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the atmosphere, and
V
a
the airspeed of the aircraft. By estimating the updraft from mass
continuity constraint, it is shown to be equivalent to:
V
W
2
h
g
x
F
(2)
xgV
a
where
V
g
is the ground speed of the aircraft, and h the altitude above ground.
For each convergence/divergence feature captured by the TDWR, the velocity change Δ
U
and the distance over which this change occurs Δ
R
are calculated. It is shown in Hinton
(1993) with reference to a microburst model that F-factor could be calculated from:
2
3
V
U
R
R
L
2
h
g
r
a
FK
f
(3)
RL
L
2
R
gV
where
K
= 4.1925,
α
= 1.1212,
h
r
the above-ground-level (AGL) altitude of the TDWR radar
beam,
L
the characteristic shear length of 1000 m, and
erf
(
y
) the error function.
The microburst model in Hinton (1993) includes a shaping function which describes the
change in microburst outflow with altitude. This function is given by:
0.22
hH
/
2.75
hH
/
e
e
ph
()
(4)
0.7386
where
h
is the altitude above ground and
H
the altitude of maximum outflow speed
(assumed to be 90 m). The F-factor
F
1
from the TDWR at the radar beam altitude
h
1
is then
related to the F-factor
F
2
of the aircraft at the altitude
h
2
by the following equation:
V
2
h
g
ph
()
2
2
gV
a
(5)
FF
2
1
V
2
h
g
1
ph
()
1
gV
a
Combining (3) - (5) and with Δ
U
and Δ
R
determined, the F-factor associated with a
divergence/convergence feature at the altitude of the aircraft along the glide path could be
calculated.
For the formulation in (1), F-factor is positive if the windshear is performance decreasing
(headwind decreasing or downdraft) and negative if the windshear is performance
increasing (headwind increasing or updraft). As discussed in Proctor et al. (2000), for
onboard windshear systems, the windshear is considered to be hazardous if
F
is greater than
0.1, and a
must alert
threshold is set to be 0.13. The must alert threshold means a wind shear
alert must be issued when that threshold is reached/exceeded.
A microburst event that affected HKIA on 18 May 2007 is considered here as an illustration
of the method. In the evening of that day, a surface trough of low pressure lingered around
the south China coast, bringing unsettled weather to the region. Between 09 and 10 UTC (5
and 6 p.m. of 18 May 2007), a band of strong radar echoes with east-northeast to west-
