Digital Signal Processing Reference
In-Depth Information
3.4.5
Diurnal PWV Variations
The significant diurnal variations of the water vapors are also found over all GPS
stations. The amplitudes of diurnal PWV variations are ranging from 0.2 to 1.2
˙
0.1 mm. The diurnal PWV cycles are stronger in summer than in winter. The
diurnal PWV cycles are closely related to the temperature. The peak times of
diurnal PWV variations are from the noon to mid-night. The semidiurnal (12 h)
PWV variations (
S
2
) are much weaker than the diurnal variations with amplitudes
of less than 0.3 mm in difference seasons. The phase of the
S
2
is noisier than
that of the
S
1
. In general, the S2 peaks occur in early morning and afternoon
(for the second cycle), or around midnight and noon. The diurnal PWV cycles are
mainly controlled by atmospheric large-scale vertical motion, atmospheric low-level
moisture convergence and precipitation, surface evapotranspiration and other factors
(Dai et al.
2002
).
3.5
3-D Water Vapor Topography
The Slant water vapor is defined as the line integral of the water density as
expressed by:
Z
W
e
.; ; h/ ds
SW V
D
(3.14)
where
W
e
(,,
h
) is the water density, , and
h
are the longitude, latitude and
height, respectively. To obtain
W
e
, the troposphere is divided into grid pixels with
a small cell where the water density is assumed to be constant, so that the SWV in
Eq. (
3.14
) along the ray path can be approximately written as a finite sum over the
pixels(
i
,
j
,
k
) as follows:
N
j
X
N
i
N
k
X
X
SW V
D
a
i;j;k
x
i;j;k
(3.15)
i D1
j D1
kD1
where
a
i
,
j
,
k
is the length of the path-pixel intersections in the pixel (
i
,
j
,
k
) along
the ray path, and
x
i
,
j
,
k
is the water density for the pixel (
i
,
j
,
k
). Each set of SWV
measurements along the ray paths from all observable satellites at consecutive
epochs are combined with the ray path geometry into a linear expression. The
unknown water densities
x
can be estimated by the water tomographic technique.
Due to the poor satellite-receiver geometry, Eq. (
3.15
) is ill conditioned, which
needs additional constraints to resolve the ill-equation, e.g., with a covariance matrix
for the correlation between the two voxels obtained from empirical water-field
models or radiosonde observations.
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