Digital Signal Processing Reference
In-Depth Information
symmetry constraint especially in the lower troposphere where horizontal gradient
could be significant. Several studies have developed computational efficient ways
of assimilating the RO observations (e.g., refractivity, bending or excess phase)
into numerical weather models by using the 2D linearized forward operator (i.e.,
to convert the model field into the RO observables) (Ahmad and Tyler
1999
;
Syndergaard et al.
2005
; Poli and Joiner
2004
; Sokolovskiy et al.
2005
).
6.2.5.3
Atmospheric Multipath
In the earlier RO missions (e.g., GPS/MET and CHAMP), relatively few soundings
penetrated into the lower half of the troposphere, in addition, significant refractivity
errors including negative biases was present in the lower moist troposphere (Rocken
et al.
1997
). The receiver tracking errors (close-loop) is one of the dominant error
sources (Ao et al.
2003
; Beyerle et al.
2003
). In addition, the presence of frequent
atmospheric multipath in the lower troposphere is another major source of retrieval
errors when applying the geometric optics retrieval method.
As discussed earlier, the geometric optics retrieval method is highly accurate
when the RO signals are monochromatic (single-tone). High accuracy in refractivity
and temperature retrieval near the tropopause and above has been demonstrated
(e.g., Kursinski et al.
1997
). In the lower troposphere, however, radio signals become
non-monochromatic (multiple-tone) and may have very complex structure due to
multipath effects mainly caused by water vapor variation. The GO retrieval method
could introduce significant errors and the radio-holographic retrieval method is
necessary to entangle the multipath problem. To a large extent, the multipath
problem has been resolved by the advanced radio-holographic inversion methods
(e.g. Gorbunov
2002
; Jensen et al.
2003
) and the implementation of the open-loop
tracking technique (e.g. Sokolovskiy
2001
).
6.2.5.4
Ducting (or Super-Refraction)
The atmospheric boundary layer (ABL, i.e., the lowest 1-2 km of the troposphere
that is directly affected by the Earth's surface) is generally capped by a stable
inversion layer with negative moisture gradient. Since the refractivity is a function
of pressure, temperature and water vapor pressure according to Eq. (
6.1
), the vertical
refractivity gradient can be expressed as
c
1
P
T
2
dT
d
z
C
dN
d
z
D
c
1
T
dP
d
z
C
2c
2
P
w
T
2
c
2
T
2
dP
w
d
z
:
(6.11)
The three terms on the right-hand-side (RHS) represent the contributions from
vertical pressure, temperature and water vapor gradients. For typical atmospheric
conditions, the first term due to the pressure gradient is approximately
30 N-
units/km near the surface and decrease in magnitude roughly exponentially with
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