Global Positioning System Reference
In-Depth Information
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This auxiliary quantity can be accurately estimated from climatologic data. Correc-
tions with surface temperature permit
T
mr
estimates to be computed to a typical ac-
curacy of
∼
3 K. Using the relationship
τ
(
∞
)
e
−τ
ds
e
−τ
(
∞
)
α
=
1
−
(6.55)
0
where we used again
d
τ
=
α
ds
, the radiative transfer equation (6.47) can be written as
T
mr
1
e
−τ
(
∞
)
T
cosmic
e
−τ
(
∞
)
T
b
=
+
−
(6.56)
which, in turn, can be rewritten as
ln
T
mr
−
[20
T
cosmic
T
mr
−
τ
∞
=
(
)
(6.57)
T
b
Lin
—
-
——
No
*PgE
The opacities and brightness temperature show similarly high correlations with the
wet delay. In fact, at low elevation angles the opacities correlate even better with the
wet delay than do brightness temperatures.
If the user measures the brightness temperatures along the slant path rather than the
zenith direction, the observed
T
b
must be converted to the vertical to estimate ZWD
using (6.53). Given the slant
T
b
measurement at zenith angle
ϑ
, and an estimate of
T
mr
, the slant opacity can be computed and converted to the zenith opacity using the
simple 1
/
cos
(ϑ)
mapping function. The equivalent zenith
T
b
follows from (6.56).
For elevation angles above 15° this conversion is very accurate.
T
mr
for a specific site is computed from (6.54) using radiosonde data that typify
the site. The variation of
T
mr
with slant angle is minimal for elevations down to about
20°. The value used for WVR calibration and water vapor retrievals can be a site-
average (standard deviation typically about 10
K
), or can be adjusted for season to
reduce the uncertainty. If surface temperatures
T
are available, then
T
mr
correlations
with
T
can reduce the
T
mr
uncertainty to about 3 K.
[20
6.
3.4 Calibration of WVR
Because the intensity of the atmospheric microwave emission is very low, the WVR
calibration is important. Microwave radiometers receive roughly a billionth of a watt
in microwave energy from the atmosphere. The calibration establishes a relationship
between the radiometer reading and the brightness temperature. Here we briefly dis-
cuss the calibration with tipping curves. This technique provides accurate brightness
temperatures and the instrument gain without any prior knowledge of either.
Under the assumption that the atmosphere is horizontally homogeneous and that
the sky is clear, the opacity is proportional to the thickness of the atmosphere. Clearly
the amount of atmosphere sensed increases with the zenith angle. For zenith angles
less than about 60° one might consider adopting the following model for the mapping
function for the opacity:
