Geoscience Reference
In-Depth Information
reflectivity is computed from both the long and short PRTs if no overlay is indicated;
otherwise only samples from the surveillance scan (long PRT) are used.
Computation of Doppler variables starts with the discrete Fourier transform. In absence of
clutter, time series data is equally weighted (uniform window) and the power spectrum
estimate (at some range location) is
2
2
mk
M
1
1
j
ˆ ( )
Sk
Vme
(
)
M
,
k
0, 1,...,
M
1
(6)
M
m
0
The discrete inverse Fourier transform applied to (6) produces the value of circular
autocorrelation function at lag 1 (i.e., T s ) which contains one erroneous term, namely the
product of first and last member of the time series (Torres et al., 2007). This term is
subtracted so that the autocorrelation at lag one (i.e., T s ) becomes
2
k
M
1
1
j
ˆ (1)
ˆ
*
R
S k e
( )
M
V
(
M
1)
V
(0),
(7)
M
m
0
and the mean velocity estimate comes out to be (Doviak & Zrnic, 2006. eq 6.19)
ˆ
ˆ
v

(
)arg[
R
(1)].
(8)
4
T
s
The spectrum width for most VCPs is estimated by combining the lag one autocorrelation
M
1
ˆ
2
and the signal power
P
V mP
()
, from which the noise power P n is subtracted, as
s
n
m
0
follows (Doviak & Zrnic 2006, eq 6.27)
1/2
ˆ
P
ˆ
s
ln
.
(9)
v
ˆ
22
T
R
(1)
s
But, if the logarithm term is negative ˆ  is set to zero. In case of phase coding and presence
of overlaid echoes equation (9) is used for the weaker signal in the surveillance scan (long
PRT). The spectrum width of the strong signal is computed for the Doppler scan using the
ratio
ˆ
ˆ
RR as in Doviak & Zrnic (2006, eq. 6.32), because it is not biased by presence of
the weak signal.
(1) /
(2)
3.5 Oversampling in azimuth (overlapping radials)
Until recent upgrades all VCPs had spacing of radials at 1 o azimuth and reflectivities were
averaged and recorded at 1 km range intervals but velocities retained inherent spacing of
250 m (Table 1). Newly added VCPs employ a strategy whereby at the lowest two elevations
time series data from overlapping (in azimuth) beams are processed to produce spectral
moments. Thus data obtained over one degree azimuth are weighted with the von Hann
Search WWH ::




Custom Search