close

Вход

Забыли?

вход по аккаунту

?

Large-scale temporal and spatial imaging of soil brightness temperature with an L-band synthetic aperture microwave radiometer

код для вставкиСкачать
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may be
from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy subm itted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely afreet reproduction.
In the unlikely event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand comer and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in reduced
form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9” black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly to
order.
UMI
A Bell & Howell Information Company
300 North Zed) Road, Ann Arbor MI 48106-1346 USA
313/761-4700 800/521-0600
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
La r g e -S c a le T
T
em poral and
e m p e r a t u r e w it h a n
L -B
S p a t ia l Im a g in g
and
S y n t h e t ic A
of
S o il B
perture
M
r ig h t n e s s
ic r o w a v e
R a d io m e t e r
A D issertation Presented
by
J o h n D . Is h a m
S ubm itted to th e G rad u ate School of the
U niversity of M assachusetts A m herst in paxtial fulfillment
of the requirem ents for the degree of
D o c t o r o f P h ilo s o p h y
February 1999
D epartm ent of Electrical and Com puter Engineering
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
UMI N um ber: 9 9 20615
C o p y r i g h t 1999 b y
Ish a m , Jo h n D .
All rights reserved.
UMI Microform 9920615
Copyright 1999, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
© Copyright by John D. Isham 1999
All Rights Reserved
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
L a r g e - S c a l e T e m p o r a l a n d S p a t ia l I m a g i n g o f S o il B
T e m p e r a t u r e w it h a n L -B a n d S y n t h e t ic A p e r t u r e M
R a d io m e t e r
r ig h t n e s s
ic r o w a v e
A Dissertation Presented
by
J o h n D . Is h a m
Approy^B as to style and content by:
C alvin T. Swift, Chair
H aluk Derin, Member
S tephen Frasier, Member
C. Read Predmore, M ember
T hom as J. Jackson, M ember
(It*
KaiTFt" R. C arver, D epartm ent Heac
Keith
Electrical and C om puter Engineering
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
D
e d ic a t io n
To m y paxents, w ithout whom none of this would have been possible,
an d to the memory o f Dr. Robert E. M cIntosh (1940-1998).
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
A
cknow ledgem ents
I would like to acknowledge the contributions of m any individuals who m ade
this dissertation possible. First, I would like to thank Professor Calvin T. Swift and
Professor R obert E. McIntosh, in memoriam, for their guidance and facilities. I
would also like to acknowledge the previous contributions of A1 Tanner, T im H iett,
A ndy Griffis, G ary Gleason, and Peter Gaiser, for giving me some very tail shoulders
to stand upon, as well as large shoes to fill. A debt of thanks is extended to Claire
Hopley, who was invaluable in the editing of this docum ent. My thanks go out to
th e post-doctoral research fellows who guided m e along the way: Mark G oodberlet,
Steven Frasier, and John Galloway; and to th e m any students who helped m e along
th e way, especially M artin Suess, Jay Eshbaugh, Mike Petronino, John Coronella,
an d Dr. Ellen M artin.
Several individuals outside the University of M assachusetts helped me. T hey in­
clude David LeVine, John Fuchs, Dick Aldridge, Ken Hersey, Ann Hsu, and M ichael
Kao of NASA G oddard, Tom Jackson of USDA, and the crew, staff, and pilots
a t NASA Wallops and NASA Ames. Thanks are also extended to the additional
m em bers of m y dissertation committee, Haiuk Derin and C. Read Predmore.
Some of th e d ata used in this dissertation were obtained from the A tm ospheric
R adiation M easurem ent (ARM) Program sponsored by the U.S. D epartm ent of
Energy, Office of Energy Research, Office of H ealth and Environmental Research,
E nvironm ental Sciences Division.
Finally, I would like to thank my mother, father, sister, and brother, for all their
assistance, encouragem ent, and inspiration along the way.
v
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
A
La r g e -S ca le T
T
em poral a n d
e m p e r a t u r e w it h a n
bstract
S p a t ia l Im a g in g
S o il B
of
L -B a n d S y n t h e t ic A p e r t u r e M
r ig h t n e s s
ic r o w a v e
R a d io m e t e r
F ebruary
1999
J o h n D . Is h a m
B .S ., R e n s s e l a e r P o l y t e c h n i c I n s t i t u t e
P h .D ., U
n iv e r s it y o f
M a ssa ch usetts A
m h er st
Directed by: Professor Calvin T. Swift
T h e Microwave Rem ote Sensing Lab (MIRSL) at the U niversity of Massachusetts
has developed a second-generation L-band synthetic ap ertu re microwave radiom eter
referred to as the Electronically Steered Thinned Array R adiom eter, or ESTAR,
which m easures soil moisture or ocean salinity from an airborne platform. This
dissertation reviews the basics of synthetic aperture microwave radiometry, then
details recent modifications to the ESTAR instrum ent, including the change to
a horizontally polarized antenna, and improvements to th e instrum ent’s therm al
control. T he dissertation discusses calibration methods, including corrections to the
null feedback radiom eter (NFR) d a ta used to form the system response m atrix, or
G -m a trix . It also describes image calibration, noting steps taken to reduce image
ripple. Results obtained during the Southern Great Plains 1997 (SG P’97) hydrology
experim ent in Oklahom a are discussed and compared to rainfall d ata obtained from
th e O klahom a Mesonet system of weather stations. This d a ta set is the largest
one of its type obtained by ESTAR to date, in terms of a re a of geographical and
tem poral coverage.
vi
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
T
able
of
C
o n ten ts
Page
A c k n o w l e d g e m e n t s ..........................................................................................................
v
ABSTRACT..................................................................................................................................
vi
L ist O f T a b l e s ....................................................................................................................
x
L is t O f F i g u r e s .....................................................................................................................xii
C hapter
1. I n t r o d u c t i o n ..................................................................................................................
1.1
1.2
1.3
1.4
I
Introduction .........................................................................................................
Chapter D e s c r ip tio n s .........................................................................................
Conventions Used in this T e x t.........................................................................
Fundamentals o f Synthetic Aperture R a d io m e tr y .....................................
1
1
2
3
1.4.1
1.4.2
1.4.3
3
4
7
Radiom etric Brightness Temperature .............................................
Interferometry ........................................................................................
Array T h in n in g ........................................................................................
2. I m p r o v e m e n t s t o t h e U n iv er sity of M a s s a c h u s e t t s E S T A R I n ­
.................................................................................................................................. 10
strum ent
2.1
2.2
2.3
T he University of Massachusetts ESTAR I n s tr u m e n t..............................
Experim ental H is to r y .........................................................................................
Hardware M odifications to the ESTAR-B In str u m e n t..............................
10
10
11
Horizontally Polarized Antenna ........................................................
Cabling and W ir in g ................................................................................
Low-Profile Calibration B o x .................................................................
D o c u m e n ta tio n ........................................................................................
R eduction o f Radio Frequency In te r fe r e n c e ..................................
Therm al S t a b ilit y ...................................................................................
Data System /G eolocation ...................................................................
11
13
13
13
14
20
31
Software Im provem ents......................................................................................
32
2.4.1
2.4.2
2.4.3
32
33
34
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
2.3.7
2.4
M odifications to the Data Collection P r o g r a m .............................
D ata Processing .....................................................................................
Data D e liv e r y ...........................................................................................
vii
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
3. C a libr a tio n
3.1
3.2
3.3
and
P r o c e ssin g
of
E S T A R D a t a ........................................ 36
O verview ............................................................................................................. 36
C o lle c tio n ........................................................................................................... 37
Antenna P attern M e a su re m e n t.................................................................... 38
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
B ackground.............................................................................................
M easurem ent of the G - M a t r i x ........................................................
N FR Correction ...................................................................................
Review of G -M atrix D ata ................................................................
Impulse Response P l o t s .....................................................................
38
40
51
56
61
Pre-P rocessing...................................................................................................
Null Feedback R adiom eter C alibration ....................................................
64
66
3.5.1
3.5.2
3.5.3
3.5.4
Basics of N FR C a lib r a tio n ................................................................
Regression for C alibration Coefficients .........................................
Selection of C alibration F i l e s ...........................................................
Com bination of N F R C alibration N u m b e rs ...................................
66
67
71
72
Image Calibration ............................................................................................
72
3.6.1
3.6.2
3.6.3
3.6.4
3.6.5
Basic Image Reconstruction Equation .........................................
Calibration E q u a tio n ...........................................................................
Regression For C alibration C oefficients.........................................
C alibrated Image R e c o n s tru c tio n ...................................................
Image R e -s a m p lin g .............................................................................
73
74
75
76
77
Image Ripple Reduction ...............................................................................
G e o -lo c a tio n .....................................................................................................
78
82
4. R e s u l t s F ro m T h e S G P ’9 7 E x p e r i m e n t .....................................................
86
3.4
3.5
3.6
3.7
3.8
4.1
4.2
4.3
Description of S G P ’97 E xperim ent ............................................................ 86
General Results .............................................................................................. 91
Brightness Tem perature Images ................................................................. 93
4.3.1
4.3.2
4.3.3
4.3.4
4.4
June 1 8 - 2 1 .............................................................................................
June 25-July 3 .....................................................................................
July 7 - 1 0 ...............................................................................................
July 11-17 .............................................................................................
Mesonet Rainfall Com parison
93
95
98
99
......................................................................117
4.4.1 Sandy Soil ............................................................................................... 118
4.4.2 Sand and Silt Soils ................................................................................119
4.4.3 Silt S o ils.....................................................................................................121
4.5
4.6
4.7
Analysis of R e su lts..............................................................................................127
Correction of July 8-10 D ata ........................................................................ 132
Conclusion.............................................................................................................135
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
5. C o n c l u sio n s a n d R e c o m m e n d a t io n s .................................................................136
5.1
5.2
A
S u m m a ry .............................................................................................................. 136
Areas for Further
S t u d y ............................................................................. 137
p p e n d ic e s
A . B asics o f T w o - D im en sio n a l A p e r t u r e S y n t h e s is ......................................142
A .l
A.2
Two Dimensioned
A perture Synthesis......................................................142
A T Sensitivity C a lc u la tio n s .......................................................................... 142
B . F a n - B e a m I n v e r s i o n ..................................................................................................145
C . M e l ’n i k T w o - D i m e n s i o n a l A p e r t u r e S y n t h e s i s .......................................148
R e fe r e n c e s
........................................................................................................................150
ix
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
L is t
of
Tables
Table
Page
1.1 Thinning factors for selected thinned array configurations........................
9
2.1
Insertion loss of first few receiver com ponents ...........................................
16
2.2
Insertion loss and RFI rejection relative to passband gain for low noise
am plifier at RF filter re-entrant pass b a n d s ...............................................
16
2.3
Receiver noise tem perature p a r a m e te rs ........................................................
19
2.4
ESTAR system tem peratures during initial UMass indoor therm al
verification tests. Temperature vs. h eater supply v o l ta g e ...................... 25
2.5
ESTAR system tem peratures during UMass outdoor therm al tests,
Tamb = 15°F= - 8°C .........................................................................................
27
2.6
ESTAR system tem peratures during initial CRREL indoor therm al
tests, Tamb = —15°F= —2 7 ° C .......................................................................... 28
2.7
ESTAR system tem peratures during final CRREL indoor therm al
tests, Tamb = —15°F= —2 7 ° C .......................................................................... 29
2.8
ESTAR system tem peratures during final UMass indoor therm al tests,
Tamb = —15°F= -2 7°C ....................................................................................
30
Experim ental conditions for data sets taken during G -M atrix calibra­
tion
42
3.2
ESTAR d a ta file type code letters
................................................................
48
3.3
G -m atrix rows, spacings, correlators, and d a ta c h a n n e ls.........................
60
3.4
Locations of synthesized beam peaks
...........................................................
65
3.5
N FR calibration numbers
...............................................................................
68
4.1
Sum m ary of ESTAR operational readiness during SG P’97...........................90
4.2
SG P ’97 rainfall events.........................................................................................
3.1
x
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
90
4.3
Relationships betw een RSC and mean tem poral changes of T q . Taken
from M attikalli et. al. [22] ................................................................................. 127
4.4
Comparison of ESTA R brightness tem peratures to M attikalli m odel. . 128
xi
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
L is t
of
F ig u r e s
Figure
Page
1.1
C orrelating receiver w ith antenna baseline d ............................................
6
1.2
O rientation and spacing of ESTAR antenna array.....................................
8
2.1
Form ation of a two dimensional ESTAR image by stacking one di­
mensional images “push-broom ” s t y l e
11
Calculated brightness tem perature for a homogeneous soil medium
w ith a specular surface a t three m oisture conditions.................................
12
2.3
Bandpass filter frequency re s p o n s e ..............................................................
14
2.4
Receiver front end block diagram, from Gaiser [1] .................................
15
2.5
Receiver low-noise am plifier frequency re s p o n s e .......................................
17
2.6
Receiver front end com ponent layout, from Gaiser [1] ............................
19
2.7
Null feedback receiver block diagram, from Gleason [2 ].......................... 21
2.8
Null feedback receiver component layout, from Gaiser [ 1 ] ....................
22
2.9
Lamont, OK C entral ARM Facility radiosonde d ata for all hours on
selected days from Ju n e 12, 1996 to July 13, 1996 ..................................
22
2.10 Lamont, OK C entral ARM Facility radiosonde d ata for 1430 hrs on
selected days from J u n e 12, 1996 to July 12, 1996 ..................................
23
3.1
Block diagram of steps used in ESTAR c a lib ra tio n .................................
38
3.2
uncorrected ESTAR N F R response during G -m atrix calibration . . . .
46
3.3
Program s and filenames used in ESTAR G -m atrix calibration
47
3.4
ESTAR N FR G -m atrix calibration response with bias correction . . .
53
3.5
ESTAR N FR G -m atrix calibration response with Venus-switch mode
c o r re c tio n ..............................................................................................................
54
2.2
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
..........
3.6
ESTAR N F R G -m atrix calibration response with first sw itching tra n ­
sient corrected ...................................................................................................
54
ESTAR N F R G -m atrix calibration response with both sw itching tra n ­
sients c o r r e c te d ...................................................................................................
55
3.8
ESTAR G -m atrix basis functions....................................................................
57
3.9
ESTAR G -m atrix basis functions, continued...............................................
58
3.7
3.10 Impulse response of center beam
3.11 Impulse responses o f all beams
.................................................................
62
......................................................................
63
3.12 Blackbody and lake calibration points
.......................................................
70
3.13 Blackbody calibration points .........................................................................
70
3.14 Downward geom etry of geo-location problem
............................................
84
3.15 Rotational geom etry of geo-location problem
............................................
84
4.1
SG P’97 experim ent axea....................................................................................
87
4.2
Landsat th em atic m apper image for S G P ’97 region..................................
89
4.3
Mesonet rainfall distribution and ESTAR.b rightness.tem p eratu re im­
age for Ju n e 18, 1997
102
Mesonet rainfall distribution and ESTAR.b rightness.tem p eratu re im ­
age for Ju n e 19, 1997
102
Mesonet rainfall distribution and ESTAR.b rightness.tem p eratu re im ­
age for Ju n e 20, 1997
103
Mesonet rainfall distribution and ESTAR.b rightness.tem p eratu re im­
age for Ju n e 21, 1997
103
Mesonet rainfall distribution and ESTAR.b rightness.tem p eratu re im­
age for Ju n e 22, 1997
104
Mesonet rainfall distribution and ESTAR.b rightness.tem p eratu re im­
age for Ju n e 23, 1997
104
Mesonet rainfall distribution and ESTAR.b rightness.tem p eratu re im­
age for June 24, 1997
105
4.4
4.5
4.6
4.7
4.8
4.9
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
4.10 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for June 25, 1997.......................................................................................... 105
4.11 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for June 26, 1997.......................................................................................... 106
4.12 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for June 27, 1997.......................................................................................... 106
4.13 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for June 28, 1997.......................................................................................... 107
4.14 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for June 29, 1997.......................................................................................... 107
4.15 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for June 30, 1997.......................................................................................... 108
4.16 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 01, 1997........................................................................................... 108
4.17 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 02, 1997.......................................................................................... 109
4.18 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 03, 1997........................................................................................... 109
4.19 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 04, 1997.......................................................................................... 110
4.20 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 05, 1997.......................................................................................... 110
4.21 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 06, 1997.............................................................................................I l l
4.22 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 07, 1997.............................................................................................I l l
4.23 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 08, 1997.......................................................................................... 112
4.24 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 09, 1997.......................................................................................... 112
4.25 Mesonet rainfall distribution and ESTAR brightness tem perature im ­
age for July 10, 1997.......................................................................................... 113
xiv
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
4.26 M esonet rainfall distribution and ESTAR brightness tem p eratu re im­
age for Ju ly 11,
1997....................................................................................... 113
4.27 Mesonet rainfall distribution and ESTAR brightness tem p eratu re im­
age for Ju ly 12,
1997...................................................................................... 114
4.28 M esonet rainfall distribution and ESTAR brightness tem p eratu re im­
age for Ju ly 13,
1997....................................................................................... 114
4.29 M esonet rainfall distribution and ESTAR brightness tem p eratu re im­
age for Ju ly 14,
1997....................................................................................... 115
4.30 M esonet rainfall distribution and ESTAR brightness tem p eratu re im­
age for Ju ly 15,
1997....................................................................................... 115
4.31 M esonet rainfall distribution and ESTAR brightness tem p eratu re im­
age for Ju ly 16, 1997............................................................................................. 116
4.32 M esonet rainfall distribution and ESTAR brightness tem p eratu re im­
age for Ju ly 17, 1997............................................................................................... 116
4.33 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net statio n A C M E ..................................................................................................118
4.34 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net station C H IC .................................................................................................... 119
4.35 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net statio n N IN N .................................................................................................... 120
4.36 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net statio n KING ..................................................................................................121
4.37 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net statio n A P A C ..................................................................................................122
4.38 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net statio n M I N C ..................................................................................................123
4.39 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net statio n ELRE ..................................................................................................124
4.40 Com parison of ESTAR brightness tem perature an d rainfall for Meso­
net statio n B L A C ..................................................................................................125
4.41 Com parison of ESTAR brightness tem perature an d rainfall for M eso­
net statio n B R E C ..................................................................................................125
xv
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
4.42 Comparison of ESTAR brightness tem p eratu re and rainfall for Meso­
net station M A R S .................................................................................................126
4.43 Comparison of ESTAR brightness tem p eratu re and rainfall for Meso­
net station M E D F .................................................................................................126
4.44 Brightness tem p eratu re change after rainfall versus RSC..........................129
4.45 ESTAR brightness tem perature change after rainfall vs. day for sites
w ith 1.0 < RSC < 1.62.......................................................................................... 131
4.46 ESTAR brightness tem perature vs. volum etric soil m oisture content
for Little W ashita site............................................................................................133
B .l
Fan beam in v e r s io n .............................................................................................146
xvi
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C
h a p t e r
1
In t r o d u c t io n
1.1
Introduction
Researchers in th e fields of hydrology, agriculture, and meteorology need synoptic
d a ta sets of soil m oisture. To this end, the Microwave Remote Sensing Lab (MIRSL)
a t th e University of M assachusetts (UMass) has developed an L-Band synthetic aper­
tu re microwave radiom eter capable of forming brightness tem p eratu re images from
an airborne platform . These images can be used to find volum etric soil moisture.
T his instrum ent is called the Electronically Steered Thinned A rray Radiom eter or
ESTAR, and has participated in a variety of recent field campaigns. This document
describes the basic theory of synthetic aperture radiometry, hardw are and software
im provem ents to the ESTAR instrum ent, and the methods and im provem ents to the
processing and calibration of ESTAR data. Finally, it presents d a ta collected during
th e Southern G reat Plains 1997 (SGP’97) experim ent that took place in June and
July, 1997 in O klahom a. This large multi-organizational field cam paign employed
great numbers of ground, airborne, and satellite measurements. T his is ESTAR’s
largest d a ta set to d ate, both in terms of the area covered and th e duration of time
over which d ata were taken.
1.2
C hapter Descriptions
The first chapter of this dissertation presents the fundam entals of synthetic
ap ertu re radiometry.
C h ap ter 2 describes the hardware improvements th at have been m ade to the
instru m en t over the past few years, including improvements to th e therm al control
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
system and th e evaluation of RFI resistance in preparation for the higher a ltitu d e
flights m ade during th e SG P ’97 experiment. It also considers im provem ents to the
data-processing system and data-collection com puter program .
C h ap ter 3 focuses on the calibration of the instrum ent from the form ation of a
G -m a trix calibration to a rough calibration of the Null Feedback R adiom eter and
calibrated image reconstruction.
C h ap ter 4 describes the Southern Great Plains (SG P’97) experim ent and the
results obtained. It presents the largest set of brightness tem peratures recorded by
ESTA R to date, and discusses the images, including a com parison of th e obtained
brightness tem peratures to in-situ rainfall m easurem ents m ade by the O klahom a
Meso-Net system .
C h ap ter 5 summ arizes the results, and suggests areas for further research.
T he appendices discuss two-dimensional synthetic-aperture radiom etry, which
seems to be a promising area for further research.
1.3
Conventions Used in this Text
In this tex t scalar quantities will be represented by a lower case letter, such as
c. V ector quantities will be represented by upper case letters, such as 7 ^ , and
m atrix quantities as bold upper-case letters, G . W henever a quantity represents a
reconstruction or an approxim ation of a quantity, rather th an a directly m easured
quantity, it will be denoted with a tilde, such as G -1 . M atrix transposes will be
denoted w ith a superscript T , as in G T. M atrix inverse will be denoted as G -1 .
Com plex conjugates will be denoted with an asterisk, as in g m(n, 0).
M any nam es of files or com puter programs are used, and are denoted in a
ty p ew riter font, such as no rm .pro.
Also note th a t in m any cases ergodicity is assum ed, and transitions between tim e
averages and ensem ble averages will be made w ithout further note.
2
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
1.4
Fundam entals of S ynthetic A perture R adiom etry
O btaining soil m oisture d a ta using ground m easurem ent techniques requires
sam pling a t many points and is a labor and tim e intensive process. Airborne and
space-borne techniques can m easure this d a ta over entire areas at once, greatly
sim plifying and speeding th e process. However, to achieve the required resolution
from a space-borne in stru m ent requires a large antenna aperture which is too heavy
to launch into space using conventional filled-array techniques. S ynthetic aperture
microwave radiom etry allows high resolution ground m easurem ents to be made with
an an ten n a that is light enough to be launched into space. ESTAR was developed
as a prototype test-bed to implem ent these techniques on a airborne platform with
th e u ltim ate goal of launching a similar instrum ent into space. This section will
present th e basics of th e microwave radiom etry and aperture synthesis techniques
th a t m ake ESTAR a valuable instrum ent for these m easurem ents.
1.4.1
Radiom etric Brightness Tem perature
Radiom eters m easure a quantity known as th e radiom etric brightness tem pera­
ture, T b (0), of a scene, which is related to its physical tem perature, Tp(9), by the
following relationship:
T b (9) = e(9)TP(Q),
( 1. 1)
where e(8) is the em issivity of the scene. It is related to to reflectivity of the scene,
provided rough surface scattering effects can be ignored, by [3]
e(0) = 1 - T(0) = 1 - R 2(9),
(1.2)
where T(0) is the scene reflectivity, and R(9) is th e Fresnel reflection coefficient of the
scene. This equation is essentially an energy-balance equation, where energy incident
upon a body is either reflected or absorbed. For a body at therm al equilibrium,
3
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
energy will be em itted at th e sam e rate it is absorbed, and this equation shows
th a t th e total incident energy is equal to th e sum of the reflected energy and the
ab sorbed/re-radiated energy.
T he scene emissivity, e{0), is a quantity th a t varies between zero and one. For
a perfect blackbody (non-reflective) radiator, e = 1 and Tg = Tp. T he value of
radiom etry lies in com paring the apparent brightness tem perature of a scene to
its physical tem perature. Assum ing a well functioning and calibrated instrum ent,
any difference between these two tem peratures is due to changes in th e emissivity,
an d w ith appropriate m odeling of the observed m edium , these values of e can be
inverted to yield some useful param eter of the scene, such as soil m oisture content
o r th e salinity of ocean w ater [4].
1.4.2
Interferom etry
T he value of ESTAR is th a t it measures the brightness tem perature across the
e n tire field of view at once, rath er than a t a single point.
To do this, it uses
interferom etric techniques to form synthetic antenna beams th at can sim ultaneously
im age an area. To understand how this works, consider two antennae separated by
a baseline d and feeding a correlating receiver, as shown in figure 1. 1. Consider a
p o int source1 in the field of view th a t radiates at a brightness tem perature of T b ( 0 ) .
T his signal is incident upon antenna 1 a t tim e t. The path length for the signal to
reach antenna 2 is longer by a distance of d sin 0/c , where d is the baseline separation
betw een antenna 1 and an tenna 2 and c is th e speed of light. Thus th e following
signals are incident upon the two antennas2:
1A point source is more convenient for illustration at this point, but the results will be extended
later to apply to area sources without loss o f generality
2T his derivation loosely follows the one presented in Tanner [5]
4
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
where
« i(0
=
r f2 VTB( 0 , t ) p l (e )e -jutd6
J - k/2
(1.3)
vi(t)
=
£ l\
(i.4)
vtb (Q)
B ( e ,, t - ^ ^ j p 2(e,) c - i< ‘- ' ^ !L)de',
is the voltage seen at th e antenna term inals due to the radiom etric
brightness tem p eratu re at 6, and Pi(0) and p2(0) are functions th at account for th e
antenna response patterns of antennas 1 and 2 respectively at angle 6.
W hen these two signals are fed into a correlating detector, it performs the
following operation:
Vi ,2(d)
=
K (* M 0 )
■
x P ' ( 0 ) P 2(0,)eiujili^ Ld0d0\
(1.5)
where x K denotes the complex conjugate of x. This can be simplified by assuming
that v r B( 0 , t ) and VTB{0',t) are independent for 0 ^ 0 ' since they are generated by
independent therm al sources, and the expectation of their product will vanish for
0 7^ O', collapsing the double integral to a single integral:
J - ir/2
/
jt/2
TB(6)P;(0)P2(9)eiu*a? ±d6.
( 1.6 )
•jt / 2
Splitting this correlation into in-phase (I) and quadrature (Q) portions obtains:
V'(d) = ® { V i M }
=
J "
TB{0)P:{0)P2{0) cos ( u ^ ^ j d O
(1.7)
VQ{d) = $ { V j ,2( d )}
= J*
TB{ 0 ) P ; { d ) P 2 { 0 ) s m ( u ^ ^ ) d0.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
( 1.8)
T„(at)
d sin 0
BPF
BPF
V, ( t )
V j(t)
90 "
LPF
V, (d)
LPF
VQ(d)
Figure 1.1. Correlating receiver w ith antenna baseline d
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
T h e antenna pairs of ESTAR are spaced at A/2 intervals. S ubstituting d = ^
into th e above equation simplifies the equation to
/•ir/2
=
V/(n)
I
Tb(0)P{ (0)Pi(9) cos(n7r sin 8)d9
(1.9)
T b {9) P f (8) P2(9) sin(nir sin 6)d9.
( 1-10)
J - i r/2
/•ir/2
^Q(n )
=
I
J-n/2
N ote th a t if th e antenna response patterns P i(5) and Pi{8) are isotropic, the
above set of equations reduces to a Fourier series [6]:
/•ir/2
V/(n)
=
/
T b {9) cos(n7r sin 0)d0
(1-11)
T b (9) sin(mrsin 8)d9,
( 1-12)
J-n/2
/•ir/2
Vq (ti)
=
I
J-n/2
which can be inverted with
TB(e) =
£
V[(n) cos(n7r s in 0)
n
+
Vcj(n)sin(ri7r s in 5).
(1-13)
n.
In the current im plem entation of ESTAR, the antenna responses are not iso­
tropic, prim arily due to interactions and scattering between adjacent an ten n a ele­
m ents, so a direct Fourier transform inversion is not possible. Instead, th e integrals
are discretized into a m atrix operator, called a G -m atrix [5], which includes the
an ten n a response functions.
1.4.3
A rray T hinning
ESTAR samples the spatial Fourier transform of the scene using an ten n a pairs
spaced at m ultiples of one half the wavelength at the operating frequency. Using
a full array of elem ents ensures th at all these antenna-pair spacings are present in
th e array, but judicious removal of antenna elements forms a new array th a t still
has all unique m ultiples of half-wavelength antenna-pair spacings w ith far fewer
elem ents. For exam ple, the current ESTAR antenna, shown in figure 1.2, is 7 A/2
wide, and covers all unique A/2 spacings with 5 antenna elem ents, while a filled
7
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
1
front
3
2
4
5
left
right
1
H
,
rear
3
2 , 1
H
I___________I 1
Figure 1.2. O rientation and spacing of ESTAR an ten n a array.
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
array of this size would use 8. Zero-redundancy configurations have been found for
small arrays, b u t do not exist for arrays of more than four elem ents [7, 8]. T he
ESTAR 5-elem ent array still has three redundant spacings, and cannot be reduced
to a zero-redundancy array, although many m inim um redundancy configurations
have been found. The ESTAR array uses only 5 elements out of 8 for a thinning
factor of | = 1.6. It is also possible to rearrange the 5 elements in th e ESTAR array
to form a new array th at covers all unique A/2 spacings up to 9A/2 which results
in a slightly higher thinning factor of | = 1.8. This rearrangem ent gives an array
with fewer redundant spacings; however, the ESTAR array must be 8A/2 wide array
because it was originally built from an 8A/2 by 8A/2 array th at had already been
developed by NASA. The presence of redundant spacings can be advantageous as
they provide m ore reliable field operation, and can be averaged to reduce the noise
statistics of d ata. These advantages are why the current ESTAR im plem entation
uses the narrow er (lower resolution) array with more redundancies instead of a larger
(higher resolution) array with fewer redundancies.
The real advantage of array thinning becomes evident when it is used for larger
arrays. For exam ple, Ruf et. al. [9] suggest the configurations shown in table 1. 1.
The thinning factors can become quite significant, especially for a space-based
platform where weight is at a prem ium .
Table 1.1. Thinning factors for selected thinned array configurations.
Number of
Elements
7
14
30
63
M aximum
Spacing xA /2
16
64
256
1032
Thinning
Factor
2.29
4.57
8.53
16.38
9
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C
h a p t e r
2
Im p r o v e m e n ts t o t h e U n iv e r s ity o f
M a ssa c h u se tts
2.1
ESTAR I n s t r u m e n t
The University of M assachusetts ESTAR Instrum ent
The Microwave Rem ote Sensing Lab (MIRSL) a t the University of M assachusetts
at Amherst has built a one-dim ensional synthetic-aperture im aging radiom eter known
as the Electronically Steered T hinned Array R adiom eter (ESTAR) [1, 2, 6, 10, 5].
This instrum ent uses ap ertu re synthesis to form a strip image perpendicular to the
flight path of an airborne platform , and then uses th e real ap ertu re of the antenna
and the m otion of the flight platform to generate an image along the flight path
of the airplane. Successive flight paths can be stacked next to each other in order
to increase the extent of th e image. In this way a two-dim ensional image can be
formed, as shown in figure 2.1. This method is referred to as th e ‘push-broom ’
m ethod since the an ten n a sweeps across the scene much like a push-broom sweeping
across a floor.
The original ESTAR instrum ent was built at th e University of M assachusetts
in 1988 by H iett [10] and T anner [5] . Later im provem ents were made 1992 by
Griffis [6], Gaiser [1], and Gleason [2], resulting in th e second generation instrum ent,
ESTAR-B. F urther refinem ents have been made to this instrum ent to improve its
reliability, therm al stability, and ease of use.
2.2
Experim ental History
The current generation ESTA R has participated in a variety of missions over
th e past few years, including extensive mapping of soil m oisture in W alnut Gulch,
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Figure 2.1. Formation of a two dimensional ESTAR image by stacking one dimen­
sional images “push-broom” style
A rizona and the Little W ashita watershed near Chickasha, Oklahoma; mapping of
th e D elm arva Peninsula in Virginia; m easurem ents of ocean salinity at the outflow
of Delaware Bay; and under-flights of the SIR-C synthetic-aperture radar mounted
aboard th e space shuttle.
2.3
H ardw are Modifications to the ESTAR-B Instrum ent
2.3.1
Horizontally Polarized A ntenna
O ver th e past few years, a variety of modifications have been m ade to the ESTAR
in stru m en t. The first of these was the installation of the horizontally polarized1
an te n n a from the ESTAR-A instrum ent into the receiver enclosure of the ESTAR-B
polarization in this context is referenced to the image plane, which runs perpendicular to
the flight path o f the instrument. The antenna dipoles are aligned parallel the flight path of the
airplane, which appears as a horizontal dipole as viewed from the side o f the plane, where the
image is formed.
11
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
instrum ent. Figure 2.2 shows the response of brightness tem perature to incidence
angle for b oth H-polarization and V-polarization. N ote th a t H-polarization drops
off as the incidence angle increases to 90 degrees, while V-polarization increases
before steeply dropping off. For a period of time, ESTAR-A (H-pol) and ESTAR-B
(V-pol) were operated together, allowing simultaneous m easurem ent of both polar­
izations [1]. However, when ESTAR-A was replaced w ith the newer, more reliable
ESTAR-B, it was desirable to return to H-polarization because it was used in prior
soil m oisture retrieval algorithms.
This an ten n a switch-out period also proved to be an advantageous tim e to mea­
sure the noise tem peratures of the receiver front ends, as the normally inaccessible
antenna feed lines were exposed.
500
I Dry Soil
~ 250
200
150
- wet
soil
v Polarization
H Polarization
£ 100
Dry Soli
HOlSt Soil
Met Soil
0.05 3 . 2 - j 0.53
0.20 9 . 5 - j 1.80
0.35 2 0 . 8 - J 3.75
Angle of Incidence e (Degrees)
Figure 2.2. C alculated brightness tem perature for a homogeneous soil m edium with
a specular surface a t three m oisture conditions. Taken from Ulaby, Moore, and
Fung [11, Fig. 19.1].
12
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
2.3.2
Cabling and W iring
The replacem ent of worn connectors on the cabling connecting the ESTAR
antenna and receiver electronics to the com puter rack enhanced reliability.
At
the same tim e the system cabling was rebuilt in a m odular fashion, thus adapting
ESTAR to installations on airplanes, which have varying cable length requirements,
and in the laboratory, where shorter lengths are more convenient.
Replacing the poorly secured wiring within the instrum ent w ith carefully laid
out wire bundles was a m ajor goal of the upgrades. In addition, care was taken to
color code the new wiring in a logical manner, and to label wires with wire m arkers
to denote their function. T he instrum ent wiring is thus now b etter organized and
easier to troubleshoot, as well as being more reliable.
2.3.3
Low-Profile Calibration Box
The addition of ex tra insulation forced the rebuilding of the internal calibration
source box so it would occupy less space. This required switching to a smaller,
commercially m ade, power splitter to distribute the system local oscillator signal,
instead of the larger, custom -m ade, microstrip power sp litter previously in use. In
addition, the cable-runs inside this box were neatly organized and well-secured to
improve reliability.
2.3.4
Docum entation
Another m ajor th ru st of work was system docum entation. Operations manuals
and reference m anuals were w ritten, requiring some reverse engineering of cabling
pin-outs and heater and therm istor locations. In addition, data-file formats were
modified to consume less disk space and keep all relevant inform ation in one file.
The final file form ats were docum ented to make further access easier.
13
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Figure 2.3. Bandpass filter frequency response
2.3.5
Reduction of Radio Frequency Interference
In th e past, ESTAR has experienced problem s with radio-frequency interference
(R F I) [6] during flights. These problems are m ostly encountered a t high altitudes,
where the platform is not as well shielded by the curvature of th e earth .
M ark
G oodberlet of Q uadrant Engineering noted problems with receiver satu ratio n at
frequencies th a t were re-entrant pass bands in his R F bandpass filters while operat­
ing an instrum ent sim ilar to ESTAR over th e Delmarva Peninsula in 1996 [12]. This
led to concern th a t the UMass ESTAR m ight experience sim ilar problem s during
th e June 1997 experim ent in Oklahoma, when it had to fly a t higher altitudes
th a n before. An analysis of the susceptibility to RFI at the re-en tran t passband
frequencies for th e UMass ESTAR on a network analyzer showed these bands to
occur a t 4.2, 7, and 8.4, and 9.6 GHz, as illustrated in Fig. 2.3. If R FI occurred
a t these frequencies, the only practical solution would have been to p u t additional
filters in the receiver.
14
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
sr
in
.*Ou*Cc
it
our
Figure 2.4. Receiver front end block diagram , from Gaiser [1]
In order to evaluate how susceptible ESTAR is to R FI, it is im portant to consider
th e full-system frequency response. T he response shown in Figure 2.3 is only one
com ponent in the receiver chain, and other nearby com ponents m ay also provide fil­
tering at th e re-entrant pass bands. Figure 2.4 shows the arrangem ent of components
within the front end of a UMass ESTAR receiver w ith the bandpass filter (B PF )
under consideration the fourth com ponent from th e top. T he three components
preceding the BPF are the calibration switch, isolator, and low noise amplifier.
They were m easured on a H ew lett-Packard 8722C network analyzer to see if they
reject the frequency bands being passed by the B P F . R ather th an removing parts
currently installed in the instrum ent, spares of an identical type were used, and
m easurem ents were m ade w ith a t least two, and as m any as five spares to ensure
the results were repeatable and typical of the part.
15
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Table 2.1. Insertion loss of first few receiver components
Component
radome
antenna
feed line
calibration switch
isolator
B PF
Insertion Loss (dB)
0.3 dB[6]
0.9 dB[6]
0.1 dB[6]
0.4 dB (measured)
0.2dB (measured)
1 dB (measured)
Table 2.2. Insertion loss and R F I rejection relative to pass band gain for low noise
am plifier at RF filter re-entrant pass bands
Frequency (GHz)
4.2
7
8.4
9.6
Insertion Loss (dB)
25
41
40
15
Rejection (dB)
46.5
62.5
61.5
36.5
This attenuation is sum m arized in Table 2.2.
As table 2.1 shows, the insertion losses of th e calibration sw itch and isolator
showed a relatively flat frequency response, at least flat enough to provide no
significant rejection at the re-entrant pass-bands of the B PF. However, th e frequency
response for the low-noise amplifier (LNA) shown in Figure 2.5 reveals significant
atten u atio n at the re-entrant frequencies. This attenuation is sum m arized in Ta­
ble 2.2. In this table, R FI rejection is figured as follows, to account for the fact that
the desired in-band signals are boosted by the gain of the LNA:
rejection (dB)
=
insertion loss (dB) + pass-band gain (dB)
=
insertion loss (dB) + 21.5
dB
16
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
(2.1)
ch i « a j
a
v
\
\
’
m
*GM*
to am/ nmr o d»_______a - i a . 8D> am
am mm •
i«g w a
ft
AIf s.
\\
i I oC
:a LSIH CHb
7?fc! tJt
k r v r*v //
VY ffI
STAJtT 1.000 OOO 000 CHb
r
r vrJ
STOP 10.000 ooo ooo SHb
Figure 2.5. Receiver low-noise am plifier frequency response
This shows th a t th e LNA provides RFI rejection of at least 36 dB which should
be sufficient when combined with the insertion losses of the isolator, calibration
switch, antenna feed line, and power combiner.
One further consideration is that a strong noise source may have enough power to
drive th e LNA into saturation, even if the source frequency is o u t of band. However,
th e LNA has a IdB compression point of + 10dBm at the o u tp u t, which equates to a
-11.5dBm level at th e input. Adding the loss of the components in front of the LNA
(1.9 dB, from table 2.1), this would require an RFI signal of approxim ately -9.5dBm
at the radome. This figure will be improved by increased range to th e transm itter,
and when the signal is received off the main peak of the ESTAR antenna response.
It is possible th at some strong RFI sources may approach these levels.
Saturation of th e calibration switch and isolator occurs only a t levels much higher
th an those for the LNA, so it is of little concern. If in-band noise is present, the
R F amplifiers following the LNA will satu rate a t lower levels th a n the LNA, and
th e d a ta will be corrupt. For out of band noise, th e gain roll-off of th e LNA and
17
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
the sto p -b an d isolation of th e BPF is enough to prevent th e RF amplifiers from
satu ratin g before th e LNA.
If sa tu ra tio n of th e LNA causes problems, the LNA and B P F could be reversed.
This jo b could easily be accomplished in an afternoon. T he filtering of the B P F
would provide additional attenuation of RFI outside the passband.
R e-entrant
passbands would still provide some attenuation, as shown in figure 2.3, w ith fu rth e r
rejection being supplied by the LNA as shown in figure 2.5 and table 2.2. R F I in
the passband cannot be rejected without affecting the desired signal. Note th a t th e
trade-off involved in this solution is the loss of the B P F is moved before th e gain of
the LNA, degrading the noise tem perature of the system . Installing additional filters
is also an option, but they would further degrade the noise tem perature, would add
to equipm ent costs, and would be difficult to install since space on the receiver is
constrained, as shown in figure 2.6. For these reasons, it is prudent to proceed w ith
the equipm ent currently in place in ESTAR.
T h e equivalent noise tem perature of the receiver can be found as follows: [13]
Ti
T-x
Te = T l + ?^ + — ^ +
Lxi
LriLi2
(2.2)
where Tn is th e effective noise tem perature of stage n and Gn is th e gain of stage
t i.
U sing th e values in table 2.3, and a system tem p eratu re of 315K, the effective
noise te m p e ra tu re of th e receiver is 219K. W ith the B P F and LNA reversed, th e
effective noise tem p eratu re is 335K. This represents a significant increase in noise
tem p eratu re, so th e filter and the LNA should probably not be switched except as
a last resort.
T h e situ atio n does not change much for the null feedback radiom eter channel.
A block diagram of this receiver is show in figure 2.7. T he circuit is essentially th e
same, w ith th e addition of a coupler for the noise injection, and a hybrid to split
off th e two parallel channels for the null feedback radiom eter. As figure 2.8 shows,
space exists for swapping the LNA and B P F as proposed for the other receivers;
18
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Table 2.3. Receiver noise tem perature param eters
component
feed line
calibration switch
isolator
LNA
BPF
RF am p 1
RF am p 2
numeric gain
0.9772
0.9068
0.9550
141
0.7943
100
100
noise tem perature (K)
7.2
27.7
14.2
130
64.8
1264
1264
Aicuua
KftL XT BPF
KHLIr I
KAfUBS
B0U10R
KXH SP4T
SWITCH
Figure 2.6. Receiver front end component layout, from Gaiser [1]
19
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
however, with th e addition of th e coupler and the hybrid to the noise tem perature
of this receiver, the degradation of th e effective receiver noise tem perature due to
reversing the LNA and B P F will be m ore significant.
2.3.6
Therm al Stability
One goal of SG P’97 was to obtain ESTAR images of soil m oisture w ith swath
width and resolution com parable to satellite images.
ESTAR therefore had to
fly at 25,000 ft. This is much higher than previous flights, and it could possibly
compromise both th e in stru m en t’s susceptibility to RFI, and its ability to m aintain
a stable therm al state. To fly at the higher level, improved insulation would therefore
be needed.
To assess th e tem perature a t 25,000 ft., and thus determ ine necessary design
changes radiosonde tem p eratu re vs.
altitude data taken from the ARM site in
Lamont, Oklahom a2 was consulted. This site is located near the northern end of the
flight lines used in SGP97. T he d a ta plotted in figure 2.9 axe from selected days from
m id-June to m id-July of 1996, th e sam e tim e of year as SGP97, and from all hours
of the day, to bracket the extrem es of diurnal tem perature variations. T he dashed
vertical line corresponds to 25,000 ft. and the range of observed air tem peratures
is —12 to —22°C. Figure 2.10 is radiosonde data from th e sam e conditions at 2:30
p.m . This indicates the range of tem peratures to be expected during th e desired
daily flight tim e. T he observed range of tem peratures at this tim e of day are similar
to those observed in figure 2.9.
When th e desired operating tem p eratu re range of ESTA R had been established,
th e ESTAR box was analyzed to determ ine its therm al fluxes. The inputs to the
system are the normal heat dissipation of the ESTAR electronics and the power
2 Data were obtained from the Atm ospheric Radiation Measurement (ARM) Program sponsored
by the U.S. Department o f Energy, Office o f Energy Research, Office o f Health and Environmental
Research, Environmental Sciences Division.
20
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
■ CAL
.SOURCE
CLOCK fU Q U V-F OH
LOOP ELECTRONICS
BOARD
rsouroti
JO dB
COUPLER
535T
VENUS
SWITCH
□a
iTi
ama
: SO 0
HYBRID
NOISE
SOURCE
C A »N «20d»
N^«II44B
f. *1.4IUCH|
RW«20MMY
JLsO.BBtfB
BPF
bpf
GAJNs20tfB
N^»7dt
GAINz 2008
I .J lJ S G H *
CONVERSION
L9SS«*M B
ft
«tOONN<
•W«20MHz
uo.
BPF
BPF
IF OUT
IF OUT
H.*O.ASdS
CAIN* JO dB
**-•749
CA JNsJOdR
NE«s7dB
Figure 2.7. Null feedback receiver block diagram , from Gleason [2]
21
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Figure 2.8. Null feedback receiver component layout, from G aiser [1]
Lam ont, OK ARM site radiosonde d ata
2000
4000
6000
8000
10000
Altitude ( m )
Figure 2.9. Lam ont, OK Central ARM Facility radiosonde d a ta for ail hours on
selected days from Ju n e 12, 1996 to July 13, 1996
22
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
L am e n t, OK ARM site radiosonde d ata
30
20
cj
ow
V
|u
i—
-10
-20
-3 0
-4 0
0
20 0 0
4000
60 0 0
8000
10000
Altitude (m )
Figure 2.10. Lamont, OK C entral ARM Facility radiosonde d ata for 1430 hrs on
selected days from June 12, 1996 to July 12, 1996
in p u t by the ESTAR heaters, which may be switched on and off in groups over
various periods of tim e to m odulate the heat input. T h e norm al heat dissipation
of the ESTAR electronics was determ ined to be 120W by measuring the current
of all power supplies in the system . Since no power is tran sm itted by ESTAR, it
was assum ed th a t all this power was dissipated as heat. T he m axim um power of
th e heaters was determ ined to be 630W by measuring th e resistance of the heating
loops and m ultiplying th at by the maximum heater supply voltage (40V). This
allows 120-750 W of power to be added to ESTAR to m aintain tem perature.
To determ ine the insulation needed to limit heat dissipation m easurem ents of all
surfaces were m ade, since all heat is lost by conduction through the receiver box
walls.
Heat loss was estim ated for various ambient tem peratures corresponding
to ground, flight, and low-level flight conditions, and w ith various am ounts of
insulation. This analysis showed th a t adding a one-inch layer of polystyrene and a
23
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
half-inch layer of Styrofoam would allow ESTAR to m aintain tem perature at flight
level, while allowing enough heat dissipation to prevent overheating on the ground.
As an added benefit, these layers were inserted w ithin rails with adjustable holding
clips, so they could be easily removed for operation on th e ground or in a w arm er
flight environm ent.
In addition to adding insulation, extensive work was done to repair or replace
dam aged heaters.
H eating groups were re-wired to utilize heaters closer to th e
therm istors th a t regulate them . In addition, a large plate covered with many heater
strips was added ju st inside the top cover of the receiver box. This plate can be
heated to 60-70°C. Since it has a large surface area and is near the electronics,
it radiates heat onto th e components. By thus adding an additional 50% to th e
available heating power, ESTAR can m aintain tem perature in the coldest of flight
environm ents. It also cuts th e long initial warm-up required to get to operating
tem p eratu re from 60-90 m inutes to 45-60.
ESTAR has had problems with overheating in the past, however; and the addi­
tional heat sources raised fears that they might recur, so several safety interlocks
were introduced into the control program. These interlocks were all designed w ith
safety in m ind, so they m ake it difficult to activate the heating plate, and tend
to de-activate it autom atically in many conditions.
T he heating plate m ust be
m anually enabled before it will power up. If the tem perature of the plate itself gets
above a certain tem perature, it will shut off to prevent burning out the heaters on
it. In addition, if any single therm istor reading is above a certain threshold, th e
heat plate will shut off.
Before th e instrum ent was mounted on an airplane, these improvements were
tested in accessible environm ents close to flight level conditions to check if they would
operate properly. The first test was done indoors at MIRSL a t progressively higher
m axim um heater voltages, to see if the instrum ent would overheat. The heaters
24
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Table 2.4. ESTAR system tem peratures during initial UMass indoor th erm al
verification tests. Tem perature vs. heater supply voltage
location
antenna
receiver 1
receiver 2
receiver 3
receiver 4
receiver 5
NFR ref
ML1
calibration
box
FE3
FE5
FE3
15 V
39.5
37.4
38.2
39.0
42.8
38.1
42.8
38.9
45.4
38.6
42.5
38.2
42.7
37.6
36.3
39.0
37.4
37.5
37.8
37.9
38.2
37.6
36.5
20 V
40.7
37.6
38.5
39.8
42.7
38.3
43.0
39.2
45.8
39.6
42.9
38.7
43.5
38.1
36.9
39.2
37.6
37.7
38.2
38.2
38.8
38.1
37.2
25 V
42.6
38.4
38.9
41.1
43.1
38.7
43.4
39.7
46.0
39.3
43.1
39.0
43.3
38.4
37.0
39.7
37.9
37.9
38.2
38.2
39.1
38.3
37.3
30 V
42.9
39.6
38.5
41.3
43.7
39.4
44.1
40.4
46.1
39.1
43.5
39.4
43.2
38.4
37.3
40.4
37.7
37.9
38.2
38.3
39.3
38.4
37.5
35 V
43.7
39.6
38.6
41.4
43.8
39.5
44.1
40.3
46.2
39.2
43.5
39.5
43.0
38.4
37.3
40.5
37.8
37.9
38.4
38.3
39.4
38.5
37.6
were sta rte d w ith a maximum voltage of 15V and allowed to stabilize for half an
hour. A t this point the voltage was increased by 5V and again allowed to stabilize
for half an hour. This was repeated up to the m axim um heater voltage of 40V.
As table 2.4 shows, the instrum ent seemed to stabilize and m aintain tem p eratu re
w ithout overheating at heater voltages up to 35V. However, a t 40V the th erm al
state begin to drift slowly higher, so th e test was term inated. T his cautioned against
extended operation on the ground w ith full heater power.
T he next test was performed outdoors at UMass on a series of cold nights in
25
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
January, 1997. T he am bient tem p eratu res on these evenings was 15°F (—8°C) which
was higher th an the nom inal flight-level tem peratures. T he instrum ent was started
at room tem p eratu re, set up out in th e cold, allowed to run, and observed to see
if it would achieve, and then m aintain, tem perature. T he results in table 2.5 show
th a t ESTA R seemed to achieve a stable operating tem p eratu re within an hour, and
then m ain tain it for a t least an o th er hour afterwards.
This experim ent provided an opportunity to adjust th e target tem peratures of
the software control loops for th e heaters so ESTAR would achieve a more uniform
therm al sta te . This reduced th e variation between the h o ttest and coldest spots by
several degrees.
T he test also showed th a t receiver 3 tended to run a few degrees warm er than
the o th er receivers because it is closest to the center of th e heating plate and has
the least o bstructed p ath to it. In addition, this receiver is used as part of th e null
feedback radiom eter, so it has nearly twice as much RF electronics as other receivers
due to th e two parallel branches involved in th e N FR design. An additional fan was
installed to circulate air over th e hottest spot on this receiver if it began to run
warm, in this way further reducing the m axim um tem p eratu re variation between
the h o ttest and coldest portions of the instrum ent.
As a final test, the instrum ent was brought to the U. S. Army Cold Regions
Research and Engineering Laboratory (C R R EL) in Hanover, New Hampshire where
it was op erated in a cold room for a couple of days at tem peratures as low as —20 to
—25°, closely approxim ating flight level tem peratures3. Table 2.6 shows th e results
of th e initial tests at CRREL. D uring this test, adjustm ents were being made to the
fan control software and these varying states axe shown. Once the fan and auxiliary
heating p late control circuitry were adjusted to im prove warm-up tim e, and the
3These temperatures are in stable air. Forced air cooling is more efficient than static air cooling,
so this is not a true test o f Sight conditions. However, this is the best that could be found before
actually flying the instrument.
26
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Table 2.5. ESTA R system tem peratures during UMass outdoor therm al tests,
Tamb = 15° F = —8°C
location
an ten n a
receiver 1
receiver 2
receiver 3
receiver 4
receiver 5
N FR ref
ML1
calibration
box
FE3
FE5
FE3
25 min
36.2
30.8
32.3
31.2
36.8
32.2
37.3
33.8
35.9
36.4
37.7
34.2
38.0
31.9
33.5
31.4
31.2
29.5
30.0
28.8
32.1
30.5
32.7
32 min
40.3
34.0
35.8
35.3
40.1
35.5
41.1
37.7
39.9
40.3
41.5
37.8
41.6
35.3
37.3
34.6
34.9
33.1
33.6
32.5
36.0
33.8
36.6
44 m in
46.1
36.3
38.4
41.5
42.3
39.2
42.9
40.2
45.0
41.2
43.3
39.4
43.8
39.0
41.1
39.3
38.7
38.7
39.0
38.4
40.9
38.5
40.9
61 min
45.2
36.8
37.4
42.3
42.6
38.8
43.3
40.1
46.3
39.0
43.2
38.6
45.6
38.2
36.6
38.8
37.7
38.3
38.5
38.9
39.1
37.1
38.9
96 min
46.2
36.1
38.1
42.4
43.8
38.1
42.1
38.2
45.9
40.8
43.6
37.9
45.6
36.8
35.0
37.9
37.9
37.7
37.8
38.3
37.6
35.5
35.7
124 m in
45.5
35.6
37.6
42.1
44.3
37.9
41.9
37.9
46.0
41.5
43.5
37.6
45.5
36.5
35.3
37.6
38.0
37.8
37.8
38.1
37.5
35.1
35.7
27
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Table 2.6. ESTAR system tem peratures during initial CRREL indoor therm al tests,
Tamb = —15°F= —27°C
location
antenna
receiver 1
receiver 2
receiver 3
receiver 4
receiver 5
N FR ref
ML1
calibration
box
FE3
FE5
FE3
near warm
43.1
36.4
38.0
38.6
41.6
39.0
41.0
39.1
40.9
39.4
41.7
39.3
43.0
37.6
39.0
39.0
35.9
34.7
35.0
34.2
38.5
37.0
38.5
fan on
45.4
35.2
37.7
42.1
42.8
40.2
42.3
40.1
40.7
39.2
42.3
38.0
44.4
36.8
37.4
40.8
38.3
37.7
38.2
38.6
37.9
35.8
37.9
stable
45.4
34.5
37.3
42.4
42.0
38.4
42.0
39.4
43.6
39.3
42.6
38.0
44.5
37.2
37.9
38.8
38.0
38.0
38.4
38.5
39.1
36.4
38.0
fan off
45.4
34.5
37.0
42.5
42.3
38.4
42.6
40.0
45.1
39.8
42.9
38.4
42.7
37.3
38.9
38.8
38.4
38.2
38.8
38.8
39.6
37.1
39.0
fan on
45.3
34.6
37.5
42.8
41.8
38.5
42.3
39.9
42.3
39.2
42.5
38.0
42.7
36.7
37.3
39.3
38.0
38.1
38.4
38.9
38.3
35.9
38.0
ability to m aintain a stable and uniform tem perature state was dem onstrated, a
final warm-up therm al test was conducted. The results are shown in table 2.7.
These tests showed th at ESTAR would heat up to, and m aintain, a stable
uniform therm al s ta te at flight level tem peratures. As a final check of th e safety
of ground operation, ESTAR was again operated indoors at UMass an d allowed to
heat for a couple of hours to make sure th a t it would m aintain tem p eratu re w ithout
overheating. These results of this are shown in table 2.8.
Finally, as part of an engineering shakedown, in April, 1997 the in stru m en t was
28
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Table 2.7. ESTAR system tem peratures during final CRREL indoor therm al tests,
Tamb = —15°F= —27°C
location
an ten n a
receiver 1
receiver 2
receiver 3
receiver 4
receiver 5
N FR ref
ML1
calibration
box
FE3
FE5
FE3
first stable
46.0
35.0
37.7
42.1
42.2
38.4
41.8
39.2
42.5
38.4
42.3
37.9
44.2
37.1
37.1
38.8
37.9
37.7
38.2
38.5
37.8
36.0
37.5
stable
45.5
35.1
37.2
42.4
42.0
38.2
42.0
39.3
43.5
38.4
42.6
38.9
42.9
36.7
37.0
38.6
38.1
37.7
38.2
38.5
38.0
36.1
37.2
room tem p
45.8
39.4
38.0
42.5
43.0
39.6
43.1
40.4
42.8
39.2
42.8
39.4
42.2
38.0
37.5
40.4
37.7
37.9
38.3
38.4
38.8
38.0
38.0
29
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Table 2.8. ESTAR system tem peratures during final UMass indoor therm al tests,
Tamb = —15°F= —27°C
location
antenna
receiver 1
receiver 2
receiver 3
receiver 4
receiver 5
N F R ref
ML1
calibration
box
FE3
FE5
FE3
1 hour
42.6
39.8
39.3
41.3
44.6
41.4
44.1
41.7
42.3
40.7
43.6
40.9
42.9
39.8
39.6
42.0
39.4
39.4
39.9
39.6
40.1
39.7
39.9
2 hours
44.7
40.2
39.4
41.6
45.1
42.0
44.6
42.2
42.9
41.3
44.2
41.6
43.6
40.6
40.2
42.5
40.6
40.6
41.0
41.0
40.7
40.4
40.5
30
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
flown in a short series of flights over the Delmarva Peninsula and the m ainland of
V irginia at altitudes com parable to the ones used in S G P ’97. During these tests,
as well as during operation in S G P ’97, the instrument easily m aintained a uniform
therm al s ta te during flight conditions, even with the presence of forced-air cooling,
which could not be replicated in any of the ground m easurem ents.
2.3.7
D ata System /G eolocation
To com pensate for the unpredictability of airplane d a ta systems and to im prove
the full-system d ata collection capability of ESTAR, a video cam era and recording
system was added to ESTAR. T his cam era provides real-tim e viewing and recording
of a full color video image bore-sighted to the ESTAR observation area. The addition
of a video character generator box allows descriptive inform ation, such as d a ta set
titles, tim e, date, location, and altitude to be superimposed on the recorded video.
The system com puter controls these functions and synchronizes the video clock w ith
the ESTA R system clock to facilitate easy comparisons between ESTAR d ata and
the video scene.
A dditionally, for real tim e determ ination of latitude, longitude, heading angle,
and speed, an Ashtec GPS unit was added to the ESTAR rack and connected to th e
ESTAR com puter. These quantities were all recorded in th e ESTAR data stream ,
and tim e-stam ped with ESTAR system tim e at the m om ent they were input to
m inim ize clock synchronization problems.
F u rth er geolocation param eters were read off the airplane Flight M anagem ent
System (FM S) and Inertial Reference Unit (IRU) using an ARINC 429 bus interface
device. This allowed the ESTAR com puter to read airplane param eters, such as
tim e, latitu d e, longitude, roll, pitch, and drift angles in near real time. As in th e
GPS system , these data were all tim e-stam ped with ESTAR system tim e and saved
as p art of th e d a ta stream .
31
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
These additions provide a full coherent picture of the airplane position, orien­
tation, and velocity in ail dimensions, from redundant systems, all tagged with a
corresponding clock.
2.4
Software Improvements
In addition to the hardware improvements m entioned above, m any improvements
were m ade to th e ESTAR software, including both the data collection program on
the airplane and the entire suite of programs used to process the d a ta and generate
images.
2.4.1
M odifications to the D ata Collection Program
Many upgrades were m ade to the ESTAR d a ta collection software to make
it easier to use in flight and to improve its performance. Therm al read-outs on
the com puter m onitor were color coded to indicate whether the tem perature in
each region was cold (blue), hot (red), or w ithin nominal lim its (green). Quick
assessments of the instrum ent’s thermal sta te can therefore be m ade in flight.
Descriptive labels of these therm al zones were also added to the display.
Many of th e functions of the data collection program are activated by pressing a
single function key, or hot-key. However, the num ber of functions used outnum bers
the keys available, so a system of hot-keys to bring up menus of functional hot-keys
was devised. Care was taken to make this m enu arrangem ent clear and logical, and
to provide prom pts to cancel accidental key presses th at could result in unwanted
operations, such as aborting a data line.
C alibration state information was added to the program so th at a t the touch of a
button nom inal values could be superimposed over actual displayed values, to check
th at the instrum ent was performing properly. These displays axe th e first diagnostic
consulted to track down a potential malfunction. By looking at w hether one, a
group, or all ou tp u ts fail to m atch their nominal values, it is possible to trace the
32
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
problem to a single channel, a subsystem such as a common receiver, or to a global
problem such as a bad com puter link or power supply failure. By thus identifying
th e p o tential source of problems, the overall complexity of ESTA R is reduced.
T he program was also modified to output various system diagnostics to a printer
a t th e end of each data line, making it easy to see how well th e instrum ent is
operating.
T hese data were also useful for determ ining where and when system
m alfunctions occurred, easing troubleshooting and providing a historical record of
operating param eters to answer future questions about ESTAR’s operating state or
th e first appearance of any problem th a t occurs.
To facilitate diagnostics, a suite of programs was w ritten to inspect every type of
file generated by th e ESTAR program, usually both in graphical and tex tu al form at.
To m ake them easier to use where they are needed, these program s were ail w ritten
in H P-BA SIC, so they can be run on the com puter that collected th e d a ta rather
th an only on a dedicated analysis com puter in the hangar or hotel. These programs
proved invaluable both in installing and interfacing new hardw are (such as the GPS
and ARIN C 429 devices), and also in looking a t d ata to begin troubleshooting after
a m alfunction.
2.4.2
D ata Processing
To analyze ESTAR data a new suite of program s was developed. W here possible,
th e design philosophy emphasized developing m odular code libraries to do basic
functions such as reading or writing the m any types of files generated by ESTAR.
This not only shortened and simplified many of th e ESTAR d a ta analysis programs,
b u t also m ade it easier to upgrade several program s at once if a bug was discovered
in code or new functionality was added. In addition, it simplified th e task of writing
new processing programs, and well-tested routines could be ‘dropped-in’ to programs
w ithout new testing.
33
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Most of the processing code was w ritten in th e IDL program m ing language,
which has m any constructs suitable for processing arrays of data and generating
plots w ith considerable ease. W here possible, calibration param eters or lists of file
nam es were stored as human readable text files.
T he use of text files made it possible to use th e rich regular expressions an d tex t
processing capabilities of Perl scripts to parse these files, and then to pass these
results to the appropriate IDL program . This technique, which was used extensively,
also tended to autom ate the use of th e IDL programs, easily specifying com m only
used default param eters. One of best examples of this was a script th a t would parse
th e ESTAR d a ta files into their constituent parts, and then run the IDL program s
necessary to generate diagnostic plots of this data, autom atically generating a web
page th a t could be used to browse these plots for diagnostic purposes. Finally, by
running this script on a battery-pow ered laptop com puter, it was possible to begin
this process on the airplane, let it run while equipm ent was secured, and be nearly
com plete by the tim e the d a ta was returned to the hotel for analysis.
2.4.3
D ata Delivery
Improvements were also m ade in delivering d a ta to the sponsor. In th e past,
d a ta had to be stored on large, bulky com puter d a ta tapes, th a t were then shipped.
T his process was improved to utilize the smaller and more convenient 4 m m /D A T
ta p e form at, but even this took tim e to be shipped to th e sponsor. Finally, th e d a ta
archives were placed in an internet-accessible area on th e MIRSL com puting system ,
w here they can be accessed using FT P. This m ake th e d ata much m ore readily
available to the sponsor, and m ake th e process of delivering it much quicker th an
it was in the past. Furtherm ore, during the SG P’97 experim ent, 8mm tap es were
used to back-up the data on th e airplane, and then tran sp o rt it to the hotel. Once
a t th e hotel, they were used to store the data on th e M IRSL processing com puter,
34
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
and th en to deliver the d ata to the sponsor within an hour or two of the end of th e
flight.
35
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C h a p t e r
3
C a l ib r a t io n and P r o c e s s in g of E S T A R D ata
3.1
Overview
ESTAR is essentially a parallel processing instrum ent, requiring th e perform ance
of many systems to produce results. Each of these system s has its own intricacies,
and as a result, there are many layers to th e ESTAR calibration. T hese include
the antenna p a ttern calibration, complex norm alization of detector o u tp u ts, cali­
bration of the null feedback radiometer o u tp u t, external blackbody and w ater scene
calibrations, image calibration, and finally image ripple reduction. Each level of
calibration corrects a possible source of error to achieve th e goal of producing reliable
d a ta output.
In a sense, even the structured operational routine in th e S G P ’97
experim ent may be thought of as a form of calibration, since this routine minimizes
the chances of introducing several system atic errors.
ESTAR is calibrated on several different tim e scales as well. Every five minutes
in flight the an ten n a is switched to the internal calibration loads, which axe used
to normalize gain variations in the instrum ent. The next scale is daily calibrations,
which include external blackbody load calibrations before and after every flight, as
well as water calibrations approximately every 1-3 days during an experim ent. Next
is regression to find N FR and image calibration coefficients, which is done for every
day of data, but seems to vary little over periods of approxim ately a week in length.
T he longest scale is th a t of the antenna p a tte rn calibration, which is usually done
only before or after an experim ent.
This chapter focuses on the steps involved in calibrating and processing ESTAR
d ata.
It outlines th e steps described above, explaining the m athem atics and the
effects of the corrections.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
3.2
Collection
Calibration can be considered as operations th at m axim ize th e quality of data.
From this liberal definition we may consider the stru ctu red operational routine
of ESTAR as a basic level of calibration. Through participating in th e S G P ’97
experim ent for a m onth, the people involved with ESTAR, from th e operators
to ground crew to pilots, developed an operational routine th a t m inim ized m any
system atic errors and reduced the risk of making operational errors from confusing
th e operational plan.
Where possible, the ESTAR flights were flown at the sam e tim e of day, at the
sam e altitu d e and speed, and with the flight lines flown in th e sam e order and
th e same direction. Flying at the same altitude and tim e of day m eant th a t the
air tem perature outside th e airplane was fairly consistent, giving ESTA R a more
stable therm al environm ent, minimizing errors caused by operating a t different
tem peratures. By flying th e sam e flight lines in the sam e order a t th e sam e speed and
at the same tim e of day, ESTAR observed each piece of ground under com parable
conditions, m inim izing any diurnal variations or dependence on ground tem p eratu re
or even any sm all residual therm al drift in the ESTAR instrum ent uncorrected by
other means.
This consistency of operation ensures th at any small residual errors w ithin the
image rem ain the sam e from day to day, and hence direct com parisons between
m ultiple days of d a ta are possible. In addition, since th e pilots, operators, and flight
crew were fam iliar with the order of operations, fewer delays and m istakes occurred,
and the num ber of lost, repeated, or mis-flown flight lines was reduced. In this sense,
operations were a preventative rath er than a corrective form of ‘calib ratio n ’.
This operation also extended to tim ing of the usual ESTA R calibrations. For
exam ple, the blackbody calibrations were taken im m ediately before and after every
flight.
37
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
G-Matrix Calibration
NFR Calibration
^^*{Real Time Average Tb Readout)
Diagnostic Single Pixel Images ]
Ripple Reduction Curves*^
Image Calibration
»•{Calibrated Images")
Figure 3.1. Block diagram of steps used in ESTAR calibration
3.3
A ntenna P atte rn M easurement
T he first step in the calibration of ESTAR is to m easure its antenna p attern .
T h e resulting discretized model of the system response is commonly referred to as
a G -m atrix following the notation used in th e original development by T anner [5].
This response is used in the image calibration and accounts for non-idealities in
th e system response.
It also measures th e im pulse response of the instrum ent,
finding the synthesized antenna beam locations. As a side benefit, such a thorough
pre-flight engineering shakedown enables researchers to com pare the system response
to well-known historical system responses.
3.3.1 Background
Recall from equation 1.6 in section 1.4.2 th a t
g
/ */2
TB{0)P;tB)P2{6)t?<—
)dB.
(3.1)
7t / 2
S ubstituting d = ^
for the half-wavelength elem ent spacing used in ESTAR
yields
vbH = r
TB{e) p;{B)p2{ e y < ^ ) d e .
(3.2)
J - k/2
Following the techniques used in previous dissertations on ESTAR, b u t most
closely following Tanner [5], this can be simplified by defining the following q u an tity
g(n,6)
=
p ^ { e ) p 2{ e y < s^ L±),
38
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
(3.3)
where g(n, 9) is referred to as a basis function or an im pulse response of th e system.
S u b stitu tin g equation 3.3 into equation 3.2 and rearranging term s inside th e integral
results in
V(n)
=
r
g(n , 9 )T B(9)d9.
(3.4)
J - i r/2
Since these quantities are only m easured at a finite num ber of angles, equation 3.4
can be simplified to
V( n)
V
=
=
(3.5)
t
G T s,
(3.6)
where G is a m atrix commonly referred to as ‘the G -m a trix ’ and is equivalent
to th e system im pulse response. The G -m atrix can be obtained experim entally by
using th e relation
g ( n ,9 0) = yO ’Ol7’B(0)_j(0_0o) ,
which may
(3.7)
be measured a t all angles of interest 0Qand for allinter-element
spacings n. Note th at without loss of generality, equation 3.3 can be modified to
include a term Pi,2(0) to account for cross-coupling effects betw een antenna elements
as follows
j( n ,« ) =
(3.8)
Thus th e m easured G -m atrix will account for antenna cross-coupling effects, even
if a model for the quantity Pi, 2 (a) cannot be derived. T his is an im portant result,
since cross-coupling is a noticeable effect in the current EST A R antenna, and the
behavior of th e coupling is currently not modeled. Note th a t it is not necessary
to specify a second angle, as in Pi,2(9,9') because section 1.4.2 assumes th a t noise
sources from any two angles 9,9' : 9
9' are independent. In th e current ESTAR
39
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
d ata processing, th e Pi^{0) is m easured empirically, b u t some work is being done
on m odeling this effect [14]. These models may also allow removal of th e m utual
coupling effects so a direct Fourier inversion can be used for image generation.
3.3.2
M easurem ent of the G -M atrix
To m easure th e G -m atrix it is necessary to find an antenna range large enough
th a t th e test source will be in ESTAR’s far field. This distance is R = 2D 2/ \ ,
where R is the required distance to be in the far field of the antenna, D is the
largest dim ension of the antenna, and A is the free-space wavelength at th e operating
frequency [15]. T he ESTAR antenna is an eight-element array with an inter-elem ent
spacing of A/2 for a total dimension of D = 7A/2. This results in a far-field distance
of R = 24.5A or 5.2 m eters (17 ft.) at ESTAR’s operating frequency of 1.4135 GHz.
The an ten n a cham ber at NASA-Goddard (GSFC) is sufficiently large for this.
ESTAR is m ounted in the antenna range by attaching a U-shaped m etal bracket
to the gussets used to m ount ESTAR on airplane installations. The m ounting plate
on the bottom of th e bracket is attached to a spacing post, which is then m ounted
to the tu rn tab le in the antenna range. W hile the ESTAR antenna is being m ounted
in such a m anner, a tem porary floor of plywood is constructed over the pit th a t
contains the range turntable. This tem porary flooring supports the weight of the
ESTAR antenna, so a wheeled hydraulic pum p cart can assist in lifting the antenna,
which weighs around 350 pounds.
Once ESTAR is m ounted in the range, care is taken to ensure th at all exposed
m etal p arts of the m ounting bracket are shielded by sheets of microwave absorber.
Any equipm ent th a t cannot be removed from the range is placed behind blocks of
absorber so they are out of the direct line of sight of the ESTAR antenna throughout
the rotation. T he cables are arranged so they will move freely and not bind over the
full range of m otion of the range turntable. A therm om eter is installed in a shielded
com er o f th e range to measure the range tem perature. To minimize th e chances
40
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission.
of interference, the range lights are turned off and the range door closed whenever
d ata axe taken.
The tu rn tab le allows accurate control of the endpoints and speed of ro tatio n of
ESTAR in th e antenna range. This is a vast improvement over th e old arrangem ent,
which used a m otor m ounted directly between the m ounting pillar and th e antennam ounting bracket. T he s ta rt and stop points had to be determ ined by observing a
scale on th e rotational bearing and could not be well controlled. T h e m otor speed
regulation was imprecise and possibly non-linear, introducing erro r into th e tim e
interpolation of an ten n a pointing angle by assuming constant velocity of rotation
between th e sta rt and stop points of rotation. Furtherm ore, care was needed to
avoid over-rotating or even rotating the antenna in the wrong direction resulting in
unw arranted stresses on the antenna cabling.
T he new range tu rn tab le controls ensure th at consistent, repeatable sta rtin g and
stopping points were used in every rotation of the antenna, and th a t th e speed of
rotation was consistent, predictable, and linear. It elim inated th e possibilities of
over-rotation or counter rotation of the antenna, which could have dam aged the
cables. F urtherm ore it elim inated the need for heavy, unreliable m otor and bearing
equipm ent on the m ounting pillar. These metallic components were an additional
possible source of error from reflecting signals.
Hand held walkie-talkies were used to communicate and coordinate betw een the
tu rn tab le controls in the antenna control room and the ESTAR com puter rack,
which was located in the hailway outside the antenna range due to restrictions in
the length of the cables between the ESTAR antenna and com puter rack.
Table 3.1 lists th e d a ta sets taken during the G -m atrix calibration. T his selection
of d ata sets was designed to m easure all im portant states of the four variables of in­
terest in an order th a t m inimizes the number of changes. The first of these variables
is the direction of rotation. M ost sets were taken in the forwaxd direction, m ainly
41
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
o u t of practicai convenience, but also in case there were any direction-dependent
system atic errors so th a t all sets would be taken under sim ilar conditions.
For
com pleteness, one set was taken in the reverse direction so the two directions could
be com pared. ‘S ta tic ’ means th at the ESTAR antenna was not rotating and was
pointed directly tow ard the range antenna (which had no source connected for this
p articu lar set).
Table 3.1. E xperim ental conditions for data sets taken during G -M atrix calibration
d a ta set
ro tatin g noise
low source
cross-pol
open loop
closed loop
reverse
ro tatin g noise
nadir noise
direction
forward
forward
forwaxd
forward
forward
reverse
forward
static
source
off
low
high
high
high
high
off
off
polarization
N /A
co-pol
cross-pol
co-pol
co-pol
co-pol
N /A
N /A
loop
closed
closed
closed
open
closed
closed
closed
closed
T he next im p o rtan t variable is the source am plitude, which is adjusted w ith
a step a tte n u a to r between the noise diode and the range antenna. The first level
tested was ‘off’, which was used for noise m easurem ents.
Note th a t when ‘off’
m easurem ents were m ade, the noise diode was not powered down, but rather con­
nected to m atched load to elim inate the possibility th a t it may stabilize at a
different am plitu d e level when powered up, and to keep it warm ed-up throughout
th e m easurem ents.
T he null feedback radiometer (NFR) works by injecting an adjustable and m ea­
surable am ount of noise into the receiver, where it adds to the noise received by the
an ten n a until th e sum equals a known reference tem p eratu re. In norm al operation,
th e unknown an ten n a noise tem perature can be found by subtracting the known
42
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
injected noise tem perature from the known reference tem perature.
However, it
is only possible to inject positive noise levels, and as a result, the system can
only m easure tem peratures up to the reference tem perature.
circum vented by the circuit arrangem ent shown in figure 2.7.
This restriction is
A switch selects
w hether the injected noise is fed to the £ (additive) or A (subtractive) branch
of a hybrid, either adding or subtracting its noise tem p eratu re to the antenna
tem perature.
This allows th e N FR to measure antenna tem peratures above, as
well as below, its reference tem perature, doubling its dynam ic range. This switch
is called the Venus switch from the proposed use of a sim ilar technique on space
probes sent to explore the planet Venus, where surface tem peratures are extrem ely
high [2].
T he state of the Venus switch determ ines the requirem ents for the two rem aining
source am plitude settings. T h e ‘low’ source level was chosen to be the m axim um
source am plitude for which th e Venus switch would not change state, rem aining in
the ‘off’, or additive position, during the entire rotation. T his results in a set of N FR
response curves without the overshoot transient th at results when the Venus switch
changes state.
The final am plitude level was the ‘high’ source level, which was
set to be the maximum level th a t the system could handle w ithout compression
of its o u tp u t.
This results in the best signal to noise ratio possible, b ut also
contains overshoot transients where the Venus switch changes state.
Ironically,
these transients are actually sm aller for larger signal am plitudes, as these result in
quicker transitions through th e unstable region for the N FR , and also present a
stronger error signal to drive th e feedback loop back into lock.
The next variable m easured was antenna polarization. ‘Co-polarized’ means th a t
both th e ESTAR antenna and the standard gain hom in the range are vertically
polarized l . ‘Cross-polarization’ denotes th at the ESTAR antenna is still vertically
^ h e ESTAR antenna in the current configuration is horizontally polarized, not vertically, but
43
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
polarized, b u t the range antenna is horizontally polarized. Once th e ESTAR antenna
is m ounted in th e range, it is not practical to change its polarization, so this is
accomplished by rotating the stan d ard gain horn, which is m ounted on a rotary'
bearing. W henever the range horn was rotated, a bubble level was used to ensure
the proper orientation. ‘N /A ’ is listed for sets where the source was set to ‘off’ and
hence no definable polarization condition exists.
The final variable deals with th e sta te of the feedback loop in the null feedback
radiom eter channel. ‘Closed’ denotes th a t the feedback loop is closed and operating
normally. ‘O pen’ means th at the feedback loop has been opened, and th a t th e NFR
is functioning more like a total power radiom eter without th e stability im provements
inherent in th e null feedback design.
The m ost im portant sets are th e closed loop set and the rotating noise set
because these are used directly in com puting the G -m atrix.
T he other sets are
collected m ainly for diagnostic purposes or as a backup set if some problem in the
closed-loop d a ta were discovered at a later date. The closed-loop set provides the
prim ary m easurem ent of the basis functions described in equation 3.3. T he rotating
noise m easurem ents are used to su b tract out the room effect, as the closed-loop
set measures the basis functions in a background equal to th e tem p eratu re of the
room rather th an in complete isolation. Measurements of th e room tem p eratu re are
also m ade and could be used, but the rotating measured noise is preferable since it
accounts for any angular non-isotropies in the background noise level.
In addition, some further steps were taken during the collection of the G -m atrix
data. W here possible, all sets were taken in a repeatable m anner. For instance, while
this is referenced to the apparent polarization o f the antenna in the across-track synthesized beams.
This is due to the alignment of the ESTAR stick antennas parallel to the long axis o f the airplane.
When ESTAR is mounted in the antenna range such that the source m ay be rotated through the
across-track synthesized beams, the resulting geometry has the ESTAR stick antennas parallel with
a line that is vertical with respect to the ground. Hence ‘co-polarized’ denotes both the ESTAR
antenna and the range antenna are vertically polarized, not horizontally
44
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
one o p erato r reset the range tu rn tab le for th e next rotation, the other operator
would go into the range to record th e tem p eratu re m easurem ent. This became
an understood procedure between th e two people taking th e m easurem ents, and
m inim ized th e chances of m istakes or repeated d a ta sets.
Similarly, a standard
script of com m unication ensured th a t th e ESTAR d a ta collection and calibration was
synchronized w ith the starting and stopping of th e range tu rn tab le w ithout losing
any d ata. A further organizational step was storing all d a ta files for a particular
G -m atrix set in a uniquely nam ed directory th a t prevents confusion and allows easy
identification of when the files were taken and to which set they belong to.
Two m ain improvements have been m ade to th e collection of the G -m atrix data.
The first is the use of the full dynam ic range of th e instrum ent to m axim ize the
signal to noise ratio of the m easurem ent. In th e past, lower levels were used w ithout
any a tte m p t to find the m axim um non-compressing signal level that could be used.
T he second m ajor improvement involves th e change in the switching criteria for
the Venus sw itch as the signal level improves. In th e past, th e Venus switch was
toggled as soon as the integrator o u tp u t went above zero. Biases in the integrator
o utput sam pling caused prem ature switching of th e Venus switch, which resulted in
a positive feedback state and drove the N F R o u tp u t into a large overshoot before
it corrected. W hen the NFR is not in lock, there is usable inform ation in th e N FR
correlator o u tp u t channel. The N FR correlator o u tp u t behaves like an error signal in
the N FR feedback loop. Normally, when th e N FR is in lock, the correlator o u tput
is a constant bias plus noise2. As antenna tem p eratu re approaches th e reference
tem p eratu re and the NFR goes o ut of lock, th e correlator o u tp u t begins to deviate
from this constant bias and tracks the increasing antenna tem perature, ju s t as if
the radiom eter were in open loop m ode [16]. W ith a little experim entation, it is
zActually, this bias appears to have a slight dependence on the level o f the integrator output,
but for the purposes o f this explanation it can be considered constant
45
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
possible to find a threshold value for the N FR correlator o u tp u t that corresponds
to an optim al switching point for the Venus sw itch m ode, which minimizes both
th e level of overshoot and the tim e to re-acquire lock in th e NFR. Figure 3.2 shows
sm all overshoots at th e Venus switching points.
ESTAR NFR r e s p o n s e (u n c o rre c te fl)
-
5 . 0 * 10'
M
<
0
500
10 0 0
1500
2000
Figure 3.2. uncorrected ESTAR NFR response during G -m atrix calibration
Once the G -m atrix d a ta has been collected in th e antenna range, further steps are
necessary to form th e G -m atrix. Figure 3.3 shows a schem atic representation of the
files and programs used in this process. The top line indicates th e processing involved
in th e forward ro tatin g set, which is the prim ary file for forming the G -m atrix. T he
nam es of the files involved are on the left. T h e file names are coded to contain an
initial letter denoting the type of information in th e file, followed by a date and tim e
code. For exam ple A 010ctl729 is a type A or A ntenna d a ta file taken on O ctober
1st at 17:29 (5:29 PM ) local tim e. Table 3.2 shows o th er files types, including
46
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
H-files which contain the internal hot calibration source d a ta used in norm alization
(described below), and B-files, which are used to initially store A, G, P and T files
for convenience in buffering while the data acquisition program is running. Each
step in th e processing adds an extension to the file nam e to denote the level of
processing th a t has been done to that file. For exam ple, when A010ctl729 has
its Venus switching transients fixed, it becomes A 0 1 0 c tl7 2 9 .fix . Thus m ultiple
versions of files with differing levels of processing exist at once. This consumes more
disk space, but when necessary, re-processing can be sta rte d at any interm ediate step
ra th e r th an from the beginning. The disk-space cost of this freedom is insignificant
since the MIRSL com puting facilities have available disk space th at is m uch larger
th an th e size of an entire ESTAR data set.
ESTAR-Bh Data Processing Schematic
Legend:
A 0 1 0 c tl7 5 9
file name
(Y u-nfr.pro)
processing program
Forward rotation sample
A Q I C c t 1 7 2 9 ~ ^ { n lr - f ix .p r o ) — ^
A Q 1 0 c t i 7 2 9 . f i x - ^ 'f n o n n .p r u ) — * ' A 0 1 O c t l 7 2 9 . f i x . n o r m - ^ t n m . p r ^ ^ ' A 0 1 0 c c i 7 2 9 . f i x . n o r m , t r i m -
• A 0 l0 c tl7 2 9 .fix -in fo .
H O l G c t 1 7 2 9 -----------HOIOCC.1737 ------------
fp
m
M
-p
n
)) —
►
put
A G lG c c l7 2 9 . i n f o "
g m a t - i n f o -------------
Rotating nobe sample
A Q lO c t.1 7 ^ 9 —
fix- afr.p tu V
A Q l O c t l7 5 9 . f i x '^ ’^ 'n u o n .p c u )
m
A 0 l G c ti 7 S 9 . f i x . n a r w * ^ m m . p r o ^ A a i Q c t n S 9 . f i x . n o r m , t r i m
A 0 1 O c tl7 2 9 . f i x - i n f o — ^
H 0 1 0 c tI 7 5 3
^
S
HO1OCC1807 -----------------------------------------------------------------
A 0 i0 c tl7 5 9 . in fo —
Reverse rotatioo sample
A 0 lo c tl7 3 9 ~
A
0
1
Q
A 0 1 0 C C 1 7 2 9 .fix -in fe
c
t
l
7
3
9
.f
tx in u .p ru )— ► A 0 1 0 c t l 7 3 9 . f i x . n o n i r - * ^ m m . p r ^ ^ - A 0 1 0 c t l 7 3 9 . f i x . n o r a . c n
__________________________ z
r
H 01C C C 1739
H Q 10C C 1748
( a x p p - o f t.p r o j
A C lO c t1 7 3 9 . i n f o *
Cold source sample
E
A 0 l O c c l 7 0 i - w ^ 6 x -n f r.p ro } A 0 1 0 c tl7 2 9 . f i x - i n f
H O lO c t1 7 0 0
H 0 l0 c tl7 0 9
A O lG c t 1 7 0 1 . i n f f o *
Opea loop sample
e
A 0 1 G c t l 7 2 0 - —(f lx - n f r p r o ) —
A 0 l0 c tl7 2 9 .f ix - in f
H 0 1 0 C C 1 7 1 9 -----------H 0 1O C C 1728 ------------
zr
zr
—1 A 0 l Q c t l 7 0 l . f i x * " C n o n n .p ro )— — A Q 1 0 c t l 7 Q l . f ix .n o m r - « * { i n n i p n ^ * ‘A 0 1 0 < :t 1 7 0 1 . f i x , n o r m , c r i a r -
__________________________
A 0 lO c tl7 2 0 . f i
x
__________________________
^
*
^
—
AO l O c t 1 7 2 0 . f i x . n o rm -* * ( ttin L p n ^ » » A0 I Q c t 1 7 2 0 . f i x . n o r a . t f i a ~
A 0 1 O C C 1 7 2 0 .l n f o "
Figure 3.3. Programs and filenames used in ESTAR G -m atrix calibration
47
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Table 3.2. ESTA R d a ta file type code letters
letter code
A
B
C
G
H
M
P
T
file type
Antenna d a ta
Bulk d ata file
Cold internal calibration source (reversed LNA) d a ta
GPS navigation d ata
Hot (noise diode) internal calibration source d a ta
Matched (50 ohm ) load internal calibration d a ta
PA-100 ARINC interface navigation d a ta
Therm istor d a ta
Before any d ata can be processed, the data contained in th e B-file m ust be split.
These files are a consequence of th e way the HP d ata com puters buffer d ata. In the
past, m ultiple buffers were kept in m em ory until the end of th e d a ta line, when they
were w ritten to disk as separate A-type, T-type, or navigation files. T his had two
prim ary lim itations. First, the am ount of memory in th e com puter placed an upper
lim it on the size of a d ata line th a t could be flown. Second, and m ost serious, if
com puter problems occurred during the d ata line, all d a ta from th a t line was lost.
To circum vent these problems, th e ESTAR data collection program was re-w ritten
to continuously dum p the d ata off to disk, rather than storing it in memory. Tests
showed th at th e com puter overhead involved in this process did not im pact the
ESTAR d a ta stream . Furtherm ore, th e m axim um data-line size is now lim ited only
by the size of the hard drive, which is sufficient for several days w orth of data.
Since the HP system only allows one file to be open a t any tim e, th e A, T, G, and
P d ata stream s were merged into a single file, which is referred to as a B-file to
avoid confusion. Before any processing can begin, this B-file m ust be split into its
constituent p arts. This task is perform ed by the IDL program p a r s e J B _ f ile .p r o .
Dr. John Galloway from UMass has worked with Perl scripts th a t will perform a
sim ilar function and write the d a ta to NetCD F form at files. W hile this approach is
48
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
not currently im plem ented in th e d a ta processing techniques used in this docum ent,
it is a m uch m ore efficient approach, and results in a fax more portable file form at.
Given th e historical problems w ith coordinating d a ta file formats with th e sponsor,
this approach is attractiv e for future processing as the self-describing n atu re of
N etCD F files would elim inate these problems altogether. It would be w orth the
tim e and effort involved to add this functionality to the data-processing program s.
T he first step in processing th e G -m atrix shown in figure 3.3 is the IDL program
n f r - f i x . p r o , which corrects th e Venus-switching transients as described in more
detail in section 3.3.3 below. T his generates two files. T he first is AOlOct 1729 . f i x ,
which is sim ply th e sam e d ata as in A 010ctl729 but w ith the Venus sw itching tran ­
sients fixed. T h e second file is A 010ctl729 . f i x - i n f o, which stores the param eters
used in fixing th e transients so th a t they may be used by a later program to correct
the N FR d a ta in other files.
The next processing step is perform ed by the IDL program n o rm .p ro which
takes the hot calibration source d a ta files taken im m ediately before and after this
file, tim e-interpolates values between them , and uses these interpolated values to
normalize th e system responses. T he idea here is th a t the hot calibration source
is therm ally stable, both by the n atu re of its circuitry and because it is located in
th e calibration box, which has th e best therm al regulation of any portion of the
ESTAR in stru m en t. By having th e receiver chains look at a known stab le source,
any gain variations m ust be due to therm al variations in the receiver chain, hence
norm alizing to these values gives a result th a t is less sensitive to gain variations.
T he resulting file-name, A 0 1 D c tl7 2 9 .fix . norm, denotes th at A 0 1 0 c tl7 2 9 .fix was
th e input file th a t has been norm alized.
In the n ext step, the file is processed by the IDL program t r i m . p r o which is
used to trim off any undesired d a ta from an early sta rt or a late stop. This is usually
m inim al for G -m a trix files. However, from a lake calibration in flight th ere m ay be
49
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
a considerable am ount of lead-in so that the calibration data is not missed while the
system is running thro u g h its internal calibrations. The output file from this step
has th e extension . t r i m , as in AOlOct 1729 .f ix .n o r m .tr im .
Before the G -m a trix can be calculated, it is necessary to run a rotating noise
sam ple through a sim ilar set of operations. In fact, the norm alization and trim ­
m ing steps are identical except that the corrections derived from the program
n f r - f i x . p r o m ust now be applied to the N FR data in this file so th a t the two can
be directly com pared. This function is performed by the IDL program f i x - n f r .p ro ,
which reads the p aram eters stored in the file AOlOct 1729.f i x - i n f o by the program
n f r- fix .p ro .
W hen both the closed loop file and the noise file have been prepared, they are
com bined by the IDL program g m at.p ro . This does the necessary interpolation to
find antenna pointing angle from time of rotation, subtracts the background noise,
an d then saves th e result in a data file, which is then read by further processing
steps for G -m atrix d ata.
Finally, the IDL program c o m p -n fr.p ro tests the reconstruction of the Venus
sw itching transients by com paring the ‘fixed’ version to the open loop, cold source,
an d reverse direction sets.
Note th at any d a ta file used in ESTAR d a ta processing must pass through at least
th e first two steps of th e above procedure. T h e program f i x - n f r . p ro is necessary
to get th e N FR d a ta in th e same format as it is in the G -m atrix d a ta stored above,
an d the program n o rm .p ro is necessary to normalize out therm al gain drifts. The
program t r i m .p r o is not normally needed, b ut may be used where convenient.
This entire process has been simplified by th e use of Perl scripts. For exam ple,
th ere is one script th a t will run norm .pro on every A-file in a specified directory
corresponding to a p articu lar day of data or a G -m atrix data set. A sim ilar script
will run parse_B_f i l e . p ro on every B-file in a specified directory.
50
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
3.3.3
N F R Correction
T he program n f r - f i x . p r o corrects the overshoot transients that occur when
the Venus switch changes state during the G -m atrix m easurem ent. This section
explains th a t process.
Figure 3.2 shows th at the set begins with the antenna facing away from th e
source and observing a constant background value. As the antenna rotates tow ard
the source, the response slowly increases. The dashed line in figure 3.2 roughly
corresponds to the reference tem perature. Since the source is so bright, this level is
quickly reached. As the response passes this level, th e N FR goes into the positive
feedback condition, which is responsible for the curved peak above the reference
line. As the N FR re-acquires lock, the signal begins to track the response curve
again. Note th a t at this point, th e Venus switch has changed state, and the N FR
is now adding injected noise to th e reference arm of the radiom eter, with th e net
result th a t increasing signal levels lower the response. This accounts for th e ‘flip’
in the m iddle portion of figure 3.2. As the antenna continues rotating tow ards the
source, th e response increases. T he dip in the m iddle of the response is due to
m utual coupling effects in the antenna, and matches those previously observed. As
the an ten n a continues to rotate past the source, the response returns upwards the
reference line. As it passes the reference line, we again see an overshoot transient,
the Venus switch toggles state, and the signal re-locks. Since the Venus switch has
changed state again, the right portion of the plot shows a decreasing signal. The
signal again drops to the background level as the antenna rotates away from the
source.
Clearly two main conditions in the NFR data m ust be addressed. T he first is
the overshoot transients, and the second is the polarity flip when the Venus sw itch
changes state. At first thought, th e correction to the Venus switch state would seem
as sim ple as reflecting the Venus-on portion of the graph about the x-axis. However,
51
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
this causes an apparent m is-alignm ent between the Venus-off and Venus-on portions
of th e graph, as if a vertical shearing had occurred. T his same effect would occur
if there were a small bias level to the entire graph, which means the Venus-on d a ta
actually needs to be flipped around some non-zero level3. T he problem now becomes
how to determ ine this bias level so th at the Venus-on and Venus-off portions of th e
curve will be aligned after the correction.
Interestingly enough, this bias level may be determ ined by th e process used to
correct th e overshoot transients, which is based on the assum ption th at the portions
where the overshoot occurs may be replaced by a sm ooth linear section. T he slope
of this section is found by m easuring the slopes of th e sections im m ediately left
and right of the transient and taking the average of the two. Next, an intercept
value is chosen for this line so th at transitions into and out of the linear region are
continuous.
This intercept value relates to the bias level. It is clarified by considering how th e
program finds the value. It first measures th e slope on either side of the transient.
T he w idth of the transient region is known, as well as the slope of the line th a t
will be used to fit across the region. This yields a height th a t will be occupied by
this linear fit. The program then calculates the am ount of vertical shift th a t m ust
be applied before the Venus-on portion is flipped about the x-axis, such th a t th e
vertical gap between the N FR traces to the left and right of the transient equal th e
height of the line fitted across the transient. This am ount of vertical shift is th e
required bias level. Since two transients m ust be corrected, th e value used is actually
the average of the two shift values, so there m ay be small ‘bends’ in the curves a t
th e edges, but in the actual d a ta these bends were too small to cause any suspicion
3A slightly more correct way of stating this is that the N FR reference level does correspond to
zero on the A /D scale, but due to A /D biases, this level has been shifted away from zero. If the
resultant curve is then flipped around zero rather than this bias level, the vertical shearing noted
above will occur.
52
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
in the technique. N ote th a t all the values used in this correction axe derived directly
from th e data; at no tim e is an arb itrary d a ta adjustm ent used.
T he first step is to isolate the regions corrupted by th e overshoot.
T he ap­
proxim ate location m ay be found by observing the uncorrected N FR plot, sim ilar
to figure 3.2 and looking for the characteristic quadratic shaped peaks near the
reference line. Once th e approxim ate location is found, it is helpful to zoom in on
this area of the plot and look for the change in slope th a t occurs as the N F R goes
from tracking the input signal to an out-of-lock condition. Using this m ethod, it
is easy to refine th e region down to th e individual 1/4 second samples where the
N F R goes in and out of lock. Finding these borders for bo th th e transients is all
th e m anual intervention this program needs. Once these regions have been isolated,
all th e other steps are performed autom atically by the program .
ESTAR-Bh Null F eedback R adiom eter R esponse, bias c o rre c te d
- 2 .0 *
iq
‘
0
500
1000
1500
2000
ESTAR d a t a in d e s
Figure 3.4. ESTA R N FR G -m atrix calibration response w ith bias correction
53
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
ESTAR—Bh Null Feedback R adiom eter R esponse, venus m ode c o rre c te d
<•
'c
3
o
0
500
1000
1500
2000
ESTAR d o t e in d ex
Figure 3.5. ESTAR N FR G -m atrix calibration response with Venus-switch mode
correction
ESTAR-0h Null Feedback R adiom eter R esponse, first transition c o rre c te d
2 . 0 * 10 *
m
c
3
<3
<
5 -0 * 10’
0
500
1000
1500
2000
ESTAR d a t a in d e*
Figure 3.6. ESTAR N F R G -m atrix calibration response with first switching tran­
sient corrected
54
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
ESTAR-Bh Null F eedback R adiom eter R esponse, both transitions co rrected
2 .5 « 104
3c
\<
C
1
0
500
1000
1
’
500
2000
ESTAR d o t s in d ex
Figure 3.7. ESTAR N FR G -m atrix calibration response with both switching
transients corrected
This process is shown in figures 3.4-3.7. Figure 3.4 shows the N FR trace with
th e bias correction applied. Com pare this to figure 3.2, which shows a sm all vertical
shift. In figure 3.5, the m iddle portion where the Venus switch is on has been flipped
ab o u t the new (bias corrected) reference line. The vertical hatched lines m ark the
m anually found edges of the transition regions. In figure 3.6 the first transient has
been corrected by a linear fit. Note the smooth appearance without any noticeable
discontinuities. In figure 3.7 the second transient has also been corrected.
This sequence shows a further benefit of the recent use of a m axim al nonsatu ratin g signal level for the G -m atrix calibration. Using such a high signal level
m eans th at the first transient occurs sooner, and the second later, shifting them away
from the main peak into a lower level portion of the antenna response. Combined
w ith the smaller size of the transients resulting from the increased signal level, this
m eans th a t a far sm aller percentage of the total beam energy is affected by the
55
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
tran sien ts and the resulting corrections.
Furtherm ore, the affected regions have
been shifted to a portion of the antenna response th a t is less im p o rtan t to overall
image form ation.
N ote th a t since the N FR has been shifted by this bias level, it is necessary
to apply this sam e shift to all NFR d ata th a t will be used in conjunction with
this G -m a trix to form images. As a result, th is information is saved to the file
A 0 1 0 c tl7 2 9 .f ix - in f o . T he IDL program f i x - n f r . p r o reads th is file and applies
this correction to the N FR data. This program also corrects for Venus-switch state
and for open-loop mode of operation for the N FR , but outside of th e G -m atrix
m easurem ent, these modes are not normally used. This whole process has been
sim plified by the Perl script f i x - a l l . p i which will run the f i x - n f r . p r o program
on all A-files in a specified directory, which again usually corresponds to either an
entire d a y ’s w orth of d ata or a complete G -m atrix m easurem ent set.
3.3.4
Review of G -M atrix D ata
Figures 3.8-3.9 show the effects of applying th e steps listed in sections 3.3.2-3.3.3.
These plots show the ESTAR basis functions in order of increasing frequency, with
the in-phase (I channel) plots on the left, and th e quadrature (Q -channel) plots on
the right. Note th a t all curves start at zero, increase to m axim um am plitude in
the m iddle, and decay back to zero, with an envelope function corresponding to the
p attern of th e individual antenna elements. As frequency increases, a larger num ber
of peaks is noticed, as expected.
Also of interest is the inverted sense of the N F R plot in figure 3.8a. T he corrected
N FR tra c e in figure 3.7 has a positive sense, but as part of the corrections mentioned
in section 3.3.3, this trace is normalized by th e internal hot calibration source,
which is a negative value. This results in an inverted sense for th e N F R row in the
G -m atrix . T he calibrations mentioned in sections 3.5 and 3.6 will take this inverted
sense into account.
56
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
fcSTA R-8* C U c t n a rgw Q
a)
\
L5TJW £ h G -M o tm row 2
tSTAH Bh G kJotna row '
b)
c)
1
x•
f
X
?
1
t
2
<00
0
<00
■oo
■00
0
tS lA B - 6 h G -M o tn a row *
tSIAH -Oh C U a tm row J
e)
d)
5
IX
1
?
j
2
<00
a
0
<00
<00
tSTAW S h S - U o tn a row 6
tSTA H-Qh C -U o tn * row ts
g)
0
*
1X
2
rX
1
2
2
<00
0
<00
90
90
0
90
<00
Figure 3.8. ESTAR G -m atrix basis functions, a) N FR , b) A/2 I, c) A/2 Q, d) 2A/2
I, e) 2A/2 Q, f) 3A/2 I, g) 3A/2 Q.
57
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
L S U R -B h C-Motnm row 1
a)
b)
?
V
tX
4
?
i
a
*
<00
o
•00
30
Q
•OO
fcSM R-Sh C - U ot't* row t o
c
d)
X
I
x
?
1
i
too
0
30
•00
•00
0
t S r A R - S h C - O o tf iB r o w
e
•00
12
0
5
iX
«
a
*
•oo
0
•00
0
<00
•oo
3
• 00
0
30
•00
g)
30
•00
Figure 3.9. ESTA R G -m atrix basis functions, continued, a) 4A/2 I, b) 4A/2 Q, c)
5A/2 I, d) 5A/2 Q, e) 6A/2 I, f) 6A/2 Q, g) 7A/2 I, h) 7A/2 Q.
58
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
The ESTA R array has redundancies since all antenna pair correlations are m ea­
sured, and th e antenna configuration is not optim ally thinned. This results in two
correlators m easuring each of the A/2, 3A/2, and 6A/2 spacings.
In the current
im plem entation, one of these two redundant channels is selected for use in th e
G -m atrix for each of the three spacings. If an instrum ent problem occurs in any of
these th ree channels, the redundant channel can be selected and the new resultant
G -m atrix used for image formation. In th e future, it m ay be worthwhile to use
all these redundant channels to improve system noise levels. This averaging m ust
be done by com puting a spatial average of m ultiple images formed using different
redundant channels. An alternative m ethod is to use a G -m atrix th at contains all
redundant rows, in which case the averaging will be perform ed by the Ieast-squares
operation used to form G -1 .
Table 3.3 shows the actual correlator outputs th a t were selected in forming th e G m atrix. T h e complex correlator outputs are split up into in-phase (I) and quadrature
(Q) com ponents, and axe listed as separate rows in the G -m atrix . The spacings run
up to 7A/2, which is the w idth of the ESTAR antenna array. T he channel num bers
listed are th e actual d ata channel numbers coming from th e ESTAR data acquisition
system.
The first row in table 3.3 has the channel spacing listed as OA/2 since this channel
is a self correlation used as p art of the NFR. While the N F R uses correlator num ber
10, the o u tp u t of this correlator is used as an error signal to drive th e NFR feedback
loop. T he actual o u tp u t of the NFR is derived from the level stored in the integrator
th at drives th e noise injection circuitry. Unlike the other d a ta channels, this channel
does not derive its o utput from a correlator, so the correlator num ber is listed as
N /A . Finally, when the N FR data is m easured, it is stored on data channel 32.
However, when th e N FR correction and norm alization pre-processing steps described
in section 3.3.3 axe applied, the new result is stored in channel 31, a previously
59
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
T able 3.3. G -m atrix rows, spacings, correlators, and d a ta channels
G -m atrix row
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A/2 spacing
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
correlator num ber
N /A
41
4Q
81
8Q
51
5Q
121
12Q
91
9Q
21
2Q
31
3Q
ESTA R channel num ber
31
7
8
15
16
9
10
23
24
17
18
3
4
5
6
unused channel, so as not to overw rite the raw d ata in channel 32, which is used as
part of th e N FR calibration steps discussed in section 3.5. Since channel 31 contains
the m ore fully corrected data, it is listed as the N FR channel in table 3.3.
Finally, note th a t only fifteen I and Q channel pairs are stored in the G -m atrix ,
covering only th e positive spacings.
In practice, the h erm itian sym m etry of th e
G -m atrix
g(~n,0) = g'(n,9)
(3.9)
is used to expand th e G -m atrix to 15 complex rows or 30 I,Q channels. Note th a t th e
NFR (zero frequency) channel is a real quantity and this has a zero Q channel. T his
sym m etry is necessary for proper image form ation, but since th e d a ta is redundant,
only th e non-negative frequency com ponents need to be stored.
In additio n to its im portance in the calibration of ESTA R, the m easurem ent
of the G -m a trix also provides a thorough engineering shakedow n, because these
60
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
m easurem ents scrutinize every ESTAR d ata channel in a predictable environm ent.
W hile tests outside the antenna range are easier to perform , they cannot usually
account for all external effects. For exam ple, sky calibrations always raise practical
questions about whether or not buildings, trees, ground, or outside transm itters are
affecting th e results. Black body calibrations minimize th e effects of these external
sources, b u t the outputs on m any d ata channels consist of a small bias value th a t
is often difficult to distinguish from a zero signal.
T he n atu re of the G -m atrix
m easurem ent yields a distinct full-scale signal in each d a ta channel th at can be
com pared to a large body of historical d ata sets to detect discrepancies th a t m ay
be present. Thus, this calibration catches many potential problem s before ESTAR
is used in flight.
3.3.5
Impulse Response Plots
A nother useful side product of th e G -m atrix m easurem ent is the determ ination
of th e ESTAR impulse responses.
I = G - l G,
(3.10)
where I is a m by m square m atrix representing the synthesized impulse response
of ESTAR. m is the number of angles measured in th e G -m atrix.
N ote th a t if G were a square m atrix, a true inverse could be found
G “ l = G _l
(3.11)
i = G ~ l G = G - l G = I,
(3.12)
and
where I is an m by m identity m atrix. However, since G is not a square m atrix, and
G -1 is formed by a least squares inversion, I ^ I. However, I does closely resemble
61
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
E S T A R -B h im p u ls e response, b e a m 7
0.08
0.06
0.04
0.02
0.00
-
0 .0 2
-1 0 0
-5 0
0
50
100
rotation angle
Figure 3.10. Impulse response of center beam
an identity m atrix, actually consisting of a series of sinc-like functions sim ilar to th e
one shown in figure 3.10.
Figure 3.11 shows the collection of ail 15 beams used in ESTAR image generation,
dem onstrating th at as the beams are synthesized farther from the bore-sight of
ESTAR, their am plitude drops, eventually tapering off to zero a t ±90 degrees. T he
m utual coupling effects between the ESTAR antennas cause a noticeable dip in
this am plitude envelope, sim ilar to th e dip observed in the N FR response shown in
figure 3.7. Also note th a t the width of th e beams spreads off axis.
T h e beams can be placed at any angle used in the G -m atrix m easurem ent.
Previous work used a 91-point G -m atrix , allowing a 2 degree resolution in beam
placem ent. The synthesized ESTAR beam s axe approxim ately 8 degrees wide, so
any sm all placement error th a t results in a position being coded into an adjacent
62
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission.
ESTAR —Bh im pulse responses
0.08
0.06
0.04
0.02
0.00
-
0.02
-1 0 0
-5 0
0
50
100
rotation angle
Figure 3.11. Impulse responses of all beams
angle bin results in a position error of approxim ately a quarter of a beam w idth. The
current im plem entation uses 401 angle points, resulting in 1/2 degree resolution over
a ±100 degree range. Any positional errors resulting in a single bin m isplacem ent
now only cause errors of 1/16 of a beam. The cost is additional storage requirem ents
and processing tim e, but the recent increases in M IRSL’s com puting power m ake
these tolerable. Note than since only 15 d a ta channels4 are used to form th e G m atrix, only 15 significant beams can be formed, so m ost of th e 401 angles are not
independent m easurem ents. This can also be seen by com paring th e 1/2 degree
angular resolution to the system resolution of 8 degrees corresponding to w idth of
47 unique spacings, plus 1 for the NFR channel, plus the 7 obtained using herm itian sym m etry
properties, for a total o f 15
63
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
th e synthesized beam s. Using a larger num ber of angles also makes for a sm oother,
less blocky-looking image.
From sam pling theory, we know th at for a regularly sam pled signal of finite
length, th e sam ples are represented as am p litu d e scaled sine or sin x /x -sh a p e d
pulses. At any sam ple point, only one sine pulse has a non-zero value. We can
use this property as an analogue for the placem ent of ESTAR beam s, since we
desire a regularly sam pled image and because th e synthesized beam s have a shape
th a t closely resem bles sine pulses. This m ay be im plem ented by placing the ES­
TA R beam s so th a t one peak occurs where th e other beam s have zero crossings.
Figure 3.11 was formed using this technique.
It gives th e beam locations listed
in table 3.4. Again, this shows the benefits of using a 401-point G -m atrix , which
gives finer resolution in the placem ent of beam s th an was possible for a 91-point
G -m atrix . W ith only 2 degrees of angle resolution, it would be difficult to align the
zero crossings of th e various synthesized beam s. These beam s determ ine where on
th e ground a p articu lar ESTAR beam is located later in th e image form ation.
3.4
Pre-Processing
T he steps outlined so far all apply to the G -m atrix generation.
However,the
steps taken in generating the G -m atrix m ust also be applied to all d ata collected by
ESTAR if th e G -m atrix is to be used in generating an image. As a result, th e first
pre-processing steps will closely m irror the steps taken in generating th e G -m atrix,
w ith only m inor variations.
T h e first pre-processing step is to split the B-file into its com ponent p arts (A,
G, P, and T files), using the program parse_B _f i l e . Once th e com ponent files have
been parsed out of th e B-files, the next pre-processing steps follow th e steps used
in section 3.3.3 to correct the N FR response in form ing th e G -m atrix. T his starts
w ith th e IDL program f i x - n f r . p r o , which is th e analogue of n f r - f i x . p r o which
corrects th e Venus switch overshoot transients. For norm al ESTAR d a ta , m ost of
64
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Table 3.4. Locations of synthesized beam peaks
beam
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
position
(degrees)
-66
-51.5
-41
-31.5
-23.5
-16
-8
1
9.5
16
23
33.5
42.5
52.5
66
this processing is not necessary, since the Venus switch stays off during normal data
taking. However, the N F R bias value th a t was determined in n f r - f i x .p r o and was
stored in the file A 010ctl729 . f i x - i n f o is used.
The program norm, p ro , and if necessary, t r i m , pro , process th e d a ta next. These
programs are identical to those used in the generation of the G -m atrix .
The Perl script p a r s e - d a y . p l performs all the pre-processing steps on a day’s
worth of data. In fact, during th e S G P ’97 experim ent, it was a com m on practice to
download the day ’s d a ta to a laptop im m ediately after finishing th e final blackbody
calibration of the day, and then run the p a L rs e -d a y .p l script.
Since the laptop
was battery powered, it could continue this processing while being transported back
to the hotel, so th at by the tim e th e d ata had been brought to th e organization
room and delivered to the sponsor, it had already been parsed and pre-processed.
A dditional functionality was added to this script to generate diagnostic plots of NFR
65
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
histories and a color image of the N FR d a ta for the entire day. It can also generate
a web page to make it easier to observe th e plots, all of which could be viewed when
th e d a ta tap e was delivered.
3.5
Null Feedback Radiom eter Calibration
T he calibration of the response of th e null feedback radiometer (NFR) is m ainly
used as a diagnostic, but it is also utilized in the ripple reduction m ethod described
in section 3.7. In addition, this step is a first look at the calibration data and filters
out som e of the potentially bad calibration sets before they are used in the image
calibration.
3.5.1
Basics of N FR Calibration
To calibrate ESTAR, two prim ary calibration scenes are used. The first is a
blackbody radiator, and the second is a water-scene calibration. The brightness
te m p eratu re of the blackbody radiator m ay be found with Tq = Tp, where Tb is the
brightness tem perature of the calibration scene, and Tp is the physical tem perature
of the calibration load.
The second scene used to calibrate ESTAR is a w ater scene. T he determ ination
of the apparent brightness tem perature of w ater is not quite as straightforw ard
as for th e blackbody, so a model m ust be used. Using the Klein-Swift model [4]
and assum ing fresh water, the dielectric constant is e = 77.802 —j’5.242. To find
th e resulting emissivity, assuming non-m agnetic m aterial, the following equation is
used [3]:
r _
cos 0i — \ J e — sin2
(3.13)
cos Q{ + y/e. — sin2 0,
resulting in a reflection coefficient of T = 0.635 and an emissivity of e = .365 a t an
incidence angle of 0t- = 0. Assuming the tem perature of the water used in calibrating
66
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
is Tp = 25° Celsius, th e apparent brightness tem perature is Tb = eTp = 108.8
Kelvin.
N ote th a t this is only th e contribution of the w ater itself. Recall from equation 1.2
th a t e(Q) = 1 — 17(0) or T(0) = 1 — e(0) = .635. This is a fairly large reflection
coefficient, so any down-welling radiation from the sky will be reflected by the w ater’s
surface contributing to the total. The contribution of th e sky is 5 Kelvin[3, Figure
5.9], which accounts for both galactic background and atm ospheric attenuation and
em ission. T h e to tal observed brightness tem perature is thus
Ta =
T ^ + TTsky
=
108.8 + 0.635(5)
=
112 K.
(3.14)
This 112 Kelvin is th e target tem perature used for th e w ater calibrations.
3.5.2
Regression for C alibration Coefficients
A fit between th e calibration d a ta and the target sets m ust be derived using th e
values determ ined from the target scenes. In th e past, 50 representative points have
been selected from each calibration file and a linear regression has been perform ed
on th em [6]. Some changes have been m ade to this technique in processing th e
S G P ’97 d ata. F irst, it was decided to use all available good d a ta points rather th a n
arb itrarily restrict them . Second, the m ethod of regression was changed slightly.
T h e equation used to fit th e raw values to the calibrated values is as follows:
67
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
N' = N - N biaa
=
Ti
Tx
(3.15)
N - 585.5
Nr
= — +b
m
(3.16)
'
=
T r-T i
.
Tr -
(
^
±
+ 6),
(3.17)
w here N ' is the bias-corrected N FR value in raw A /D units, N is th e uncorrected
N F R value in A /D u n its, and Afaas is the N FR bias value found in section 3.3.3
an d stored in the file A 0 1 0 ctl7 2 9 . f i x - i n f o. T\ corresponds to the calibrated NFR
injected noise tem p eratu re, 7 r to the measured N FR reference load tem perature,
an d T \ the calibrated N FR antenna brightness tem perature in Kelvin, m and 6
are th e desired calibration coefficients and are listed in table 3.5.
Note th a t m
has been inverted from th e usual sense used in a linear regression, giving a more
conveniently sized value for the result. The qu an tity 1/m is the one actually used in
th e regression, and it is inverted before it is displayed in the sum m ary in tab le 3.5.
Table 3.5. NFR calibration numbers
dates
13J un97-25J un97
26Jun97-30Jun97
01Jul97-04Jul97
07Jul97
08Jul97-14Jul97
08Jul97-18Jul97
Jun97
Jul97
SG P—Jun97-Jul97
m
-80.132
-79.032
-82.576
-68.135
-80.482
-80.342
-79.734
-79.228
-78.987
b
-18.520
-23.337
-14.921
-23.326
-19.292
-20.047
-20.179
-18.735
-19.645
Figure 3.12 illu strates the collection of all calibration points and th e lines formed
68
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
by the regressions. W hen taken as a whole, this structure appears as dense clouds of
points on either end of the calibration lines. However, a close-up of th e blackbody
calibrations in figure 3.13 shows th a t the individual calibration files do not always
form a linear trend and when they do, the slope occasionally diverges from th e
slope of the calibration lines observed in figure 3.12. Conversely, when considered
in com bination with a w ater calibration file, the proper slope is obtained w ithout
depending on th e slope of any individual file. In fact, the individual files can be
reduced to a single point at the centroid of the data in the file, w ith a weight equal to
th e num ber of points in the file. This greatly simplifies the bookkeeping associated
w ith the calibration files. The calibration line can then be found by fitting a line to
two endpoints, where each one is a weighted average of th e centroids of all desired
w ater or blackbody calibration points. When the steps listed below are used to
elim inate bad calibration sets, removing a bad set is as easy as zeroing the weight
of its centroid.
W hen using this m ethod, it is very im portant to have reliable calibration scenes
on either end of the operating range (approximately 150-270 K), or the results
are unpredictable. The blackbody calibration provides the upper end of the range
(approxim ately 290-310 K), while the water calibration brackets the lower end
(approxim ately 90-120 K). If the blackbody calibrations alone are used, the slope of
th e calibration line tends to diverge wildly, but the water calibrations at the lower
end of the operating range anchor the slope to reliable values.
Using as many different types of points spread as far as possible across th e
operating range of the instrum ent should improve the results of the regression. For
exam ple, if a third point were included within the operational area, it would be
possible to model a second order non-linear effect by fitting a quadratic function
to th e calibration curve. The internal ‘cold’ calibration source (reversed LNA [17])
m ay provide a suitable calibration point for this, if the am plitude of its response
69
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
injected Noise T em p eratu re vs. raw NFR
250
200
o»
4)
"O
0)
cl
E
4>
►
—
4)
(O
*o
z
50
-2 0 0 0 0
-1 5 0 0 0
-1 0 0 0 0
-5 0 0 0
U calib rated d e —b ia s e d NFR re s p o n s e (A /0 u nits)
Figure 3.12. Blackbody and lake calibration points
Injected Noise Tem perature vs. raw d e —biased NFR
■T
20
o ' 15
4)
■o
E 10
4)
O
z
0
-6 0 0 0
-5 0 0 0
-4 0 0 0
-3 0 0 0
-2 0 0 0
U calib rated d e - b ia s e d NFR re s p o n s e (A /D u n its)
Figure 3.13. Blackbody calibration points
70
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
-1 0 0 0
can be b e tte r m odeled. It m ay also be possible to use th e internal m atched-load
calibration source, but this is very close in am plitude to the external blackbody
load. F urtherm ore, the m atched calibration load serves as a convenient source of
noise th a t is uncorrelated between different receivers, and as a result may be b e tte r
exploited for a bias m easurem ent.
3.5.3
Selection of Calibration Files
T he n ex t step was to elim inate calibration files th a t detracted from the quality of
the calibration. F irst, the tim e histories of the calibration data were observed. Any
files w ith obvious large spikes or drifts were elim inated, though occasionally some
good-looking d a ta from these files were salvaged by trim m ing and used. In some of
the early m orning blackbody calibrations a large drift caused by warm ing-up of th e
instrum ent were noted and elim inated. A plot sim ilar to figure 3.12 was observed,
and any glaring outliers were elim inated.
It was th en possible to form rough calibration coefficients, and to use these to
plot th e tim e histories of the calibration files against th e trial calibration line. If the
calibration file deviated from the trial line by more than 3 Kelvin5 it was elim inated.
T he post-flight blackbody calibrations were abandoned in favor of the pre-flight
calibrations because they were m ade when the instrum ent was quite warm com pared
to th e pre-flight calibrations. T his is a com bination of m any factors, including the
higher am bient tem p eratu re during descent and approach to the airport, significantly
decreased airflow over the instrum ent while on the ground, heat radiated onto the
instrum ent from tarm ac th a t had been baiting in th e afternoon O klahom a sun,
and finally th e large am ounts of insulation required to m aintain tem perature in
the flight environm ent. Since th e pre-flight calibrations more closely approxim ated
5This error bound was selected since it corresponds to an error o f 1 part per thousand in soil
moisture, considered to be the acceptable error for the experiment.
71
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
th e therm al sta te of the instrum ent, they were used instead of th e post-flight
calibrations.
In some places it was noted th a t some o f the w ater calibrations read high
com pared to the expected values. Presum ably, this is due to leakage of land in
th e extrem es of the footprint into the image. If this difference was slight (only a few
Kelvin), and th e shape of the response looked sim ilar to other w ater calibrations
over the sam e lake, it was assum ed th at a sm all constant level of leakage into the
beam was present, and a correction was applied. If this correction needed to be more
th an 3-5 Kelvin, the file was assum ed to be corrupt and not used in th e calibration.
3.5.4
C om bination of N FR Calibration Num bers
The process of generating the calibration num bers ran in several steps. First,
calibration num bers were generated for each day.
However, w ater calibrations
were not taken every day, and w ithout a w ater calibration set it is not possible
to generate calibration num bers, so these were grouped with the nearest w ater
calibration.
Regions where the calibration num bers varied little were grouped,
providing calibrations th at were good for approxim ately a week.
T he resulting
groupings are shown in table 3.5. The labels for m and b correspond to th e quantities
in the calibration equation shown in equation 3.16.
As table 3.5 shows, the calibration numbers for Ju ly 7th differ a fair bit from the
others. As discussed in chapter 4, this is the result of a hardware m alfunction. At
th e bottom of th e table are listed sum m ary values for th e first and second halves of
the experim ent, as well as the entirety of the experim ent. Note th a t th ere is little
variation in th e calibration values over this range.
3.6
Image Calibration
Thus far, we have dealt with measuring the G -m atrix or impulse response of the
instrum ent, pre-processing d ata, and finding a calibration for the N F R to generate
72
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
diagnostic data. However, th e great value of ESTAR is in generating images, and
these m ust be calibrated as well.
3.6.1
Basic Image Reconstruction Equation
ESTAR image reconstruction uses the G -m atrix as an approxim ation to th e
system response. As a result, we can write the operation of taking ESTAR d a ta as
Kneas = G 7 /imeas,
(3.18)
where T[<meas is the brightness tem perature vector representing the scene, and Vmeas
is the m easured visibility vector. Note th at T[<meas cannot be measured directly6,
and th a t \/meas is the direct o u tp u t of ESTAR. Since the N FR measures injected
noise tem p eratu re, an additional step is required later to find th e resulting antenna
brightness tem perature, so the notation T/imeas is used where th e subscript I denotes
th a t this q u an tity is a an injected noise measure.
Equation 3.18 can be inverted as follows:
T/,meas
=
G _1 V'meas
(3.19)
=
G - l(G7V,meas),
(3.20)
where
G T 1 = G r (G G r )-1
(3.21)
is a least squares inverse of G [5]. Since G is not a square m atrix, this is not a
direct inversion but rather an approxim ation, and th e no tatio n G ~ l denotes this
6It can be measured directly for the zero frequency term, which is in fact the NFR output, but
for non-zero frequency terms the inversion process outlined here needs to be followed
73
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
approxim ation, in contrast to th e exact quantity G 1. N ote th a t if G -1 were a
direct inverse, G -1 G = I and equation 3.20 would reduce to
Tl, mens =
=
G ' 1(G T /tmeaa) = IT />meas
77,mcas.
(3.22)
Finally th e reconstructed scene tem perature can be reconstructed using
Tscene
where
3.6.2
T
r
=
T
=
T r - G ~ l Vmeaa,
r
— 7 / ,meas
(3.23)
is th e N FR reference load tem perature.
Calibration Equation
T he equations is section 3.6.1 form the basis for im age inversion, but they do
not take into account any form of calibration. The calibration involves at least
two scenes w ith brightness tem perature distributions th a t can be modeled.
For
blackbody targets, this is simply th e physical tem perature of th e target. For w ater
calibrations, this can be found using the Klein-Swift m odel [4].
The m easurem ent of these scenes can be described by th e equation
Vmodei
~
CrTmodel — G T / ilnodeI
=
G ( 7 f t >tnodel — T a,model),
where Vmodei is the modelvisibility vector derived from th e
is the model scene brightness
(3-24)
calibration scene, T^modei
tem perature distribution, a n d Tfl>model is the N FR
reference tem perature at the tim e of the calibration.
Vmodei is the ideal response obtained by looking at th e calibration scene. In order
to calibrate the instrum ent, it is assumed that what the in stru m en t really measures
74
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
is a version of V^,otiej modified by a scalar gain constant and a bias in each term , as
follows:
l^meaa — d^rnodel "1" l^bias-
(3.25)
Kneas is the measured visibility vector including the scale a bias effects. The cali­
b ratio n constants are th e scalar gain c, and a vector of bias values Vbias- Expanding
term s in equation 3.25 results in
I'meas =
3.6.3
cG
(T
r
—T a ,model) + Hrias-
(3.26)
Regression For C alibration Coefficients
Since th e calibration model in equation 3.25 is a linear fit, th e calibration coef­
ficients may be found by a simple linear regression. Note th a t Vmodei is a calculated
quantity, but it may be easily found from equation 3.24 as a function of T^.modei»
th e calculated model scene brightness tem perature, and T r , th e measured N FR
reference tem perature.
T he regression can be performed using a slightly modified version of the regres­
sion equations from Griffis [6], which are included below for reference.
u =
p =
u
=
P =
Sx =
J^K.m odel
t
(3.27)
Sy =
^K m eas
(3.28)
-z ^ ]
E
—^ ]
E
N •u - (sx, S X) = N ■u~sT
xsx
N •p - <
s„Sy) = N P ~ S Tx Sy
(I'i’.model) ^t,model)
K,model K,model
K,meas^«.model
(l^’.measj 1 model)
•
75
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
(3.29)
(3.30)
(3.31)
(3.32)
These can be easily solved for c and Vbiag.
Note th at in the equations for
calibrated image reconstruction given in section 3.6.4, it is more convenient to deal
with th e 1/c, the inverse of th e scale factor, rather th an c, so that is listed as well.
3.6.4
C alibrated Image R econstruction
T he quantities derived above can be used to reconstruct a calibrated image.
R e-arranging equation 3.25 allows us to solve for a reconstructed visibility vector,
Vscene 3-S follows:
K eene =
^ (K n e a , ~
H ia s )-
(3 .3 5 )
This visibility vector m ay be used to find th e corresponding reconstructed tem per­
atu re vector, T/,scene using th e G -m atrix inverse, G -1 .
T[,scen e
=
Gr
V scene
=
~ G ~ l (V^neas “ Vhiaa).
(3.36)
Again, like other ESTAR m easurem ents, this is an injected noise m easurem ent,
so one fu rth er step is necessary to reconstruct the scene brightness tem perature
distribution, T^scene, using th e N FR reference load tem perature,
T
a , scene
=
T
=
Tr
r
Tr
— 7 / iScene
c
G - 1 ( K n Cas — V b ia s).
(3 .3 7 )
Note th a t this equation consists of the calibration coefficients - c and Vbias, the
G -m atrix inverse - G - 1 , the quantities m easured by th e instrum ent and results in the desired o u tp u t - Ta,scene76
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
T
r
and Vmeas,
3.6.5
Image Re-sam pling
Even though the ESTAR instrum ent only synthesizes 15 beam s, some benefits
accrue from using more th an 15 points during the image generation. Initially, in the
proposal for dissertation, it was suggested th a t using only th e 15 points generated
by ESTAR could improve th e side lobe levels and result in lower com putational
requirem ents to form images. This, however, has been found to not be the case.
The problem of associating an azim uth angle with a corresponding beam position
crops up in several spots in the ESTAR processing. It is involved in the angle binning
used to to form the G -m atrix basis, and in geolocation to place th e m easurem ents
on ground coordinates. W hile using fewer beams requires fewer com putations, it
also increases th e error in beam placement, either due to random noise or motion of
the aircraft platform . Since MIRSL’s com puting power has increased, the am ount
of processing required was deemed to be a secondary consideration to the beam
placement accuracy.
Previous im plem entations of ESTAR used a 91-point G -m atrix, resulting in angle
bins 2 degrees wide covering from —90 to +90 degrees. In the proposed system , these
91 points would have been replaced by 15, resulting in angle bins approxim ately 8
degrees in size. Any error resulting from quantizing down to th e larger bins would
generate four tim es the am ount of placement error. In the current im plem entation,
401 points are utilized covering a swath from —100 to +100 degrees w ith a bin size
of 0.5 degrees. Most of these 401 points are not significant d ata points, however the
smaller bin sizes result in easier location of d a ta points with respect to beams, and
may be easily averaged down to the 15 significant data points. T h e extension to a
200-degree sw ath from a 180-degree swath catches some of the energy at the most
extrem e edges of the tails of the antenna response. However, since th e level of energy
involved in this region is so low compared to the peak levels, th e improvement is
only slight.
77
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
T he ESTAR images axe also re-sampled in other ways.
All ESTAR data is
collected at a rate of 4 samples per second. However, at the flight speeds and alti­
tudes utilized during the SG P’97 experim ent, it takes approxim ately 25-30 seconds
for the aircraft to travel a distance equal to th e size of the an te n n a footprint. To
reduce some of this volume, ESTAR pixels are averaged down to one second samples,
resulting in a four-fold improvement in processing tim e and storage requirements.
More points could be averaged giving even g reater improvements, b u t it was decided
th a t this was an adequate compromise between fine spatial resolution and storage
requirem ents, which again are not serious w ith the available com puting power.
T he final note on image re-sampling is th a t some of the ESTA R beams are
discarded. Initially, the two outerm ost beams were discarded because of the large
am ount of off-axis beam spread noticed in figure 3.11. This produced am effective
sw ath w idth of approximately ±55°. On forming some images using these beams, it
was noticed th at th e remaining two outer beam s were often noticeably brighter than
th e other beams. This may be due to the larger am ount of atm ospheric emissions
picked up near the horizon as the antenna views a larger volume of sky. A second
sim ilar effect is th a t near-grazing beams observe a large area on the ground and
become more susceptible to terrestrial emissions. To elim inate these effects, the
next two outerm ost beams were not used in the image form ing, resulting in am
effective swath of approximately ±45° degrees covered by 11 beam s approxim ately
8 degrees wide.
3.7
Image Ripple Reduction
T he images produced by the steps described above contain a fair am ount of
ripple due to windowing effects. To get any meaningful images out of this data,
the ripple had to be reduced. This section explains the steps taken to do this on
ESTAR d a ta used in the SG P’97, which are based on a m ethod used in processing
78
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
ESTA R d a ta at NASA G oddard Space Flight C enter, but have been extended to
su p p o rt am plitude-dependent corrections.
T raditional ways of windowing seem to have little effect on ESTAR images. Since
ESTA R looks at relatively flat scenes, th e visibility vectors produced are m ainly
com posed of a large spike at zero frequency, w ith very little energy at th e higher
frequencies. Since traditional signal-processing windowing functions reduce side-lobe
levels by tapering off higher frequencies w here these images have little energy, the
effects are minimal.
To correct this image ripple by a new approach, we devised a m ath em atical
representation of it. We denote the reconstructed scene brightness tem p e ra tu re as
Tmeas(0). N ext, we consider this to be com posed of an ideal tem p e ra tu re vector,
Tcorr(8), which has been distorted by a linear, angle-dependent operator. Two of
these are used. The first, R (6), accounts for th e angle-dependent effect of th e image
ripple, and th e second, A{0) accounts for the effect of incidence angle on th e d ata,
represented m athem atically as
T in e a s {B,t)
= [R {0 ,t)A {6 ,t)\T con{0,t).
(3.38)
T h e m ain assum ption in this ripple reduction m ethod is th a t any single fan
beam im age is composed of a flat scene w ith random detail variations about this
m ean level. We further assum e th at these random variations are zero m ean7, and
if an appropriately large num ber of scenes are averaged, we will obtain a flat image
around this average level expressed as
< W M ) > = (Tavg(OTriPPle(0, 0> = Tavg(f).
(3.39)
If we solve equation 3.38 for the ripple and incidence angle term s
(3.40)
rOr have a mean equal to the average scene level
79
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
then invert this an d average over all scenes, we obtain
where Tavg(£) is th e average tem perature across the scene.
Note th a t this is es-
sentially equal to th e N FR output8, and accordingly the N F R d a ta is used as this
term .
Equation 3.41 is an expression for our m ain ripple-correction term , and may be
used to find a reduced ripple image using
W f l.i)
=
([« (» ,
o r 1) r TO„ ( « .i )
(3.42)
GSFC currently uses a technique sim ilar to this one, using only two correction
curves — one for w ater, and one for land. To process the S G P ’97 d ata, this technique
wets varied slightly, employing an entire range of curves based on the am plitude
of Tavg(i).
This has th e advantage of also correcting any am plitude dependent
effects, but at th e expense of having fewer points to average in the form ation of each
correction curve. Since the SG P’97 flights were fairly long an d covered a large area,
th ere were sufficient points in each am plitude level bin to m aintain the assum ption
th a t the random d etail variations of the scene average to zero. Ju st as a precaution,
the program was w ritten to print a warning message if any am plitude bin were used
th a t had an insufficient num ber of sam ple points. In almost all cases these warnings
were only generated a t th e high end of th e operating range, where radio frequency
interference (R F I) was already corrupting the data, or at th e very low end of the
operating range in transitions from land to w ater during lake calibrations, which are
not utilized as p a rt of th e calibration data.
8T he NFR output is actually an average temperature weighted by the antenna pattern of the
center antenna, but this is sufficient for these purposes
80
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
T his raises the question of how m any bins axe sufficient for this technique. Too
few bins do not adequately correct for any am plitude dependent effects in the
corrections curves. Too m any bins reduces the num ber of available points to average,
an d increases processing and storage requirem ents.
The processing and storage
requirem ents were unim portant because MIRSL has adequate com puting power. A
b in size of 5 Kelvin was used, chosen to be approxim ately twice the operational
requirem ent of 3 Kelvin accuracy to achieve 1 part-per-thousand accuracy in soil
m oisture m easurement.
F urther research may point out th e num ber of levels needed to correct for am pli­
tude-dependent effects in th e data. W hile variations were observed between curves
w ithin the operating range, these were fairly small and possibly due to noise varia­
tions. If this is true, th an a far sm aller num ber of am plitude bins may be adequate.
However, an interesting phenom enon was noted at th e upper end of the operating
range. As the response increased to levels where R FI was beginning to satu ra te
th e instrum ent, the correction curves flattened out, and then eventually retu rn ed to
th e ir norm al variation, but with inverted phase. A likely explanation is the presence
o f a large RFI source at th e edge of the image producing sidelobes within th e image.
W hen these axe superim posed on the correction curves they reduce the characteristic
variation of these curves, and eventually invert th e phase of this variation as the
R F I am plitude increases. This provides promise for a future technique to ex tract
this level and use it as a threshold for an autom atic RFI-removal filter, sim plifying
a process th a t has been a largely m anual to date. To improve the estim ate of this
threshold level, the am plitude bin size m ust be reduced, as th e error in determ ining
this threshold level will be half the bin size9.
An im portant lesson learned the hard way while im plem enting this technique, is
9T his is similar to estim ating rounding error in m athem atics, or quantization error in digital
system s
81
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
th a t th e correction curves m ust be calculated according to equation 3.41 and not
according to th e formula
< [ * • . 1M («, o r 1) =
= ^ L (IN C O R R E C T ).
(3.43)
E quation 3.43 incorrectly averages th e tem perature vectors by am plitude bin, then
scales th e average scene to TaVg(0-
Averaging the scene first has the effect of
quantizing the scenes to the am plitude bin size, arbitrarily adding an error of half
the bin size. The correct m ethod finds th e scaled correction curve according to
equation 3.41, then averages these normalized curves by bin. Since the curve is
norm alized before averaging, no quantization noise is added to the image.
3.8
Geo-location
O nce the images have been generated, th e next question is how to register th e
image pixels into ground coordinates th a t can be used to plot the data onto a m ap
or com pare it with other d ata sets. A wealth of inform ation is available for this
process, including the flight m anagem ent unit (FMU) and inertial reference unit
(IRU ) on the airplane, as well as th e GPS integrated into ESTAR provide m any
positional and orientation param eters.
O f these, th e GPS provides the easiest interface, producing d a ta with the sm allest
tim e lag and the best understood error. It is therefore used to find the latitude,
longitude, and altitu d e of the airplane, thus fixing the antenna in three dimensions.
O nce th e center of the antenna is identified, the centers of th e synthesized beam s
m ust be located. The first step is to calculate the cross-track distance between
the center of the beam and the point directly below the aircraft. The geom etry
of this is shown in figure 3.14, where the vertical direction in the plot corresponds
to altitu d e, and the direction of travel of the plane is into th e page. This shows a
typical synthesized antenna beam at angle 0* off th e vertical intersecting the ground
82
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
with a cross-track distance of /*. Note the ground is not a t zero a ltitu d e , but rather
at hg, an d th e airplane is at altitu d e ha. The resulting cross tra ck distance is
l'k = (ha - ha) tan(flfc),
(3-44)
which m ay be corrected for a ltitu d e variations with
=
4
•
<3 ' 4 5 >
Note th a t since degrees of latitu d e do not equal degrees of lon g itu d e10, this cross
track distance m ust be broken up into equivalent values in the la titu d e and longitude
directions as follows
lx,k =
Ik
(3.46)
=
'»•* -
<3-47>
The latitu d e of the S G P ’97 experim ent area is around 35-37 degrees north, so the
value of 0.8 is used.
The next step in locating th e synthesized beams is to handle th e rotation of
the airplane as th e heading angle changes. T he geom etry of th is step is shown in
figure 3.15, which is a top view with north up, where the cross-track beam distance
Ik is shown ro tated by th e heading angle <j>. The corresponding x a n d y components
of this ro tatio n are found by
Xk =
lr,k cos(-<f>) = lX'k cos(<t>)
(3.48)
Vk =
ly,k sin(-<f>) = - l y<ksin(<t>),
(3.49)
and the resulting positions by
Px,k =
Ion + lx<k cos(<£)
(3.50)
Py,k =
lat —ly<k sin(<£),
(3.51)
10Except at the equator
83
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Ha
Ha-Hg
Hg
Lie
Ho
Figure 3.14. Downward geom etry of geo-location problem
where lat and Ion are the GPS latitude and longitude, respectively, and denote
the center of th e rotation, assum ing negligible pitch and roll angles. T he subscript
k denotes th a t this applies for the fcth beam. Note th a t th e GPS latitu d e and
longitude is only accurate to within approxim ately 300 ft. However, this is not a
problem since when flying at an altitude of 25000 ft. an ESTAR synthesized an te n n a
beam is approxim ately 3500 ft. by 4400 ft. or larger.y
Xk
Lk
Yk
Figure 3.15. R otational geom etry of geo-location problem
84
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Note th a t the distance used in equation 3.44 scales linearly in altitu d e and tan 0,
so a com putational simplification can be made. Assuming a stan d ard altitu d e of 7.62
km (25000 ft), and a standard beam angle of 45° (ta n # = 1), we find a normalized
beam distance of 0.0686 degrees of latitu d e from th e point directly below the aircraft.
If the locations of the synthesized beams are stored as tan 0k rath er th an 0k, their
locations m ay be easily found by scaling this constant by the ratio of th e operating
altitude to the standard altitude, and the ratio of tan(0jt)/ tan 45 = tan(fljt). Using
the beam locations found from the G -m atrix and listed in table 3.4, we can form a
vector of these standard beam locations
B = HU U = [(*. - *o) tan(fl4) l L . .
(3.52)
which can be used in com bination w ith the altitu d e and latitude corrections to find
the beam positions as
Px =
Ion + cos(<£) | j' ^
„
Py =
,
la t
B
(3.53)
sin(<£) f h a — h a\ „
JTTTlr
7t ) B cos(lat) \ h a — h0J
3.54
These geo-location steps do not correct for drift angle variations, b ut this may
be easily added as
Adrift
=
Ion + cos{<ph + <f>d)
/U tt
=
lat +
cos(lat)
\ h a — hQJ
B
(3.55)
B,
(3.56)
where 4>h is the heading angle, and 4>d is the drift angle11. This drift angle correction
is not currently im plem ented in the images displayed in chapter 4. These images also
assume th a t roll and pitch angles are negligible. Corrections for these m ay be found
using E uler angles, as discussed in m any mechanics texts, such as G oldstein [18]
1'T his correctly follows the sense used on the airplane where a left facing drift angle is negative
85
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
C
h a p t e r
R esu lts F r o m T
4.1
he
4
S G P ’97 E x p e r i m e n t
Description of SG P’97 Experim ent
T h e Southern G reat Plains (S G P ’97) experim ent, a large, m ulti-organization
hydrology experim ent, took place in Oklahom a in June and July, 1997. It involved
several aircraft, m any teams of people on the ground, a variety of microwave, laser,
and satellite instrum ents, and extensive ground sampling. The experim ental area
of approxim ately 10,000 square kilom eters over central Oklahoma was also chosen
because it has extensive ground m easurem ent facilities. These include the USDA
A gricultural Research Service (ARS) facility in the Little W ashita w atershed near
Chickasha, the ARS facility near El Reno, and the ARM CART C entral Facility near
Lam ont [19]. In addition, an extensive network of ground m easurem ent stations,
including the Mesonet, cover th e state of Oklahom a, while the M icronet has even
denser coverage of the Little W ashita W atershed.
T his experim ent area is quite large compared to past experim ents concentrating
on th e L ittle W ashita W atershed, an area of approxim ately 600 square kilom eters, an
order of m agnitude smaller than th e SG P’97 area [19]. In addition, past experim ents
were briefer, spanning only a few days or a couple of weeks, rath er th an an entire
m onth.
T he S G P ’97 experim ent area is outlined in figure 4.1. The borders of Oklahom a
are included for scale. The main experim ent area is maxked by the laxge rhomboid
in the central region. This axea o f approxim ately 40 km by 280 km was covered by
four parallel flight lines extending the length of the region and overlapping slightly.
T he axea is inclined so it covers b o th the Little W ashita in the south and th e ARM
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
CART C entral Facility in the north. T he four le tte r names on the m ap are the
locations an d identifiers of th e M esonet stations. N ineteen of these stations were
m easured w ith over-flights during th e course of the m onth-long experim ent, eleven of
th em being over-flown on a regular basis. Section 4.4 compares the d a ta from these
stations to d a ta obtained from ESTA R. In addition to th e m ain experim ent area,
th e trapezoidal area to the north is th e CASES stu d y area, covering approxim ately
2000 square kilometers in Kansas.
It was over-flown with two overlapping flight
lines on 3 occasions during the experim ent.
S G P'97 C overage Area
7 280 km
ts
4Qkro
Figure 4.1. S G P ’97 experim ent area.
Figure 4.2 shows a Landsat th em atic m apper im age1. Taken on July 25, 1997,
it roughly corresponds to the m ain SG P experim ent area. To quote th e Landsat
T hem atic M apper Data User’s G uide [20]:
lrThis image was obtained from the S G P ’97 web-site at
h t t p : / / h y d r o l a b . a rsu sd a . g o v /s g p 9 7 /tm /tm . htm l
87
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Typically, TM Bands 4, 3, and 2 can be com bined to m ake false-color
com posite images where band 4 represents the red, band 3 represents the
green, and band 2 represents the blue portions of th e electrom agnetic
spectrum . This band combination makes vegetation appeax as shades of
red, brighter reds indicating more vigorously growing vegetation. Soils
w ith no or sparse vegetation range from w hite (sands) to greens or browns
depending on m oisture and organic m atter content. W ater bodies will
appeax blue. Deep, clear water appears dark blue to black in color, while
sedim ent-laden or shallow waters appeax lighter in color. Urban areas
appeax blue-gray in color. Clouds and snow appeax bright white. Clouds
an d snow are usually distinguishable from each o th er by th e shadows
associated w ith clouds.
As this description makes clear, the SGP axea covers m any kinds of vegetation.
In addition, large lakes, visible as dark patches, are scattered across the image.
O klahom a City appears as the bluish-gray axea approxim ately 1/3 of the way up
and to th e right of center of the image, with a couple of dark lakes located to the
northw est of th e city.
Table 4.1 shows th e operational availability of ESTA R during th e experiment.
It collected d a ta on 23 of 30 allocated experim ent days, acquiring full data sets on
16 days, and nearly com plete data sets on three additional days. T he 4 remaining
days consisted of partial d ata sets shortened either by inclem ent flying conditions
on 2 days, experim ental requirements of other instrum ents on the airplane on 1 day,
and an in-flight instrum ent malfunction th a t term inated operations on another day.
G round conditions varied considerably. Initially, it was fairly wet, and through­
out the experim ent a variety of precipitation events and dry-down periods occurred.
Table 4.2 records th e m ost notable rainfalls.
88
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Figure 4.2. Landsat them atic m apper image for SG P’97 region.
89
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Table 4.1. Sum m ary of ESTA R operational readiness during S G P ’97.
16 full
d a ta sets
30 experim ent days
23 d ata days
7 partial d a ta sets
1 day
3 mostly 2 days
1 day
full sets w eather LASE malfunction
7 down days
1 day
6 days
w eather
repairs
( 2 x 3 days)
Table 4.2. S G P ’97 rainfall events.
date
Ju n e 18
Ju n e 23
Ju n e 24
Ju n e 26
Ju n e 28
Ju n e 29
Ju n e 30
July 4
Ju ly 10
Ju ly 11
Ju ly 16
Ju ly 17
rainfall
trace north
light rain south and central
light to m oderate rain central and east
m oderate to heavy rain north
m oderate to heavy rain central, scattered light rain
light rain south and east
heavy rain north, m oderate rain east of south
light rain central, trace south
trace south
heavy south, m oderate central and n o rth
trace south
heavy north
90
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
4.2
G eneral Results
Section 4.3 includes a detailed chronological account of the brightness tem pera­
tu re images o btained during th e S G P ’97 experim ent, while this section notes general
results th a t apply to all the d ata.
Radio-frequency interference (R F I), observed as colored bands in th e image, was
consistently observed in the El Reno area, located north of th e southern end of
the experim ent area, near 35.5 degrees north latitude. Closer inspection revealed
th a t this R F I is actually two sm aller regions - a larger one on th e west end of the
experim ent area near El Reno, and a sm aller one on the east near O klahom a City.
T he O klahom a C ity RFI is likely caused by a RADAR or beacon a t th e Oklahom a
C ity airp o rt, which caused large R FI when it was over-flown. T h e cause of the
El Reno R F I is not quite as clear, but either an em itter from Vance AFB or an
atm ospheric sounder used by th e ARM program axe possible sources.
Both are
consistent w ith th e RFI over El Reno on the usual flight line orientation.
Extensive ground sampling occurred near El Reno. Uncorrupted d a ta from this
area was needed. To achieve this, we used ESTAR’s real (not synthesized) antenna
p attern , which is a fan-beam oriented perpendicular to the direction of travel of the
airplane. T his is far more sensitive to R FI from the side than it is to R FI from the
front or rear. W hen the airplane flew past the El Reno area on a north-south leg,
these R F I sources would leak in to the side of the antenna p attern and corrupt the
data. We therefore decided to fly th e lines from east to west, hoping th a t positioning
th e front or rear of the antenna tow ards the R FI sources would m inim ize or elim inate
th e effects. Tw o east-west lines flown in this experim ent axea from Ju n e 25 until
th e end of th e experim ent produced uncorrupted data.
In past ESTA R field cam paigns, the flight lines were short so th e internal cali­
bration cycle of th e instrum ent could be deferred until the end of th e flight line with
no significant im pact. However, for S G P ’97 the flight lines were significantly longer
91
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
(30-40 m inutes). A full cycle of all th ree internal calibration loads on ESTAR takes
45 seconds, thus in-flight calibration would cause an unacceptably large gap within
the im age. To obviate this, only th e attenuated noise diode or “hot” calibration
load was sam pled. This takes only 15 seconds, approxim ately the tim e it takes
for ESTA R to traverse an antenna footprint on the ground. This was deemed an
acceptable loss of d ata. These calibrations were taken every five m inutes in flight. In
the im ages, th e produce the occasional bar-shaped dropouts oriented perpendicular
to the flight path. Since the flight lines overlap, in the middle two flight lines these
bar-shaped dropouts are partially filled in by overlap from adjoining flight lines,
resulting in a dot-shaped dropout. T his effect also reduces th e size of the dropouts
on the o u te r two flight lines, but since they are only partially filled in by th e overlap
from th e one adjoining flight line, they still retain their bar shape.
A nother general result was th at th e some cooler regions appear as small dots,
ranging from blue to black. They occur in the southwest and northern portions of
the experim ent region, as well as northw est of Oklahoma City. During the course of
the experim ent, these dark spots were noted consistently in the same places. Those
ju st northw est of O klahom a City proved interesting, as the author had spotted lakes
in this region of th e city. The Landsat image shown in figure 4.2 also has black spots
in these locations, confirming th at these axe lakes. The fact th a t ESTAR observed
these lakes in consistent locations, even though their size approxim ately equalled an
ESTAR resolution pixel, served as a coarse confirmation of th e correct operation of
the in stru m en t, as well as the geo-location of the data.
Some striping rem ains in the images. One cause is imperfections in th e image
ripple reduction used. This may be improved by using fewer ripple averaging bins,
or averaging bins across several days to increase the number of scenes used for the
ripple correction. T he issue of w hether these bins axe am plitude dependent and
which size bin is optim al has yet to be determ ined. If larger bins can be used, the
92
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
num ber of scenes averaged will increase, and this should improve the image rippling.
A nother possible cause of rippling is that the cross-track images axe averaged down
to 11 independent beams from a full swath of 90 or even 400 beams, which are not
independent. While this removes the smooth transitions from data point to d ata
point present in past images, and makes tem perature changes look more like jum ps
or stripes, it ensures th a t all pixels in the image are independent m easurem ents.
This ripple may be improved by using a convolution mask to average pixels, an
operation which is common when gridding d ata to a geo-referenced array. In this
processing we choose to keep raw data values th a t are not smeared, and represent
independent d ata points, ra th er than to optimize the smoothness of the image. This
approach also made it easier to catch processing errors during the developm ent of
th e d a ta analysis program m ing code.
4.3
Brightness Tem perature Images
T he brightness tem perature images produced by ESTAR are the most interesting
d a ta product generated by the instrument. This section describes them , pointing
out their significant features by following the tim e series obtained during the S G P ’97
experim ent. The plots are arranged in a continuous group beginning with figure 4.3
to facilitate comparison as a continuous tim e series.
Section 4.4 com pares the
d a ta obtained in these plots with ground measurements obtained by the O klahom a
M esonet. Since that section considers the detailed comparisons between th e two,
this section focuses prim arily on general trends and features, rather than accurate
extraction of d ata points.
4.3.1
June 18-21
A fair am ount of rain fell in the week preceding the experim ent, so conditions
were wet on June 18. In addition, in the 24 hours preceding the Bight on June
18, there was trace rainfall in the central and north regions. These conditions are
93
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
reflected in figure 4.3, where th e north is depicted in dark blues, corresponding to wet
conditions w ith brightness tem peratures ranging between 180 and 210 K. Additional
wet areas occur the central (190-210 K) and southern (200-220 K) regions, separated
by m oderately dry areas (220-250 K). This day serves as a baseline to com pare the
day-to-day changes to th e observed rainfall. N ote th a t the RFI in th e El Reno and
O klahom a city areas is present in this image, as it is before the additional El Reno
flight lines were flown. T h e dark purple or black areas correspond to lakes in the
southw est portion of the im age and just northw est of Oklahoma City.
T here was no m easurable rainfall between Ju n e 18 and June 19, and figure 4.4
reflects this in general drying/w arm ing of the im age. The wet areas in th e southern
and central regions have begun to dry to cyan or lighter blue (200-230 K). In
addition, while the north rem ains primarily wet (180-210 K), th e drier areas in
the n orth have expanded and warmed up (210-240 K) compared to th e previous
day. RFI is still present in th e El Reno and O klahom a City areas, and the contrast
provided by drier conditions m akes the lakes in the southwest and O klahom a City
areas more noticeable.
Once again, no m easurable rain fell between June 19 and June 20. Figure 4.5
shows th e general drying over m ost of the image. T he southern and central regions
have drier tem peratures (210-240 K), and while th e north is still wet, th e drier
areas have again expanded and warmed (210-240K). The dividing dry areas appear
drier, w ith some areas beginning to show in th e oranges and reds (240-275 K). RFI
is still present in the El Reno area, however it is not noticeable near Oklahom a
City, supporting the theory presented in section 4.2 th a t two separate em itters were
responsible. Lakes are still noticeable in the south, although the resolution of these
lakes appears degraded by leakage of the w arm er surroundings into th e pixels. The
two lakes northwest of O klahom a city are easily visible in these drier conditions.
T he flights on June 21 were term inated after only half of the first flight because
94
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
airplane vibrations had loosened the thermal control card in th e ESTAR an ten n a
box, thus losing th e voltage reference for all tem p eratu re m easurem ents w ithin th e
ESTAR shell, and shutting down the data collection program . W hile it was possible
to m odify th e program to operate without the therm istor reference voltage, th e
therm al control and measurement would have been inaccurate, resulting errors, o r at
worst, dam age to the instrum ent electronics. D ata collected prior to the m alfunction
were not affected.
No m easurable rain fell between June 20 and Ju n e 21, so conditions were d rier
across th e area, as shown in figure 4.6. The north and central regions show a fair
am ount of drying (210-250 K). T he RFI in the El Reno area is clearly noticeable
on this day, as well as a well-defined lake near the southern edge of the m easured
experim ental area.
T h e instrum ent was down for repairs between Ju n e 22 and June 24.
4.3.2
Ju n e 2 5-July 3
T here was no measurable rainfall in the region on Ju n e 22, however June 23 and
24 saw light to m oderate rain over much of the experim ental region, as depicted
in figures 4.7-4.9. There was no additional rainfall on Ju n e 25. The brightness
tem p eratu re image obtained for June 25 in figure 4.10 shows a fair am ount of drying
and w arm ing, w ith most brightness tem peratures in the 230-260 K range, while
w etter areas in th e north and central regions have tem peratures of 190-230 K. T his
was th e first day th a t the El Reno lines were flown, and they have removed th e
observed R F I in th e El Reno area, although small am ounts rem ain near O klahom a
City, and further sources were observed north and south of the lines. As in th e o th e r
d ay ’s d ata, lakes are observed in th e southwest and near O klahom a City.
T he M esonet recorded heavy rainfall in the n orth between June 25 and Ju n e
26, as reflected in much cooler brightness tem peratures, as figure 4.11 shows. Tem­
peratu res in the north dropped to th e 180-220 K range.
T he south appeaxs to
95
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
have dried, with tem peratures around 230-270 K. W hile th e recorded rainfall is
shown n o rth of the central region, this area, especially around El Reno, appears to
have cooled significantly, w ith tem peratures in the 190-240 K range. Much of the
rainfall in Oklahoma during this tim e of year occurs during thunderstorm s, often
very localized, so a lot of rain can fall in one area while none drops at a M esonet site
only a few miles away. This could explain the decrease in brightness tem p eratu re
in th e central region, despite lack of indicated rainfall. M oderate rainfall to the
west of th e experim ent axea m ay have traversed the central region, cooling it down,
w ithout affecting the El Reno or Minco Mesonet stations. Little RFI shows on this
day since the El Reno lines were flown. T he lakes in the Oklahom a C ity region are
discernible, b u t the lakes in th e southwest axe not, probably due to leakage from the
noticeably warm er surrounding axea washing out any distinct signature from them ,
although slightly cooler (230-250 K as opposed to 250-270 K) areas may be noticed
in th e correct places.
Ju n e 26-27 had no m easurable rain across most the region. Some further cooling
is shown in the brightness tem perature image in figure 4.12, likely due to rain th a t
fell during th e previous day’s flight.The north region is quite wet, with brightness
tem p eratu res in the 175-210 K range. The central and southern regions also cooled
slightly, w ith 190-240 K tem peratures in the central axea, and 240-260 K tem p era­
tures in th e south. RFI was m ostly absent, except in a sm all axea south of O klahom a
C ity th a t was not corrected by th e El Reno flight lines. T h e lakes in th e southw est
and O klahom a City areas axe easily discernible.
B rightness tem perature d a ta were not collected on Ju n e 28, but the M esonet
rainfall d a ta is shown in figure 4.13. M oderate to heavy rain fell in the central
portion o f th e experim ent axea, w ith additional light rain in the north and south.
T he cum ulative June 28-29 rainfall shows only light rain in the south and east.
T he brightness tem perature image is shown in figure 4.14. The north has w arm ed
96
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
slightly, with tem peratures in the 180-240 K range. The El Reno axea cooled to
175-210K, as expected following the heavy rainfall on June 27-28. The rem aining
regions dried slightly, w ith tem peratures of 230-260 K in the south, and 220-250
K between El Reno and the north. Some RFI is noticeable near O klahom a City,
ju st south of the El Reno lines, and the usual lakes are discernible in th e southwest
and Oklahom a City areas. Bad weather term inated the easternm ost line early so a
portion in the northeast corner of the experiment region is missing.
Ju n e 30 had very heavy rain in the north (approxim ately 4 inches), with dry
conditions over the rem ainder of the experiment axea. Figure 4.15 depicts the effects.
T he north region is very wet, with indicated tem peratures of 170-210 K. T he El
Reno region dried slightly to 190-230 K, while remaining areas dried to 230-260 K.
Only a slight am ount of RFI is noticeable south of Oklahoma City, and the lakes
are discernible as usual in the southwest and Oklahoma City axeas.
July 1 had no m easurable rainfall. The brightness tem perature image in fig­
ure 4.16 shows only sm all changes, with moderate warming in th e north and El Reno
regions.
O ther areas are essentially unchanged, with perhaps m oderate cooling,
possibly because the Ju n e 30 flight began at 11:18 am, while the July 1 flight
began at 08:52 am. Since the diurnal tem perature variations are not corrected in
this d ata, the earlier flight would yield cooler ground tem peratures and brightness
tem peratures. This highlights the importance of consistent operations. RFI was
light on this day, with sm all affected axeas neax Oklahom a City, and farther south.
T he lakes are discernible.
July 2 continued the drying trend with no rainfall, as shown in figure 4.17.
Tem peratures in the n orth range from 190-220 K, and tem peratures in the central
and southern portion range from 230-275 K. T he El Reno region is still slightly
w etter th an the surrounding axeas, with tem peratures from 200-240 K. A small bit
of R F I is visible south of Oklahoma City, and the lakes are visible as usual.
97
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Ju ly 3 further extends the drying trend, with no m easurable rainfall. As fig­
ure 4.18 shows, all regions show warming, w ith tem peratures of 190-230 K in th e
north, 200-240 K near El Reno, and 240-270 K across the rest of the image. Some
R FI is noticeable south of Oklahoma City. T he four lakes, while noticeable, axe not
nearly as d istinct due to leakage from the w arm er surrounding ground.
From Ju ly 4 to July 6 the instrum ent was down for repairs to the control lines
to th e calibration switch at the front of the N FR receiver chain.
4.3.3
Ju ly 7-10
M oderate rain fell across the central portion of the experim ent region on July 4,
but none was measured on July 5-7. Figure 4.22 is the image obtained on July 7.
C om pared to the other images, this image suffers from excessive streaks, noticeably
higher levels, and some saturation in parts. This data appears to be corrupted and
unusable. T he suspected cause was a continuation of the problem noted w ith th e
N FR receiver calibration switch on July 4-6. A fter the July 7 flights this switch
was replaced, and the problem went away.
T h e instrum ent flew again on July 8, and the resulting image is shown in
figure 4.23. No significant rainfall was recorded. For comparison, the best previous
image is th a t of July 3, shown in figure 4.18. Noticeable rainfall occurred on July
4. T h ere appears to have been considerable drying in the north, w ith tem peratures
now in th e 200-240 K range. The rem ainder of th e experim ent area seems to have
cooled to 220-250 K. Again there is some sm all R FI south of O klahom a City, and
the lakes are noticeable. The lakes in the southw est are especially noticeable, likely
due to th e m oist surrounding ground.
Ju ly 9 again saw no observed rainfall, and general drying across the region is
apparent in figure 4.24, with tem peratures fairly uniform in th e range of 220 to
260K across th e image. Some RFI is evident south of O klahom a City and El Reno,
and th e lakes are visible. There appears to be a slight warming as th e airplane moves
98
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
from west to east. This was initially thought to caused by instrum ent th erm al drift,
but this hypothesis has now been abandoned, as discussed in section 4.6.
July 10 again saw no m easurable rainfall, except for trace am ounts in th e south­
west. As figure 4.25 shows, this image shows little change from th e Ju ly 9 image,
indicating th a t this drying cycle has likely run its course. Again some slight warming
appears as the airplane progressed from west to east. M ost noticeable is th e rapid
warming, and eventual loss of d a ta in the region of th e El Reno flight lines. The
source was an antenna box heater supply wire th a t had worked loose and shorted to
a receiver ground plane, causing a drop in many system voltage supplies lasting for
approxim ately 10-15 minutes until the short circuit b u rn t out and norm al operation
returned. This was responsible for th e reddish areas observable in th e im age near
th e El Reno lines, as well as th e saturated data, which has been rem oved from the
image. This supply wire was replaced on July 10, and does not affect d a ta after
th a t date. Considerable RFI is noticeable in the corridor from O klahom a C ity to El
Reno. VVe could not correct this because the data from one of the El Reno lines were
corrupted. The lakes in the southw est axe noticeable, b ut those in th e O klahom a
C ity area were not observed due to th e instrum ent m alfunction. The d a ta from these
four days as well as possible instrum ent problems affecting them will be discussed
in further detail in section 4.6.
4.3.4
July 11-17
It rained significantly on Ju ly 11 with especially heavy rain in th e south. This
rainfall was associated with thunderstorm s passing through the area during the
flights on this day, resulting in m any truncated flight lines, as observed in th e image
in figure 4.26. Not surprisingly, this am ount of rainfall caused noticeable cooling in
th e image when compared to th e dry conditions of Ju ly 10. T em peratures across
th e image range from 180-240 K. T he lake signatures axe again present, although
99
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
not as noticeable on such a wet background. RFI was only present in two very small
areas ju st south of Oklahoma C ity and El Reno.
July 12 showed only a trace of rainfall west of the experim ent region, w ith general
drying in th e image in figure 4.27. W et areas axe noticeable in the north, betw een
Oklahom a City and El Reno, and west of the Chickasha watershed in th e south, w ith
tem peratures in the 190-240 K range. The remaining areas show some drying from
July 11, w ith tem peratures in th e 230-260 K range. T he small strips in th e east
are d ata from low-altitude legs flown while neax the lake used for water calibration.
The lakes in the Oklahoma City region axe clear, as well as the northernm ost of the
southwest lakes. The southernm ost lake is lost in the wet axea in the south.
July 13 had no recorded rainfall, with general drying across the im age shown
in figure 4.28.
The wet axeas in th e south and central regions have dried to
tem peratures of 225-250 K, while the one in the north still remains som ew hat m oist
with tem peratures of 190-230 K. T he remaining portion of the image has dried to
230-270 K. Once again, some additional low altitude d a ta have been plotted to th e
east of th e experim ent area. The lakes are clear, and R FI is essentially non-present.
July 14 continues the drying trend, with no m easurable rainfall. T he im age in
figure 4.29 shows slightly wet areas in the north as well as neax the southernm ost
lake, while th e rest of the experim ent axea is fairly dry with tem peratures around
230-275 K. T he lakes can be seen, along with some slight R F I ju st south of O klahom a
City and El Reno. In addition, some low altitude flight lines were flown across the
experim ent region in the south, over th e Chickasha watershed.
July 15 further extends this drying cycle, with only a trace rainfall northw est
of the experim ent axea. The image in figure 4.30 shows shortened lines to avoid
thunderstorm s th at passed through th e axea w ithout generating rain. T h e axea
appears dryer than the previous day, with tem peratures in the 240-275 K range.
The lakes in th e south axe visible, although the southernm ost lake is nearly lost in the
100
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
dry background. The El Reno lines were not flown, so there is a noticeable am ount
of RFI in th e central region, and the O klahom a City lakes were not m easured. An
additional series of low-altitude lines was flown over the Chickasha watershed.
July 16 recorded light rain scattered over the south. The im age in figure 4.31
shows some slightly noticeable cooling in this region. An additional low-altitude
flight line in the east is included. This line intersects one of the lakes northw est of
Oklahoma City, showing th at there are no altitude-dependent problem s w ith beam
placement in the image. The other lakes are easily noticeable and only a trace of
RFI is visible south of Oklahoma City.
July 17 was a day prim arily driven by the LASE instrum ent on board the P-3,
so the norm al flight path and calibration process were not followed. Nearly all of
the second m ost western flight line was flown repeatedly, for a to tal of nine times.
This line is shown in figure 4.32. Since the normal flight lines and calibrations were
not perform ed on this day, the data are not readily comparable to th e other days’
data; they are included here to show th e slight drying in the southw est region.
101
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
18Jun97
Figure 4.3. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for Ju n e 18, 1997.
Figure 4.4. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for Ju n e 19, 1997.
102
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Figure 4.5. M esonet rainfall distribution and ESTAR brightness tem perature image
for June 20, 1997.
21 Jun 97
Figure 4.6. M esonet rainfall distribution and ESTAR brightness tem perature image
for June 21, 1997.
103
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Figure 4.7. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for June 22, 1997.
2 B 0 a ^ M !5 0
23Jun97
i........
.
JI-
mjc
2 55 F
1100—
E
e
2501
8.
ffi
o
E
p
■CQ
150
<i8
t
2051
50
-9 LSQ
M 80
1801
.J4
.J 4 ..
Figure 4.8. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for June 23, 1997.
104
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
24Jun97
Figure 4.9. Mesonet rainfall distribution and ESTAR brightness tem perature image
for June 24, 1997.
Figure 4.10. Mesonet rainfall distribution and ESTAR brightness tem perature image
for June 25, 1997.
105
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
26Jun97
Figure 4.11. M esonet rainfall distribution and ESTAR brightness tem perature im age
for June 26, 1997.
Figure 4.12. M esonet rainfall distribution and ESTAR brightness tem p eratu re im age
for June 27, 1997.
106
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
2 8 Ju n 9 7
Figure 4.13. M esonet rainfall distribution and ESTAR brightness tem perature image
for Ju n e 28, 1997.
29Jun97
Figure 4.14. M esonet rainfall distribution and ESTAR brightness tem perature image
for Ju n e 29, 1997.
107
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
2 B 0 |^ ^ M 1 5 0
30Jun97
.J R ..
255f
100 -
8
,i\\V - 7
&
23 0 1
4
f t
•?
o
X3
c
15 0
&
8
20 5 1
-90JO
-9C 50
-97.30
•J 4 . .
1801
Figure 4.15. Mesonet rainfall distribution and ESTAR brightness tem perature image
for June 30, 1997.
280
150
97Q U 0-4707Q 1 «M e»
01 Jul97
J7.
255 F
| 100~
E
J6.
23 0 1
150
<I8
2051
97.50.___ 1 ........ r^e 30
-9*30
1801
-97.30
.34..
Figure 4.16. Mesonet rainfall distribution and ESTAR brightness tem perature image
for Ju ly 01, 1997.
108
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
02vJul97
Figure 4.17. Mesonet rainfall distribution and ESTAR brightness tem perature im age
for July 02, 1997.
0 3Jul97
>97.50
Figure 4.18. Mesonet rainfall distribution and ESTAR brightness tem perature image
for July 03, 1997.
109
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
04vlul97
Figure 4.19. M esonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 04, 1997.
2 8 0 ■ ■ i H 150
0 5 J u l9 7
•7070*—f7Q7QS x W o l
J7.
255F
1100
.
J6.
S 230|
iso 2051
-9 lsq
-9^30
18 0 1
;..« * -9 U 0 .
tMSQ
9 7 .5 0
.J 4 .,
Figure 4.20. M esonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 05, 1997.
110
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
0 6 J u l9 7
Figure 4.21. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 06, 1997.
0 7 J u l9 7
Figure 4.22. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 07, 1997.
Ill
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
08Jul97
Figure 4.23. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 08, 1997.
09Jul97
Figure 4.24. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 09, 1997.
112
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
10wiul97
Figure 4.25. Mesonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 10, 1997.
11 Jul97
Figure 4.26. M esonet rainfall distribution and ESTAR brightness tem p eratu re image
for July 11, 1997.
113
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
1 2 Ju l9 7
Figure 4.27. Mesonet rainfall d istribution and ESTAR brightness tem p eratu re image
for July 12, 1997.
13wiul97
Figure 4.28. Mesonet rainfall d istrib u tio n and ESTAR brightness tem perature image
for July 13, 1997.
114
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
14Jul97
Figure 4.29. Mesonet rainfall distribution and ESTAR brightness tem perature image
for Ju ly 14, 1997.
15Jul97
9 7 .5 0
Figure 4.30. Mesonet rainfall distribution and ESTA R brightness tem perature image
for July 15, 1997.
115
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
280
?
0
3
16Jul97
255
Q
S.
1
8 230
«
c
£
5*
ffl
•o
c
<I8
205
180
Figure 4.31. Mesonet rainfall distribution and ESTAR brightness tem perature image
for Ju ly 16, 1997.
1 7Jul97
Figure 4.32. Mesonet rainfall distribution and ESTAR brightness tem perature image
for Ju ly 17, 1997.
116
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
4.4
M esonet Rainfall Comparison
T he rainfall d a ta previously discussed were obtained from th e O klahom a Meso­
net meteorological stations. They autom atically take a variety of m easurem ents,
including tem p eratu re and wind speed, although rainfall is th e only quantity used
in this discussion. T he d a ta are recorded and available over th e Internet2. During
th e experim ent, 19 of these stations were over-flown, 11 of them regularly. T his
analysis focuses on these eleven stations.
T he Mesonet rainfall d a ta are available as accum ulated rainfall for a 15-minute
period. Since the flight schedule was daily, these d ata were totaled as accum ulated
rainfall for th e 24 hour period from noon on the day prior to th e flight to noon on
th e day of the flight. T he Mesonet rainfall d ata is indexed w ith G M T rath er th an
local tim e, and this analysis now properly takes this into account. These d a ta are
p lo tted on the left in the brightness tem perature plots included in section 4.3. These
are com pared to the ESTAR brightness tem perature d a ta by accepting any pixel
th a t falls w ithin a 0.5 nautical mile radius3 of a Mesonet statio n on a given day
and recording its value. T he average of all the values is th en com puted, and used
as th e brightness tem p eratu re datum for th at station on th a t day. These pixels are
ex tracted after the image inversion and ripple reduction steps, and any pixels th a t
have unreasonably high or low values axe discarded from th e average. Approxim ately
5-15 d a ta points being used to form each average.
T h e soil com positions as percentages of sand, silt, and clay at each Mesonet
statio n used in this com parison were obtained from Dr. T . J . Jackson. T he eleven
M esonet stations th a t were regularly over-flown may be broken down into one of
2 D ata were obtained from the Atmospheric Radiation M easurement (ARM ) Program sponsored
by the U.S. Departm ent of Energy, Office of Energy Research, Office of H ealth and Environmental
Research, Environm ental Sciences Division.
3T his is the smallest radius th at can be used while still allowing a m odest number of image
pixels to be averaged
117
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
th ree basic soil types — those composed prim arily of sand, silt, or approxim ately
equal proportions of both.
4.4.1
Sandy Soil
O nly th e A cm e Mesonet station, located in the southwest comer of th e experi­
m ent area, is located on predom inantly sandy soil. Figure 4.33 compares its mea­
sured rainfall w ith the m easured ESTAR brightness tem perature in the surrounding
region. T his indicates minor rainfall on June 23 and 25, and July 4 and 16, w ith a
significant rainfall in July 11. T he small rainfall events show small dips in brightness
te m p eratu re w ith gradual recoveries over the next few days. The rainfall event
on Ju ly 11 shows a larger drop (15 K) in brightness tem perature. These results
qualitatively seem good, although th e drops in brightness tem perature axe less than
m ight be expected.
Mesonet station ACME (RSC «.67: S6X sand. J2X silt. 12X clay) (3<,81.-98.01)
200
260
2*0
®
220
tsoL_
9706< 6
970623
970626
970703
Oar
970706
970 6 1 8
970623
970628
970703
970708
Day
970713
970718
Figure 4.33. Com parison of ESTAR brightness tem p eratu re and rainfall for M esonet
statio n ACM E
118
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
4.4.2
Sand and Silt Soils
Three of th e over-flown M esonet stations, Chickasha (C H IC ), Kingfisher (K IN G ),
and Ninnekah (NINN), are located on soil composed of approxim ately equal pro­
portions of sand and silt. T he Chickasha and Ninnekah stations are in the south of
th e experim ent area, and Kingfisher is ju st north of the central region.
T he Chickasha site received light rainfall, less than 10 m m , on three occasions as
shown in figure 4.34. Each tim e, the rainfall caused a m oderate drop in brightness
tem perature (15-30 K), and drying seemed to occur over a period of 2-6 days. T his
site shows good agreem ent between ESTAR data and the rainfall data.
Mesonet stotion CHIC (RSC 1.50: 30X sond. 50% silt. 20% cloy) (55.03,-97.9!)
280
260
a
970616
97062.3
970 6 2 8
970703
Day
970708
970713
970718
_
-
-
:
-
-
f
970618
W W
W W
„
970623
-
w
-X’S . It— 'W
970628
W
970703
w
y \
970708
:
970 7 1 3
97Q718
Figure 4.34. Com parison of ESTAR brightness tem perature and rainfall for Mesonet
station CHIC
T he Ninnekah site was m ore difficult to characterize.
It received only trace
am ounts of rainfall (less th an 4 m m ) on three occasions, each producing a negligible
change in brightness tem p eratu re. On July 11, the brightness tem perature dipped
119
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
significantly with no indicated rainfall; however, the nearby Chickasha station re­
ported a m oderate am ount of rainfall in this tim e period, which m ust have caused
these changes in brightness tem perature in the surrounding region, even though the
statio n itself did not receive any rain. This exemplifies past hypotheses concerning
the comparison of point measurements w ith area measurements.
O therw ise the
perform ance of the instrum ent appears fine in comparison with the d a ta from this
site.
M e s o n e t a t o t i o n NINN (R S C 2 .4 7 : 3 7 X s e n d . 4 5 X s ilt. 1 5 * c to y ) ( 3 4 . 9 7 . - 9 7 . 9 5 )
280
9
ii
200
(80
970703
Day
-
-
-
_
_
-
970703
Day
Figure 4.35. Comparison of ESTAR brightness tem perature and rainfall for Mesonet
statio n NINN
T he Kingfisher site had rainfall on five different occasions as shown in figure 4.36.
Ju n e 29, July 4, and July 11 recorded light rainfall of less than 5 m m w ith only
slight drops in brightness tem perature. M oderate rainfall of 15 m m occurred on
Ju n e 26-27 resulting in a 30-35 K drop in brightness tem perature, w ith drying
taking 6 days. A slight rainfall on June 23-24 did not cause a noticeable change
120
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
in brightness tem perature.
T h ere is good agreem ent between th e rainfall and
brightness tem p eratu re d ata for this site.
Mesonet station KING (35.68,-97.91)
280
260
a 2*0
9
1
200
9 70 6 1 8
970623
970628
970 7 0 3
970708
970713
970 7 1 8
_
-
-
-
_
-
C__ ____ HC__ XC__ w — * r
9706 1 8
970623
*
/
--*£----3K--
\
970628
970703
Dc*
970708
970713
97071 8
Figure 4.36. Com parison of ESTAR brightness tem perature and rainfall for M esonet
station KING
A g reater change in brightness tem p eratu re after a rainfall is observed for all
three of these sites as com pared to ACM E, the single sandy soil site. W ith th e
exception of th e rainfall sam pling problem m entioned for the NINN station, these
three statio n show a good agreem ent between rainfall and changes in brightness
tem perature.
4.4.3
Silt Soils
The rem aining seven Mesonet stations axe located on soil prim arily composed of
silt: A pache (APAC), Blackwell (BLA C), Breckenridge (BREC), El Reno (EL R E ),
M arshall (M A RS), Medford (M E D F), and Minco (MINC). These m ay be further
121
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
broken up into three groups — those in th e south (APAC and M IN C ), one in the
central region (EL R E), and those in the north (BLAC, BREC, M ED F, and MARS).
T he A pache Mesonet station received significant rainfall (55 m m ) on July 10-11
and sm all am ounts on four other occasions, w ith a m axim um of 15 m m of rain on
June 28, as shown in the comparison plot in figure 4.37.
In ail these cases the
brightness tem p eratu re drops, followed by a slow rise as the ground gradually dries
out. T he drying process seems to take a little longer than for the m ore sandy soils.
The largest rainfall causes the largest drop in brightness tem p eratu re (40 K) and
the sm aller rainfall am ounts cause smaller drops in brightness tem p eratu re (15-30
K), m atch in g expectations. The drop caused by the July 16 rainfall seem s a little
bit large for th e indicated am ount of rainfall, but not large enough to cause concern.
Mesonet s to tio n APAC (RSC t.6 2 : 21% se n d , 66% s ilt, ' I X clo y) ( 3 4 .9 1 ,-9 8 .2 9 )
2 00
200
970703
Ooy
00
E
6,
*e
6
20
9707 0 3
Oay
970700
970710
Figure 4.37. Com parison of ESTAR brightness tem p eratu re and rainfall for Mesonet
station APAC
The o th e r southern Mesonet station w ith silty soil, MINC, received 10-15 mm
122
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
of rainfall on th ree occasions, and light rainfall on one o th er occasion, as shown
in figure 4.38.
Again we observe th e expected response with dips in brightness
tem perature, and a gradual recovery over 4-5 days.
Mesonet stotion MINC (RSC I.Jfl: I8X sond, 69% silt. TJX cloy) (35-27.-97.96)
290
260
A
I
T 220
200
>60
970618
970623
970628
970703
970708
970 7 1 3
970718
Ocy
6E,
c
o
970623
970628
970703
970708
Figure 4.38. Com parison of ESTAR brightness tem perature and rainfall for Mesonet
station MINC
The only central Mesonet site with silty soil is at El Reno. As figure 4.39 show,
significant rainfall (60 mm) was recorded on June 29, w ith four smaller rainfall
events occurring on various days. Each results in the expected dip in brightness
tem perature, however the rate of drying seems to be faster. T he unique feature
of this site is th e consistently wet conditions over m ost of th e experim ent, with
brightness tem peratures typically axound 200-230 K. Since th e conditions are so
wet, it is likely th a t drying is negligible. After the heavy rainfall on June 29, the
brightness tem p eratu re increases on June 30, but then decreases on July 1-2, which
is a slightly odd. A trace of rainfall was recorded on Ju n e 30, so it is possible th a t
123
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
this is another case of rainfall occurring in the vicinity of the site and lowering the
measured brightness tem perature w ithout actually raining at the rain-gauge itself,
again raising th e issues of com paring point m easurem ents to area m easurem ents.
280C
Mesonet stotion £ifl£ (RSC 1.31:
sang, 69% silt.
\7X
MX
cloy) (35.55,-98.04)
260
x
a
T>
I
970 6 1 6
470623
970 6 2 8
970705
970708
970713
970710
Ooy
60
60
e 40
o
*<3
20
970616
970623
970628
970708
Figure 4.39. Comparison of ESTAR brightness tem perature and rainfall for Mesonet
station ELRE
T he rem aining four sites, BLAC, BREC, M EDF, and MARS, ail located in the
north, show sim ilar responses, as displayed in figures 4.40-4.43. They all experienced
m oderate to heavy rainfall, with the expected dip in brightness tem p eratu re and
gradual w arm ing as the ground dried. These stations range between wet and dry
conditions, showing a much richer variation than the other stations. T he unique
behavior here is th at the dips in brightness tem perature seem to be larger in
m agnitude th an those for sand or sand-silt soils, and the recovery tim e is longer.
This study only considers few soil textures, with silty textures being observed at
a m oderate num ber of sites. However, even this lim ited sampling shows reasonable
124
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Mesonet stotio n BLAC (RSC 1,20: 18% song. 67% silt, 15% cloy) ( 3 6 .7 5 ,- 9 7 .2 5 )
28 0
260
a
1T 220
970623
9707Q3
Oey
97Q718
80
E
E
1o «
o
a
20
970628
970708
970718
Oar
Figure 4.40. Com parison of ESTAR brightness tem perature and rainfall for Mesonet
station BLAC
Mesonet station BREC (RSC 1.20: IBS send, 67% silt. 15% cloy) (36.41,-97.69)
280
-G
— 2*0
a
o
e
7 M0
180
97Ui18
970623
970628
970703
970708
970713
970716
970708
970713
970718
Oar
80
60
T
£
io «
<2
970628
970703
Oar
Figure 4.41. Com parison of ESTAR brightness tem perature and rainfall for Mesonet
station BREC
125
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
M esonet statio n MARS (RSC 1.00: 20% san d . 60% silt, 20% cloy) (3 6 .1 2 .-9 7 .6 0 )
280
a
e
I
2 20
-
200
970628
970703
Of
970708
80
60
E
6,
1*0
O
*
3
20
970618
970708
970628
970718
Of
Figure 4.42. Comparison o f ESTAR brightness tem p eratu re and rainfall for M esonet
statio n MARS
Mesonet stotion MEOF (RSC 1.20: 18% acnd. 67% silt. 15% cloy) (36.79.-97.7S)
2 80
260
a
i
970618
970623
970628
970703
Ooy
970708
970713
970718
80
60
E
E
40
3
20
970628
Ooy
970708
970718
F igure 4.43. Comparison o f ESTAR brightness tem p eratu re and rainfall for M esonet
statio n M EDF
126
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
agreem ent between ESTAR brightness tem peratures and the am ount o f recorded
rainfall, with a few exceptions which are likely a result of only sampling th e rainfall
a t a small num ber o f points rather than as an area m easurement. Furtherm ore,
it is apparent th a t th e texture of the soil affects the m agnitude of th e change in
brightness tem p eratu re and the rate at which th e soil dries out. T he next section
exam ines soil tex tu re effects in more detail.
4.5
Analysis of Results
This section presents more quantitative comparisons, comparing th e d a ta ob­
tained to a model presented in the literature.
M attikalli et.
al. [22] used extensive ground sam pling in the L ittle W ashita
area in 1992 to derive a model of the change in the observed L-band brightness
tem p eratu re in the days following a rainfall versus a soil texture m etric known as
RSC (Ratio of Sand to Clay). Table 4.3 presents the num bers from this model.
Table 4.3. Relationships between RSC and mean tem poral changes of 7b- Taken
from M attikalli et. al. [22]
period of change, days
1
2
3
4
5
6
7
8
estim ation of RSC
1.3025 x 1041 • T ^ m
1.8563 x 1025 • T g 23 95
2.2083 x 1018 • T b 16 64
5.6516 x 1017 • T b 14 67
2.2211 x 1016-T b 1298
1.0450 x 1017 • Tg 12'51
1.0819 x 1018 • Tg 12'46
8.0543 x 102° •
13 46
r2
0.95
0.29
0.45
0.86
0.83
0.70
0.40
0.49
Figure 4.44 plots ESTAR brightness tem p eratu re against soil tex tu re (RSC),
w ith the M attikalli m odel overplotted as a dashed line. T he brightness tem p eratu re
extraction was perform ed using a 0.5 Nm. radius as in the previous section. T he
127
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
RSC values were calculated using th e soil textural com positions provided by Dr. T.
J. Jackson.
T h e first thing to note in figure 4.44 is th at th e brightness tem p eratu re change
predicted by th e model increases as tim e passes from th e rain, as would be expected
from drying. T he second thing to note is that as RSC increases, the predicted change
in brightness tem perature decreases, even if slightly. Increasing RSC corresponds to
a larger fraction of sand-size particles in the soil, and th e resulting decreased change
in brightness tem perature m irrors the observations m ade in th e previous section
about th e site with sandy textured soil showing less change after rainfall.
Table 4.4 shows a q u an titative analysis of the agreem ent between th e ESTAR
ex tracted brightness tem peratures and brightness tem peratures predicted from RSC
using th e M attikalli model. Standard errors are less th an 15 K, w ith 7-11 K typical.
W hile th e standard error is large, the table shows th a t th e d a ta from this experim ent
is com parable to data obtained in previous experim ents.
T he sim ilarity of the
stan d ard errors to the mean m odeled tem peratures causes th e high error percentages
noted in th e table.
Table 4.4. Comparison of ESTAR brightness tem peratures to M attikalli model.
day
1
2
3
4
5
6
7
8
num ber
of points
13
17
10
9
3
2
3
4
standard
error (K)
9.2
10.9
10.9
14.7
8.4
7.6
4.0
7.1
mean m odeled
7 b change (K)
7.9
11.2
12.2
15.6
16.9
21.0
27.7
42.0
percent
error
116.9
97.9
89.1
94.3
49.7
36.2
14.6
17.0
Several effects may contribute to the high stan d ard error values.
128
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
F irst, this
'b c n a n q e vs. RSC. * days
a)
c n an q e vs. RSC. 2 acys
C
;
;
i
*0 -
*o-
&
A
A
A
2 0 -
A
2
^
** A A
A ^
20 -
A
__ £ .......
*
-
A
A
*
a
A
i
2
4
A
*
0
2
RSC
C c nanqe vs. RSC. 4 aays
A\
" ’
bC
5
RSC
' t c n an q e vs. RSC. j acys
c)
A
4
bU
A
*0 -
4 0 a
A*
c
A
o
a>
A
2
A
20 -
2 0 - . . .
- v
a
_ . . .
A
-
a
r
A
2
f
J
A
0
»
*b
e)
.
A
.
4
2
RSC
A
RSC
c ^ cn q e vs. RSC. b aays
'6 cn an q e vs. RSC. 6 days
n
to
*o -
60
£.
‘
4Q -
c
A
«*
A*1
2 20-
20 - ' - -
A
*
0
i
2
J
4
0
*b
g)
c n an q e vs RSC.
T
2
4
6
RSC
rsc
/
aays
M
'b cnanqe vs. RSC. B days
Figure 4.44. Brightness tem perature change after rainfall versus RSC. a) one day
after, b) two days after, c) three days after, d) four days after, e) five days after, f)
six days after, g) seven days after, and h) eight days after rainfall.
129
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
m odel does not tak e into account the am ount of rain that fell. T h e M attikalli model
is based on d a ta th a t were gathered after a thorough wetting of th e soil, while the
ESTAR d ata were collected under varying soil wetness conditions, ranging from wet
to dry. In addition, the d a ta used in the M attikalli model covered a large variety of
soil textures, while the ESTAR data were from a fairly narrow range of soil texture,
w ith RSC values below 5, and clustered m ainly around 1. T h e M attikalli model
was m ade to be effective over a large range of soil textures, and is not necessarily
optim ized for th e soil textures covered in this experim ent.
Moreover, th e d a ta recorded here were obtained at a higher altitu d e th an those
used in the M attikalli model. The larger ESTAR footprint has a greater chance
of observing non-homogeneous soil, w ith differing soil tex tu re or rock fraction,
or possibly even w ith differing amount of vegetation, forestation, or even bodies
of w ater or u rban areas appearing in th e beam .
These will affect th e observed
brightness tem p eratu re. T he increased altitu d e also makes th e instrum ent more
susceptible to R F I. Normally RFI is strong enough to com pletely overpower the
usable signal, b u t it is possible th at it could also cause a sm all bias tem perature
superim posed on th e data.
One possible problem with the plots shown in figure 4.44 is th a t the d a ta cannot
be easily inverted to predict RSC values from observed brightness tem perature
changes. Given th e flat slope of the model curves, very small changes in brightness
tem p eratu re will result in extrem e variations of th e resulting RSC values, and with
th e am ount of s c a tte r observed in the brightness tem perature d a ta m ost of the RSC
values would be off the curve. This lim its th e use of brightness tem p eratu re to
ob tain soil tex tu ra l properties, however th e model can still be used to show the
am ount of agreem ent with the ESTAR data.
Figure 4.45 shows th e change in post-rainfall brightness tem p eratu re plotted
against the num ber of elapsed days.
T his plot only includes d a ta from around
130
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
th e Mesonet sites th a t have RSC values between 1 and 1.62, which represents the
m ajority of the d ata p lotted above. T he error bars extend one stan d ard deviation
above and below the m easurem ents and are calculated from the actual sam ple points
used. T he small error bars for the d a ta at 5 and 6 days after th e rainfall occur
because those days had only 2 and 1 closely valued data points, respectively. The
values expected from th e M attikalli m odel, based on the RSC values at the points
used, are plotted as th e dashed line on th e plot. T he most obvious feature noticed
on this plot is th at th e brightness tem perature changes towards drier and warm er
tem peratures following a rainfall, leveling off after 4-6 days, and having a small rise
after 7-8 days. The ESTA R d ata tracks th e model values fairly well, even exhibiting
th e sam e small peaks and dips as the model. However, the ESTAR d a ta seems to
consistently be one stan d ard deviation higher th an the model values. This is likely
due to the explanations listed above.
Brightness T em p e ra tu re Change vs. Day
50
ESTAR SG P'97
Mattikalli m odel
4)
O'
o
c
CJ
C
a, 30
3
a
4)
CL
£
£
20
cn
in
4>
c
cO'
m
0
2
4
6
Days of c h a n g e
8
10
Figure 4.45. ESTAR brightness tem perature change after rainfall vs. day for sites
w ith 1.0 < RSC < 1.62.
131
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
4.6
Correction of July 8-10 D ata
Dr. T. J. Jackson of USDA in Beltsville, MD has expressed concern over the
images for the days of Ju ly 8-10, 1998. He notes th a t th e brightness tem peratures
shown, and the overall contrast of the images, were lower th an he expected when
com pared to other images taken in the experim ent [21].
Figure 4.46 shows the
relationship between brightness tem perature and volum etric soil m oisture content
a t th e Little W ashita site over the course of th e experim ent. T he July 8-10 data
points, depicted as triangles in the plot, can clearly be seen to lie below th e trend
established on all the o th er days, which were dry across m ost of the area. They also
serve as a transition between the June and July data, forming one large d a ta set as
opposed to two smaller ones. As such, there is considerable interest in correcting
these days. The brightness tem perature d a ta plotted in figure 4.46 were obtained
from d a ta processed at GSFC so it is possible th a t there m ay be differences in the
way th e d ata were processed, however, since the values shown are com parable to
th e values in the images presented in this docum ent, this is unlikely.
These d a ta were collected immediately following the replacem ent of the calibra­
tion switch on July 7, 1998 and precede the repair of a faulty antenna box heater
power supply wire on Ju ly 10, 1998. Therefore, the initial concern was the possibility
of an instrum ent m alfunction. The new calibration switch seems unlikely as an
explanation, as this sam e switch was in place when good d a ta were collected on the
days following July 10. It is possible th at a connection to this switch might have been
left loose during the replacem ent on July 7, and may not have been tightened until
the heater repair on July 10. This could have introduced a small loss into th e RF
chain, which would have have the effect of compressing dynam ic range and shifting
levels. However, this should have been corrected by the calibration procedure, as
long as it were present in d a ta taken on the ground. T he lack of correction suggests
th a t it was not present on th e ground, and it seems unlikely th a t a poor connection
132
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
SGP97ESTAP
•#
Figure 4.46. ESTAR brightness tem p eratu re vs. volum etric soil m oisture content
for L ittle W ashita site. Courtesy of Dr. T. J. Jackson.
would occur only in the air w ithout an obvious transition or apparent in term itten t
response. Thus, a different failure m echanism seems to have been at work. Even if a
sm all loss of this type were present, its disappearance prevents a direct correction for
it. Using an em pirical fit sim ilar to th e one described below is th e only alternative.
T he second possibility, th at of a loose heater power supply wire, is not quite so
straightforw ard. The prim ary indication of this faulty power supply wire was th e
satu ratio n of the image during th e flights on th e El Reno lines on July 10, when
th e loose power supply wire grounded itself to a receiver backplane, causing a short
circuit th a t drained several system power supplies. The short circuit burned o ut
th e wire after approxim ately 10 m inutes, and th e system returned to its norm al
133
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
operational state. However, th e antenna box tem peratures slowly cooled over the
rem ainder of the experim ent, which was the initial indication o f a fault in the antenna
box power supply.
W hile no effects quite this drastic were noted on July 8-9, later analysis of the
d a ta showed a gradually drifting increase in the observed brightness tem peratures
over th e course of each day’s flight indicating th a t the power supply wire was already
loose or failing, producing the image drift as the antenna cooled. However, later
analysis of the tem peratures in th e antenna box, as well as in th e calibration box and
receiver planks, show therm al drifts far sm aller than th e level of the discrepancies
noted in figure 4.46. Even though the d a ta images suggest a therm al drift as the
m ost likely explanation, analysis of these therm al diagnostic d a ta seem to suggest
otherwise.
T he calibration num bers for these days are reasonably consistent w ith the num ­
bers on other days, and the level shift and compression of dynam ic range cannot
be a ttrib u te d to a known instrum ent problem th at can be m odeled and corrected.
However, following suggestions from Dr. Jackson, it may be possible to correct the
dynam ic range and level of the d a ta on these days to fit values derived from ground
m easurem ents.
Let us define th e following error model relating the m easured brightness tem per­
atu res to those corrected to m atch ground samples:
T c o ft
=
^
T
m e a s -f- t b i a a i
(4 -1 )
where it is assumed th at the error is neither angle nor tim e dependent, unlike the
im age ripple and incidence angle effects presented in section 3.7. W hile a timedependent drift was observed, it cannot be corrected unless an error mode can be
determ ined. It does not appear to be any of the error m odes described above, and
short of determ ining an applicable error mode, the m ethod in equation 4.1 can be
used in preference to discarding th e uncorrected data.
134
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Since equation 4.1 represents a simple linear fit with two scalar unknowns, a
sim ple linear regression will suffice to obtain th e constants. However, th e tem pera­
tures extracted from th e ESTAR d ata m ust correspond to the actual ground areas
sam pled. Due to the large footprint of the synthesized ESTAR beam s, it is likely th at
th e sam pled ground points will be sm aller than an ESTAR pixel, possibly creating
some co-registration problems, but it should be possible to pick an averaging radius
so th a t a sufficient num ber of ESTAR pixels are averaged over an area close in size
to th e sam pled ground area. Note th at these corrections have not been applied in
generating th e images depicted in figures 4.23-4.25.
4.7
Conclusion
T he S G P ’97 experim ent covered a larger area than previous experim ents, and
over a longer period of tim e. T he ESTAR d a ta obtained shows internal consistencies,
and reasonable response to environm ental effects. The instrum ent was capable of
repeatedly measuring small features on th e ground, such as lakes. T he brightness
tem p eratu re d a ta obtained by ESTAR was com pared to rainfall m easured at eleven
O klahom a M esonet autom ated weather stations. These data agreed w ith previously
published models within 15 K, and typically w ithin 7-11 K, and exhibited similar
features to th e model, within one standard deviation.
135
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
C
h a p t e r
C o n c l u s io n s
5.1
and
5
R e c o m m e n d a t io n s
Sum m ary
This dissertation has discussed th e basic theory of operation of the Electronically
Steered T hinned Array Radiom eter (ESTAR); improvements to the in stru m en t
hardware, software, processing, and calibration; and the th e d a ta obtained from
the participation of ESTAR in Southern G reat Plains 1997 (S G P’97), a large,
m ulti-organization hydrology experim ent.
C hapter 1 covered the basic theory of synthetic ap ertu re radiom etry, including
radiom etric brightness tem perature, interferom etry, and array thinning.
C hapter 2 dealt w ith improvements to th e ESTAR instrum ent over the past few
years, specifically the switch to a horizontally polarized antenna, im provem ents to
the system cabling and wiring, analysis of the susceptibility of ESTAR to radio
frequency interference (RFI), and im provem ents to the th erm al stability of th e
instrum ent. Modifications to the d a ta collection and d a ta analysis program s were
also discussed.
C hapter 3 focused on the processing and calibration of ESTAR data.
T his
included th e theory and operation of collecting antenna p a tte rn calibration d a ta ,
and the use of this d a ta to form a G -m atrix.
A new m ethod to correct th e
transients caused by changes in the s ta te of the Venus sw itch makes it possible
to measure high signal-to-noise ratio G -m atrix data w ithout discontinuities. T h e
chapter also discussed pre-processing steps and a m ethod of calibrating th e null
feedback radiom eter (N FR ), which has great utility in establishing the quality of
ESTAR d a ta , as well as generating quick-view d ata products for establishing proper
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
operation and flight planning during the course of an experim ent. The theory and
m ethods of perform ing an ESTAR image calibration were discussed as well, detailing
the use o f 401 image points during d a ta processing, as well as the steps used to reduce
th e effects of im age ripple. In addition, the chapter described th e m athem atics and
mechanics used to geo-locate ESTAR data.
C hapter 4 presented a brief overview of the S G P ’97 experim ent, and presented
th e d a ta collected by ESTAR during its course. Brightness tem perature images of
th e S G P ’97 region were obtained on 23 days during Ju n e and Ju ly of 1997. This
is the largest d a ta set of its type collected by ESTAR, in both geographical and
tem poral term s. These images and dropouts caused by brief in-flight calibrations
were discussed, as well as th e modification of flight lines to avoid RFI. Several lakes
w ithin th e S G P ’97 experim ent area were consistently detected over the course of the
experim ent, indicating th a t ESTAR performed properly. T he chapter also described
problems discovered during Ju ly 7-10 and a m ethod to correct the apparent shift in
the level of th e d ata, so th a t it can be used to generate soil m oisture images. D ata
points were ex tracted from these images and com pared to rainfall d a ta obtained from
the O klahom a Mesonet, a series of weather stations located across the experim ent
area. Good agreem ent was found between am ounts of rainfall and changes in the
microwave brightness tem perature. This data was com pared to a published model
and was found to agree w ithin 15 K, and typically w ithin 7-11 K.
5.2
Areas for F urther Study
Several further im provem ents can be made to th e ESTAR instrum ent or the
processing of its data.
O ne of these is the correction of the ESTAR d a ta for
tem p eratu re variations in th e system . Currently, only the tem perature of the N FR
reference load is used in processing.
While great care is are taken to m aintain
the system at a stable, repeatable therm al state, minimizing the effects of any
tem p eratu re variation, no m echanism is actually used to correct for variations of
137
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
these tem peratures. An indication of this can be seen in the July 8-10 d ata, where
an instrum ent m alfunction allowed the antenna box to cool over the course of the
flight. This caused a sm all drift in the measured brightness the day’s m easurem ents.
These tem perature corrections can be made by starting the instrum ent when it is
cold, and m easuring the response to a stable, well characterized target, such as the
hot calibration load, as it warms up.
Repeating this process over several cycles
produces d a ta th a t can be regressed to m atch system tem peratures with system
outputs. These tem peratures will most likely be associated with the com ponents in
th e receiver chain closest to th e antenna. Such components have the greatest effect
on the system noise characteristics, and include the antenna itself, the various feed
lines, and th e first am plifier in th e chain. There will likely be a lot of cross-coupling
in this data, w ith various system outputs seeming to respond to changes in various
system tem peratures. A possible way to minimize this cross-coupling would be to
warm-up ESTAR several tim es, using only one bank of heaters each tim e. T his will
tend to isolate therm al regions so more direct measurements can be m ade. Since
there are approxim ately 15 h eater banks within ESTAR, and the instrum ent m ust be
allowed to cool between these m easurem ents, this would result in a long, painstaking
series of m easurem ents.
Another possible source of improvement would be the incorporation of infrared
m easurem ents of the ground tem perature. The d ata set presented in this dissertation
relies upon attem p ts to fly over the same area on the ground at the same tim e of
day during th e same tim e of year to minimize variations in ground tem peratures,
b u t it does not actually correct for measured changes in the ground tem p eratu re
th a t an infra-red instrum ent could provide. Indeed, on June 30 the flight took place
later when th e ground tem p eratu re was warmer, possibly causing slight variations
in brightness tem perature. T h e airplane had an infrared device, but at th e tim e
th e d ata for this dissertation was processed, no reliable, well-calibrated version its
138
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
d ata was available. However, in the best of circumstances, infrared does not provide
ground tem perature through cloud banks, and since several of th e days during the
experim ent saw m oderate to heavy cloud cover over parts of the experim ent area, it
can never provide a to tal solution. Indeed, this is one of the strengths of microwave
instrum ents, such as ESTAR. Nonetheless, even if the ground tem p eratu re can only
be measured at a couple of points across the experiment area, these can be used to
form day-to-day correction factors for variations in tem perature.
Further im provem ents to ripple reduction methods may be possible as well.
Traditional windowing m ethods seem to have little effect, since they rely upon
tapering off the high frequency components th a t cause the ripple, and ESTAR
images have relatively little energy in these high frequencies.
ESTAR currently
uses a method sim ilar to the one used at NASA Goddard, which has been extended
to allow correction curves th a t vary with am plitude. Further research into this
technique may allow for a theoretical derivation of these correction curves, rather
th an an empirical m easurem ent of them . It may also give some insight into the
am plitude dependence, or possible lack of this dependence, on these curves. Further
research into o th er techniques to lower the image ripple may prove fruitful as well.
Additional im provem ents to the geo-location of ESTAR pixels m ay be made by
incorporating the yaw, pitch, and drift angles of the air platform . These param eters
are available from the navigation and data systems on the airplane, and may be
incorporated by using the equations and techniques associated w ith Euler angles
presented in G oldstein, or a similar mechanics text [18].
Modification o f the ESTAR data-processing programs to support the NETCDF
file formats may be worthwhile as well. This is a platform -independent and self­
describing file form at th a t eases the transfer of data across com puter networks and
m edia. The m ethods employed in this format would have solved or prevented many
139
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
of th e problems associated w ith changing file formats th at have historically presented
them selves whenever ESTAR d a ta has been shipped off-site.
T h e comparison of ESTAR brightness tem perature to M esonet rainfall statistics
has also shown much promise. However, some further refinem ents are necessary for
proper operation at this altitude. A greem ent with prior models was only w ithin 15
K. Possibly, incorporation of internal therm al corrections or corrections for ground
tm p era tu re may improve this figure somewhat, but it is likely th a t th e bulk of
this error lies in oth er effects. To refine the model further, access to radar rainfall
estim ates, possibly from the N exrad w eather radar, would elim inate some of the
point sampling issues. Access to a greater number of raingauges, ideally located on
a wider variety of soil types, would also help. Inclusion of th e O klahom a Micronet
system may fulfill some of this need. F urther work also needs to be done to correct
th e d a ta for variations in land cover, including vegetation, forest, bodies of water,
and urban areas.
O ne lim itation to the ESTAR inversion process has always been system non­
idealities th a t result in non-orthogonal system basis functions. This prevents the
use of straight Fourier inversion techniques to recover brightness tem p eratu re maps
from th e ESTAR visibility functions. A possible area of im provem ent m ay be in
separating the ESTAR system response into two components. O ne com ponent would
be composed of orthogonal basis functions so simple Fourier transform techniques
could be used for image inversion. T he other component would account for non-ideal
system responses, such as m utual coupling between antennas, and would require an
approach sim ilar to the current G -m atrix, or measured system im pulse response,
m ethod. W ith further research, it m ay also be possible to derive a theoretical de­
scription of these effects, elim inating th e need for empirical m easurem ent. However,
it would be unwise to elim inate all em pirical measurements from the calibration pro­
cess, since this process is one of th e m ost intense scrutinies of ESTAR perform ance
140
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
and operation, and historically it has shed light on some subtle m alfunctions th a t
m ay not otherw ise have been noticed. At the very least, some empirical m easurem ent
will be necessary to find scaling and offset coefficients to fix the real-world range of
ESTAR d ata.
141
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
A
B a sic s
of
T
p p e n d i x
A
w o - D im e n sio n a l
A
perture
S y n t h e sis
A .l
Two Dimensional A perture Synthesis
The images produced by ESTAR use aperture synthesis in only one dimension,
and rely upon the real ap ertu re of the antenna and motion of the observing platform
to generate two-dimensional images.
It is possible to generate two dimensional
images with a stationary platform using two-dimensional aperture synthesis. Ruf
et. al. [9] derives the visibility integral for the two dimensional case:
V { u , v ) = [ 2 [ 7 g ( 0 ,0 )ei 27r(usin«CO8^+"s*n®«n^) sin8ddd<t>,
Jo Jo
(A .l)
where u = Dx /X and v = Dy/ \ describe the two-dimensional antenna baseline,
which is analogous to d in th e one-dimensional case. This equation is sim ilar in
form to th at for the one-dimensional case, and is essentially a two dimensional
Fourier transform .
There are many m ethods of performing two-dimensional ap ertu re synthesis.
These appendices will take a cursory look a t two of them , nam ely fan-beam inversion
and Mel’nik coherent processing.
A.2
A T Sensitivity Calculations
Central to the evaluation of any radiom etric system is the radiom etric sensitivity,
or A T , equation, which describes the minimum change in the observed radiom etric
brightness tem perature detectable at the receiver output, given th e noise statistics
of the receiver. The range of brightness tem perature variation for m any practical
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
rem ote sensing applications can be as low as a few degrees Kelvin,so A T ’s on
th e
order of a tenth of a Kelvin degree can be required in m any instances.
T h e basic form for most A T equations is [3]
AT ^ AT sy s = —
(A.2)
-l l ? ? ;
v Bt
w here T a is the brightness tem perature observed at the antenna, T r e c is the receiver
equivalent noise tem perature, B is the bandw idth over which observations are m ade,
and
t
is the length of the observations.
T his basic form of the A T equation varies for specific designs of radiom eters
and assum ptions m ade on their operating param eters.
For instance, for a zero-
redundancy, large array ( i V > 1) ESTAR with identical noise tem peratures in each
receiver, it takes the following form[9]
A T = ( T A + T a£c ) \ f j ^ ,
(A.3)
where N is the num ber of elements in the array. This is very similar in form to
equation A.2, but with the additional multiplying factor of \ / N to account for
dependence each image pixel on the entire field of view, which is an order of y /N
brighter than the individual pixels. While the specific form of th e A T equation
for this specific case differs from that in equation A.2, they are of the basic form
com m on to all radiom eters, allowing many conclusions to be drawn.
E quation A.2 shows th a t the sensitivity of a m easurem ent improves as th e
bandw idth and observation times are increased.
In im plem enting a radiom eter
system it would be desirable to use as large a bandw idth and as long an observation
tim e as possible but in practice there are lim itations to how much these quantities
can be increased. Large bandwidths increase RFI susceptibility and increase cost of
com ponents.
Long observation times degrade image u p d ate tim es. For moving
platform s, observations m ust be made before the an ten n a footprint moves past
the area being observed, or no further benefit is gained from a longer observation
143
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
tim e. Thus, at the core of any serious radiom eter systems design or analysis is the
determ in atio n of the sensitivity equation.
Any m ajor design param eter m ust be
chosen to achieve an adequate system sensitivity.
144
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
A
p p e n d i x
Fa n - B
eam
B
In v e r s io n
One m ethod of forming a two-dimensional image uses a one-dimensional in­
terferom eter to form a linear image, and then rotates the linear array to form
a two-dimensional image in a process known as rotational synthesis. Wiley [23]
describes a m ethod of this type known as fan-beam inversion, which is the method
used in CAT scanners as well as th e Hughes SPINRAD system . In this m ethod
a fan beam is swept across a scene. Each fan beam integrates th e scene intensity
over the footprint o f the fan beam, called a Radon transform , and as the fan beam
sweeps across the scene a profile of these Radon transform s is generated.
The
Fourier transform of this profile is taken, and then the an ten n a array is rotated
and the fan beam s sweeps across th e scene again, and is repeated until a half
rotation has been m ade. The resulting one-dimensional transform s axe assembled in
a two-dimensional space.
Taking the two-dimensional inverse Fourier transform
results in the reconstructed scene.
This process is dem onstrated in figure B .l,
reproduced from Wiley [23].
One im provem ent to this technique would be to use a synthetic aperture inter­
ferometer to m easure the radial scene profile w ithout sweeping a fan beam, cutting
sweep tim e for th e scene by an order of m agnitude. The interferom eter could then
be rotated to collect additional radial profiles and generate an image.
Many issues would have to be addressed before this technique could be used
to generate high-resolution images. F irst, an equation to evaluate the sensitivity
A T of these system s would have to be derived so the relative m erits of various
im plem entations of this system could be evaluated. This will affect the choice of
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
IMAGE RECONSTRUCTION
VO
Figure B .l. Fan beam inversion
an ten n a types, as well as perm it calculation of allowable rotational speed, and hence
im age generation tim e. For high resolution, large antenna arrays will be necessary,
an d they will require careful mechanical design so they can be rotated. Using higher
frequencies will allow sm aller arrays to be used, but increase the total cost o f the
system .
O ne possible antenna type was presented in a sem inar on the U niversity of
M assachusetts campus by Dr.
Debabani Choudhury of Millitech C orporation in
South Deerfield, Massachusetts[24]. This 94 GHz antenna uses a monolithic diode
array over a reflective substrate. By adjusting the bias voltage on the diode array,
an adjustable linear phase taper can be applied to signals reflecting off the su b stra te
o f th e array, resulting in a steered beam . This system was proposed by M illitech as
p a rt of a compact contraband detection system. W hile this system is only capable of
scanning a fan beam in one dimension, the antenna itself is only a few feet across, and
146
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
as such could be easily rotated to use the fan beam inversion techniques described
above. W hile this antenna system m ay not be the best for im plem entation of a fan
beam inversion system , it does show th at the implementing a high-resolution fan
beam inversion system might be feasible.
147
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
A
M
e l ’n i k
T
C
p p e n d i x
w o - D im e n sio n a l
A
perture
S y n t h e sis
A nother m ethod of obtaining two-dimensional radiom etric images has been pro­
posed by M el’nik [25]. In this m ethod, an object moving according to some known
law w ithin the neax field of an antenna system can be imaged in both azim uth and
range. This differs from previously suggested system s, which image in azim uth and
elevation. T h e known law of the motion of th e object is used to calculate a variable
delay r,(2) such th a t the following phase balance relationship is m aintained:
c
+r,(()=
c
+ r 2(l),
(C .l)
where Ri{t) is the range to antenna i, and c is th e speed of light. When this balance
is m aintained, the signals from both antennas correlate w ithin the receiver. For
objects at different ranges, or moving according to other known laws, th e signals
from both antennas will not be in phase and will tend to cancel within the receiver.
If the phases of the incoming signals can be adjusted appropriately, th e resolution
th at can be obtained using this technique is
AX
= f f
(C.2)
AK
=
(C.3)
for m otion perpendicular to the antenna baseline, and
AX
= W‘ ~D
^C'4^
AK
= f f
(C.5)
for m otion parallel to th e antenna baseline, w here 0 is th e angle through which the
target moves during th e tim e of observation, and D is th e length of th e an ten n a
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
baseline. Note th a t for ranges where
~ 1, these resolutions are com parable to
those of a synthetic ap ertu re radar (SAR)
A -V
=
g .
(C .6 )
T here are lim itations to achieving this resolution. First, th e object being ob­
served must be close to the antenna. For large values of ^ the resolution degrades,
but by using larger an ten n a baselines the range can be increased, to th e point where
such a large baseline becomes mechanically im practical. Further, th e object m ust be
moving according to som e known law, which allows the phase correction factors r,(<)
to be calculated. This may not be a problem for an airborne instrum ent th a t is flying
straight and level a t a constant altitude and speed over ground-based targets. This
m ay also be possible for satellite system s, where well-known physical laws describe
th e m otion of the satellite (and hence the m otion of the ground w ith respect to the
satellite), however th e ranges involved are large, and may require an ten n a baselines
too large to be practical. There are m any advantages to m ounting an instrum ent
on a satellite as opposed to an airborne platform , so it will be necessary to research
w hether it will be practical to mount such an instrum ent on a satellite platform .
M el’nik’s technique requires an instrum ent th a t can generate th e required phase
corrections at a rate th a t allows the image to be formed properly. O ne possibility
is to digitize the signal received from the antennas, and then th e phase corrections
can be added off-line in post-processing. T his will simplify the hardw are, b ut at the
expense of being unable to view real-tim e images. Another possible technique will
be to find a m atched filter to provide the proper phase correction.
149
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
R eferences
[1] Gaiser, P. The Development o f a Second Generation Electrically Scanned
Thinned A rray Radiometer. PhD thesis, University of M assachusetts, Amherst,
MA, M ay 1993.
[2] Gleason, G. The design and development of an analog complex correlator and
other subsystem s for a thinned array microwave radiom eter. M aster’s thesis,
U niversity of M assachusetts, A m herst, MA, February 1993.
[3] Ulaby, F., Moore, R., and Fung, A. Microwave Rem ote Sensing; Active and
Passive vol. I. Artech House, 1982.
[4] Klein, L. A. and Swift, C. T. An improved model for th e dielectric constant
of sea w ater at microwave frequencies. IE E E Journal o f Oceanic Engineering,
OE-2(1):104-111, January 1977.
[5] Tanner, A. Aperture Synthesis fo r Passive Microwave Remote Sensing, the
Electronically Scanned Thinned Array Radiometer. PhD thesis, University of
M assachusetts, Am herst, MA, February 1990.
[6] Griffis, A. Earth Remote Sensing with an Electrically Scanned Thinned Array
Radiometer. PhD thesis, University of M assachusetts, A m herst, MA, February,
1993.
[7] Moffet, A. T. M inim um -redundancy linear arrays. IE E E Transactions on
A ntennas and Propagation, AP-16(2):172-175, M arch 1968.
[8] Bracewell, R. N. Radio astronom y techniques. In Fliigge, S., editor, Handbuch
Der Physik, volume 54, pages 42-129. Springer-Verlag, Berlin, 1962.
[9] Ruf, C. S., Swift, C. T., Tanner, A. B., and LeVine, D. M. Interferom etric
synthetic aperture microwave radiom etry for the rem ote sensing of th e earth.
IE E E Transactions on Geoscience and Remote Sensing, 26(5), Septem ber 1988.
[10] H iett, T . T he construction of an electrically scanned thin n ed array radiom eter.
M aster’s thesis, University of M assachusetts, A m herst, MA, February 1988.
[11] Ulaby, F ., Moore, R., and Fung, A. Microwave R em ote Sensing; Active and
Passive vol. 3. Artech House, 1982.
[12] G oodberlet, M. personal com m unications, December 1996.
[13] Pozar, D. M. Microwave Engineering. Addison-Wesley Publishing Company,
Reading, M assachusetts, 1990.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[14] Weissman, D. E. and LeVine, D. M. The role of m utual coupling in the
performance of synthetic ap erture radiom eters. In 5th Specialist Meeting
on Microwave Radiom etry and Rem ote Sensing o f the Environment, Boston,
November 1996.
[15] Balanis, C. A. Antenna Theory: Analysis and Design. John Wiley & Sons,
New York, 1982.
[16] Frasier, S. personal communications, w inter 1996.
[17] Frater, R.
H. an d Williams, D. R. An active ”cold” noise source.
Transactions on Microwave Theory and Techniques, m tt-29(4), April 1981.
IE E E
[18] Goldstein, H. Classical Mechanics. Addison-Wesley Publishing Company, Inc.,
second edition, 1980, 1950.
[19] Southern great plains 1997 (sgp97) experim ent plan, 1997. USDA A gricultural
Research Service.
[20] Land-sat th em atic m apper data user’s guide. Online document located at
h t t p : / / edcwww. c r . u s g s . g o v /g lis /h y p e r /g u id e /la n d s a t_ tm .
[21] Jackson, T. personal communications, July 1998.
[22] M attikalli,
N. M ., Engman, E. T ., Jackson, T . J., and Ahuja, L. R.Mi­
crowave rem ote sensing of tem poral variations of brightness tem perature and
near-surface soil w ater content during a watershed-scale field experim ent, and
its application to th e estim ation of soil physical properties. Water Resources
Research, 34(9):2289-2299, Septem ber 1998.
[23] Wiley, C. Microwave radiometer five year plan, unpublished internal docum ent,
August 1989.
[24] Choudhury, D. A millimeter wave m onolithic diode array beam controller
and its applications, seminar presented at th e University of M assachusetts
at Amherst, M arch 1996.
[25] Mel’nik, Yu. A. Potential applications of coherent processing of random signals.
Radio Engineering and Electronic Physics, (4):575-578, 1972.
151
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
IMAGE EVALUATION
TEST TARGET (Q A -3 )
* •>
i
%
1.0
l£m
U£
13.2
12.2
2.0
l.l
.8
1.25
1.4
1.6
150 m m
IIV U B E . In c
1653 East Main Street
Rochester. NY 14609 USA
Phone: 716/482-0300
Fax: 716/288-5989
0 1993. Applied Image. Inc.. All Rights Reserved
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.
Документ
Категория
Без категории
Просмотров
0
Размер файла
6 609 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа