Geoscience Reference
In-Depth Information
water vapor content the frequencies close to the 22.235 GHz line are normally the
most suitable ones since this line is not too strong. For very dry conditions (e.g. high
altitudes) higher frequencies (e.g. 183 GHz) will give higher sensitivity, however for
normal conditions the attenuation is too high.
The sensitivity to the different atmospheric quantities also varies with height, e.g.
some frequencies have a higher sensitivity to humidity close to the ground (frequen-
cies on the edge of awater vapor absorption line) while others aremore sensitive to the
humidity at high altitudes (frequencies close to a water vapor absorption line). Thus
it is in principle possible to estimate the humidity profile using radiometer measure-
ments at several different frequencies having different sensitivity to humidity with
height, a so-called radiometric profiler (Askne and Westwater
1986
; Scheve and
Swift
1999
). This humidity profile could then be taken to calculate the tropospheric
delay. However, the need for using many channels makes the radiometric profilers
expensive, and it is difficult to find a set of frequencies from which the humidity pro-
file can be estimated without running into any singularity problems. Furthermore,
if only the integrated amount of water vapor—or the wet delay—is of interest we
do not necessarily need to know the profile. If a frequency can be found where the
sensitivity to the refractivity is constant with height, this is sufficient.
Normally the brightness temperature is not used directly to estimate the wet delay.
Instead the opacity
is calculated from the brightness temperature, which is
then used for the wet delay estimation. By introducing the effective temperature of
the atmosphere
T
eff
τ (
∞
, ν)
S
e
−
τ (
s
,ν)
d
s
(
) α(
, ν)
T
s
s
S
T
eff
(ν)
=
,
(174)
α(
s
, ν)
e
−
τ (
s
,ν)
d
s
we can write
T
B
as
1
e
−
τ (
∞
,ν)
T
bg
e
−
τ (
∞
,ν)
+
T
B
(ν)
=
T
eff
(ν)
−
.
(175)
Thus the opacity can be estimated by
ln
T
eff
−
T
B
τ (
∞
, ν)
=−
.
(176)
T
eff
−
T
bg
Some WVR retrieval algorithms to estimate the wet delay from
directly (Westwa-
ter et al.
1989
; Bosisio and Mallet
1998
). However, this requires that the effective
temperature
T
eff
is accurately estimated. An alternative way is to use the linearized
brightness temperature
T
B
(Wu
1979
)
τ
T
B
(ν)
=
T
bg
[1
−
τ (
∞
, ν)
]
+
T
(
s
) α(
s
, ν)
d
s
.
(177)
S
The linearized brightness temperature can be calculated from the opacity by
