In the correction of satellite Doppler data for tropospheric effects the precipitable water vapor (PWV) is inferred at the tracking site. The technique depends on: (1) an ephemeris for the satellite; (2) an analytic model for the refraction range effect that is good to a few centimeters; (3) Doppler data with noise level below 10 centimeters; and (4) a surface pressure/temperature measurement at the tracking site. The PWV is a by product of the computation necessary to correct the Doppler data for tropospheric effects. A formulation of the refraction integral minimizes the necessity for explicit water vapor, temperature and pressure profiles

Black, H. D.

Eisner, A.

English

NASA Technical Reports Server

/[1 84 2T2, 3
Q
A NEW TECI[NIQUE FOR MONITORING TIIE
_"- WATER VAPOR IN THE ATMOSPIIERF
_ , Harold D. Black and Arie Eisner
. The Johns Hopki**s University
_ "_ Applied Physics Laboratory
Johns Hopkins Road
Laurel, MD 20707
; (USA)
- ABSTRACT
In correcting satellite doppler data for tropospheric effects,
we have found that we can infer the precip_table water vapor (Pg_)
at the tracking site. The determination proceeds via a least-squaresl'
. _ fit of a refraction parameter to each fifteen-_inute pass of data.
,2
,- For its success, the technique depends on having: i) an ephem-
eris for the satellite, 2) an analytic model for the refraction range
' effect that is good to a few centimeters, 3) doppler (range differ-
_ ence or cycle count) data with noise level below i0 centimeters, and
., 4) a surface pressure/temperature measurement at the tracking site.i
The P_ is a by-product of the computation necessary to corzect
• the doppler data for tropospheric effects. We have tried for a num-
_ ber of years to reliably isolate the tropospheric refractive effect :
in the doppler shift measurement. It is only recently that we have {
succeeded in doing this. Our rec_nt success was due to a formulation :
of the refraction integral which minimized the necessity for explicit
_. water vapor, temperature and pressure profiles.
1. THE DOPPLER SHIFT AND THE REFRACTIVE EFFECT
_ A common and convenient model of the doppler shift measurement !
contains the range to the satellite at two contiguous times. These i
} ranges are corrupted by tropospheric effects which can be written: {
I
/ i6s = I0 -6 (Nd+N w) do (i) '
_ wherein I
Nd is the "dry" refractivity : _I
i
Nw is the "wet" refractivity I
i I
The Smith-Weintraub expressions for these are: i
q
327
1984019194-329
https://ntrs.nasa.gov/search.jsp?R=19840019225 2020-03-22T09:29:03+00:00Z
_d = 77.6 P/T
_ = (3.73 x 105 °K2/mbar) e/T 2
." W
wherein
: (e,T,P) are the (water vapor pressure, temperature total atmo-
spheric pressure) at a point within the troposphere.
Units consistency requires e and P in millibars and T
Physical rigor (Fermat's principle) insists that the integration path
be an extremum. Except at low elevation apgles, this requirement is
not important as ray-tracing studies show; we can use the instanta-
neous straight line connecting the satellite and observer for the
integration path. If we then change variables from p to h (see
Fig. i), we obtain
_- hd£
ts = 10 -6 1 (Nd+Nw) dh (2)
°
Since both the wet and dry troposphere extend to heights that are
small compared to the radius of the earth; h/Re < hd/Re = 0.007, we
replace eq. (2) with
•/hdAs = 10 -6 Idw (Nd+N w) dh (3)
0
wherein
! i -'12Idw _ 1 -- i + Xdw hd/R (4)
and
.. 0 < IXdw = Xdw (e,T) I < 1
I
J
i
328
J
1984019194-330
3F POOR QUALITY
E
J
¶
i
i
J
Fig.1 Troposphericgeometry, i
t
i
l
L
!
Ii
i
i
!
!
!
l329 [
i®'
_ .... ,;° . , , t.
o-
1984019194-331
Using explicit models of Nd and Nw which, in turn, require models for
: the atmospheric state, we were able to show that eq. (3) and (4)
_',_ could be written
4,
I0-6 .,_ .. cos E
= (_,_d+_w) dh i - 1 _ O.O01 (5)
with an error which did not exceed a few centimeter_ if we do not use
elevation angles les_ than 7.5 ° . Above 20 ° the form l_-spractically
exact, i._., the error is, at most, a few millimeters.
Equation (5) is a convenient separation (amplitude . geometry),
moreover, in the amplitude
/d_s h = 10 -6 (Nd+N w) dh (6)
0
! We have absorbed, "buried", the difficult problems of modeling the
atmospheric state as a function of the surface conditions. We say
difficult'; the water vapor is not uniformly distributed in the half
space above the observing site, and modeling has fundamental limita-
tions.
We used eq. (5) as a model of the tropospheric range effect and
- associated an amplitude, eq. (6), with each fifteen-.minute pass of !
data. We fitted the amplitude without any a priori constraints on the
value of ASh; although we have, with a surface pressure measurement, a
lower bound i
hd?
(the dry effect = 10 -6 J Nd dh) which is 85-90 percent of the
0 _
i
combined wet-dry integral. This dry integral is very closely 2.305 i
(meters) times the surface pressure in atmospheres. To isolate the i
tropospheric amplitude, we performed a four-parameter fit; the three I
• iadditional parameters absorbed orbit, position and frequency biases
- 2. RESULTS I
I
_" We have used doppler data characterized as follows: I
I
Obtained at a globally-distributed set of tracking sites I
_ from two of the Transit satellites, 30140 and 30180. !
2. O_e two-day data span was obtained during February 1980 !
| (days 48-49) and another during July 1982 (days 197-198)• Each span I
• contained approximately eighty passes, i
! A
330
I
' _,,_e-.,_
J9840J 9J94-332
• Results of the amplitude fitting for days 197-198 are sho%_ in
Fig. 2. The lower bound, the straight line, is a consequence of the
Hopfield theory (see Refs. 2 and 4). Data points falling below this
straight line are "wild" (invalid). There are four of these. The
distance from each of the _alid data points to the straight line is
the wet term
i0 _ _;w dh
We then computed the mean value (for the valid data) at each of the
sites; mean over two days for each of the two data sets. Four sta-
tions were represented in both data sets: Johannesburg, Seuth Africa;
Las Cruces, New Mexico; San Jose Dos Campos, Brazil; and Herndon,
Virginia. The data at these four sites agree with the (usually true)
; finding that the atmosphere contains more water vapor in the sum_er
than it does in the winter, Fig. 3. A tabulation of the results shown
in Fig. 3 is given in Table i. From Fig. 3 we see that synoptically
the wet term is about I0 percent of the dry.
M
, 3. PRECIPITABLE WATER VA_OR
!|_ii The 'wet' range integral for a vertic_l path can be written,
using the Smith-Weintraub expression for the refractivity:
?
5
0
I: and assuming the water vapor obeys the perfect gas law:
T
e = Pe RT (8)
we have
/ PeAS w -- 0.373 R _--dh (9)
and, in turn, a linear decrease of tem_eratui-e with height facilitates
' an expansion in terms of the mo_e_ts of the water vapor distribution.
0. 373 1 dh + L
i ASw = T0 RPw _ Pe _ h Pe dh + ... (i0)
alternately,
i
331 •
1984019194-333
_JRIGINAL PAGE |g
OF POOR QUALITY
!.

334 ......
] 9840] 9] 94-336
1.722 X 103 1 /'r | L hwv
'Sw -- _ Ow ]'e dh I 1 +"0 TO
Dw is the density of (liquid) water. TO is the surface temperature
(°K) ,_nd L is the (absolute value of the) temperature lapse rate
(= 6.5°/Pro), hwv is the scale height of the water vapor in the atmo-
sphere (_ 5.2 kin). Each of the terms in the expansion, eq. (10), has
units of height. T_e first term, the dominant one, is the "precipi-
table water vapor" The dimensionless term in front is about 6.0.
It is precisely 6.0 for TO = 287°K. The second term (the first moment
in the expansion) is approximately 5 percent of the precipitable water
vapor (Ref. 3). The second moment is a factor of ten less than the
first. Consequently, we can, with surface temperature and pressure
measurements, interpret our results for the (wet) range effect in
terms of precipitable water vapor.
4. CO_CLUDI_G RE_RKS
In keeping with the spirit of this meeting, the significant find-
ings from this study are:
i. It is possible to determine the total atmospheric water vapor
using microwave doppler measurements. This measurement differs from
the water vapor measurements made with radiosondes or with microwave
radiometers. The latter two produce water vapor estimates along a
profile through the atmosphere. The doppler technique produces a
different sort of estiPate; it is a 'bulk' estimate over that fraction
of the trol:osphere swept out by the satellite-observer vector.
Typically a region extending out to 150 km, on the satellite side of
the observing site, will be s<impled (see Ref. I). Each of these kinds
of measurements have their uses.
It would be interesting and useful to study the correlation
between the different kinCs of measurements. The data currently
exists to do this.
2. It is possible to derive a model of the tropospheric range
effect which is accurate to a few centimeters. The 'thinness' of the
troposphere (compared with the radius of the earth) is an essential
fact in developing the model. By model we mean one in which there is
a clear separation of geometry on the one hand and an atmospheric-
state-_ependent amplitude on the other.
3. The tropospheric range amplitude is (demonstrably) separable I
|
from the otber errors affecting the doppler shift. The accuracy with
which the tropospheric range effect is isolated depends on the I
accuracy of the modeling and the noise level of the data. The exist- Ii
ing data noise is about i0 cm (in range difference), and we are cur- i
rently unable to fully exploit the accuracy implicit in the theory. I
J
I
335
1984019194-337
_; It is easily within the current state-of-the-art to build
satellites and ground equipment which will reduce the noise level of
the data. Equally important for these purposes would be raising the
frequency pair from 150/400 MHz to (say) 400/1200 MHz to reduce the
higher order ionospheric effects in the data.
5. REFERENCES
Black, H.D., 1978: An easily implemented algorithm for the tropo-
spheric range correction. J. Geophys. Pes., Vol. 83 (B4).
Goldfinger, A.D., 1980: Refraction of microwave signals by water
vapor. J. Geophys. Res., Vol. 85 (C9).
Hopfield, H.S., 1971: Tropospheric effect on electromagnetically
measured range: Prediction from surface weather data. Radio
Science, Vol. 6, _o. 3, pp. 357-367•
This paper is a synopsis of: Black, H.D., and Eisner, A., 1983:
Correcting satellite doppler data for tropospheric effects.
! APL/JHU Report SDO-6777 Also in press in the J Geo_hys. Res.
%
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mm
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1984019194-338


A new technique for monitoring the water vapor in the atmosphere

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