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The Constants in the Equation for Atmospheric Refractive Index at Radio Frequencies

01 Aug 1953-Vol. 41, Iss: 8, pp 1035-1037
TL;DR: In this paper, a relation 77.6 e N = ~ p + 4,810-T T where p = total pressure in millibars e=partial pressure of water vapor in millibrars T=absolute temperature=°C+273
Abstract: Recent improvements in microwave techniques have resulted in precise measurements which indicate that the conventional constants K1 = 79°K/mb and K22?=4,800°K in the expression for the refractivity of air, N=(n-1) 106=[K1/T](p+ K2'e/T) should be revised. Various laboratories appear to have arrived at this conclusion independently. In much of radio propagation work the absolute value of the refractive index of the atmosphere is of small moment. However, in some work it is important and it seems highly desirable to decide upon a particular set of constants. Through consideration of the various recent experiments this paper arrives at a relation 77.6 e N = ~ p + 4,810-T T where p=total pressure in millibars e=partial pressure of water vapor in millibars T=absolute temperature=°C+273 This expression is considered to be good to 0.5 per cent in N for frequencies up to 30,000 mc and normally encountered ranges of temperatures, pressure and humidity.

Content maybe subject to copyright    Report

Journal
of
Research
of
t
he
Noti
onal
Bureau
of
Standard
s Vol. 50, N
o.1,
Januar
y 1953
Research
Paper
2385
The
Constants
in t
he
Equation for Atmospheric
Refractive
Index
at
Radio Frequencies
Ernest K. Smith, Jr.,
and
Stanley
Weintraub
Re
cent
improv
e
ment
s
in
microwav
e
tec
hniqu
es
hav
e
resulted
in
precise meas
urem
e
nt
s
at
th
e
Nationa
l
Bur
eau
of
Standard
s, the
Nationa
l
Phy
sical
Laboratory
,
and
elsewhere,
which
indicat
e t
ha
t t he conve
ntional
constants
K
\=
79
° K/
mb
and
K
2
'=
4,800° K
in
the
expression for
the
refractivity
of
air
, N = (n - 1) 10
6
= (K d T )
[p
+ K
2
'
(e
/T)] s
hould
be
revi
sed .
Variou
s
laboratori
es
app
ea
r
to
hav
e
arriv
ed
at
this conclus
ion
ind
ep
en
de
ntly,
wi
t.h
the
result
t
ha
t there
are
seve
ral
differ
ent
sets
of
constants
in
c
urr
ent use.
In
much
of
propagation
work
the
absolute
value of
the
refractive
in
dex of the
atmosphere
is of small
moment.
Howev
er,
in
s
om
e
work
it
is
imp
o
rtan
t,
and
it
seems highly desiI
abl
e to decide
upon
a
particular
set
of
con
sta
nt
s.
Through
conside
rat
ion
of the
various
r
ecent
ex
perim
ents
a rel
ation
N = (77.6/ T)
[p
+ 4810
(e/ T)] is deriv
ed,
where p is t he
tota
l
pr
e s
ur
e,
in
millibars, e is t he
par
tia
l
pre
ss
ur
e of
wat
er
vapor,
in
millibars,
an
d T is
ab
solu
te
te
mperature
(O
C+ 273
).
Thi
s
expre
sion is con-
sidere
d
to
be
good
to
0
.5
pe
rc
ent
in
N f
or
fr
eque
ncies
up
to
30,000 megacycles
and
normally
enco
un
tere
d
range
s of
temperature,
pI' ssure,
an
d h
umidity.
R ece
nt
improve
ment
s in microwave techniques
hav
e
re
sulted
in
measureme
nts
at
the
National
Bur
ea
u of
Standard
s [1]/ the National
Phy
sical
Laborator
y
[2],
a
nd
elsewhere
[3
, 4, 5
],
which
hav
e
indi
cate
d
that
the
conventional constants
in
the
ex
pre
ss
ion for the refractive index of air
at
radio fr
e-
qu
encies shou
ld
be
revised. Various laboratories
appear
to
ha
ve arrived
at
this conclusion indepen-
de
ntl
y,
with
the
result
that
there are seve
ral
differe
nt
sets
of
constants in
current
use
[6
, 7, ,
9]
.
Th
e
sources of these recent changes, such as
hav
e been
run
to earth,
have
b
ee
n found to be
ba
ed on indivi-
dual
rather
than
co
ll
ecLive
r
es
ults. Almost all the
proposed c
onstant
s seem to re
pr
ese
nt
a sub
sta
ntial
improvement
over the former values.
Th
e
authors
propose a
set
of
constanLs derived from
what
is fe
lt
to be the
most
reliable 0f
Lh
e rece
nt
microwave
and
optical measure
ment
s of
the
refractive index of
I .
.
dry
air
and
from a rece
nt
s
urv
ey
of
wat
er
vapor
Debye constants.
It
is hoped t
hat
these new con-
sta
n ts will provide a common meeting g
round
for
the
laboratories desiring change
rath
er
than
inje
ct
ju
st
another
set
of
va
lu
es
int
o the field.
For
an
accuracy of 0.5 percent in N, the scaled-
up
refractiv
it
y of moist air
[N
=
(n-
l )
10
6
],
where n
y is
the
refractive index, some simplifying ass
umption
s
m
ay
be
made
if the use of
the
relation is to
be
re-
st
ri
cte
d to certain limits of the variabl
es.
The
limits
in
this case restrict
its
use to
temperat
ur
es
of
-5
0 to + 40° C,
total
pressures
of
200 to 1,100
mb
,
water-vapor
partial
pr
ess
ur
es
of 0 to 30
mb
,
and
a
frequency range of
0 to 30,000
Me
.
Th
e
co
ns
tituent
s
of
dr
y air
and
even
water
vapor
may
be assumed to
obey the ideal gas law
[10]
.
Th
e refractive index
of
water
vapor, a polar molecule
with
an
electric
dipol
e,
may
be
represented
by
a two-term Debye
relation
[ll]
.
The
permeability of air
at
radio fre-
quencies due to oxygen
may
be taken as 1 +
O.4
X
10
-
6
[
J]
.
Di
spersion
ma
y
be
neglected.
Th
e
Lor
e
ntz
polarization term
ma
y
be
ignored.
\.b
sol
ut
e zero
.
Fi
gures
In
brackets in
di
cate the literature references
at
the
end
of this pa.per.
39
for
tempera
Lur
e
ma
y be
taken
as - 273° C
rath
er
than
- 273.16° C [12].
Ther
e
ha
s b
ee
n no proof of
var
iation in
tbe
co
m-
position of the
dry
gases
of
Lhe free atmosphere
e
ith
er
with
l
at
itud
e or
with
heig
ht
up
to
the
iono-
s
ph
ere [13].
Th
e
water
vapor
c
ontent
, of course,
var
i
es
widely. A contributions to
Lh
e
tota
l re-
fra
ct
iv
e
ind
ex obey
an
acldiLive
rul
e,
a
th
r
ee
-t
erm
ex
pression
ma
y be formulated
[ll],
in
which
the
fir
st
te
rm
ex
pr
esses the
um
of the distortion of
el
ectronic c
har
ges of
the
dr
y-gas mol
ec
ules
und
er
the
influence of
an
applied electromagnetic field ;
the
second term,
th
ese di
st
ortions for
water
vapor
;
and
the third term, the e
fT
ect
of
the
orien
tat
ion of
the
electric dipol
es
of
water
vapor
und
er
the
influence of
a
fi
e
ld
.
Thu
s,
us
in
g N for the scaled-up
refractivity
[N
=
(n-
l )106
],
=K
1
(~)+K
2
(
f)+
Ka (;2} (1)
where n i
Lb
e refractive
ind
ex
at
radio fre
qu
encies;
P
a
,
the partial press
ur
e
of
the
dr
y gase ;
e,
the
partial
pr
e sure of
wat
er
vapor;
and
T, the absolute tem-
peratur
e.
In
radio work one is
inte
rest
ed in propagation
through
th
e free atmosphere.
Ther
efore, the com-
position of air should
be
taken
to include
an
average
amount
of carbon dioxide. However,
labora
tory
meaSUl'
e
ment
s usually are
made
on
COrfree
air
because of variable
co
n
ce
ntration
s of CO
2
in
th
e
laborator
y. Hence, those values
of
- 1 originall
published for
CO
2
-free air
ha
ve been
ad
ju
sted
for
0.03 perce
nt
CO
2
content
by
raising
them
0.02 per-
ce
nt
.
Th
ese values are al
so
g
iv
en on a real
ratb
er
than
an
ideal gas basis.
Three
determinations s
hown
in
table 1 are considered.
Th
e fir
st
shown,
that
of
Barrell
[14], is
an
average
of
the
constant
term
(n
for A=
00)
of
the
optical
Cauchy
dispersion e
qua-
tions for
standard
air used
in
three
of
the principal
metrology laboratories of the
wo
rld.
Theor
et
ical
co
nsiderations indicate th
at
the dielectric
constant

for
dr
y ail' will be the i
sa
me for optical and radio
fre
qu
enc
ie
s. Barrell's value is
co
nverted to dielec-
tric c
on
s
tant
from the relation n=w
with
Il
, the
permeability,
ta
ken as uni
ty
at
optical fre
qu
encies.
Th
e second valu
e,
th
at
of
Birnbaum
,
Kr
yder, a
nd
Lyons
[1]
,was originally pu blished on
an
ideal
ba
sis
but
ha
s here been
co
n
verte
d to the
va
lue per tinent to
real gases.
Th
e
last
deter
min
at
ion,
that
of
Ess
en
a
nd
Froom
e
[2],
ha
s been
adju
sted to include
CO
~
.
Th
e
un
cer
ta
inties li
ste
d are
sta
nd
a
rd
e
rr
ors.
TAB
LE
1. D
Ty
-ai
r Tefractive
index
and
diel
ec
tric constant at
0° C
an
d 1 atmosphere
Frequency
of measure-
Mea
sw'ed N
(.--
1)10
6
Year
ment
-----
--
Barrell
[14J
____
.
__
.
__
.
OpticaL
____
28
7.7
0.0"
fi75
.6± 0.1 3 1951
Birnbaum, Kryder
9,000
Mc
_
__
_
575.8± 0.36 1951
"nd
Lyons
tiJ.
Essen and roomc
24
,000 M c
___
288
.2
0.1 57
6.
0.2 1
951
[2J
.
Mean
'·"
Iu
e
___________
_
_________
288.0
0.0, 575.7
0.
10
--._-.--
Ut
ilizing the
tota
l press
Ul"C
, p= P d+
c,
one
ma
y
write
For
use in the limited te
mp
erature
range - 50° to
+ 40° C, negligible e
rror
is incurred
thro
ugh lumping
th
e seco
nd
and third terms
in
(7).
Thi
s m
ay
be
accomplished by dividing these t
er
ms by cfT and
solving for the composite con
st
ant
, K
4
,
in the rel
at
ion
(8) ,
which, for T= 273 ° K, results in
(9) \
Th
e t
wo
-te
rm
formula for dry air is now
N =
77.6
~ +
3.73
X
I0
5
;2'
(10)
a
Derived
Il'om
n=
..;;;.
where
,,
- 1= OAXIO-6 is taken
for
radio frequenci
es
to
accou
nt
for the permeab
ili
ty
. which
ma
y be
wr
i
tten
Th
e
stat
i
st
ical me
an
value of dielect
ri
c
co
n
sta
nt is
then
co
nver ted to
re
fra
ct
ive ind
ex.
Th
e cons
tant
K 1 is eva
lu
ate
d from
(2)
which
ste
ms from (1) when
c=
o.
Sett
ing N = 2S8.04,
p = 1013.25
mb
, T=
273
° C
and
solving for K
1
:
. (3)
A rece
nt
s
urv
ey of dete
rmin
at
ions of the dielectric
cons
tant
of
wat
er
vapor
in
th
e
mi
crowave region
b~
Birnb
a
um
and
C
ha
tte
rjee [
15]
is used to e
valuat
e
the
wat
er-
vap
or con
sta
nts K z
and
K s in (1). As-
s
umin
g ideal gas behavior, which is permissible here
as only low
partial
pre
ss
ur
es are of
int
er
es
t,
th
e
co
nstants
m
ay
be
eva
lu
ate
d from the Dcbye con-
s
tant
s .!l a
nd
B (molar polarization P= .!l
+Hf
T)
dete
rmined
by Bi
rnb
aum a
nd
C
hat
terj
ee.
Th
is
results in
(4)
(5)
where the
un
certa
inti
es are again
sta
ndard errors.
Substituting
the
va
lues of (3), (4),
and
(
5)
in (1),
and
reducing
th
e
va
lu
es
to t
hr
ee
fi
gures
wh
ere
signifi
ca
n t
N = 77.6
~+72
f+3.
75 X
10
5
;2
' (6)
40
(
ll
)
Th
ese
la
st
two rel
at
ions are the ones proposed for
gen
era
l radio meteorological use.
Li
ste
d
in
ta
ble 2 are s
om
e of the values of K
1
,
K
z
,
and
K
a
,
t
ha
t
hav
e been used by
author
s throu
gh
the years. In examples 1 tlu'ough 7 the cons
tant
K I
wa
s
drawn
from
th
e Smithsonian
Ph
ysical Tables
(1933).
Th
e
water-vapor
co
n
st
ants K2 a
nd
K s in
examples 2 to 7
represent
an
averag
e of the deter-
mination
s of several, differe
nt
workers
in
each case.
Essen a
nd
Froom
e in example 8 relied on their own
excellent experime
nt
al work
to
eva
lu
ate
Kl
a
nd
K
s.
Th
eir value of K
t
is seen from table 1
to
be in excel-
lent agreement
with
the
va
lu
es
of
Barr
ell a
nd
of
Birnbamn
,
Kr
yder,
and
Lyons. However, their
value for
Ka is low because of the fact th
at
their
measured
va
lue of the dielect
ri
c c
on
sta
nt
of
wat
er
vapor
is
about
1 perce
nt
lo
we
r
than
those dete
rmin
ed
TABLE
2. Consta
nts
used by diffel'ent authors
N=(n-
l )
10
6
=
Kl
'!!...
+ K
2
!...
+
](
3
~
l ' 'T
']'2
1
_____
A_ut_h_
Ol
_.
____
!I
__
'"_
'ea
_r
1
~
1
__
I
(.
_'_I
___
K
_3
__
1
I.
Sc
be
ll
eng,
BW
Tow
s,
and
Ferrell [
16J
________________ 1
933
2.
En
glund, Crawford,
and
Mumford
[17
J_ ____________ 1935
3. 'Waynick
[1
8]
________
.
_______
1940
4. S
mith
-Rose a
nd
Stickla
nd
[1
9J
__
______________
________
1943
5.
NDRC,
Burrows a
nd
Att·
wood
[201
__________
__
______
1946
6.
Meteorological Factors in
P
ro
pagation [
21J
____
__
_____
1946
7.
Radi
ation
Laboratory, vol.
13 (Kerr)
[lll
______________ 1951
8. Essen and
Fr
oome
[2
1
_______
1
91\
1
9.
Smith a
nd
W eintra
ub
_
______
1952
79
G75
1. 35 x
10
'
79
. 1 68. 3 3. 81
79
68
.5
3.
72
79 68
3.77
79
68
3.8
79
e8 3. 8
79
(
79
) 3. 8
77
. 64
64
. 68 3. 718
77.
6
72
3. 75

by
other
recent workers
in
the
fi
eld.
It
is true
that
their meas
ur
eme
nt
s were performed in a region
ad
ja
cent to the 1.35-cm
water-vapor
absorption
band
,
but
this effect
ha
s been shown to be too small
to acco
unt
for
the
discrepancy. As Essen
and
Froome did
not
hav
e refra
ct
ive-ind
ex
determinations
over the wide
temperature
range
necessary to
eva
l-
u
ate
K2
and
K3 indepe
nd
e
ntl
y,
they
utilized an
opt
ical
va
lue of re
fra
ctive
ind
ex
(K
3
= 0) to d
ete
r-
mine K
2
Consequently, their value for K2 is
about
10
pe
rc
e
nt
low
at
radio
frequencies.
How
ever, the
e
ff
ect of this on the e
quation
is negligibl
e.
Th
e
authors
thank
George
Birnbaum
,
Arthur
1ifary
ott
,
Jack
W. H erb
streit
,
and
Kenn
e
th
A.
N orton for their ad
vi
ce
and
assistance
in
this work.
References
[1]
G.
Birnbaum
, S. J .
Kr
yder,
and
H .
Lyon
s, J.
App
lied
Phy
s.
22,
95 (1951
).
[2]
L. Ess
en
and
K.
D .
Froo
me,
Pro
c.
Ph."
R.
Soc. (London)
[B]
64, 862 (1951) .
[3]
C. M.
Cra
in,
Phy
s. R ev. 74, 691 (1948).
[4]
W. F .
Gab
riel,
Pr
oc.
In
st.
Radi
o
Eng
rs. 40, 940 (Aug.
1952
).
[5)
W.
E.
Phillip
s,
Pro
c.
In
st.
Radi
o
Eng
rs. 3
8,
786 (1950
);
C. M.
Crain
,
Pr
oc.
In
st.
Radi
o E ngrs. 40, 164 (Feb.
1952
).
2
33
150
-
5R
- -4
41
[6]
C.
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As
lak
s
on
and
O. O.
Fickei
ssen,
Tran
s. Am. Ge
op
hys.
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ion 31, 819 (1950
).
[7]
Cornell
E.
E . Research
Int
e
rim
E ngin eering Re
por
t
No
. 13, p. 23 (
Octob
er 27, 1951
).
[
8]
L.
Essen
and
K.
D .
Fro
ome,
Na
t
ur
e
167,
512 (1951).
[9]
L. J.
And
erson,
NEL
Re
port
No. 279 (1952).
[10]
H.
Barr
ell
and
J. E.
Sea
rs,
Phil
os.
Tran
s. [A] 23
8,
2
(1940) .
[11] P
ropagat
ion of S
hor
t Radio
Wave
s,
Edit
ed
by
D .
E.
Kerr
, R
adiat
ion
Laboratory
Se
ri
es 13, p. 189 (
McGraw-
H ill
Book
Co
.,
I
nc
., New
Yo
rk, N .
Y.,
1951
).
[12]
ibid
. p. 643.
[13] I
onosp
heric
Radi
o
Pr
opagation,
NBS
Circ. 462, p. 35
(J
une
1948
).
[14] H .
Barr
ell, J.
Optical
Soc.
Am.
U,
295 (1951
).
[1
5]
G.
Birnbaum
and
S.
K.
Cha
tte
rjee, J.
App
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Citations
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Book
01 Jan 1996
TL;DR: In this paper, the authors discuss the effects of RF interference on GPS Satellite Signal Receiver Tracking (GSRSR) performance and the integration of GPS with other Sensors, including the Russian GLONASS, Chinese Bediou, and Japanese QZSS systems.
Abstract: Fundamentals of Satellite Navigation. GPS Systems Segments. GPS Satellite Signal Characteristics and Message Formats. Satellite Signal Acquisitions and Tracking. Effects of RF Interference on GPS Satellite Signal Receiver Tracking. Performance of Standalone GPS. Differential GPS. Integration of GPS with other Sensors. Galileo. The Russian GLONASS, Chinese Bediou, and Japanese QZSS Systems. GNSS Markets and Applications.

4,475 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a new approach to remote sensing of water vapor based on the global positioning system (GPS) for estimating the extent to which signals propagating from GPS satellites to ground-based GPS receivers are delayed by atmospheric water vapor.
Abstract: We present a new approach to remote sensing of water vapor based on the global positioning system (GPS). Geodesists and geophysicists have devised methods for estimating the extent to which signals propagating from GPS satellites to ground-based GPS receivers are delayed by atmospheric water vapor. This delay is parameterized in terms of a time-varying zenith wet delay (ZWD) which is retrieved by stochastic filtering of the GPS data. Given surface temperature and pressure readings at the GPS receiver, the retrieved ZWD can be transformed with very little additional uncertainty into an estimate of the integrated water vapor (IWV) overlying that receiver. Networks of continuously operating GPS receivers are being constructed by geodesists, geophysicists, government and military agencies, and others in order to implement a wide range of positioning capabilities. These emerging GPS networks offer the possibility of observing the horizontal distribution of IWV or, equivalently, precipitable water with unprecedented coverage and a temporal resolution of the order of 10 min. These measurements could be utilized in operational weather forecasting and in fundamental research into atmospheric storm systems, the hydrologic cycle, atmospheric chemistry, and global climate change. Specially designed, dense GPS networks could be used to sense the vertical distribution of water vapor in their immediate vicinity. Data from ground-based GPS networks could be analyzed in concert with observations of GPS satellite occultations by GPS receivers in low Earth orbit to characterize the atmosphere at planetary scale.

2,011 citations

Journal ArticleDOI
TL;DR: In this article, the authors present the first systematic, extensive error analysis of the spacecraft radio occultation technique using a combination of analytical and simulation methods to establish a baseline accuracy for retrieved profiles of refractivity, geopotential, and temperature.
Abstract: The implementation of the Global Positioning System (GPS) network of satellites and the development of small, high-performance instrumentation to receive GPS signals have created an opportunity for active remote sounding of the Earth's atmosphere by radio occultation at comparatively low cost. A prototype demonstration of this capability has now been provided by the GPS/MET investigation. Despite using relatively immature technology, GPS/MET has been extremely successful [Ware et al., 1996; Kursinski et al., 1996], although there is still room for improvement. The aim of this paper is to develop a theoretical estimate of the spatial coverage, resolution, and accuracy that can be expected for atmospheric profiles derived from GPS occultations. We consider observational geometry, attenuation, and diffraction in defining the vertical range of the observations and their resolution. We present the first systematic, extensive error analysis of the spacecraft radio occultation technique using a combination of analytical and simulation methods to establish a baseline accuracy for retrieved profiles of refractivity, geopotential, and temperature. Typically, the vertical resolution of the observations ranges from 0.5 km in the lower troposphere to 1.4 km in the middle atmosphere. Results indicate that useful profiles of refractivity can be derived from ∼60 km altitude to the surface with the exception of regions less than 250 m in vertical extent associated with high vertical humidity gradients. Above the 250 K altitude level in the troposphere, where the effects of water are negligible, sub-Kelvin temperature accuracy is predicted up to ∼40 km depending on the phase of the solar cycle. Geopotential heights of constant pressure levels are expected to be accurate to ∼10 m or better between 10 and 20 km altitudes. Below the 250 K level, the ambiguity between water and dry atmosphere refractivity becomes significant, and temperature accuracy is degraded. Deep in the warm troposphere the contribution of water to refractivity becomes sufficiently large for the accurate retrieval of water vapor given independent temperatures from weather analyses [Kursinski et al., 1995]. The radio occultation technique possesses a unique combination of global coverage, high precision, high vertical resolution, insensitivity to atmospheric particulates, and long-term stability. We show here how these properties are well suited for several applications including numerical weather prediction and long-term monitoring of the Earth's climate.

1,249 citations

Journal ArticleDOI
TL;DR: In this paper, the time-varying zenith wet delay observed at each GPS receiver in a network can be transformed into an estimate of the precipitable water overlying that receiver.
Abstract: Emerging networks of Global Positioning System (GPS) receivers can be used in the remote sensing of atmospheric water vapor. The time-varying zenith wet delay observed at each GPS receiver in a network can be transformed into an estimate of the precipitable water overlying that receiver. This transformation is achieved by multiplying the zenith wet delay by a factor whose magnitude is a function of certain constants related to the refractivity of moist air and of the weighted mean temperature of the atmosphere. The mean temperature varies in space and time and must be estimated a priori in order to transform an observed zenith wet delay into an estimate of precipitable water. We show that the relative error introduced during this transformation closely approximates the relative error in the predicted mean temperature. Numerical weather models can be used to predict the mean temperature with an rms relative error of less than 1%.

1,112 citations

Journal ArticleDOI
TL;DR: In this article, the authors used the longest radar wavelengths possible, within ionospheric scintillation and Faraday rotation limits, for topography, maximize interferometer baseline within decorrelation limits, and use multiple observations and average the derived products.
Abstract: Interferogram images derived from repeat-pass spaceborne synthetic aperture radar systems exhibit artifacts due to the time and space variations of atmospheric water vapor Other tropospheric variations, such as pressure and temperature, also induce distortions, but the effects are smaller in magnitude and more evenly distributed throughout the interferogram than the wet troposphere term Spatial and temporal changes of 20% in relative humidity lead to 10 cm errors in deformation products, and perhaps 100 m of error in derived topographic maps for those pass pairs with unfavorable baseline geometries In wet regions such as Hawaii, these are by far the dominant errors in the Spaceborne Imaging Radar-C and X Band Synthetic Aperature Radar (SIR-C/X-SAR) interferometric products The unknown time delay from tropospheric distortion is independent of frequency, and thus multiwavelength measurements, such as those commonly used to correct radar altimeter and Global Positioning System (GPS) ionospheric biases, cannot be used to rectify the error In the topographic case, the errors may be mitigated by choosing interferometric pairs with relatively long baselines, as the error amplitude is inversely proportional to the perpendicular component of the interferometer baseline For the SIR-C/X-SAR Hawaii data we found that the best (longest) baseline pair produced a map supporting 100 m contouring, whereas the poorest baseline choice yielded an extremely noisy topographic map even at this coarse contour interval In the case of deformation map errors the result is either independent of baseline parameters or else very nearly so Here the only solution is averaging of independent interferograms, so in order to create accurate deformation products in wet regions many multiple passes may be required Rules for designing optimal data acquisition and processing sequences for interferometric analyses in nondesert parts of the world are (1) to use the longest radar wavelengths possible, within ionospheric scintillation and Faraday rotation limits, (2) for topography, maximize interferometer baseline within decorrelation limits* and (3) for surface deformation, use multiple observations and average the derived products Following the above recipe yields accuracies of 10 m for digital elevation models and 1 cm for deformation maps even in very wet regions, such as Hawaii

921 citations

References
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Journal ArticleDOI
01 Oct 1951
TL;DR: In this paper, the authors measured the refractive indices of air and its principal constituents at a frequency of 24,000 Mc/s with a precision comparable with that obtained in the optical range.
Abstract: The refractive indices of air and its principal constituents have been measured at a frequency of 24,000 Mc/s. with a precision comparable with that obtained in the optical range. The method is based on the measurement of the resonant frequency of a cavity resonator first when it is filled with the gas and then when it is evacuated. The source of oscillations used is a Pound-stabilized velocity-modulated oscillator, and its frequency is measured by reference to a high harmonic of a quartz standard, with a precision of 1 part in 108. The cavity is provided with a tuning plunger, which changes the resonant frequency through a range of about 10 Mc/s, and is calibrated to an accuracy of within 1 kc/s. Most of the measurements were made by the frequency-change method and the plunger was used in a narrow region only for a precise setting to resonance. It is possible by a larger movement of the plunger to compensate for the whole frequency change due to the removal of the gas and thus to work at a fixed frequency. The following results were obtained for (n - 1)106 where n is the refractive index at 0°C., 760 mm Hg: dry CO2-free air, 288.15 ± 0.1; nitrogen, 294.1 ± 0 1; oxygen, 266.4 ± 0.2; argon, 277.8 ± 0.2; carbon dioxide, 494 ± 1; and the value for water vapour at 20°C., 10 mm. Hg pressure was 60.7 ± 0.1 The dielectric constants can be calculated from the relationship μ = n2, where μ is the magnetic permeability and the dielectric constant, the values of (μ - 1) 106 being taken as 0.4 for air, 1.9 for oxygen and zero for the other gases. Accurate formulae are given for obtaining the refractive index of moist air at different atmospheric conditions, and are reduced to the following simple formula which is applicable for normal atmospheric conditions: (nt,p - 1)106 = (103.49/T)p1 + (177.4/T)p2 + (86.26/T)(1 + 5748/T)p3, where p1, p2, p3 are the partial pressures of dry air, carbon dioxide and water vapour, t is the temperature in degrees c., and T = 273 + t is the absolute temperature. A value of 1.839 ± 0.002 × 10-18 E S.U. was derived for the dipole moment of the water vapour molecule.

160 citations

Journal ArticleDOI
TL;DR: The first accurate laboratory determination was made about the same time by Biot and Arago (1806), who measured the deviation of white light passing through air enclosed in a hollow glass prism.
Abstract: (a) Note on previously recorded values of the refractive index of air. For many centuries astronomers have recognized the effect that the refraction of the earth’s atmosphere has upon observations of the positions of celestial bodies. From the time of Tycho Brahe, when astronomical technique became sufficiently refined for the purpose, attempts have been made to apply corrections for the deviation of light in its passage through the earth’s atmosphere, and ultimately, in 1805, Delambre (1806) determined, by comparing a large number of astronomical observations, a value of the refractive index of atmospheric air for white light. The first accurate laboratory determination was made about the same time by Biot and Arago (1806), who measured the deviation of white light passing through air enclosed in a hollow glass prism. In 1857 Jamin (1857 b) made his original application of the methods of interferometry to the measurement of the refractive index of a gas. The increased accuracy obtainable by the use of the principle of the Jamin refractometer enabled Ketteler (1865) to determine the refractive indices of air for the red, yellow and green lines in the visible spectra of lithium, sodium and thallium respectively, and thus to make some of the earliest measurements of the dispersion of air.

159 citations

Journal ArticleDOI
01 Mar 1933
TL;DR: In this paper, a method of measuring attenuation and field strength in the ultra-short-wave range is described, and a resume of some of the quantitative experiments carried out in the range between 17 megacycles (17 meters) and 80 megacecles (3.75 meters) with distances up to 100 kilometers is given.
Abstract: Part I of this paper first describes a method of measuring attenuation and field strength in the ultra-short-wave range. A resume of some of the quantitative experiments carried out in the range between 17 megacycles (17 meters) and 80 megacycles (3.75 meters) and with distances up to 100 kilometers is then given. Two cases are included: (1) "Optical" paths over sea water and (2) "Nonoptical" paths over level and hilly country. An outstanding result is that the absolute values of the fields measured were always less than the inverse distance value. Over sea water, the fields decreased as the frequency increased from 34 megacycles (8.7 meters) to 80 megacycles (3.75 meters), while the opposite trend was found over land. As a rule, the signals received were very steady, but some evidence of slow fading was obtained for certain cases when the attenuation was much greater than that for free space. Part II gives a discussion of reflection, diffraction, and refraction as applied to ultra-short-wave transmission. It is shown, (1) that regular reflection is of importance even in the case of fairly rough terrain, (2) that diffraction considerations are of prime importance in the case of nonoptical paths, and (3) that refraction by the lower atmosphere can be taken into account by assuming a fictitious radius of the earth. This radius is ordinarily equal to about four thirds the actual radius.

123 citations

Journal ArticleDOI
TL;DR: In this article, an accurate and sensitive method for measuring the complex dielectric constant (e′−ie) of gases in the microwave region is described and critically investigated for sources of error.
Abstract: An accurate and sensitive method for measuring the complex dielectric constant (e′‐ie″) of gases in the microwave region is described and critically investigated for sources of error. A resonant‐cavity method is used in which the cavity response curve is displayed on a cathode‐ray tube. The variation of resonance frequency and Q of the cavity when filled with gas are determined from measurements with two frequency markers. The equipment is operated at 9000 Mc, and cavities with Q's of 1×104 are used. In the determination of e′‐1 (dimensionless) of very low loss gases, an accuracy of 0.4 percent and a sensitivity of 4×10−7 can be obtained. In the determination of the loss factor e″, an accuracy of 2 percent and a sensitivity of 5×10−7 can be obtained. This method is useful for measuring dispersion and absorption in solids and liquids as well as gases.Experimental results are given and briefly discussed for e′‐1 of O2, N2, CO2, He, and air, and for e″ of NH3 as a function of pressure up to 20 cm Hg.

53 citations

Journal ArticleDOI
TL;DR: In this paper, the dielectric constant of water vapor was determined at 9280 Mc by a cavity comparison method at 10 temperatures ranging from 32 to 103°C, and observations were made at 24,800 Mc at the single temperature of 24.5°C.
Abstract: The dielectric constant of water vapor was determined at 9280 Mc by a cavity comparison method at 10 temperatures ranging from 32 to 103°C. In addition, observations were made at 24,800 Mc at the single temperature of 24.5°C. Although the vapor pressure was raised to within 10 percent of the saturation value at 24.5°C and 103°C, the variation of (e′−1)/(e′+2) with pressure remained linear, contrary to observations made at radiofrequencies. These data are discussed in relation to the questions of association and adsorption of the vapor. The present results are in agreement with those obtained at radiofrequencies (sufficiently below saturation pressures) and do not show the dispersion reported in an early microwave experiment. Results obtained here and those obtained by others are used to determine mean values for the constants in the Debye equation: namely, P=[3.96±0.32]+[(2.077±0.016)104/T]. This gives a dipole moment of (1.846±0.005)10−18 esu.

48 citations