Geoscience Reference
In-Depth Information
of two-color SLR measurements. When the water vapor and the curvature effects are
neglected, the new formula reduces to the 2C-SLR formula, Eq. (
164
). Further detail
of this new formula can be found in Wijaya and Brunner (
2011
).
4.4 Water Vapor Radiometry
A Water Vapor Radiometer (WVR) is an instrument that can be used to estimate the
atmospheric wet delay. It does this by measuring the thermal radiation from the sky
at microwave frequencies where the atmospheric attenuation due to water vapor is
relatively high. These measurements can then be related to the wet delay.
Equation (
9
) describes the attenuation of radio signals caused by the atmosphere.
The attenuation will depend upon frequency, as well as on temperature, pressure,
humidity, and liquid water content. For details about how
can be modeled as
function of these quantities, see e.g. Liebe et al. (
1993
) and Rosenkranz (
1998
).
Normally the radiation power from the sky is expressed using the brightness
temperature
T
B
, which is defined as the physical temperature a black body would
have if it radiates the same amount of power as the sky. For low frequencies
T
B
is
related to
W
sky
by
α
W
sky
(ν)
=
k
b
T
B
(ν)
B
,
(171)
where
k
b
is Bolzmann's constant and
B
the observed bandwidth. This relation is
valid for frequencies
ν
/
h
, where
h
is Planck's constant. This requirement is
fulfilled at microwave frequencies for normal atmospheric conditions.
The brightness temperature can be calculated from the equation of radiative
transfer
k
b
T
T
bg
e
−
τ (
∞
,ν)
+
e
−
τ (
s
,ν)
d
s
T
B
(ν)
=
T
(
s
) α(
s
, ν)
,
(172)
S
where
T
bg
is the brightness temperature of the cosmic microwave background
(
≈
τ (
, ν)
2.7 K). The opacity
s
is given by
s
0
α(
s
, ν)
d
s
.
τ (
s
, ν)
=
(173)
T
B
depends upon the pressure, temperature, humidity, and liquid water density pro-
files. The dependencies on these quantities will vary with frequency; for some fre-
quencies (e.g. close to the center of a water vapor absorption line like 22.235 or
183 GHz) there will be a high sensitivity to water vapor while other frequencies (e.g.
close to the center of the oxygen absorption lines around 60 and 120 GHz) are more
sensitive to the pressure and temperature. For good sensitivity to these parameters,
the attenuation needs to be high but not too high. If the attenuation is too high the
brightness temperature will approach the physical temperature of the atmosphere,
thus the sensitivity to the atmospheric properties will be lost. For retrieval of the
