Geoscience Reference
In-Depth Information
T
eff
(ν)
−
T
bg
T
B
(ν)
=
T
bg
+
τ (
∞
, ν),
(178)
where the linearized effective temperature
T
eff
is given by
S
T
(
s
) α(
s
, ν)
d
s
T
eff
(ν)
=
.
(179)
τ (
∞
, ν)
If
T
eff
and
T
eff
are consistently modeled, the error in
T
B
caused by an error in
T
eff
will be approximately canceled by the error in
T
eff
. Thus the linearized brightness
temperature can normally be estimated with higher accuracy than the opacity.
The linearized brightness temperature can be divided into four parts
T
B
(ν)
=
T
wv
+
T
lw
+
T
ox
,
T
bg
+
(180)
where
T
wv
,
T
lw
, and
T
ox
are the contributions fromwater vapor, liquid water, and oxy-
gen, respectively.
T
bg
is constant and well known. The oxygen part can be accurately
modeled using measurements of the surface pressure and temperature (Jarlemark
1997
), while the liquid water contribution is approximately proportional to the fre-
quency squared (if the water droplets are much smaller than the wavelength). If the
frequencies are properly chosen,
T
wv
is proportional to the wet delay. Thus the wet
delay can be estimated by a combination of measurements at two different frequen-
cies
ν
1
and
ν
2
ν
2
ν
1
2
T
B
(ν
1
)
−
T
B
(ν
2
)
−
Δ
L
w
=
c
b
T
bg
,
ox
,
(181)
where
T
bg
,
ox
is the contribution from oxygen and the cosmic microwave background.
For the estimation of the wet delay we need to know the retrieval coefficient
c
b
,
as well as
T
bg
,
ox
,
T
eff
, and
T
eff
. Normally these parameters are modeled as functions
of the surface pressure, temperature, and humidity. To model
c
b
, one can use WVR
measurements and simultaneous observations of the wet delay made by another
instruments. Then the model coefficients can be obtained by fitting the radiometer
observations to the wet delay observations. The disadvantage of this method is that
it requires a long time series of measurements, ideally longer than one year in order
to be able to take seasonal variations into account. Furthermore, any systematic
error in the wet delay measurements will cause systematic errors in the retrieval
coefficient. Amore commonly usedmethod is to use profiles of pressure, temperature
and humidity obtained from e.g. radiosondes to calculate the theoretical values of
T
B
,
T
bg
,
ox
,
T
eff
,
T
eff
, and
L
w
. These can then be used to estimate appropriate models
for the parameters. For details, see e.g. Elgered (
1993
) and Jarlemark (
1997
).
Several studies have been performed where WVRs have been used to correct for
the wet tropospheric delays in space geodetic (mostly VLBI) data analysis. Examples
of such studies are Elgered et al. (
1991
), Kuehn et al. (
1991
), Ware et al. (
1993
),
Δ
