residual Brightness Tem peratures of Venus from Nadir to th e
Equatorial Limb.
F re q u e n c y
M ean A T b m
Peak A T b m
M e a n A T Bm
of
at
a t th e
a t th e
a t th e
O b se rv a tio n
N a d ir
E q u a to r ia l
E q u a to r ia l
E q u a to r ia l L im b
E q u a to r ia l L im b
L im b
L im b
R e la tiv e to N ad ir
R e la tiv e to N a d ir
AT
bm
P*»k
a t
Bm
a t th e
(G H t )
<K>
(K )
(K>
(K )
<K )
1494
+ 1 .T
-1 2 .9
-14 4
-1 4 6
-16.1
22.46
•2 3
'1 2 .6
-17.0
-10 3
-1 4 .7
Table 5.4: C om puted Residual B rightness T em peratures of Venus from Nadir to th e
Equatorial Limb using th e ISAV1 SO 2 A bundance Profile and th e M ariner 10 H2SO4
Abundance Profile.
Frequency
AT bc
Mean AT bc
Mean AT bc
of
at
at the
at the
Observation
Nadir
Equatorial
Equatorial Limb
Limb
Relative to Nadir
(GHz)
(K)
(K)
(K)
14.94
-22.4
-45.1
-22.7
2*2.46
-30.2
-43.8
-13.6
109
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Table 5.5: Com puted Residual B rightness Tem peratures of Venus from N adir to the
E quatorial Limb using a Uniform SO 2 Abundance Profile of 75 ppm Below th e Main
Cloud Layer and using th e M ariner 10 H 2 SO 4 A bundance Profile.
Frequency
AT bc
Mean ATbc
Mean AT bc
of
at
at the
at the
Observation
Nadir
Equatorial
Equatorial Limb
Limb
Relative to Nadir
(GHz)
(K)
(K)
(K)
14.94
-24.4
-41.2
-16.8
22.46
-28.8
-34.2
-5.4
110
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Table 5.6: M easured Residual Brightness Tem peratures of Venus from Nadir to th e
Polar Limbs.
F req u en cy
A T bm
at
a t bm
of
a t th e
A T bm
a t th e
O b e e rv a tio R
N a d ir
N o rth P o le
S o u th Pole
N o rth P o le L im b
S o u th P o le L im b
L im b
L im b
R e la tiv e to N a d ir
R e la tiv e t o N a d ir
T Bm
a t th e
a
Bm
a t th e
a t
(G H a )
(K )
(K )
(K )
(K )
(K )
14.94
+ 17
-21.1
-2 3.5
-22 .6
-2 S 2
22 46
-2 .3
-24 2
-22 .3
-2 1 .9
-2 0 .0
Table 5.6 shows th e measured residual brightness tem peratures (A T b m ) of Venus
from nadir to the p o lar limbs at II- and K-band. In this table, th e m easured darkening
at th e north and south poles represent pixels on th e VLA emission m aps with look
angles of 72° and 63.1°, respectively.
The northern pixel corresponds to the 67°
north latitude at which the Magellan spacecraft radio occultation experim ents were
conducted for orb its 3212, 3213, and 3214. Note th a t the su b-earth point of Venus
during the VLA observation was at a la titu d e of -4.6°. Thus, a look angle of 71.6° n ear
the north pole (th e closest on the VLA emission m aps is 72°) corresponds to a latitu d e
of 67°. This pixel w ith a look angle of 72° is represented with an V on th e contour
m aps for the residual brightness tem peratures of Venus at U- and K -band as shown
in Figures 5.7 and 5.8. T he reason for being very specific in selecting the proper
pixel in the north polar region is th a t th e vertical abundance profiles for gaseous
SO2 and gaseous H2SO4 vary significantly for latitudes above 60° (K olodner et a/.,
1997) [2]. Tables 5 .7 ,5 .8 , and 5.9 show th e com puted residual brightness tem p eratu res
( A T b c ) of Venus a t th e north pole relative to nadir. A t the nadir pixel, th e com puted
residual brightness tem peratures have been obtained by using th e equatorial ISAVl
SO2 abundance profile and the equatorial M ariner 10 H2SO4 abundance profile. At th e
north pole pixel, th e com puted residual brightness tem peratures have been obtained
by using the SO2 and H2SO4 vertical abundance profiles inferred from th e Magellan
spacecraft radio occultation experim ents for orbits 3212, 3213, and 3214 (see C hapter
111
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Table 5.7: C om puted Residual Brightness T em peratures of Venus from Nadir to the
Polar Limbs using the SO 2 and H 2 SO 4 A bundance Profiles Inferred from the M agellan
Spacecraft Radio O ccultation E xperim ents for O rb it 3212.
Frequency
AT bc
AT bc
AT bc
AT bc
of
at
at the
at the
at the
Observation
Nadir
North Pole
South Pole
North Pole Limb
Limb
Limb
Relative to Nadir
(GHz)
(K)
(K)
(K)
(K)
14.94
-22.4
-50.7
-48.0
-28.3
22.46
-30.2
-45.9
-46.3
-15.7
Table 5.8: C om puted Residual Brightness T em peratures of Venus from Nadir to th e
Polar Limbs using th e SO 2 and H 2 SO 4 Abundance Profiles Inferred from the M agellan
Spacecraft Radio O ccultation Experim ents for O rb it 3213.
Frequency
AT bc
AT bc
AT bc
AT bc
of
at
at the
at the
at the
Observation
Nadir
North Pole South Pole
North Pole Limb
Limb
Limb
Relative to Nadir
(GHz)
(K)
(K)
(K)
(K)
14.94
-22.4
-54.8
-51.9
-32.4
22.46
-30.2
-45.9
-46.3
-2 0 . 2
112
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Table 5.9: C om puted Residual Brightness T em peratures of Venus from N adir to th e
Polar Limbs using th e SO 2 and H2SO4 A bundance Profiles Inferred from th e M agellan
Spacecraft Radio O ccultation Experim ents for O rbit 3214.
Frequency
AT bc
ATbc
AT bc
AT bc
of
at
at the
at the
at the
Observation
Nadir
North Pole
South Pole
North Pole Limb
Limb
Limb
Relative to Nadir
(GHz)
(K)
(K)
(K)
(K)
14.94
-22.4
-56.6
-53.6
-34.2
22.46
-30.2
-51.9
-52.5
-21.7
3 for the derived SO 2 and H 2 SO 4 vertical abundance profiles). Note th a t below an
altitude of 35 km it has been assumed th at H2SO4 dissociates and its abundance
is 0 ppm .
Above 50 km , it has been assumed th a t H 2 SO 4 follows th e satu ratio n
abundance profile (Kolodner and Steffes, 1997) [2]. In addition, note th a t for orbits
3212. 3213, and 3214, it has been assumed th a t SO 2 has a uniform abundance of 150
ppm below 37 km and between 43 and 50 km. Above 50 km , it has been assum ed
that SO 2 decays exponentially with a scale height of 3.3 km (N a et a/., 1994) [60].
Note from Tables 5.7, 5.8. and 5.9 th a t th e com puted and m easured n o rth pole lim b
darkening relative to nadir using abundances from orbits 3212, 3213, and 3214 are
consistent a t K -band. At U-band, the com puted n o rth pole lim b darkening relative
to nadir is higher th an the measured darkening by 6-10 K when abundances from
orbits 3212, 3213, and 3214 are assumed.
From these results, we conclude th a t in th e equatorial and m id-latitudinal re­
gions of Venus, th e SO 2 abundance profile derived from th e ISAV -1 ultraviolet spec­
troscopy experim ent (B ertaux et al., 1996) [1 ] and the H 2 S 0 4 abundance profile
derived from the M ariner 10 radio occultation experim ents (Kolodner an d Steffes,
113
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1997) [2] are representative of th e atm ospheric conditions. However, in th e polar
regions, larger abundances of both gaseous S 0 2 and gaseous H 2S 0 4 are indicated,
as represented by th e H2S 0 4 abundance profiles derived from th e Magellan space­
craft radio occultation experim ents (K olodner and Steffes, 1997) [2] and by th e S 0 2
abundance profiles derived in this work (i.e., as p er Magellan S 0 2 abundance profiles
above 37 km . and 150 ppm below 37 km ).
One final com m ent is that m ore precise stu d y of the latitu d in al variations in
the vertical abundance profiles of S 0 2 and H2S 0 4 could be inferred from th e U- and
K-band emission m aps of Venus once th e S- and X-band abso rp tiv ity profiles of the
Venus atm osphere are obtained from th e 1994 Magellan spacecraft radio occultation
experim ents at latitudes of 62° south (S). 87° S, 49° north (N ), 74° N, and 82° N.
In the next chapter, th e microwave effects of S 0 2 on INSAR im aging of terrestrial
volcanoes are discussed.
114
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115
CHAPTER 6
LIMITS OF THE EFFECTS OF S 0 2 ON
INSAR IMAGING OF TERRESTRIAL
VOLCANOES
6.1
Introduction
In recent years, interferom etric synthetic ap ertu re radar (INSAR) techniques have
been applied to th e rem ote sensing of the terrestrial surface. These techniques provide
digital topographic maps with a high spatial resolution on the order of a few tens
of m eters and a high vertical accuracy on th e order of a few m eters as compared
to conventional synthetic aperture radar (SA R)-techniques (Rodriguez and M artin,
1992) [82]. Am ong the various terrestrial targ ets th a t have been im aged by INSAR
systems to study th e ir topography and the topographic change due to new eruptions
are volcanoes (Zebker et al., 1994, M ouginis-M ark, 1995) [9, 10]. T he assumption for
the INSAR topographic m apping is th a t th e atm osphere does not effect the rad ar
reflected signal. However, the atm osphere is a refractive m edium especially over an
active volcano w here gaseous SO 2 is released. T hus, th e refractive atm osphere m ay
introduce significant phase errors (i.e., increasing th e path length between the S 0 2
source and INSAR) which could degrade the quality of th e image. Some concerns have
been expressed (Zebker H. A., private com m unication, 1997) [83] th a t measurable
errors in INSAR height m easurem ents may b e caused by th e refractive effects of
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S 0 2. In this chapter, th e potential microwave refractivity effects of S 0 2 on INSAR
imaging of terrestrial volcanoes are discussed, bu t first a brief theoretical background
on INSAR is presented.
6.2
O verview o f IN SA R T heory
The theory of INSAR was first introduced by G raham (1974) [84] and la te r used by
Zebker and G oldstein (1986) [85] and Li and G oldstein (1990) [86] to analyze th e
perform ance of IN SA R system s for th e topographic m apping of terrestrial regions. A
topographic m ap can be obtained by either using two SAR receivers in a single-pass
mode (Zebker and G oldstein. 1986) [85] or by one SAR receiver in a repeat-pass m ode
at different tim es (Li and Goldstein, 1990, Zebker et al., 1994) [86, 9]. T h e INSAR
topographic m ap displays the three-dimensional location (horizontal position and
height) of the terrestrial object, whereas a conventional sideward-looking SAR m ap
displays the horizontal position coordinates of th e object w ithout any inform ation
about its height. T his is because a conventional sideward-looking SAR utilizes only a
single antenna w ith which the height of the im aged object can not be derived due to
the inability to m easure th e differential phase. By adding a second receiving a n ten n a
as in INSAR. th e differential phase can be m easured and used to derive an e stim ate
of the height of th e object. Figure 6.1 shows a schem atic of a typical airborne INSAR
system . T he interferom eter system employs two antennas A l and A2 sep arated by
the baseline distance B. T he radar signal is tra n sm itte d from each an ten n a and is
received sim ultaneously by th e two antennas. W hen th e rad ar signal is tra n sm itte d
from antenna A l an d is received simultaneously by antennas A l and A2, th e slant
range difference 6 at an ten n a A2 (see Figure 6.1) is given by (Zebker and G oldstein,
1986) [85]
6 = p - p' = B c o s(9 4- a )
116
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(6.1)
(a)
(b)
Figure 6.1: D iagram of a typical airborne INSAR sy ste m with th e im agin g geom etry
shown (Zebker and G oldstein. 19S6) [So].
where p ' and p are th e line-of-sight distances, or th e slant range d ista n ces from the
target point to th e an tennas A l and A 2. respectively, 9 is the a n g le o f th e baseline
w ith respect to th e horizontal, and a is the look a n g le o f the target p oint. N o te that
th e sam e path difference results at antenna A l w h en a radar sig n a l is transm itted
from antenna A 2 and is received sim ultan eou sly by antennas A l an d A2.
Now the difference in the electrical path len gth 6 is related t o th e relative phase
difference o (in radians) at each antenna as
( 6 .2 )
< =
where A is th e w avelength o f the radar signal.
Based on th e relative phase difference betw een th e two a n ten n a s o f th e INSAR
sy stem , an e stim a te of th e height o f th e imaged ta rg et can be d eriv ed . N o te from
Figure 6.1 that th e height h of point P relative to th e aircraft a n ten n a s can be written
117
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in term s of th e slant range p and the look angle a as
h = p sin a
(6.3)
Solving for o from 6.1 and 6.2, and su b stitu tin g in 6.3 yields the following
expression for th e height of th e target relative to th e aircraft antennas
h = p sin
cos" (s i)
(<u)
- e]
Upon determ ining th e height h. the slant range p and th e along-track d istance x,
th e three-dim ensional coordinates (x.y.h) for each targ et point on the terrain will be
known. Then th e measured d a ta is interpolated onto a square grid and an accu rate
topographic m ap of the height of imaged region is produced. N ote th at the ground
range y is calculated using
y
= sjp2 — h 2
(6.5)
From 6.4. it can be noticed th a t u n certain ties in each o f th e param eters p , 4>,
and 6 will determ ine the accuracy of th e topographic height m easurem ent. T hese
sources of uncertainty in th e height m easurem ent have been discussed thoroughly by
Zebker and G oldstein (1986) [85], Li and G oldstein (1990) [86], and Rodriguez and
M artin (1992) [82]. The accuracy of the topographic height m easurem ent (A h) due
to uncertainties in th e INSAR phase m easurem ents (A<f>) is determ ined using (Li and
Goldstein, 1990) [86]
Aocos
------------------ A
d>
- 2rBsin(a
—ca
+
a
6)
where A<f> is in radians.
118
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(6 6 )
^
!
In th e next section, th e potential effects o f SO 2 microwave refractivity to uncer­
tainties in INSAR phase m easurem ents and to topographic height accuracies when
imaging terrestrial volcanoes are discussed.
6.3
Effects of S 0 2 R efractivity on IN S A R Im aging
o f Terrestrial Volcanoes
The uncertainties in the INSAR phase m easurem ents are due to lim ited signal-to-noise
ratios, lim ited num ber of looks, pixel m isregistration, and baseline decorrelation (Li
and Goldstein. 1990) [86]. A nother potential co ntributor to th e uncertainty in th e
INSAR phase m easurem ents is the tim e delay caused by th e refractive atm osphere
through which th e radar signal propagates. T h is refractivity effect could be especially
im portant when INSAR system s are used for th e topographic m apping of terrestrial
volcanoes where refractive S 0 2 clouds extending for several kilom eters are released.
Table 6.1 gives the characteristics of am airb o rn e INSAR system which was used
for the topographic m apping of terrestrial regions (Zebker and G oldstein, 1986) [85].
For this airborne INSAR system , it was reported th a t the difference in th e electrical
path length p — p' is determ ined to an accuracy of 1 cm which corresponds to a phase
error of 0.257 radians (or 14.69 degrees) at a frequency of 1.225 GHz (A = 24.5cm).
The corresponding tim e delay is 33.39 pico-seconds. For a phase error of 0.257 radians,
th e uncertainty in the height m easurem ents is on th e order of a few m eters. For
example, using Equation 6.6 and th e values from Table 6.1, where th e wavelength
A = 24.5 cm . p a th length p = 10 km, baseline B = 11 m , baseline angle 5 = 0,
look angle a = 53°, and th e phase error A 4> — 0.257 radians, yields an error in th e
height m easurem ent of 6.9 m . Note th at higher phase errors give higher inaccuracies
in the topographic height m easurem ents. Now to determ ine th e abundance of SO 2 in
volcanic clouds required to produce tim e delays on th e order of 33.39 pico-seconds, we
have used th e results from our laboratory m easurem ents of th e S 0 2 density norm alized
119
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refractivity. A value of 1.588 x 10~ 16 for the SO 2 density norm alized refractivity has
been used. This value is an average of our refractivity m easurem ents at a frequency
of 2.25 GHz and a te m p e ratu re of 295 K. Assuming a p ath length of 10 km betw een
the tra n sm ittin g an ten n a and th e target point to be imaged which is typical for the
above airborne IN SA R sytem , then th e velocity of the propagating wave th ro u g h the
SO 2 cloud has been determ ined, which in turn, has been used to calculate th e SO 2
index of refraction (assum ing uniform SO 2 abundance along th e p ath length). Using
the relationship betw een th e index of refraction and refractivity, th e SO 2 refractiv ity
has been found to b e 1.0017 which corresponds to a SO 2 m olecular num ber density
of 6.31 x
1 0 15
m olecules/cm 3. As a result, the abundance of SO 2 (based on uniform
SO 2 m ixing ratio along th e p ath length) required to give a tim e delay of 33.39 pico­
seconds has been determ ined to be 253 ppm. However, it should be noted th a t the
m easured abundances of SO 2 in volcanic clouds range from
8
ppm to
20
p p m near
volcanic surfaces to few p arts per billion (ppb) of SO 2 as the cloud extends for several
kilom eters in the vertical and horizontal directions away from th e position of the
volcano (Jaeschke et al., 1982, Hobbs et a l, 1991, and M artin et al., 1986) [87,
88,
89]. T hus, the microwave refractivity due to SO 2 in volcanic clouds is 'not significant
to induce tim e delays on th e order of 33.39 pico-seconds. Consequently, th e q u a lity of
INSAR imaging of terrestrial volcanoes using the airborne system shown in T able
will not be degraded by volcanic
802
6 .1
-
In th e next ch ap ter, th e sum m ary and conclusions of this thesis are provided.
120
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Table 6.1: C haracteristics of an A irborne INSAR System used for th e Topographic
M apping of T errestrial Regions (Z ebker and G oldstein, 1986) [85].
Frequency
1.225 GHz
W avelength
24.5 cm
Peak Pow er
5 KW
B andw idth
20 MHz-
Look Angles
25°-55°
Baseline
11
Baseline Angle
A ltitu d e
0°
8
R esolution
m
10
to 14 km
m x
10
m
121
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CHAPTER 7
SUMMARY AND CONCLUSIONS
7.1
U niqueness of W ork
T his research has provided significant and unique contributions to th e understand­
ing of the microwave effects of gaseous SO 2 in the atm ospheres of Venus and E arth.
New higher accuracy laboratory m easurem ents of the tem p eratu re dependence of the
microwave opacity of gaseous SO 2 u nder sim ulated Venus conditions have been con­
du cted at tem peratures from 290 to 505 K and at pressures from
1
to 4 atm for
th e following frequencies (wavelengths): 2.25 GHz (13.3 cm ), 8.5 GHz (3.5 cm), and
21.7 GHz (1.4 cm ). T he high-accuracy opacity m easurem ents have been achieved by
m atching the refractive indices of the lossy and lossless (non-absorbing) gases used
in th e experim ent. Thus, the effects of dielectric loading on th e q u ality factor of
th e resonator have been removed. B ased on these m easurem ents, a new empirical
microwave opacity m odel using the Ben Reuven spectral line shape theory has been
derived. This new B en Reuven model predicts the absorption of gaseous SO 2 in th e
V enus atm osphere as a continuous function of frequency, tem p eratu re, pressure, and
abundance. F urtherm ore, it has been shown th a t the new Ben Reuven opacity model
provides a more a cc u ra te characterization of SO 2 opacity in th e Venus atm osphere
as com pared to previous models. In ad d itio n , it has been shown th a t th e new Ben
Reuven opacity m odel is consistent w ith th e previous m illim eter-w avelength labora­
to ry m easurem ents of gaseous SO 2 opacity.
One application of the new Ben-Reuven model for gaseous SO 2 microwave ab­
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
sorption has been in in terp retin g the S-band (2.3 GHz or 13 cm) and X -band ( 8 . 4
GHz o r 3.6 cm) absorptivity profiles which w ere obtained from th e 1991 M agellan
spacecraft radio occultation experim ents of Venus for orbits 3212, 3213, an d 3214.
A ccurate vertical abundance profiles of gaseous SO 2 in th e Venus atm osphere have
been inferred. One com m on feature among th e derived vertical abundance profiles of
gaseous SO 2 for the th re e orbits is the variation of SO 2 abundance between altitu d es
of 35 k m and 50 km. T hese longitudinal variations (orbit to orbit) among th e SO 2
vertical abundance profiles for th e three o rb its are statistically significant a t some
altitu d e s which indicate th e presence of local dynam ical mechanisms in th e Venus
atm osphere.
In addition to the o pacity measurem ents o f gaseous SO 2 , a new radiative transfer
model for Venus which includes th e Ben R euven opacity model for gaseous SO 2 has
been developed. This new emission model provides a more accurate in terpretation of
the microwave and m illim eter-w ave emission sp ectru m of Venus. On a disk-averaged
basis, it has been shown th a t a uniform SO 2 disk-averaged abundance of 75 ppm
below th e base of the m ain cloud layer provides an excellent fit to the m easured
disk-averaged brightness tem peratu res at m icrow ave and millimeter-wave frequencies
(including those obtained from our VLA observation of Venus). Furtherm ore, a new
uniform upper limit of 150 ppm on the disk-averaged abundance of gaseous SO 2
below th e base of the m ain cloud layer has been derived. This new upper lim it is in
agreem ent with recent infrared Earth-based observations of Venus and com pares well
with previous spacecraft in situ m easurem ents.
B ased on the sensitivity of subcloud SO 2 to th e frequency windows as determ ined
using th e new radiative tran sfer model, a dual-frequency observation of Venus using
the Very Large Array (V LA ) at frequencies (wavelengths) of 14.94 GHz (2 cm ) and
22.46 G H z (1.3 cm) was conducted. This m icrowave observation of Venus has resulted
in two high spatial resolution continuum em ission maps. Based on the new em ission
model, these VLA emission m aps have been used to detect potential spatial variations
123
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in th e abundances and distribution of gaseous SO 2 and gaseous H 2 SO4 across th e disk
of Venus. It has been concluded th a t in th e equatorial and m id-latitudinal regions of
Venus, th e SO 2 abundance profile derived from th e ISAV-1 ultraviolet spectroscopy
experim ent (B ertaux et al., 1996) [1] and th e H2SO4 abundance profile derived from
the M ariner 10 radio occultation experim ents (Kolodner and Steffes, 1997) [2] are
representative of th e atmospheric conditions. Additionally, in th e polar regions, larger
abundances of both gaseous S 0 2 and gaseous H2SO4 are indicated, as represented by
the H 2 SO 4 abundance profiles derived from th e Magellan spacecraft radio occultation
experim ents (Kolodner and Steffes, 1997) [2] and by th e SO 2 abundance profiles
derived in this work (i.e., as per M agellan SO 2 abundance profiles above 37 km , and
150 ppm below 37 km).
In addition, the new emission model has been used in determ ining regions in
the Venus microwave emission spectrum th a t are m ost sensitive to detecting subcloud
SO 2 . Specifically, it has been shown th a t observations in th e frequency ranges between
15 GHz and 26 GHz and between 65 GHz and 75 GHz are m ost sensitive to detecting
subcloud SO 2 .
A nother unique contribution of this research has been th e determ ination of the
microwave refractivity of SO 2 at th e sam e frequencies, tem peratures, and pressures
used for m easuring its opacity. T his SO 2 refractivity m easurem ent has been applied
to th e in terpretation of th e refractivity profiles of the Venus atm osphere obtained
from th e M agellan spacecraft radio occultation experim ents. Furtherm ore, th e SO 2
refractivity m easurem ent has been used to investigate the effects of SO 2 on th e INSAR
images of terrestrial volcanoes.
7.2
Publications
This research has culm inated in th e publication of one journal paper. A second journal
paper has been recently subm itted and a th ird one is being prepared. In addition,
124
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this research has been presented a t several conferences with published abstracts. A
list of the journal papers and the conference presentations is shown below:
1.
Marc A. K olodner, Shady H. Suleim an, Bryan J . B utler, an d P aul G. Steffes,
“Microwave rem ote sensing of th e distribution of sulfur com pounds in th e Venus
atm osphere” , to be subm itted to Icarus.
2. Shady H. Suleim an. Marc A. Kolodner, and Paul G. Steffes, “L aboratory m ea­
surem ent of th e tem perature dependence of gaseous sulfur dioxide (SOj) m i­
crowave absorption w ith application to the Venus atm osphere” , Jo u rn al of
Geophysical Research: Planets (special issue on Venus), vol. 101, no. E2, pg.
4623-4635. February, 1996.
3. Bryan J. B utler. Paul G. Steffes, Shady H. Suleiman, and M arc A. Kolodner,
“Accurate and consistent microwave observations of Venus an d th e ir implica­
tions”, to be su bm itted to Journal of Geophysical Research .
4. Marc A. K olodner, Shady H. Suleim an, Bryan J. B utler, and Paul G. Steffes,
“The abundance and distribution of sulfur-bearing com pounds in th e lower
Venus atm osphere.” EOS Transactions of the American G eophysical Union, vol
77, no. 46. pg. F439, November, 1996.
Presented D ecem ber 16, 1996 at th e Fall M eeting of the A m erican Geophysical
Union, San Franciso, California.
0.
Shady H. Suleim an, Marc A. K olodner, Bryan J. B utler, and P au l G . Steffes,
“VLA images of Venus a t 1.3 cm and 2 cm w avelengths.” B ulletin of th e Ameri­
can A stronom ical Society, vol. 28, no. 3, pg. 1117, October, 1996. Presented at
th e 28th annual m eeting of the Division for P lan etary Sciences o f th e American
Astronom ical Society, Tucson, A rizona, O ctober 24, 1996.
6. Shady H. Suleim an and Paul G. Steffes, “R adiative transfer m odels for Venus
microwave and millimeter-wave emission using a Ben-Reuven form alism for S 0 2
125
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
absorption.” B ulletin of the American A stronom ical Society, vol. 27, no. 3, pg.
1071, October, 1995. Presented at th e 27th annual m eeting of th e Division for
P lanetary Sciences of th e American A stronom ical Society, M auna Lani, Hawaii,
O ctober 9. 1995.
7. Paul G. Steffes, M arc A. Kolodner, and Shady H. Suleiman, “Sensing of the
abundances and distributions of sulfur-bearing com pounds in the Venus a t­
m osphere at m illim eter and centim eter w avelengths.” Venus II conference on
geolog}', geophysics, atm osphere, and solar wind environm ent, pg. 95, January,
1995. Presented a t th e Venus II conference on geology, geophysics, atm osphere,
and solar wind environm ent, Tucson, AZ, Jan u a ry 4-7, 1995.
8.
Shady H. Suleiman and Paul G. Steffes. “L aboratory m easurem ent of th e tem ­
perature dependence of gaseous sulfur dioxide (S O 2 ) microwave absorption un­
der simulated conditions for the Venus atm osphere.” Program of th e Sixth In­
ternational Conference on Laboratory Research for P lanetary A tm ospheres, pg.
29. October 1994. Presented a t th e Sixth In tern atio n al Conference on Labora­
tory Research for P lanetary Atm ospheres, B ethesda, MD, O ctober 30, 1994.
In addition to the above publications and as p art o f this research, a form al pro­
posal to observe Venus using the VLA was w ritten a n d subm itted to the N ational
Radio Astronomy O bservatory (NRAO). T he proposal was reviewed by a panel of
scientists and later accepted by the NRAO scheduling com m ittee:
Shady H. Suleiman, M arc A. Kolodner, B ryan J. B u tler, and Paul G. Steffes, “M ap­
ping SO 2 and H 2 SO 4 variations on Venus.” S u b m itted to the N ational R adio As­
tronom y Observatory (N R A O ), Septem ber, 1995, accepted January, 1996.
126
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7.3
Suggestions for Future Work
Recent therm ochem ical equilibrium models for th e lower atm osphere (i.e, below 12
km) and surface of Venus show SO 2 abundances of 100-130 ppm - T he recent eq u ato ­
rial SO 2 abundance profile obtained from the ISAV -1 ultraviolet spectrom eter carried
aboard the e n try probe which was released by th e VEGA -1 spacecraft shows S 0 2
abundances of 20-25 ppm a t 12 km and below. To resolve th is contradiction and to
investigate th e latitu d in al and longitudinal variations in th e v ertical abundance pro­
files of SO 2 in th e m iddle and lower atm osphere of Venus, a new NASA m ulti-probe
mission capable of in-situ m easurem ents of SO 2 which could cover various eq u ato ­
rial. m id-latitudinal, and th e polar zones is suggested. In ad d itio n , once th e 1994
Magellan S- and X-band absorptivity profiles of th e Venus atm osphere are obtained
from the spacecraft radio occultation experim ents, th e newly developed Ben Reuven
model for SO 2 microwave absorption should be applied to th e ir interpretations. This
will provide m ore insight into the latitudinal variations in th e vertical abundance
profiles of SO 2 for altitudes betw een 35-50 km . Finally, it is suggested to conduct
an interferom etric observation of Venus in th e frequency range between 75-85 GHz.
Although the peak sensitivity of subcloud SO 2 is a t 70 GHz, th is frequency is u n su it­
able for observing Venus due to th e integrated absorption from th e oxygen line in th e
terrestrial atm osphere. This observation will provide an em ission m ap which would
be most useful in detecting equatorial variations in th e abundances of S0 2 -
127
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128
APPENDIX A
PROPOSAL TO OBSERVE VENUS
USING THE VLA
This appendix presents the proposal which was su b m itted to th e National R adio
Astronomy Observatory (N RA O ) to observe Venus using th e Very Large A rray a t 15
and 22 GHz. T he proposal consists of two parts. T h e first part is the VLA observing
application which highlights th e specifics of the observation. The second p a rt is a
scientific justification which discusses th e goals of th e observation and its im p o rtan ce
to our research.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A .l
VLA O bserving A pplication
1l S
H
w
VLA OBSERVING APPLICATION
A
DEADLINES: 1st of Feb.. June.. Oct. for next configuration following review
INSTRUCTIONS: Each numbered item must have an entry or N/A
SEND TO: Director NRAO. 520 Edgemont Rd.. Charlottesville. VA 22903-2175
rod:
(1) Date Prepared: September 25. 1995
(2) Title of Proposal: Mapping SOj and IlySO* variations on Venus.
(3)
AUTHORS
INSTITUTION
Shady II. Suleiman
Georgia Institute of Technology
Marc A- Kolodner
Bryan J- Butler
Paul G. Steffes
Georgia Institute of Technology
National Radio Astronomy Observatory
Georgia Institute of Technology
For Grad Students
Only
Who Will Observations
Come To
For Ph.D.
Anticipated
The VLA? Thesis?
Ph.D. Year
X
Yes
1996
X
Yes
1996
X
(4) Related VLA previous proposal number(s): AS330
(5) Contact author
(6) Telephone: (101)391-3123
for scheduling: Prof. Paul G. Steffes
Telex:
address: School of Electrical and Computer Digineering
Internet:
Georgia Institute of Technology
Other E Mail:
Atlanta. Ga. 30332-0250
Telefax:
N/A
paul-steffes'itee.galecb.edu
psJ l«prisra.gatecfa.edu
(104)353-9171
(7) Scientific Category': O astrcmetry.geodesy A- techniques. O solar. O propagation. ® planetary. Qstellar. O pulsar.
O ISM. O galactic center. Q galactic structure k dynamics (III). O normal galaxies. O active galaxies. Q cosmology
(6) Configurations (one per column)
(A. B. C. D. BnA. CnB. DnC. Any)
(9) Wavelength(s)
(100.90.20. IS. 6. 3-5. 2.1.3. 0.7 cm)
(10) Time requested
(hours)
C
1.3 and 2 cm
12
(11) Type of observation: ® mapping. O point source. O monitor. ® continuum. O itn poln. Q arc poln. O solar. O VLBI.
(check all that apply) O spectroscopy. O multichannel continuum. O phased array. O pulsar. O higb-time resolution
O other_________________________
(12) ABSTRACT (Do not write outside this space. Please type.)
An observation of Venus is proposed to obtain high resolution continuum maps at frequencies of 15 and
22 GHz. These emission maps will be used to detect potential spatial (logitudinal and latitudinal) variations
in the abundances of gaseous sulfur dioxide (SOy) and gaseous sulfuric acid (II2SOr) across the disk of the
planet. The suggested observation time is in early April 1996 while the VTA is in the C-configuration. The
time requested for this observation is 12 hours which can be divided on two consecutive days if necessary (6
hours per day).
NRAO use culy
129
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(1 3 ) Observer present for observations?
®Yes 0 b °
Data reduction at?
(1 4 ) Help required: ® None O Consultation
Q Friend (extensive help)
( 1 5 ) Spectroscopy Only:
line J
line 2
O Home ® AOC or CV (2 weeks notice)
line 3
_________
_ _ _ _ _
line i
_ _ _ _ _
T ransition (III. O il. etc.)
______
Rest Frequency (MHz)
_______
_______
_______
_______
Velocity (km/s)
_____
_____
______
_____
Observing frequency (MIlz)
_______
_______
_______
_______
Correlator mode
_____
_____
______
______
IF bandw idtb(s) (M Ilz)________________ _________
_________
_________
_________
H anning smoothing (y /n )
_________
_ _ _ _ _
_________
_________
N um ber of channels per IF
_________
_________
_________
_________
Frequency Resolution (kHz/channel)
_______
_______
_______
_______
R m s noise (m Jy /b m . n a t. weight . 1 h r ) _________
_________
_________
_________
_________
_________
_________
R m s noise (K nat. weight..
(1 6 ) Num ber o f sources
(17) NAME
J
I h r)
_________
(If m o re th a n 10 please a tta c h list. If m ore th a n 30 give only selection criteria and LST range(s).)
Epoch: 1950 O 2000 ®
RA
Dec
bhmm
± xx.x*
Config.
Band­
Band width
(cm) (MIlz)
line
tfyr
Venus
3 37 •
22.7
C
C
1.3
2
50
50
Largest Required
angular ■ rms
cent.
size (mJy/bm)
(J))
66
0.072
26"
39
0.012
26"
Total Flux
N/A
N/A
Time
requested
(hours)
12
'this should be the total flux at the peak of the line
Notes to the table (if any):
(16)
Restrictions to elevation (other than hardware limits) ot HA range (give reason): None
(19) Preferred range of dates for scheduling (give reason): Preferred: April 1-15.1996- Acceptable: Feb. 9-Aprii 15.1996.
(20) Dates which are not acceptable: All other times.
(21) Special hardware, software, or operating requirements: N/A
(22) Please attach a self-contained Scientific Justification not in excess of 1000 words. (Preprints or reprints will be IGNORED!)
Please include the full addresses (postal and e-mail) for first-time users or for those that have moved (if not contact author).
When your proposal is scheduled, the contents of the cover sheets become public information (Any supporting pages are for
refereeing only).
v3.0 6/91
130
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A.2
Scientific Justification
We propose to observe Venus using th e Very Large A rray (VLA) a t 15 GHz and 22
GHz sim ultaneously. T h e objective of this observation is to obtain high resolution
continuum maps of Venus. These emission m aps will be used to detect po ten tial
spatial (longitudinal and latitudinal) variations in th e abundances of gaseous sulfur
dioxide (SO 2 ) and gaseous sulfuric acid (H 2 SO 4 ) across th e disk of th e planet. S ta ­
tistically significant large-scale variations in th e 13 cm absorptivity profiles of th e
sub-cloud Venus atm osphere were observed from th e Pioneer-Venus radio occultation
data (Jenkins et al., 1991). In addition, sm all-scale variations in th e 3.6 cm and 13
cm opacity profiles were detected from th e 1991 M agellan radio occultation m easure­
m ents (Jenkins et al., 1994). Finally, sm all and large-scale variations in the em ission
from th e lower atm osphere of the planet were observed in the n ear infrared im ages
of th e nightside of Venus during th e Galileo encounter (Carlson e t al., and Crisp e t
al.. 1991). These features are likely caused by variations in the sulfur-bearing gases
in th e lower Venus atm osphere where strong dynam ical forces are present.
The frequencies of observation were selected based on th eir sensitivity to these con­
stitu en ts. as determ ined using our radiative transfer m odel. This m odel incorporates
a newly developed Ben-Reuven form alism which provides a more accu rate characteri­
zation of th e microwave absorption of gaseous S 0 2 [Suleiman et al., 1995]. The m odel
also uses th e most current spectral line catalog [Poynter et al., 1994] to com pute th e
microwave absorption of gaseous H 2 SO 4 . A 150 ppm m ixing ratio of gaseous SO 2 b e ­
low th e m ain cloud layer (based on uniform m ixing) is used which is in agreem ent w ith
recent infrared Earth-based observations [see Bez-ard e t al., 1993]. T his SO 2 m ixing
ratio also compares well w ith previous spacecraft in situ m easurem ents [see O yam a e t
al., 1980 and Gelman e t al.. 1979]. A 20 ppm m ixing ratio of gaseous H 2 SO 4 between
38 and 48 km is used which is consistent w ith th e results from th e 1991 Magellan
radio occultation experim ents [see Jenkins et al.. 1994]. Figure
1
shows th e range of
131
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
projected differences in th e flux density per beam for a viewing angle of 0 ° (nadir)
as a function of frequency between a Venus atm osphere with only carbon dioxide
(CO 2), nitrogen (N2), and w ater vapor (H 20 ) and a Venus atm osphere w ith C 02.
N2, H2O, and S 02. Figure 2 shows th e range of projected differences in th e flux
density per beam for a viewing angle of 0 ° (nadir) as a function of frequency betw een
a Venus atm osphere w ith only CO 2, N2, H2O, and S 02 and a Venus atm osphere w ith
CO2. N2. H2O, SO2, and H2SO4. Note from Figures
1
and
2
th a t the largest drop
in th e flux density at nad ir due to th e absorption from gaseous SO 2 and gaseous
H 2 SO 4 occurs in the K -band (20-25 GHz) and U-band (12-16 GHz) portions of th e
emission spectrum , respectively. Thus, simultaneous observations in these regions
would be m ost sensitive to detecting potential spatial variations in the abundances
of gaseous SO2 and gaseous H2SO4 which are correlated in position and tim e an d are
both contributing to th e integrated opacity at each frequency.
Although an observation of th e Venus emission was conducted with th e VLA in
December 1981 at 15 GHz and 22 GHz [Janssen et al., 1982], images obtained a t b o th
frequencies had large rm s noise levels ( ± 10 Kelvins or m ore). Thus, m easurem ents of
the effects of gaseous SO 2 a t 22 GHz and gaseous H 2 S 0 4 at 15 GHz from these im ages
were difficult since th e possible variations in the brightness tem perature are only on
the order of 5-10 Kelvins a t both frequencies. The current system is significantly
more sensitive and thus, less noisy images could be obtained.
These observations could be perform ed a t any time from February through m id A pril
of 1996. However, in order to get th e best resolution, we request tim e as la te as
possible in th e C-configuration (th e distance to Venus is ~ 1.14 A.U. on Feb.
1,
and
~ 0.60 on Apr. 15). The declination is m ore favorable on la te r dates as well (6 ~ -5°
on Feb.
1,
and 6 ~ -5° on A pr. 15). We request 12 hours for this observation, w hich
can be divided on two consecutive days
(6
hours per day), if necessary. This should
give us 4-5 hours on Venus at each frequency, giving us sensitivity which m ight be
somewhat b etter th an 0.1 m J y /b m . This would give us th e ability to see variations
in SO 2 and H 2S 0 4 of a few ppm .
132
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References
Bezard, B., C. de Bergh, B. Fegley, J.P. Miallard, D. Crisp, T. Owen, J. B. Pollack, and D. Grisspoon, The
Abundance of Sulfur Dioxide Below the Clouds of Venus, Geopby. Res. Lett., 15, 1587-1590, 1993.
Carlson, R. W., K. H. Baines, T. Encrenaz, F. W. Taylor, P. D rouart, L. W. Camp, J. B. Pollack, E.
Lellouch, A. D- Collard, S. B. C&lcutt, D. Grinspoon, P. R. Weissman, W. D. Smythe, A. C. Ocampo,
G. E. Danielson, F. P. Fan ale, T. V. Johnson, H. H. Kieffer, D. L. Matson, T. B. McCord, and L. A.
Soderblom, Galileo infrared imaging spectroscopy measurements at Venus, Science, 253, 1541-1548,
1991. .
Crisp, D., S. McMuldroch, S. K. Stephens, W. M. Sinton, B. Ragent, K. W. Hodapp, R. G. Probst, L. R.
Doyle, D. A. Allen, and J. Elias, Ground-based near-infrared imaging observations of Venus during
the Galileo encounter, Science, 253, 1538-1541, 1991.
Gelman, B. G-, V. G. Zolotukhin, L. M. Mukhin, N. I. Lamonov, B. V. Levcbuk, D. F. Nenarokov, B. P.
Okhotnikov, V. A. Rot in, and A. N. Lipatov, Gas Chromatograph Analysis of the Chemical Compo­
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Janssen, M. A., M. J. Klein, G. L. Berge, and D. O. Muhleman, High resolution Microwave Imagery of
the Venus Atmosphere, Presented at the XVIII General Assembly of the International Astronomical
Union, Patras, Greece, August 17-26, 1982.
Jenkins, J. M. and P. G. Steffes, Results for 13 cm absorptivity and H2 SO4 abundance profiles from the
Season 10 (1986) Pioneer-Venus orbiter radio occultation experiment, Icarus, 90, 129-138,1991.
Jenkins, J. M., P. G. Steffes, D. P. Hinson, J. D. Twicken, and G. L. Tyler, Radio Occultation Studies of
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Icarus, 110, 79-94, 1994.
Oyama, V. I., G. C. Carle, F. Woeller, J. B. Pollack, R. T. Reynolds, and R. A. Craig, Pioneer Venus Gas
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133
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
'0
5
10
1S
20
2S
90
36
40
AS
CO
Frequency (GNU
Figure 0.1: Range of projected differences in flux density per beam for a viewing angle
of 0° (nadir) as a function of frequency between a Venus atm osphere w ith only C 0 2.
X2. and H20 and a Venus atm osphere with C 0 2. N2. H20 . and S 0 2. The mixing
ratio for gaseous S 0 2 is 1-50 ppm (uniform ly m ixed) below 48 km.
20
IS
X
F re q u e n c y (GHz)
Figure 0.2: Range of projected differences in flux density per beam for a viewing angle
of 0° (nadir) as a function of frequency betw een a Venus atm osphere with only C 0 2.
X2. H20 . and S 0 2 and a Venus atm osphere w ith C 0 2. X2. H20 . S 0 2. and H 2S 0 4.
The mixing ratio for gaseous H2SO.j is 20 p p m for altitudes between 38 and 48 km.
134
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135
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VITA
Shady H. Suleiman was born on Ju n e 8, 1967 in Youngstown, O hio. He gradu­
ated from the Ohio S tate University w ith a bachelor’s degree in Engineering Physics
in August 1990. followed by a m a ste r’s degree in Electrical Engineering in August
1992. also from th e Ohio S tate University. He obtained his doctorate in Electrical
Engineering from th e Georgia In stitu te of Technology in May 1997.
As a M aster’s stu d en t. Shady Suleim an conducted research in th e area of com­
pact range technology where he developed a new electrom agnetic m ethod to estim ate
the root mean square surface error in com pact range reflectors. As a P h.D . student,
he conducted research in th e area o f microwave rem ote sensing of p lan etary atm o­
spheres. His dissertation research involved laboratory m easurem ents of th e microwave
absorbing and refracting properties of gaseous sulfur dioxide (SO 2 ) w ith application
to the atmospheres of Venus and E a rth .
144
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