Probabilistic Forecast of Solar Particle Fluence for Mission Durations
and Exposure Assessment in Consideration of Integral Proton Fluence at High Energies
SM23C-2332
AGU2012 Fall Meeting
Myung-Hee Y. Kim1, Allan J. Tylka2, William F. Dietrich2,3, and Francis A. Cucinotta4
Space Research Association, Division of Space Life Sciences, SK/SRPE/B37, 2101 NASA Parkway, Houston, TX 77058, USA myung-hee.y.kim@nasa.gov
2Space Science Division, Naval Research Laboratory, Washington, DC 20375, USA allan.tylka@nrl.navy.mil
3Consultant
4NASA Johnson Space Center, SK/B37, 2101 NASA Parkway Houston, TX 77058, USA francis.a.cucinotta@nasa.gov
Introduction
1.
2.
3.
4.
5.
6.
7.
8.
References
Hu, S., Kim, M.Y., McClellan, G.E., Cucinotta, F.A., Modeling the acute health effects of astronauts from exposure to large
solar particle events, Health Phys., 96(4), 465-476, April 2009.
Cucinotta, F.A., Kim, M.Y., Willingham, V., George, K.A., Physical and biological organ dosimetry analysis for International
Space Station Astronauts, Radiat. Res., 170, 127-138, 2008.
National Research Council of the National Academies, Committee for Evaluation of Space Radiation Cancer Risk Model Space
Studies Board, Division on Engineering and Physical Sciences. Technical Evaluation of the NASA Model for Cancer Risk to
Astronauts Due to Space Radiation, The National Academies Press, 2012.
Kim, M.Y., Hayat, M.J., Feiveson, A.H., Cucinotta, F.A. Prediction of frequency and exposure level of solar particle events.
Health Phys., 97(1), 68-81, July 2009.
Kim, M.Y., Hayat, M.J., Feiveson, A.H., Cucinotta, F.A. Using high-energy proton fluence to improve risk prediction for
consequences of solar particle events. Adv. Space Res., 44, 1428-1432, 2009.
Tylka and Dietrich, the 31st International Cosmic Ray Conference, Lodz, Poland, July 7-15, 2009.
Cucinotta, F.A., Wilson, J.W., Badavi, F. F. Extension to the BRYNTRN code to monoenergetic light ion beams. Washington DC,
NASA Report No. TP-3472, 1994.
Billings, M.P., Yucker, W.R. The computerized anatomical man (CAM) model. Washington DC, NASA CR-134043, 1973.
Functional Form of Event-Integrated GLE Proton Spectra
for Radiation Analysis
Band Function with 4 Parameters (J0, γ1, γ2, R0)
for Double Power Law in Rigidity
Φ (> R) = J 0 R
−γ 1
Φ(> R) = J 0 R
−γ 2
e
for R ≤ (γ 2 − γ 1 ) R0
− R / R0
{[(γ
− γ 1 )R0 ]
(γ 2 −γ 1 ) (γ 1 −γ 2 )
2
e
}
for R ≥ (γ 2 − γ 1 ) R0
Differential Energy Spectra of Band Function
1  − R / R0  dR
dΦ dΦ dR 
−γ 1 −1 − R / R0
−γ 1 
e
e
=
= J 0(γ 1 ) R
+ J 0(γ 1 ) R  −

 dE
dE dR dE 
R
0



1  −γ 1 dR
γ
− R / R0 
1
R
 +
for R ≤ (γ 2 − γ 1 ) R0
= J0 e
R R 
dE
0 

dR
dΦ dΦ dR
for R ≥ (γ 2 − γ 1 ) R0
=
= J 0(γ 2 ) R −γ 2 −1 [ (γ 2 − γ 1 ) R0 ] (γ 2 −γ 1 ) e (γ 1 −γ 2 )
dE
dE dR dE
{
dR
A
−3
= 10
dE
Z × β (E)
}
Where,
R in GV, E in MeV, and β(E) is the proton velocity relative to the speed of light.
95 percentile
SPE onset date
Propensity of SPEs: Hazard Function of
Offset β Distribution Density Function
1.E+10
1.E+09
λ0
K Γ( p + q )  t 
λ (t ) =
+


4000 4000 Γ( p)Γ(q )  4000 
(0 ≤ t ≤ 4000)
1.E+08
1.E+07
1.E+10
p −1
t 


1 −
 4000 
q −1
Median
25 percentile
10 percentile
5 percentile
1.E+10
1.E+09
1.E+08
1.E+07
1.E+06
1.E+05
1.E+04
-2
Φ60, protons cm
-2
Φ60, protons cm
75 percentile
1.E+11
160
1.E+09
140
1.E+08
120
1.E+07
1.E+10
1.E+09
1.E+08
1.E+07
1.E+06
1.E+05
1.E+11
40
20
1.E+07
2/
1/
19
54
2/
1/
19
57
2/
1/
19
60
2/
1/
19
63
2/
1/
19
66
2/
1/
19
69
2/
1/
19
72
2/
1/
19
75
2/
1/
19
78
2/
1/
19
81
2/
1/
19
84
2/
1/
19
87
2/
1/
19
90
2/
1/
19
93
2/
1/
19
96
2/
1/
19
99
2/
1/
20
02
2/
1/
20
05
1.E+09
80
60
1.E+08
1.E+10
1.E+04
100
λ (t)
Φ100, protons cm
90 percentile
1.E+11
-2
Φ30, protons cm
-2
Φ30, protons cm
1.E+11
-2
• Exposure to solar particle events (SPEs) presents significant
acute radiation risk (ARR)(1) during extra-vehicular activities
(EVAs) or in lightly shielded space vehicles for space missions,
and the exposure to large SPEs with high energy levels poses
cancer risks to astronauts(2,3).
• Improved forecasting capability and/or early-warning systems
and proper shielding solutions are required to avoid ARR and
stay within NASA’s short-term dose limits.
• Using SPE onset dates for the past 5 solar cycles, the
propensity for SPE occurrence with large proton fluence was
estimated as a function of time within a typical future solar
cycle from a non-homogeneous Poisson model(4).
• Using historical database of proton fluence with E>30, >60,
and >100 MeV, total fluence distributions of Φ30, Φ60, and
Φ100 were simulated ranging from its 5th to 95th percentile for
each mission durations(5) for random event size of SPE, ΦE.
• Band fit parameters(6) for most of the ground-level enhanced
events (GLEs) observed since 1956 have been applied as an
accurate functional representation of Major SPEs.
• NASA BRYNTRN code system(7) was used for transport
properties of the shielding materials and the astronaut’s body
tissues with computerized anatomical man (CAM) model(8).
• The dependencies of BFO dose and Effective dose were
evaluated and unconditional probability of BFO dose
exceeding the NASA limit was calculated as a function of
proton fluence at a given energy threshold of 30, 60, and 100
MeV.
Probabilistic Forecast of Solar Particle Fluence for Mission durations
-2
Φ100, protons cm
1Universities
0
2/1/54
2/1/58
2/1/62
2/1/66
2/1/70
2/1/74
2/1/78
2/1/82
2/1/86
2/1/90
2/1/94
2/1/98
2/1/02
2/1/06
1.E+10
1.E+09
1.E+08
1.E+07
1.E+06
1.E+05
1.E+04
0
Date
50
100
150
200
250
300
350
400
Mission duration, d
Exposure Assessment in Consideration of Integral Proton Fluence at High Energies
Exposure Assessment from GLE’s
Band Fit Parameters of Recorded GLE’s and Exposure Assessment
during Extra Vehicular Activity and Inside 5 g/cm2 Aluminum
GLE’s
1956
1959
1960
1960
1960
1960
1960
1961
1967
1968
1969
1971
1971
1972
1972
1973
1976
1977
1977
1977
1978
1978
1981
1981
1982
1982
1984
1989
1989
1989
1989
1989
1989
1989
1989
1989
1990
1990
1990
1990
1991
1991
1992
1992
1997
1998
1998
1998
1998
2000
2000
2001
2001
2001
2001
2001
2002
2003
2003
2003
2003
2005
2005
2006
Date
Feb
Jul
May
Sep
Nov
Nov
Nov
Jul
Jan
Nov
Mar
Jan
Sep
Aug
Aug
Apr
Apr
Sep
Sep
Nov
May
Sep
May
Oct
Nov
Dec
Feb
Jul
Aug
Sep
Sep
Oct
Oct
Oct
Oct
Nov
May
May
May
May
Jun
Jun
Jun
Nov
Nov
May
May
Aug
Aug
Jul
Jul
Apr
Apr
Nov
Nov
Dec
Aug
Oct
Oct
Oct
Nov
Jan
Jan
Dec
23
17
04
03
12
15
20
18
28
18
30
24
01
04
07
29
30
19
24
22
07
23
10
12
26
08
16
25
16
29
29
19
19
22
24
15
21
24
26
28
11
15
25
02
06
02
06
24
24
14
14
15
18
04
04
26
24
28
28
29
02
17
20
13
Official No.
5
7
8
9
10
11
12
13
16
19
21
22
23
24
25
26
27
28
29
30
31
32
35
36
37
38
39
40
41
42
42
43a
43b
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58a
58b
59a
59b
60
61
62a
62b
63
64
65a
65b
66
67
68
69
70
Band Fit Parameters
γ1
γ2
R0 (GV)
J0,
8.790E+08
0.584
5.04
0.3207
7.590E+09
0.218
6.08
0.1030
8.156E+05
1.527
4.88
0.5850
1.240E+08
0.319
5.56
0.1410
7.540E+08
1.154
6.54
0.2160
1.780E+08
1.595
7.00
0.2628
3.070E+07
1.112
5.21
0.1970
6.302E+08
0.755
6.13
0.1312
1.066E+07
1.896
5.62
0.3720
7.286E+06
2.822
6.91
0.2405
9.315E+07
0.353
4.32
0.1536
7.423E+06
3.256
6.58
0.2874
2.336E+08
0.701
7.38
0.1807
1.450E+15
-3.636
7.95
0.0345
6.340E+06
3.260
6.27
0.2980
7.240E+06
1.073
4.44
0.1628
7.620E+06
1.710
6.33
0.2054
1.388E+06
2.995
7.95
0.3163
4.324E+06
1.730
5.40
0.3390
3.020E+06
2.533
5.41
0.4238
6.424E+06
1.549
3.87
0.1806
8.151E+09
0.473
5.61
0.0682
9.509E+04
4.210
6.49
0.8169
6.800E+08
1.344
5.11
0.0768
2.211E+05
3.365
4.87
0.8655
4.169E+05
3.706
5.04
1.2680
2.506E+07
0.760
5.05
0.1644
1.290E+07
0.544
6.60
0.1822
7.270E+07
1.914
5.86
0.1845
1.799E+05
2.060
2.63
3.6593
2.027E+10
-0.109
4.58
0.0945
1.220E+09
0.528
5.81
0.1621
9.090E+09
0.911
4.43
0.08435
1.090E+09
1.226
7.25
0.1352
4.420E+07
2.176
5.65
0.3850
3.850E+06
0.970
5.53
0.2200
1.131E+08
0.554
4.31
0.1366
5.579E+07
0.797
4.91
0.1832
4.685E+07
0.333
5.72
0.1829
7.659E+07
0.417
4.98
0.1433
8.360E+08
0.974
5.14
0.1052
2.525E+07
2.182
5.98
0.2362
8.621E+05
3.117
6.12
0.3496
1.965E+09
0.462
6.91
0.0951
8.150E+08
0.284
5.38
0.1159
8.980E+06
1.306
6.51
0.1962
1.640E+06
1.921
7.46
0.2018
2.096E+05
2.977
5.27
0.6769
1.630E+04
5.285
7.74
0.983
2.940E+09
0.506
7.46
0.1230
6.010E+07
3.235
7.85
0.226
5.220E+07
1.388
5.69
0.2604
8.390E+06
1.852
5.02
0.2366
2.140E+09
0.242
6.67
0.0934
4.780E+08
2.363
11.2
0.129
2.170E+07
1.806
7.86
0.1803
5.060E+06
2.356
6.70
0.2253
8.440E+09
0.009
6.48
0.0888
1.120E+08
2.812
8.92
0.171
7.620E+07
2.044
6.86
0.2062
2.270E+06
3.501
7.01
0.3212
3.508E+07
2.649
8.29
0.1619
3.803E+08
0.719
5.78
0.2040
1.330E+08
1.045
5.80
0.1765
p/cm2
BFO dose, mGy-Eq
EVA
5 g/cm2 Al
557.23
405.37
244.51
120.9
2.15
1.49
12.65
7.35
442.75
266.83
217.48
129.45
14.5
8.53
76.96
40.35
26.81
16.42
23.55
11.35
12.37
7.42
46.8
22.09
63.14
38.38
597.63
174.29
42.17
20.06
2.14
1.18
6.74
3.67
7.85
3.94
8.42
5.2
15.5
8.8
3.73
2.03
47.78
19.82
3.54
1.68
20.38
9.14
3.93
2.13
11.7
6.17
5.73
3.32
3.08
1.93
61.88
31.49
1.35
0.95
340.46
170.34
218.18
130.52
279.49
139.03
223.54
110.72
148.88
87.9
1.98
1.23
12.95
7.14
16.96
10.21
9.32
6.02
8.94
5.15
57.97
26.44
44.27
23.42
6.15
3.09
56.97
25.71
43.16
22.71
5.02
2.86
1.7
0.89
2.3
1.29
1.76
0.72
233.32
122.83
253.73
112.74
52.07
31.92
10.93
6.08
47.02
21.66
238.11
96.65
15.92
8.17
9.57
4.86
120.04
55.23
181.15
78.04
91.92
47.66
20.73
9.66
42.84
18.51
134.68
85.16
46.6
26.64
NASA E, mSv
EVA
5 g/cm2 Al
589.73
446.77
231.38
118.38
2.26
1.63
12.31
7.42
436.55
273.61
214.59
132.94
14.21
8.7
73.59
39.95
26.77
17.11
22.67
11.23
12.17
7.61
45.17
21.85
62.15
39.26
581.48
172.36
40.73
19.87
2.08
1.19
6.53
3.69
7.6
3.93
8.41
5.42
15.26
9.02
3.65
2.09
46.62
19.59
3.46
1.68
20.03
9.11
3.86
2.17
11.49
6.28
5.58
3.37
3.06
1.98
59.45
31.27
1.45
1.07
325.06
171.02
213.69
132.77
274.34
140.6
212.84
108.81
147.49
90.76
1.97
1.28
12.54
7.22
16.69
10.44
9.32
6.26
8.7
5.21
55.15
26.17
42.85
23.47
5.96
3.09
53.57
24.88
41.24
22.51
4.89
2.9
1.63
0.89
2.27
1.33
1.74
0.71
222.7
121.36
244.28
110.58
51.72
33.01
10.65
6.16
44.21
21
227.43
93.47
15.29
8.11
9.22
4.84
112.88
53.69
173.62
76.07
88.58
47.49
20.04
9.55
41
18.03
134.18
88.24
45.34
26.92
BFO dose Fit for Males with 90% Tolerance
Limits as a Function of Φ100
NASA Effective dose Fit for Males with 90% Tolerance Limits as a
Function of Φ100
Probability Exceeding the BFO limit as a Function of Φ30, Φ60, and Φ100 of Proton Fluences
Conclusion
1. Total fluence of solar particle events (SPEs) for a given mission period was estimated from a non-homogeneous Poisson process model with a non-constant hazard function
and a random draw from a Gamma distribution representing energy above 30, 60, and 100 MeV fluences.
2. The exposure levels of GLE’s were calculated from corresponding observed spectral characteristics of Band function, which are found to be modeled based solely on integral
proton fluences at high energies by a linear trend on a log-log scale with an assumed Gaussian distribution of the exposure level around the regression line attributable to
variability of each GLE spectra.
3. By taking into account the distribution of integral proton fluence at high energies for a given mission period as the predictor of estimating exposure level:
• The overall predictions of BFO dose and NASA effective dose were estimated at the median as well as the 5th and 95th percentiles.
• The unconditional probability of a BFO dose exceeding the NASA defined limit of 250 mGy-Eq was calculated.
4. The results can be applied to the mission planning and shielding optimization for future space missions.