Geoscience Reference
In-Depth Information
2
2
2
2
2
2
2
(
rk
)
(
rk
)
rr
(
k
,
)
(8)
s
s
s
sr
0
0
where
r
2
= (0.35c/2)
2
,
2
=
1
2
/16ln2, and
2
=
1
2
/16ln2. Here c/2 is range resolution,
and
1
is the one-way angular resolution (i.e., beamwidth).
k
,
k
, and
k
r
are the components
of shear along the three orthogonal directions.
In order to use
t
to estimate eddy dissipation rate (EDR) , it must be assumed that within
radar resolution volume turbulence is isotropic and its outer scale is larger than the
maximum dimension of the radar's resolution volume (which is indicated as V
6)
. Under
these assumptions, in the case of
the relation between turbulence spectrum width
t
and EDR can be approximately written as (Labitt, 1981)
r
r
3
3/2
0.72
t
,
(9)
r
where A is constant (i.e., about 1.6). When
r
, the relation can be approximated by
r
23
2
2 2
11
4
r
t
3/2
(10)
[
](
)
3/2
2
15
15
(1.35
A
)
r
r
Eqs. (9) and (10) are used to estimate EDR using Hong Kong TDWR observed spectrum
width.
In hazardous weather mode, the Hong Kong TDWR conducts sector scans from azimuth
182
o
to 282
o
(i.e., confined to the approach and departure paths). Each sector scan takes
about 4 minutes. Thus, the low altitude wind shear can be detected within a minute. The
range and angular resolutions of the radar are 150 m and 0.5
o
respectively. The maximum
range reaches 90 km. The radar data includes reflectivity, Doppler velocity, spectrum width,
and signal-to-noise ratio (SNR) recorded with the azimuth interval of 1
o
.
Based on the Eqs. (9) and (10), EDR can be estimated when spectrum width observation is
available. In this feasibility study, EDR estimation is only performed at the lowest elevation
angle of 0.6
o
. The vertical wind shear contribution to the EDR is calculated by using spatially
averaged mean Doppler velocity at two lowest elevation angles. Because the closest two
elevation angles at lowest level are 0.6
o
and 1.0
o
at scans 11 and 12, vertical wind shear is
calculated by using the Doppler velocity fields at these two scans. For simplicity, EDR is
estimated at scan 17 with elevation angle of 0.6
o
. Azimuthal and radial wind shear is also
calculated at this scan. So in the current algorithm, one EDR field at elevation angle of 0.6
o
will be generated for each volume scan.
The control of the TDWR spectrum width data quality is very important for EDR estimation.
It has been found that there is a variety of sources of errors in spectrum width
measurements in previous studies (Fang et al. 2004). Especially if signal to noise ratio (SNR)
is low, spectrum width measurements have large variance. In this study, SNR > 20 dB is
assigned as a simple and straightforward threshold for the EDR estimates. In other words,
EDR at the gate with SNR < 20 dB is marked as missing data (MD) in our algorithm. In the
future, more comprehensive quality control processor will be designed and implemented in
our algorithm to deal with other error sources.
