NG23A-1467
Statistical Projection of Solar Cycle 24 for the Exposure Estimates
Myung-Hee Y.
1Division
1
Kim ,
John W.
Statistical Estimation of Future Solar Activity Levels and Projection of Solar Cycle 24
Approach
Sunspot number cycle:
Correlated well with many observable space quantities
Represents variation in the space radiation environment
A solar cycle statistical model(1-3) for the estimation of solar activity
(SA) levels and the cycle 24 projection is based on:
Accurately defined solar minimum 24 in December 2008
Up-to-date sunspot data of current solar cycle 24
Using the accumulating sunspot data of numbered even cycles
⇒ The resultant projection of solar cycle 24: a basis for estimating
exposure in future space missions by the degree of disturbance in
the solar surface
⇒ Projection errors of solar cycle 24: self-corrected with the
progression of the cycle 24
Observable Space Quantities
0.8
140
Up-to-date mean with standard deviation
2012.3
150
SA=25.3% ± 7.9%
0.4
0.3
0.2
0.1
0
Dec-08
Mar-09
Jun-09
Sep-09
Dec-09
Mar-10
Jun-10
Sep-10
Dec-10
Mar-11
20
1800
1850
1900
1950
0.8
22
24
0.5
SA=25.3%[28.0%, 22.6%]
0.3
0.2
0.1
Jun-09
Sep-09
Dec-09
Mar-10
Jun-10
Sep-10
Dec-10
Group Sunspot Number and Solar Particle Event
Impulsive Nitrate Event(5)(■) and Space Era Event(6) (■)
2.0E+10
1.8E+10
1.6E+10
1.2E+10
1.0E+10
100
8.0E+09
6.0E+09
50
4.0E+09
1660
1710
1760
1810
Year
1860
1910
1960
2.0E+09
2010
Φ30, cm-2
1.4E+10
Dalton
Minimum
60
Cycle 12
Cycle 14
0
2010
2012
2014
Year
2016
2018
0
2020
Mar-11
Jun-11
Even Cycle Parameters
ΦIMP Data
160
140
ΦACE Data
120
100
800
80
400
1972
60
40
Sunspot
Cycle
Number
2
4
6
8
10
12
14
16
18
20
22
24
1992
Year
2002
0
2012
BO10 GCR Model: A predictive model for GCR radiation environment(7,8)
Fokker-Planck equation
- steady-state, spherically symmetric
- diffusion, convection, and adiabatic deceleration
Local Interstellar Spectrum (LIS) - GCR Spectrum at outer edge of heliosphere
Solar Modulation Parameter, Φ (~solar activity, sunspots)
- determines GCR's rigidity to overcome heliosphere
- derived from sunspot number accounting for time delay as solar wind
carries the magnetic disturbances outward
⇒ Prediction of GCR environments by the projection of sunspot cycles for
future space exploration missions.
SPE Onset Dates: 1 January 1956 - 31 December 2007
Solar Minimum
Solar Maximum
Year
Month
Year
Month
1766
1784
1810
1833
1856
1878
1901
1923
1944
1964
1986
2008
7
9
8
12
1
12
9
8
3
11
10
12
1769
1788
1816
1837
1860
1883
1907
1928
1947
1968
1989
2011*
9
2
5
4
2
12
1
5
7
11
8
8*
Cycle 19
2/1/54
Cycle 20
2/1/62
Cycle 21
2/1/70
2/1/78
Cycle 22
2/1/86
Cycle 23
2/1/94
2/1/02
Propensity of SPEs
Hazard Function of Offset β Distribution Density Function
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
SA in Rising Phase
20
1982
60
90
Month from Solar Minimum
120
150
⇒ A statistical model to predict future solar activity with self-correcting projection errors as cycle’s progression is a useful analysis tool for exploration mission
design studies.
180
500
30
• Mean solar activity level (SA) of cycle 24 is estimated as 25.3%[22.6%, 28.0%] with 95% confidence interval based on up-to-date measurement of sunspot
numbers.
• Future development of cycle 24 at a given solar activity level is projected based on accumulating sunspot data of numbered even cycles.
• Cycle 24 with the recent deep extended solar minimum is more active than cycle 6, which is the latter cycle of Dalton minimum recorded as the least active cycle
among numbered even cycles with SA= 11.3%[ 9.4%, 13.1%].
• The predicted trajectory of cycle 24 is peaked in early 2014, and similar to cycle 14 and 12 in the rising and declining phases, respectively.
• The amplitude of cycle 24 is expected to be the 2nd or 3rd inactive solar cycle among historical even cycles.
• A temporal forecast of GCR radiation environment(7,8) and the probability of solar particle events(9) for a given mission period can be derived by implementing the
resultant projection of sunspot numbers.
0.6
Mar-09
2014.1
Conclusion
0.7
2000
(4)
Maunder
Minimum
0
2008
Up-to-date mean activity level with 95%CI
0.4
80
40
2014.3
Activity level of measurement
600
200
10% level
Measured
sunspot number
Application of a Solar Cycle Statistical Model to the Prediction of Radiation Environments for Future Space Exploration Missions
Year
250
2013.9
0.9
700
0
1750
30% level
Sunspot
Cycle
Number
2
4
6
8
10
12
14
16
18
20
22
24*
2/1/54
Solar Activity Levels of Rising Phase,
SAR
70.6%[64.8%, 76.5%]
81.5%[78.1%, 84.9%]
11.3%[ 9.4%, 13.1%]
71.7%[65.3%, 78.0%]
38.2%[34.5%, 41.9%]
35.6%[32.2%, 39.0%]
27.5%[24.1%, 30.9%]
41.9%[37.9%, 45.9%]
68.3%[62.6%, 74.0%]
63.6%[59.4%, 67.8%]
92.3%[87.2%, 97.4%]
25.3%[22.6%, 28.0%]
*For solar cycle 24, up-to-date measurements until August 2011
are accounted for SAR.
2/1/62
2/1/70
2/1/78
Date
2/1/86
2/1/94
2/1/02
Cumulative Occurrence in a Solar Cycle
1
Cycle 19
0.9
Cycle 20
0.8
Cycle 21
Cycle 22
0.7
P
18
50% level
Cycle 24 projection at the 25.3% level
20
BO_GCR Modulation Parameter
and International Sunspot Number
16
70% level
λ(t), events/d
14
2012.5
100
100
Cycle 6
Smoothed Sunspot Number
12
90% level
Jun-11
Mean Activity Level with 95% Confidence Interval
based on Up-to-Date Measurements
1
Even cycle
10
100% level
50
900
8
2012.3
Measurement
70
6
Smoothed Monthly Sunspot Number
0.5
1200
4
120
0.6
Smoothed Sunspot Number
Solar Activity
0.7
Φbar, MV
Smoothed Monthly Sunspot Number
2012.3
1000
0
1610
200
Activity level of measurement
0
Dec-08
International Sunspot Number(4)
2
Cycle 24 Projection from Even Cycle Distribution
160
1100
150
Current Trend to Even Cycle Distribution with Estimated Maximum Date
0.9
140
Group Sunspot Number
Solar Cycle 24 Progression Trend
based on Up-to-Date Measurements
1
Solar Activity
A solar cycle statistical model(1-3) has been developed based on
the accumulating cycle sunspot data to estimate future levels of the
solar cycle activity. Since the current solar cycle 24 has progressed
about three years(4), the mean solar activity levels of the cycle 24 are
estimated with an accurately defined solar minimum 24, and then
solar cycle 24 is projected with the cycle activity levels using the
statistical model. The projection of solar cycle 24 will be coupled to
space related quantities of interest to radiation protection, because
interplanetary plasma and radiation fields are modulated by the
degree of disturbance in the solar surface. Radiation doses received
by astronauts in interplanetary space are likewise influenced.
Therefore, the resultant projection of solar cycle 24 provides a basis
for estimating exposure in future space missions. Projection errors
will be corrected as the cycle progresses and the observations
become available, because the model is shown to be self-correcting.
Odd cycle
and Francis A.
3
Cucinotta
of Space Life Sciences, Universities Space Research Association, Houston, TX 77058, USA (myung-hee.y.kim@nasa.gov)
2Distinguished Research Associates, NASA Langley Research Center, Hampton, VA 23681, USA
3NASA Johnson Space Center, Houston, TX 77058, USA (francis.a.cucinotta@nasa.gov)
Abstract
210
2
Wilson ,
Cycle 23
Impulsive Nitrate Events
0.6
Nitrate Events with Correction
Space era
0.5
0.4
0.3
0.2
0.1
0
104
105
106
107
Φ30, p cm-2
108
109
The randomness of each event size of ΦE and SPE occurrence
⇒ Simulation of total ΦE distribution for each mission period
by random draw from a Gamma distribution(9).
1010
References
(1) J. W. Wilson, M. Y. Kim, J. L. Shinn, H. Tai, F. A. Cucinotta, G. D.
Badhwar, F. F. Badavi, and W. Atwell, Solar Cycle Variation and
Application to the Space Radiation Environment. NASA/TP-1999209369, 1999.
(2) M. Y. Kim and J. W. Wilson, Examination of Solar Cycle Statistical
Model and New Prediction of Solar Cycle 23. NASA/TP-2000210536, 2000.
(3) M. Y. Kim, J. W. Wilson, and F. A. Cucinotta, A Solar Cycle
Statistical Model for the Projection of Space Radiation
Environment. Advances in Space Research, 37, 1741-1748, 2006.
(4) International sunspot Number, National Geophysical Data
Center, NOAA,
http://www.ngdc.noaa.gov/stp/spaceweather.html
(5) McCracken KG, Dreschhoff GAM, Zeller EJ, Smart DF, Shea MA.
Solar cosmic ray events for the period 1561–1994. 1.
Identification in polar ice, 1561–1950. J Geophys Res 106:21585–
21598; 2001.
(6) Shea MA, Smart DF. A summary of major proton events. Solar
Phys 127:297–320; 1990.
(7) P. M. O’Neill, Badhwar – O’Neill Galactic Cosmic Ray Model
Update Based on Advanced Composition Explorer (ACE) Energy
Spectra from 1997 to Present, Advances in Space Research, 37,
1727-1733 (2006).
(8) P. M. O’Neill, Badhwar-O’Neill 2010 Galactic Cosmic Ray Flux
Model – Revised, IEEE Transactions on Nuclear Science, 57, No.
6, 3148-3153 (2010).
(9) M. Y. Kim, M. J. Hayat, A. H. Feiveson, and F. A. Cucinotta,
Prediction of Frequency and Exposure Level of solar Particle
Events, Health Physics, 97(1), 68-81 (2009).