For some prediction purposes it is useful to know how many X-ray flares
of a given energy might be expected. For example, if the predicted
yearly sunspot number for 1994 is 30, how many flares of class M1-2 or
X1-2 might be expected during the year. These sort of estimates have particular
value when combined with other information to yield estimates of fadeout effects
on HF circuits.
Two equations are useful in making such estimates. Firstly, the following
equation, derived from flare data between 1976 and 1991, connects
sunspot number R12 and the total number of M Class
flares (Nm) in a
year. Equation (2) is a similar relationship, but between sunspot
number and the total number of X Class flares in a year.
Nm = 2.86 R12 (1)
Nx = 0.23 R12 (2)
A second equation gives the distribution of flares in X-ray class
as derived from
flare data from 1976 to mid 1993.
N = Nm DELTA 1.26 X ** (-2.12) (3)
where,
X is the X-ray class measured as 1.0 for M1, 5.0 for M5,
and 10.0 for X1 and so on;
N is the expected number of flares in a range DELTA centred on
an X-ray class of X.
and ** indicates a power - i.e. X raised to the power -2.12.
To calculate the number of flares in a range M1-2, the above equation
can be used with X = 1.5 and DELTA = 1.0. Similarly, for a range
X1-2, X = 15 and DELTA = 10.
Figure 1 shows flare occurrence plotted against X-ray class, indicating that
equation (3) gives a good fit right from class M1 through to X5.
It should be stressed that equations (1), (2) and (3) are statistical
in nature whilst flares, even at solar minimum, come in clumps where the
expected yearly occurrence may be produced within several weeks. Nevertheless,
in the absence of more detailed knowledge, the equations produce estimates
which are useful for planning purposes. Naturally, the random nature of
flares is more apparent and the equations less useful, when
short time intervals are used.
Educational