Solar Wind High-Speeds Observed Near the Earth
V.M.Silbergleit +, *
+
Departamento de Física, FIUBA , Av.Paseo Colón 850, Piso 2 – C1063ACV Capital Federal – Argentina
*
CONICET of Argentina
Abstract. To predict the occurrence of major solar wind velocities near the Earth, hourly solar wind speed magnitudes
from November 1963 to May 2000 are considered by applying Gumbel’s first distribution. According to the present
study a maximum value equal to (1017 ± 50) km/sec is expected to observe during the current solar cycle as a
consequence of this result, we infer the possibility to detect intense geomagnetic storms on the Earth.
Sudden commencements (SCs) are the sign
of one of the most important facts that are a
consequence of the interaction of the solar wind
with the Earth’s magnetosphere.
Siscoe [4], studied Gumbel’s first distribution
to the first, second and third largest geomagnetic
storms in nine solar cycles. He used the average
half-daily of the aa indices.
To study the prediction of the major solar wind
speeds Gumbel’s [2] asymptotic distribution
extreme values is considered.
INTRODUCTION
During active periods, fast streams of energetic
particles are ejected from the place of a flare, a
coronal hole, or other variable solar-surface CME
region. Studies of the statistical properties of the
solar wind were understanding using available
spacecraft data., most from spacecraft near Earth
orbit. Interesting results were obtained focalizing
the correlations between plasma parameters and
the solar cycle variations. Solar cycle variations
were observed in the solar wind speed and
pressure [3].
Dynamic processes on the Sun release a plasma
charged particles (mainly protons and electrons)
and associated fields to the Earth´s environment,
being an important cause
of geomagnetic
disturbances at the Earth´s surface. Large
nonrecurrent geomagnetic storms, shock wave
perturbations in the solar wind, and energetic
particle events in interplanetary medium
frequently appear in close connection with
coronal mass ejections. Geomagnetic activity is
vitalized by high solar wind speed and by a
southward
direction of the interplanetary
magnetic field, in solar- coordinates.
SOLAR WIND SPEED PEAKS
The temporal distribution of hourly solar
wind speed values (V ) from November 2, 1963
to May 31, 2000 as obtained by NASA home
page is considered. For each event, the solar
wind speed peaks (Vi, here i =1, ...n is the
number if each solar cycle) is used. The data set,
is constructed by:
i- The compilation of hourly data from November
2, 1963 to May 31, 2000 as they are presented via
homepage of NASA at http://www. NASA.com/
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
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ii- The data processing is applied to digital hourly
V values (to obtain the higher Vi values as
selected in part i).
iii- The selection procedure to obtain the
maximum Vi peaks related to each solar cycle
(using the data recorded in ii) is considered.
Solar cycles
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EXTREME VALUE DISTRIBUTION
T
Gumbel’s first distribution includes most
credible distributions, such as the normal,
lognormal and exponential distributions. The
distribution function is given by Gumbel [2]:
G1(x) = exp {- exp [ - (M1 x-M2) ]} =
exp {- exp [ - α ( x-m) ]}
T'
10
(1)
where m is the mode and A, B and α are
constants. The best fitting adjustment obtained
for solar wind speed peaks considering the
Gumbel’s asymptotic distribution give us the
parameter values M1 = (156 ± 3)10-4 sec/km and
M2 = 15.4 ± 0.3.
Extreme values of the absolute magnitude of the
Vi (with i = 1,2 and 3) are obtained by using the
Vi values detected for each solar cycle and
considering these data in ascending order. Each
observed value was assigned a probability
according to the mean ranking method as
published by Gringorten [1]. A frequently used
approximation is:
Pi = (i-0.44) ( N +0.12) -1
with
i = 1,2...N
1
950
1150
FIGURE 1. The descending /ascending branches
show the waited number of periods required to detect
one with extremes less than /equal to or exceeding x.
distribution function [2]. The arithmetic mean
(am, which is the average of all possible results),
is related to m by the expression:
(4)
am = m + 0.57722 A-1
The relative dispersion (rd) acording to Siscoe [4]
is :
(2)
rd = π (A √6 m) -1
where i is the ordinal number related to the
observed value.
The return intervals T(x) between such extreme
values are calculated by using the expression:
T(x) = [1- exp {- exp [ - (M1 x- M2) ]}]-1
1050
Solar Wind Speed (km/sec)
(5)
The statistical characteristics of the largest Vi
peaks per solar cycle obtained are: m = 987
km/sec, mv = 1012 km/sec, am = 1024 km/sec
and rd = 0.083 km/sec.
The hourly maximum Vi values for the last
three solar cycles are: 951 km/sec, 1021 km/sec
and 1090 km/sec. Although it is interesting to note
that the level of mean hourly Vi peaks is now
much higher that some years ago.
(3)
T(x) is the expected time required to have one
event with the extreme equal to or exceeding x.
The median value is estimated by plotting the
observations ( Fig. 1 shows the ascending
curveT(x) and the descending one
T(x)[T(x)-1]-1 ).
When the ordinate is equal to 2, the abscissa is
equal to the median value (mv).
The standard statistical parameters of the
variable (M1 x-M2) are found from the
CONCLUSION
The results obtained to study the Vi magnitudes
are shown in Fig. 1.
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For the three cycles studied, the solar wind
velocity peaks considered are equal to 951
km/sec, 1021 km/sec and 1090 km/sec
respectively, showing that the level of magnitude
from cycle to cycle was increasing. According to
the present study we conclude that during the
current solar cycle (23) it is predicted an observed
maximum value of the hourly solar wind speed
between 967 and 1067 km/sec, this interval
indicates a predicted value less that the maximum
observed during the prior solar cycle but
sufficiently
strong
to
cause
important
geomagnetic disturbances.
The predicted values obtained for the solar wind
speed peaks indicate that the solar wind particles
are expected to be numerous enough and fast to
modify the Earth´s magnetic field and cause
effects on Earth.
To increase the confident results more
extended data intervals are demanded.
REFERENCES
1. Gringorten, ,I. I., A Plotting Rule for Extreme
Probability Paper. J. Geophys. Res. 68, 813,
(1963).
2. Gumbel, E. J., Statistical Theory of Extreme
Values and Some Practical Applications. Nat.
Bur. Standards Appl. Math. Ser. 33, Washington
D.C., 51,.(1954).
3. Neugebauer, M., Large scale solar cycle
variations of the solar wind. Space Sci. Rev.
17, 221, (1975).
4. Siscoe, G. L., On the Statistics of the Largest
Geomagnetic Storms per Solar Cycle. J.
Geophys. Res., 81, 4782, (1976).
_______________
V.M.Silbergleit, Departamento de Física de la
Facultad de Ingeniería (UBA) and CONICET.
Av.
Paseo Colon 850 - C1063ACV-Buenos Aires Argentina
Fax: 54 11 49 63 20 62.
email: vsilber@fi.uba.ar
ACKNOWLEDGMENTS
This work was partially supported by
agreements of Facultad de Ingenieria
(Universidad de Buenos Aires) and CONICET
of Argentina.
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