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It is desirable to convert the distributions of gusts into probability
distributions, giving the probability that a gust from a particular bin would
occur. For the GE0 true-direction gusts, this would simply be a matter of
normalizing the distributions by 
, the total number of records for each
sensor. Since there are the same total number of records for each sensor
(unless there is a local fault at a particular instrument), a table of the
probability density functions of GE0 true-direction gusts would look just like
the table of numbers of true-direction gusts
(table 1).
However, when operations-relevant gusts and thresholded gusts are considered,
more possibilities emerge. Two types of probabilities can be computed:
absolute probabilities and conditional probabilities. The absolute probability
of a particular type of gust 
at sensor 
is given by
where, at sensor , 
is the number of gusts
in the particular gust bin required by gust type , and is the total
number of valid records. For example, the absolute probability of
operations-relevant gusts of type `along track gust between -6.0 and
-7.0 
experienced during landing in direction 07' is therefore the
probability that such gusts occurred at sensor 1 and that the local mean
conditions meant aircraft would have been operating in the 07 runway direction
at the time. For the example day of 13 April 1994, the probability above is
, because there were, from
table 2, 220 gusts fitting the
criteria and a total 
of 46140 valid records at sensor 1.
The conditional probability is given by
where 
is a particular gust bin, 
refers to the type of operation,
such as `landing in direction 07' and 
is the number of records for
which would have occurred. For example, the conditional probability of
operations-relevant gusts in the bin for `along track gusts between -6.0 and
-7.0 ' for operations type `landing in direction 07' is the
probability that such gusts occurred at sensor 1 given that aircraft
would have been operating in the 07 runway direction at the time. Continuing
the above example, the conditional probability is 
since there
was a total of 6941 records under conditions when aircraft would have
landed in direction 07. Formally, the two probability types are related by
Conditional probabilities will be of more interest in assessing the risk factors due to gusts, associated with a particular direction of runway usage. For example, it may be of interest to estimate the probability of an aircraft stalling, given that it is landing on runway 07. Absolute probabilities are always smaller than conditional probabilities and enable an assessment of the overall risk of a particular incident. For example, the overall chance of an aircraft stalling on approach 07 would be estimated using an absolute probability.
R. Manasseh Papers
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