The approach used in JPL models, JPL85 and JPL91 [RD.68] [RD.69], is based on a combined consideration of:
•
the distribution of fluences
seen in SEP
events and
• the probability of occurrence of an event (irrespective of magnitude) over a given period.
A normal probability distribution function, f, is employed to describe the log10 of individual event fluences, F,
|
|
(I-5) |
where
μ is the mean of the distribution of the log10 of fluence values
σ is the standard deviation
The probability p of n events occurring in time τ is given by a Poisson distribution such that
|
|
(I-6) |
where
w is the average number of events occurring per active year
The probability, P, of exceeding a selected fluence level, F, during a mission lifetime, τ can be expressed analytically as,
|
|
(I-7) |
where
Q(F, n) is the probability that the sum of all fluences due to n (n = [1, ∞]) events will exceed 10F
The
derivation of P requires an estimate
of the parameters w, μ and σ to perform computer based
JPL-91
has been a de-facto standard for many years. However, it was recently shown
that the values of the parameters μ,
σ and w derived from the data for JPL-91 lead to an underestimation of
the fluence [RD.70]. Updated values of these parameters have been
proposed for the fluence specification in the energy ranges >10 MeV and
>30 MeV [RD.70], [RD.71]. The values of the parameters μ, σ and w of the model that are recommended to
be used are given in Table
I-2.
The
complete calculation of 
has been coded in IDLTM
and the source code can be found in [RD.70].