Solar Radiation Alert 

System 

Kyle Copeland1

Herbert H. Sauer2

Wallace Friedberg1

1

Civil Aerospace Medical Institute

Federal Aviation Administration

Oklahoma City, OK 73125

2

CIRES, University of Colorado and 

National Geophysical Data Center 

NOAA, Boulder, CO 80305

July 2005

Final Report

DOT/FAA/AM-05/14

Office of Aerospace Medicine

Washington, DC 20591
NOTICE

This document is disseminated under the sponsorship of

the U.S. Department of Transportation in the interest of

information exchange. The United States Government

assumes no liability for the contents thereof.
Technical Report Documentation Page 

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. 

DOT/FAA/AM-05/14 

4. Title and Subtitle 5. Report Date 

Solar Radiation Alert System July 2005 

6. Performing Organization Code 

7. Author(s) 8. Performing Organization Report No. 

Copeland K,1 Sauer HH,2 Friedberg W1

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) 1

FAA Civil Aerospace Medical Institute 2CIRES, University of Colorado & 

P.O. Box 25082 National Geophysical Data Center 11. Contract or Grant No. 

Oklahoma City, OK 73125 NOAA, Boulder, CO 80305 

12. Sponsoring Agency Name and Address 13. Type of Report and Period 

Covered

Office of Aerospace Medicine 

Federal Aviation Administration 

800 Independence Ave., S.W. 

Washington, DC 20591 14. Sponsoring Agency Code 

15. Supplemental Notes 

This work was accomplished under the approved tasks TOXLAB.AV9000. 

16. Abstract 

A solar radiation alert (SRA) system has been developed to continuously evaluate measurements of 

high-energy protons made by instruments on Geosynchronous Operational Environmental satellites. 

If the measurements indicate the likelihood of a substantial elevation of effective dose rates at aircraft 

flight altitudes, the Civil Aerospace Medical Institute issues an SRA to the aviation community via the 

National Oceanic and Atmospheric Administration Weather Wire Service. This report describes the 

methodology of the SRA system. A Monte Carlo particle transport code was used to estimate the 

fluences of secondary particles (protons, neutrons, pions, kaons, photons, electrons, and muons) in 

selected energy ranges at specific altitudes. Coefficients to convert particle fluence to effective dose 

incorporate radiation-weighting factors and tissue-weighting factors recommended by the 

International Commission on Radiological Protection, except that the radiation-weighting factor for 

protons was changed from five to two, as recommended by the National Council on Radiation 

Protection and Measurements. Effective dose rates from solar-proton-induced ionizing radiation in the 

earth’s atmosphere at high geomagnetic latitudes were calculated for the solar proton event of 20 

January 2005. The event started at 06:50 Universal Time, and within 5 minutes, dose rates at 60,000, 

40,000, and 30,000 ft (relative to mean sea level) reached maximum values of: 140, 55, and 21 

microsieverts per hour, respectively. 

17. Key Words 18. Distribution Statement 

Solar Radiation, Monte Carlo Particle Transport Code, Solar 

Protons, Solar Particles, Space Weather, Solar Flare, Coronal Mass 

Ejection

Document is available to the public through 

the Defense Technical Information Center, 

Ft. Belvior, VA 22060; and the National 

Technical Information Service, Springfield, 

VA 22161

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price 

Unclassified Unclassified 13 

Form DOT F 1700.7 (8-72) Reproduction of completed page is authorized 

iii

ACKNOWLEDGMENTS

For editorial and technical contributions to this report, we thank: E.B. Darden, Jr., 

Oak Ridge Associated Universities (Ret.), Oak Ridge, Tennessee; M.E. Wayda and F.E. 

Duke, Civil Aerospace Medical Institute, FAA, Oklahoma City, Oklahoma; D.E. Parker, 

University of Oklahoma Health Sciences Center, Oklahoma City, Oklahoma; and M.A. 

Shea and D. F. Smart, University of Alabama, Huntsville, Alabama. 



Solar Radiation Alert System

INTRODUCTION

Aircraft passengers and crew are constantly exposed 

to ionizing radiation at higher dose rates than normally 

received by the general population. The principal ionizing radiation is galactic cosmic radiation, a main source 

of which is believed to be supernovae (exploding stars). 

Occasionally, a disturbance in the sun (solar flare, coronal 

mass ejection) leads to a large flux of solar protons with 

sufficient energy to penetrate the earth’s magnetic field, 

enter the atmosphere, and increase ionizing radiation 

levels at aircraft flight altitudes. For a primer on aircrew 

exposure to ionizing radiation, see report by Friedberg 

and Copeland (1). 

A system (Figure 1) has been developed for the continuous evaluation of proton flux measurements made 

by instruments on Geosynchronous Operational Environmental Satellites (GOES). At present, the primary 

data source is GOES-11 while GOES-10 measurements 

are used if they are more current or if GOES-11 is not 

operating properly. If the measurements indicate the 

likelihood of a substantial elevation of ionizing radiation levels at aircraft flight altitudes at high latitudes, 

the Civil Aerospace Medical Institute (CAMI) issues a 

Solar Radiation Alert (SRA) to the National Oceanic 

and Atmospheric Administration Weather Wire Service 

(NWWS) (2). Information given with the alert includes 

estimated dose rates in microsieverts per hour (μSv/h), 

based on 5-minute averages, at 30,000, 40,000, 50,000, 

60,000, and 70,000 ft (relative to mean sea level). The 

dose rates are updated at 5-minute intervals for the duration of the SRA. 

The specific criteria for issuance of an SRA are that 

the estimated effective dose rates induced by solar 

protons at any altitude from 30,000 to 70,000 ft in 

the earth's atmosphere are equal to or greater than 20 

microsieverts per hour for each of three consecutive 5-

minute periods. The three 5-minute periods need not 

be at the same altitude. Because of the potential for a 

delay of 3 to 20 minutes in communication processes 

and the three 5-minute periods, notification of the start 

of SRA conditions may be 18 to 35 minutes after the 

start of the first 5-minute period. Possible effects on the 

dose rate caused by ions other than protons (e.g., alpha 

particles) in the primary solar particle flux, shielding 

by the earth's magnetic field, and shielding by aircraft 

structure are not taken into account in the calculations. The SRA is canceled when the average effective 

dose rate at all altitudes from 30,000 to 70,000 ft is 

less than 20 microsieverts per hour for six consecutive 

5-minute periods. 

METHOD USED TO ESTIMATE 

EFFECTIVE DOSE RATES AT FLIGHT 

ALTITUDES

Basis of SRA System 

The Primary Solar Proton Spectrum. Observations of fluxes of high-energy protons used to estimate 

solar radiation dose rates in the earth’s atmosphere are 

obtained from GOES proton flux measurements. These 

measurements are recorded in several “channels”: P4 to 

P7 (15 to 900 MeV energy, 168 to 1581 MV rigidity), 

P10 (510 to 700 MeV, 1103 to 1343 MV), and P11

(greater than 700 MeV, greater than 1343 MV). Protons 

in channels P4 through P10 are in terms of differential 

flux (particles/cm2/steradian/second/MeV). Protons in 

channel P11 are in terms of integral flux (particles/cm2

/

steradian/second). 

The proton fluxes currently available from the Space 

Environment Center (SEC) are derived from satelliteinstrument count rates using conversion factors appropriate for GOES-7 instruments (3). In Steps 1 to 3, 

below, these fluxes are converted to count rates and then 

reconverted to flux using the conversion factors specifically intended for GOES-10 and GOES-11. Channels 

P8 and P9 are excluded from the analysis because their 

correction algorithms are more complex than those of the 

other channels, and excluding them does not significantly 

affect the calculated dose rates. 

The data are available in near real-time from the file 

transfer protocol (ftp) server at the SEC and are also 

on the Internet (4). Protons flux observations are from 

solar plus galactic cosmic radiation. The contribution of 

galactic protons is subtracted from the total as part of the 

correction process described below. The initial 5-minute 

average galactic background count rate (B, counts/second) 

for a channel is the average of the preceding 12 hours 

of data (144 5-minute periods) collected when no solar 

particle event or Forbush decrease (sudden reduction 

in galactic background radiation as a result of scattering of low-energy galactic particles by magnetic fields 
carried by solar particles) is occurring. Once the system 

is operating, the background is changed as described in 

Step 10, below.

In each channel, solar protons of sufficiently high energy to cause an increase in ionizing radiation levels in the 

atmosphere have a flux spectrum (f) across the channel’s 

energy acceptance band that can reasonably be expressed 

as a power law function of rigidity (R): 

f (R) = α R-γ (Eq. 1)

where the proton spectrum is characterized in terms of 

time-dependent constants, intensity (α) and spectral 

hardness index (γ) (5,6). Six spectra in the form of Eq.1, 

each spanning a different rigidity range, are created in 

Steps 1 to 7 (below) using GOES data.

These six spectra are combined in Step 8 to form a complete spectrum used to calculate effective doses in Step 9. A 

piecewise-continuous spectrum is needed because during 

solar proton events, γ increases at higher rigidities.

Radiation Transport.Monte Carlo radiation transport 

code MCNPX2.4.0 (7) was used to calculate the fluences 

(particles/cm2) of secondary particles (protons, neutrons, 

pions, kaons, photons, electrons, and muons) in selected 

energy ranges for specific altitudes, which were generated 

by mono-energetic isotropic fluences of protons at an 

altitude of 100 km. Solar proton fluences at 100 km were 

assumed to be isotropic because there is no directional 

information in the GOES data. The atmospheric pressure density at 100 km is 0.0003 g/cm2

. Using a higher 

altitude to more closely approximate the free-space environment of the satellite would not significantly improve 

dose estimates. The earth was modeled as a sphere of 

liquid water with a radius of 6371 km and a density of 

1g/cm3

. The atmosphere was modeled as a series of 100 

spherically symmetric 1-km thick layers surrounding the 

earth. The composition (a gaseous mixture containing 

nitrogen, oxygen, argon, and carbon atoms) and density 

of each layer were assumed to be that reported for the 

middle of the layer (8), resulting in an atmosphere with 

a vertical depth of 1035.08 g/cm2

. Altitudes in Table 1

were calculated from the atmospheric depth. Geomagnetic 

effects were neglected. 

Fluence-to-Effective Dose Conversion. With one 

exception, fluence-to-effective-dose conversion coefficients reported by Pellicioni (9) were used to convert 

the secondary particle fluences generated by the transport 

code to effective doses. The reported coefficients incorporate radiation-weighting factors and tissue-weighting 

factors recommended by the International Commission 

on Radiological Protection. The one exception is the 

radiation-weighting factor for protons, which was changed 

from five to two, as recommended by the National 

Council on Radiation Protection and Measurements 

(10). The effective dose from kaons was not calculated 

because its contribution to the total dose would have 

been negligible. Table 1 shows, at selected altitudes, the 

dose rate per unit flux of primary solar protons of selected 

rigidities. The transport code automatically converts a 

fluence below 10-25 particles/cm2

 to zero fluence, which 

would lead to a zero dose rate per unit flux (Table 1). To 

avoid this, any zero dose rate per unit flux was changed 

from zero to 1x10-12

. Table 1, as presented, is applicable 

to any solar particle event.

Calculating Effective Dose Rate at Specific Altitudes

Step 1. Convert the incorrect fluxes obtained from 

the SEC to instrument count rates (C), by multiplying 

the flux (φ) for each channel used (φP4, φP5, φP6, φP7,

φP10, and φP11) by the appropriate conversion factor (k) 

from Table 2: 

C = φk (Eq. 2)

GOES-10 and GOES-11 have identical instruments and 

therefore use the same conversion factors.

Step 2. Subtract the galactic background count rate 

(B) from the total count rate (C, galactic plus solar) to 

obtain the solar-induced count rate (C′): 

C′= C–B (Eq. 3)

If C′ is negative, assign it a value of 1% of B. Calculation of B is described earlier, in the section entitled “The 

Primary Solar Proton Spectrum.”

Step 3. Divide the background corrected solar count 

rate (C′) by the appropriate conversion factor (k′) from 

Table 2 to obtain the differential flux (f (R)): 

f(R) = C′/k′ (Eq. 4)

Step 4. Calculate a preliminary spectral hardness index 

(γ) for each pair (i,j) of channels (P4 and P5, P5 and P6, 

P6 and P7, P7 and P10, P10 and P11) using Eq. 5, which 

was derived from Eq. 1:

Variables f(R)P4 through f(R)P11 are differential proton 

fluxes derived from values in channels P4 through P11

(Steps 1 to 3). The characteristic rigidities of the protons 

in these channels are RP4 through RP11 from Table 2. 

ln( ) ln( )

ln( ( ) ) ln( ( ) ) ,

Pj Pi

Pi Pj

Pi Pj R R

f R f R

−

− γ = (Eq. 5) (Eq. 5)
Step 5. Further correct the differential fluxes (f(R)Pi),

using spectral hardness index correction factors(s) in 

Table 3: 

f(R)corrected = f(R)s (Eq. 6)

Use the γPi,Pj values from Step 4 to find the appropriate 

s values. Thus, use γP4,P5 to find the s value to correct 

f(R)P4, use γP5,P6 to find the s value to correct f(R)P5, etc. 

This selection procedure weights the spectral response 

towards the higher energies. f(R)P11 does not require this 

correction.

Step 6. Recalculate γ values with Eq. 5, using fluxes 

f(R)Pi and f(R)Pj that were corrected in Step 5. If γ is 

negative, assign it the value 0. If γ equals 1, assign it the 

value 1.000001.

Step 7. Calculate α for each channel with Eq. 7 using 

the characteristic rigidities from Table 2, the differential 

fluxes f (R)corrected from Step 5, and the recalculated γ values 

from Step 6: 

α = f(R)corrected /R−γ	 	 	 (Eq. 7)

with f (R)P4 use γP4,P5, with f(R)P5 use γP5,P6, etc. For channel P11, use the α found for P10. Convert channel P11

count rate (C′) to integral flux (FP11), irrespective of γ, by 

dividing C′ by its geometric factor 0.73 (3). Use Eq. 8 to 

find the γ that best describes FP11. Start with γ equal to 

γP10,P11 and, if necessary, decrease γ in steps of 0.000001

until the relationship is just satisfied.

(Eq. 8)

The upper and lower limits in Eq. 8 are the rigidity bounds 

set for channel P11. The upper limit is the upper rigidity 

limit of the Monte Carlo calculations, 32545 MV (Table 

1), and the lower limit is 1343 MV, the lowest rigidity 

of data in P11. 

Step 8. Construct a piecewise-continuous description 

of the solar proton spectrum (ψ(R)) for primary solar 

protons with rigidities above 137 MV (10 MeV) based 

on results of Steps 1 to 7, with each piece having the 

form of Eq. 1. With the exception of the upper rigidity 

limit of channel P11, the upper and lower rigidity limits 

used with the parameters calculated for each channel are 

shown in Table 4. The upper rigidity limit for channel 

P11 (and thus for ψ(R)) is Rmax and is found by replacing 

the upper rigidity limit in Eq. 8 with 1344 MV, then 

increasing the upper limit in steps of 1 MV until the 

relationship is just satisfied. 

Step 9. For a specific altitude (H), the effective dose 

rate per unit flux of primary solar protons (∆(R,H)) is 

generated from the data in Table 1. For intermediate R

values, ∆(R,H) is generated using linear interpolation of 

Log(R) and Log(∆(R,H)). Primary solar protons in bins 

with rigidities less than 183.5 MV (17.78 MeV), the 

lowest rigidity in Table 1, are assigned the same ∆(R,H)

as primary solar protons of 183.5 MV. The effective 

dose rate (E(H), microsieverts per hour) at a particular 

altitude is the integral 

(Eq. 9)

where Rmin is the lower limit of channel P4 (Table 4) 

and Rmax is from Step 8. The numerical integration is 

performed using 1 MV-wide flux bins. For each bin, the 

∆(R,H) value used is the mean of the ∆(R,H) values at 

the extreme rigidities of the bin.

Dose rates at altitudes between those listed in Table 1

are estimated using a cubic spline interpolation.

Step 10. If C from Step 2 does not exceed twice B in 

any channel, C is used to update B in each channel:

B= (143B+C)/144 (Eq. 10)

Thus, the background count rates will always be the 

averages of the last 12 uneventful hours. 

To examine solar proton events using proton flux 

data from satellites other than the current GOES series 

(GOES-8, GOES-9, GOES-10, GOES-11, GOES-12), 

minor modifications are necessary: any satellite data set 

may be used that allows the reasonable construction of 

a solar proton spectrum spanning the rigidity range 137 

MV to above 1343 MV.

RESULTS AND DISCUSSION

In estimating dose rates for the SRA system, only 

solar protons are used because they are the dominant 

contributor to the ionizing radiation from the sun at 

aircraft flight altitudes and data are available in near 

real-time. Other radiation information, such as GOES 

alpha particle measurements and data from the worldwide 

network of neutron monitors, would enable more complete calculations, but not with the immediacy required 

of an alert system.

During the early stages of a solar proton event (solar 

particle event where the proton flux with energies equal 

to or greater than 10 MeV exceeds 10 particles/second/

steradian/cm2 (11)), solar radiation in the vicinity of the 

earth is usually somewhat anisotropic, as indicated by 

ground-level neutron monitor data (12). However, anisotropy is not particularly evident in GOES data. The 

3 

5 d

MV

MV

F R dR

32545

1343 11

J D Eq. 8) 

3 ' max

min

( ) ( ) ( , ) R

R E H \ R R H dR (Eq. 9)
15 largest solar proton events from 1996 through 2003 

for which data were available from two or more satellites 

were examined to compare event onset times and flux 

measurements. Apparent event onset times at the satellites 

were the same (within 5 minutes). The largest differences 

in fluxes measured by the satellites, typically 20%, were 

observed at energies greater than 350 MeV during the first 

few 5-minute periods of an event. As the event proceeded, 

differences decreased. Longitudinal separation of the most 

widely separated satellites was about 60 degrees. The low 

anisotropy effects observed at the satellites indicate that 

doses generated by the system are reasonable first estimates 

at aircraft flight altitudes at polar latitudes (i.e., where 

the cutoff rigidity is close to 0 MV).

Figure 2 shows effective dose ratesfrom solar protons 

in the earth’s atmosphere during the solar proton event 

of 20 January 2005. The calculations do not take into 

account geomagnetic shielding (i.e., shielding by the 

earth’s magnetic field) and shielding by aircraft structure. 

Inclusion of aluminum shielding afforded aircraft occupants in a B-747 (using a skin thickness of 0.6 g/cm2

), for 

example, would not change the effective dose estimates at 

40,000 ft by more than a few percent (depending on the 

specific energy spectrum, the effective dose could increase 

or decrease). The event started at 06:50 Universal Time 

(UT), and by 06:55 UT dose rates at 60,000, 40,000, 

and 30,000 ft had reached maximum values of: 140, 55, 

and 21 microsieverts per hour, respectively. The dose rates 

then dropped rapidly: at 07:55 UT, they were 17, 4, and 

1 microsieverts per hour at the three altitudes. 

The SRA system provides timely, quantitative information for the aviation community on potentially 

hazardous solar radiation levels at aircraft flight altitudes 

in high-latitude regions. This information enables users 

to decide whether or not reducing aircraft flight altitudes 

is appropriate. 

Future work includes: (a) improve estimates of dose 

rates in Table 1 by improving Monte Carlo calculations, 

(b) improve estimates of radiation levels at neutron monitor locations by including geomagnetic and anisotropy 

effects on dose rates, (c) possible incorporation of dose 

rates from alpha particles and any other significant heavier 

ions in the solar particle flux, and (d) calculation of dose 

rates, flight doses, and neutron monitor counting rates 

during past solar proton events.

REFERENCES

1. Friedberg, W., and Copeland, K. What Aircrews 

Should Know About Their Occupational Exposure 

to Ionizing Radiation. Washington, DC: U.S. 

Department of Transportation, Federal Aviation 

Administration, Office of Aerospace Medicine, 

Technical Report no. DOT/FAA/AM-03/16 

(2003). Available through the National Technical 

Information Service, Springfield, VA 22161 and 

at: http://www.faa.gov/library/reports/­medical/

oamtechreports/2000s/media/0316.pdf (date accessed: 7 July 2005). This publication and all Office 

of Aerospace Medicine technical reports are available in full-text from the Civil Aerospace Medical 

Institute’s publications Web site: http://www.faa.

gov/library/reports/medical/oamtechreports/

2. National Weather Service. Solar Radiation Alerts 

are distributed to subscribers of the NOAA Weather 

Wire Service (NWWS). The NWWS is administered for the National Weather Service by DynCorp 

Systems and Solutions, LLC; 1500 Conference 

Center Drive, Chantilly, VA 20151-3808, phone: 

(703) 818-4000.

3. Sauer, H.H. Analysis of GOES Particle Data and 

the Development of a Processing Procedure in Support of FAA Requirements for Radiation Exposure 

Estimation at Aircraft Altitudes, Boulder, CO: 

CIRES/NOAA-NGDC (2003). Prepared for the 

FAA under contract number DTFA0201P09198. 

6973H5 FAA Aero Center AMQ-300. Appendix C 

contains the instrument manufacturer’s calibration 

report “Calibration Report for the EPS DOME Sensor Response to Protons” NXT-CAL-102, May 30, 

1995, Panametrics, Inc. for Space Systems/Loral, 

Inc. The FAA contracted report is in the library of 

the Civil Aerospace Medical Institute, Oklahoma 

City, OK.

4. National Oceanic and Atmospheric Administration, 

Space Environment Center Web site: http://www.

sec.noaa.gov/ftpmenu/lists/pchan.html. Files to 

select are G11pchan_5m.txt and G10pchan_5m.txt 

(date accessed: 7 June 2005).

5. Ellison, D.C. and Ramaty, R. Shock Acceleration of 

Electrons and Ions in Solar Flares. The Astrophysical 

Journal 298: 400-408 (1985). 
6. Brown, J.C., Smith, D.F., and Spicer, D.S. Solar 

Flare Observations and Their Interpretations. 

In The Sun as a Star, Jordan, S. (Ed./Author), 

Washington, DC: National Aeronautics and Space 

Administration Science and Technical Information 

Branch, Technical Report no. NASA SP-450, pp. 

81-227 (1981).

7. Los Alamos National Laboratory. Monte Carlo NParticle Transport Code System for Multiparticle 

and High Energy Applications (MCNPX 2.4.0), 

released August 2002. Available from the Radiation 

Safety Information Computational Center at the 

Oak Ridge National Laboratory. 

8. National Oceanic and Atmospheric Administration, 

National Aeronautics and Space Administration, 

and United States Air Force. U.S. Standard Atmosphere, 1976. NOAA S/T 76-1562, Washington, 

DC: U.S. Government Printing Office (1976).

9. Pellicioni, M. Overview of Fluence-to-Effective 

Dose and Fluence-to-Ambient Dose Equivalent 

Conversion Coefficients for High Energy Radiation 

Calculated Using the FLUKA Code. Radiation 

Protection Dosimetry 88(4): 279-297, (2000). 

10. National Council on Radiation Protection and 

Measurements. Limitation of Exposure to Ionizing 

Radiation. NCRP Report No.116 (p. 20, Table 4.3) 

(1993). 

11. National Oceanic and Atmospheric Administration, 

Space Environment Center Web site: http://sec.

noaa.gov/tiger/SolarProtons.html (date accessed: 

6 June 2005). 

12. Smart, D.F. and Shea, M.A. The Local Time Dependence of the Anisotropic Solar Cosmic Ray 

Flux. Advances in Space Research 32(1): 109-114 

(2003).

FIGURES AND TABLES

Figure 1. Solar radiation alert system: (1) Occasionally, a disturbance in the sun (solar flare, coronal mass 

ejection) leads to a large flux of high-energy particles in the vicinity of the earth. (2) Instruments on a GOES 

satellite continuously measure the radiation and the information is transmitted to NOAA. (3) From there it 

is sent to CAMI. A computer at CAMI analyzes the measurements. (4) If the measurements indicate the 

likelihood of a substantial elevation of ionizing radiation levels at aircraft flight altitudes, a Solar Radiation 

Alert is issued to the NOAA Weather Wire Service within 10 minutes. (5) NOAA Weather Wire Service 

subscribers are provided estimated effective dose rates for 30,000, 40,000, 50,000, 60,000, and 70,000 ft. 

This information is updated at 5-minute intervals for the duration of the alert. 

Table 1. Effective dose rate per unit flux of primary solar protons, as related to incident rigidity 

and energy at selected altitudes in the atmosphere relative to mean sea level.

Dose rate per unit flux, ҞΔ(R,H), җѽ microsieverts per 

hour/(protons/cm2

/steradian/second) at altitude (H) a

Rigidity (R), MV Energy, MeV H= -50 ft H=9722 ft H=19,588 ft H=29,378 ft 

 183.5 17.78 1.000x10-12 1.000x10-12 1.000x10-12 2.901x10-9

 245.6 31.62 1.000x10-12 1.000x10-12 1.404x10-10 1.256x10-8

 329.7 56.23 1.000x10-12 1.000x10-12 2.978x10-9 2.063x10-7

 444.6 100 1.000x10-12 9.739x10-9 2.251x10-7 7.796x10-6

 604.4 177.8 9.040x10-8 1.919x10-7 7.713x10-6 1.271x10-4

 832.7 316.2 5.281x10-7 2.489x10-5 2.935x10-4 1.960x10-3

 1171. 562.3 7.556x10-6 2.383x10-4 2.267x10-3 1.207x10-2

 1696. 1000 4.294x10-5 1.122x10-3 9.903x10-3 5.130x10-2

 2549. 1778 2.173x10-4 4.428x10-3 3.625x10-2 0.1469 

 3991. 3162 7.719x10-4 1.495x10-2 9.106x10-2 0.3009 

 4848. 4000 1.122x10-3 1.915x10-2 0.1147 0.3651 

 6495. 5623 1.885x10-3 2.356x10-2 0.1319 0.4335 

 10898. 10000 7.433x10-3 4.966x10-2 0.2413 0.7315 

 18695. 17780 2.202x10-2 0.1064 0.4464 1.277 

 20917. 20000 2.751x10-2 0.1227 0.5025 1.410 

 32545. 31620 6.046x10-2 0.2178 0.7942 2.110 

H=39,197 ft H=48,977 ft H=58,749 ft H=68,511 ft H=78,260 ft 

 183.5 8.348x10-8 1.282x10-6 7.556x10-6 1.937x10-5 3.215x10-5

 245.6 9.257x10-7 1.521x10-5 7.390x10-5 1.699x10-4 2.622x10-4

 329.7 1.199x10-5 1.223x10-4 4.873x10-4 1.004x10-3 1.456x10-3

 444.6 1.511x10-4 7.832x10-4 2.407x10-3 4.436x10-3 6.602x10-3

 604.4 1.046x10-3 4.495x10-3 1.129x10-2 1.165x10-2 2.446x10-2

 832.7 8.491x10-3 2.470x10-2 5.079x10-2 0.1116 0.2307 

 1171. 4.331x10-2 0.1298 0.2748 0.3850 0.4490 

 1696. 0.1731 0.3447 0.4922 0.5712 0.5900 

 2549. 0.3629 0.5957 0.7517 0.7941 0.7719 

 3991. 0.6252 0.9125 1.064 1.077 1.004 

 4848. 0.7475 1.079 1.243 1.242 1.150 

 6495. 0.9214 1.379 1.621 1.653 1.518 

 10898. 1.484 2.100 2.357 2.296 2.075 

 18695. 2.418 3.234 3.451 3.241 2.835 

 20917. 2.638 3.499 3.711 3.450 3.006 

 32545. 3.792 4.795 4.884 4.425 3.762 

a

 Geopotential altitude in feet is converted from atmospheric depth in g/cm2 using ref. 8.
10

Table 2. Conversion factors (k, k' ) and characteristic rigidities for 

measurements in GOES-10 and GOES-11 proton channels (3) 

 Channel 

Conversion

Factor k a

Conversion

Factor k' b

Characteristic

Rigidity, MV c

 P4 4.64 22.25 225.1 

 P5 15.5 43.04 338.2 

 P6 90. 252.8 563.9 

 P7 300. 1210. 950.0 

 P10 162. 175.6 1225. 

 P11 1565. 1103. 1700. 

a k: counts/(particles/cm2

/steradian/MeV)

b k': counts/(particles/cm2

/steradian/MV) c When calculating a spectral hardness index, a single rigidity value, called the 

characteristic rigidity, is assigned to the entire channel. 

Table 3. Spectral hardness index correction factors (s) for 

differential fluxes derived from measurements in GOES-10

and GOES-11 proton channels (3) a

 γ P4 P5 P6 P7 P10 

 0 1.0000 1.0000 1.0000 1.0000 1.0000 

 1 0.9565 0.9775 0.9733 0.9300 0.9968 

 2 0.8777 0.9350 0.9233 0.8050 0.9904 

 3 0.7751 0.8764 0.8553 0.6502 0.9808 

 4 0.6609 0.8060 0.7753 0.4913 0.9683 

 5 0.5458 0.7284 0.6888 0.3485 0.9529 

 6 0.4380 0.6476 0.6011 0.2329 0.9348 

 7 0.3428 0.5674 0.5161 0.1473 0.9142 

 8 0.2623 0.4904 0.4366 0.08856 0.8914 

 9 0.1969 0.4186 0.3645 0.05089 0.8666 

10 0.1453 0.3533 0.3006 0.02811 0.8400 

a Intermediate correction factors are obtained by linear interpolation.

Table 4. Lower and upper rigidity limits associated with parameters α and 

γ calculated for each channel.

P4 P5 P6 P7 P10 P11 

Lower Rigidity 137 338 564 950 1225 1343 

Upper Rigidity 338 564 950 1225 1343 See Step 8