Probabilistic Solar Particle Flux
Forecast Modeling
Myung-Hee Y. Kim and Francis A. Cucinotta
Date
05
20
1/
22
2/
02
20
1/
2/
99
19
1/
2/
96
19
1/
21
2/
93
19
1/
2/
90
19
1/
2/
87
19
1/
2/
84
19
20
1/
1.E+09
2/
81
19
1/
20
20
1/
2/
1/
2/
19
19
1/
2/
1/
2/
19
1/
2/
19
1/
2/
19
1/
2/
19
19
1/
2/
1/
2/
19
19
1/
2/
1/
2/
19
1/
2/
19
1/
2/
19
19
1/
2/
1/
2/
19
19
1/
2/
1/
2/
19
-2
1/
2/
F60, protons cm
05
02
99
96
93
90
87
84
81
78
75
72
69
66
63
60
57
54
F30, protons cm
-2
1.E+11
2/
78
19
1/
2/
75
19
1/
19
2/
72
19
1/
2/
69
19
1/
2/
66
19
1/
2/
63
19
60
19
1/
2/
1/
57
19
1.E+07
1.E+10
2/
1/
1
2/ 954
1/
1
2/ 956
1/
1
2/ 958
1/
1
2/ 960
1/
1
2/ 962
1/
1
2/ 964
1/
1
2/ 966
1/
1
2/ 968
1/
1
2/ 970
1/
1
2/ 972
1/
1
2/ 974
1/
1
2/ 976
1/
1
2/ 978
1/
1
2/ 980
1/
1
2/ 982
1/
1
2/ 984
1/
1
2/ 986
1/
1
2/ 988
1/
1
2/ 990
1/
1
2/ 992
1/
1
2/ 994
1/
1
2/ 996
1/
1
2/ 998
1/
2
2/ 000
1/
2
2/ 002
1/
2
2/ 004
1/
20
06
-2
1.E+10
2/
1/
2/
54
19
1/
2/
F100, protons cm
SPE Database for the Recent Solar Cycles
SPE onset date
1.E+10
1.E+09
1.E+08
1.E+07
1.E+09
Date
1.E+08
23
Date
1.E+08
1.E+07
Model-based Prediction of SPE Frequency
based on the Measurements of SPE Flux
Propensity of SPEs: Hazard Function of Offset b Distribution Density Function
l0
K ( p  q )  t 
l (t ) 



4000 4000 ( p)(q)  4000
19
20
21
22
23
p 1
t 

1 

 4000
q 1
for (0  t  4000)
0.04
160
0.035
140
0.03
120
160
140
120
m=1783rd day
0.025
100
0.02
80
0.015
60
0.01
40
0.005
20
80
60
40
20
0
0
2/1/54
0
0
2/1/58
2/1/62
2/1/66
2/1/70
2/1/74
2/1/78
2/1/82
Date
2/1/86
2/1/90
2/1/94
2/1/98
2/1/02
500
1000
1500
2000
2500
3000
2/1/06
Elapsed time, d
Typical Nonspecific Future Cycle
3500
4000
l(t)
l (t)
100
Approaches
1. Cumulative frequency distribution of recorded SPEs
2. Model for the realistic application and the dependence
of multiple SPEs:
 Non-constant hazard function defined for the best
propensity of SPE data in space era
 Non-homogenous Poisson process model for SPE
frequency in an arbitrary mission period
 Cumulative probability of SPE occurrence during a
given mission period using fitted Poisson model
3. Simulation of F30, 60, or 100 distribution for each mission
periods by a random draw from Gamma distribution