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Conditional probability distributions were calculated by adding up the operations-relevant gust bin data for ten days when strong gusty winds occurred. The winds on these days were caused by synoptic conditions rather than thunderstorms.
Overall, the probability distributions are quite uniform. There is no obvious
skewness to the distributions, which appear very close to normal distributions.
This should be expected, since sample sizes over 30 of a randomly distributed
variable should give approximately normal distributions
, and here
there are several thousand records. As examples, distributions of along-track
gusts for take-offs in direction 07 and cross-track gusts for take-offs in
direction 34 are plotted in
figure 2. These are the
distributions with the greatest and least variance respectively. All the
distributions have equally smooth curves. Generally, the probability of a gust
of magnitude greater than 8.0 
(16 knots) is small, for either
along-track or cross-track gusts, where `small' for this dataset is a 1 in
chance.
Figure 2: Probability distributions of along-track gusts for take-offs in
direction 07 (lower, broader curve) and cross-track gusts for take-offs in
direction 34 (taller, narrower curve), for
a compilation of 10 days of strong synoptically-generated
winds. These are the distributions with
greatest and least variance respectively.
`Bin number' can be read as knots, approximately; divide by 2 to
get . This is a normalized probability density function
whose integral is 1.0 when integrated over bin number.
The equivalent distributions shown in figure 2 are also shown in figure 3 for the single day, 13 April 1994, that was analysed in §2.3; figure 2 is effectively obtained from the third and sixth columns of table 3. It can be seen that the distribution curves, although rougher, are still fairly symmetric. The data from 13 April 1994 was included in the 10-day compilation.
Figure 3: Probability distributions of along-track gusts for take-offs in
direction 07 (lower, broader curve) and cross-track gusts for take-offs in
direction 34 (taller, narrower curve), for 13 April 1994.
As figure 2.
Quantitative comparisons between the gust distributions for various operations
can be made by considering their variances. Because of the large number of
records used (over 
) even the closest variances from the 10-day
compilation are significantly different at confidence levels higher than
99.9%. Hence inferences can be drawn by comparing any distributions, with
very high statistical confidence.
There are some interesting systematic differences when landing and take-off
operations for a particular direction are considered together. For directions
07, 25 and 34, the probabilities of the higher along-track gusts are greater
than those for the cross-track gusts. For example, the summed probability of
along-track gusts between 7.0 and 8.0 in direction 07 is about
2.3
, while the equivalent cross-track gusts have a probability
of about 6
. There is a tendency for strong easterly, westerly
and northerly winds to blow in a reasonably consistent direction, so that the
gusts are either with or against the wind direction. A fluid-dynamical
interpretation is that the turbulence structure of these winds in the boundary
layer consists of rolls with axes normal to the wind direction, rather than
spherical eddies. For direction 16 the distributions reverse; higher
along-track gusts are less probable than higher cross-track gusts. This may be
due to the lower friction a southerly wind experiences because it blows over
the water (Botany Bay), meaning that the boundary layer and any coherently
structured rolls within it are lower than the height of the anemometers.
Comparing directions overall, 07 has the greatest variances and hence the
greatest risk of a higher magnitude gust; direction 34 has the least risk.
The high variance in direction 07, particularly for along-track gusts, may be
caused by the easterly winds being in a less-developed boundary layer, with the
coastline only 6 km away acting as a vortex-generating `trip-wire'. The lower
risk in direction 34 is harder to explain, but is probably associated with the
fact that northerly winds in Sydney are generally weaker than southerly or
westerly winds, and gust magnitudes for strong steady winds are
known
to be proportional to mean wind strength. Details are
summarized in table 4. Recall that for
along-track gusts, negative gusts are lift-reducing; for cross-track gusts,
negative gusts push the aircraft to the left of its path.
Table 4: Standard deviations and probabilities of gusts greater than
5 for a compilation of 10 days of strong synoptically-generated
winds. `A': gusts along the aircraft track; `C': cross-track
gusts; 
: standard deviations in ; 
:
probability of a negative gust of magnitude greater than or equal to
5 ; 
: probability of a positive gust of magnitude
greater than or equal to 5 .
R. Manasseh Papers
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