This science fair project develops a correlation between yearly solar flare X-ray Irradiation and worldwide yearly tropical cyclone activity; where Accumulated Cyclone Energy, Major Hurricane Days, and Hurricane Days, are graphed in an effort to estimate future year tropical cyclone activity.
Google was accessed to locate and download yearly Geostationary Operational Environmental Satellite (GOES) X-ray 5-minute data which measures solar flare X-ray irradiance in W/m2 at Earth. Similarly Google was also accessed to locate yearly sums of worldwide Accumulated Cyclone Energy (ACE), Major Hurricane Days (MHDs), and Hurricane Days (HDs).
Nine figures are used to demonstrate that an exponential relationship exists between the slow release of stored electrons in the Inner Van Allen Belt inward over time and a one-year time delay in tropical cyclone activity.
As the sum of each year's 5-minute X-ray GOES data representing irradiances above 1E-05 W/m2 [M&X Flares only] are plotted against worldwide yearly ACE, MHDs, and HDs for each successive year [i.e. 1997-2017 X-ray, 1998-2018 ACE, MHDs, HDs]; a time-independent exponential relationship is formed which estimates future year worldwide ACE, MHDs, and HDs. The accuracy of the models is presented statistically and graphically.
The year 2018 has been a quiet year with regard to solar flare activity with no M or X class solar flares being recorded by NOAA. The exponential regressions contained in Figures 7, 8 and 9 return 2019 tropical cyclone activity estimates: ACE2019= 628 +/- 124 knots2; with 43 +/- 17 MHDs2019, and 134 +/- 27 HDs2019.
Is there a correlation between the X-ray energy received at Earth from our sun’s most powerful solar flares and worldwide tropical cyclone activity?
This science fair project sets out to establish a correlation between the arrival of M-Class and X-Class solar flare energy summed over the course of a calendar year and the energy expended the following year through worldwide tropical cyclone activity as measured by these parameters: Accumulated Cyclone Energy per year, Major Hurricane Days per year, and Hurricane Days per year.
My reasoning is that the solar wind developed by Coronal Holes on the surface of the sun and the two most powerful classes of solar flares, M-Class and X-Class, emit billions of tons of charged particles every year. The negatively charged particles interact with the Earth’s magnetic field and become trapped in the Earth’s Outer Van Allen Belt. Continual solar flaring populates the Inner Van Allen Belt’s stable region with low energy electrons near 1.5 Earth radius and directly above the magnetic equator; the larger the solar flare the more electrons populate the Inner Belt. As identified by James A. Van Allen in his remarkable work in 1965, the population of the Inner Belt electrons decay inward by an e-t/T relationship; transferring the majority of the charged particles into the Earth’s upper atmosphere (Thermosphere) over one year creating an imbalance. The net effect of the imbalance creates successive year worldwide tropical cyclone activity, regulating Earth’s atmospheric energy system.
Beginning in 1958 and ending in 1962, scientists detonated a series of high altitude nuclear weapons, and unknowingly created a key to unlock the secret of forecasting yearly worldwide tropical cyclone activity. The discovery of electrons trapped in a stable inner belt encircling the equator [Reference 6, 15, 33] gave rise to estimates of electron lifetimes within the belt, and similarly, established processes for their removal. The belts are now known as the Van Allen Radiation Belts. In August of 2012, the Van Allen Probes were launched by NASA and remain in service today. The Van Allen Probes have given us a wealth of knowledge about the sources of electrons [Reference 2,3,16,18] and how the electrons move inward following solar flare events [References 3,4,16,18,19,26,39,40] and populate the Inner Van Allen Belt. Today the only confirming sources of information available regarding estimated electron leakage rates from the Inner Van Allen Belt are the high altitude nuclear tests of 1958-1962. This slow leakage rate, measured as e-t/T, forms a major underlying assumption of this science fair in that the electron leakage from the Inner Van Allen Belt over time is influencing the tropical cyclone activity; allowing successive year tropical cyclone activity data to be paired with current year solar flare data.
Geostationary Operational Environmental Satellites (GOES) also provide data. Solar flares from our sun are measured by the strength of the X-rays [W/m2] they emit as measured at the Earth by the GOES satellite [Reference 10, 21] using special detectors. The GOES data is available on the internet for analysis. Reference 20&32 rank the flares into the Top 50 for each year while Reference 29 indicates that only the two highest classes of solar flares, M-class and X-class, create radio interference effects noted within the Ionosphere, suggesting these two classes need to be examined in more detail.
Lastly, the tropical cyclone data for this science fair (which are also measured using GOES) originates from References 7, 8 & 9, where Colorado State University places the NOAA tropical cyclone tracks [Reference 17] into bins related to tropical cyclone activity for each ocean basin; these are Accumulated Cyclone Energy, Major Hurricane Days, and Hurricane Days.
This science fair correlates yearly solar flare X-ray Irradiation, which is created by summing the GOES 5-min X-ray irradiance data over each year, with worldwide successive-year tropical cyclone activity; where Accumulated Cyclone Energy, Major Hurricane Days, and Hurricane Days are graphed to estimate future year tropical cyclone activity.
Nine figures are used to show an exponential relationship existing between the slow release of stored electrons in the Inner Van Allen Belt inward over time and a one-year time delay in worldwide tropical cyclone activity. Where the greater the number of electrons pushed into the lower stable belt by solar flaring, the greater the number of electrons leaking inward over e-t/T, and the greater the Accumulated Cyclone Energy expended the following year.
The results of this science fair represent original research, where the results have never been published.
In order to develop a correlation between yearly solar flare X-ray energy measured at the Earth and yearly tropical cyclone energy expended, a graph must be produced.
The classification system for solar flares uses the letters A, B, C, M or X, according to the peak X-ray flux in watts per square meter (W/m2) with wavelengths between .100 to .800 nanometers, as measured at the Earth by the Geostationary Operational Environmental Satellite (GOES).
Figures 1-3 utilize the Top 50 Solar Flare events for each year for years 1997-current [Reference 32: https://www.spaceweatherlive.com/en/solar-activity/top-50-solar-flares/]. Prepare Figures 1-3 by summing only the M-class and X-class (i.e. >1E-05 W/m2) events from the top 50 solar flare events for each year. Record one sum in W/m2 for each year in Excel.
Figures 4-9 utilize GOES Satellite data for 5-Min X-ray (0.5-0.3 nm & 0.1-0.8 nm) to produce years 1997-current [Reference 21: https://satdat.ngdc.noaa.gov/sem/goes/data/avg/]. Prepare Figures 4-9 by cutting and pasting each year’s GOES Satellite data for 5-Min X-ray into two Excel columns, one for each detector (104,800 data points/column for a non leap year). Replace any null sets created when the detectors were not working (-99999) with a zero (0). If more than 1/10th of the data set is null, use another satellite’s data for that year.
For the Figures 4-6 sum only the M-class and X-class data present in each column (i.e. >1E-05 W/m2). Then add each detector’s result together to get a combined total for each year. Record one sum in W/m2 for each year. Similarly for Figures 7-9, sum all the continuous data from the 5-Minute X-ray GOES for both detectors and then add each detector’s result together to get a combined total for each year. Again, record one sum in W/m2 for each year.
Figures 1-9 utilize the total Accumulated Cyclone Energy (ACE), Major Hurricane Days (MHDs), and Hurricane Days (HDs), for all worldwide tropical cyclones occurring each year [Reference 7: http://tropical.atmos.colostate.edu/Realtime/]. Prepare Figures 1-9 by recording one worldwide total for ACE, MHDs, and HDs for each year, placing the each yearly total in separate columns in the same Excel file as the abscissa information.
Van Allen’s Key [Reference 33]:
Offset each column of tropical cyclone activity data (ACE, MHDs, HDs) by one year, such that 1997 X-ray sum creates the 1998 observed tropical cyclone data point, up to the current year, where the 2017 X-ray sum creates the 2018 tropical cyclone data point.
Using the shifted tropical cyclone columns with the annual X-ray sums create the time-independent relationship depicted in Figures 1-9. Each representing the worldwide yearly ACE, MHDs, and HDs (as dependent variables) versus the solar flare X-ray sums (as independent variables). Plot the abscissa using a logarithmic scale. Create an exponential regression for Figures 1-9 to estimate future year worldwide tropical cyclone ACE, MHDs and HDs per year based on current year X-ray totals.
Assess the error of the regression using a 90% confidence about the mean as determined from http://www.xuru.org/Index.asp.
• Figures 1-9 reveal that yearly worldwide tropical cyclone activity; measured as ACE, MHDs and HDs, are exponential functions of solar X-ray Irradiation as measured at Earth during the previous year; where the use of three different approaches presenting the solar flare data resulted in similar exponential functions with similar ordinate-intercepts and associated modeling error.
• Of the A, B, C, M, & X classes of solar flares that arrive at Earth, only the M-Class and X-Class flares (i.e. greater than 1E-05 W/m2) have a noticeable effect. Note – the effect is similar to the NOAA radio communication interference scale-which is where my idea to graph only M&X classes (Figures 1-6) came from.
• Figures 1-3 document the response of tropical cyclone activity to a previous year’s sum of peak solar flare events that are M-Class and X-Class, i.e. with peak irradiances above 1E-05 W/m2. Exponential breakout begins when the sum reaches 2E-03 W/m2 for tropical cyclone activity ACE, MHDs and HDs; the 2E-03 W/m2 is lower than the breakout in Figures 4-9 as the number of events being summed is 50 or less.
• Figures 4-9 document that tropical cyclone activity ACE, MHDs and HDs breakout begins when the yearly sum of GOES 5-min X-ray data reaches 2E-02 W/m2. Meaning that a yearly increase in M-Class and X-Class solar X-ray Irradiation above the sum 2E-02 W/m2 initiates a corresponding exponential growth in observed formation of ACE, MHDs and HDs the following year.
• Figures 7-9 are created using the continuous sum of full year GOES 5-min X-ray data sets, regardless of any solar flare event classification; representing true solar flare X-ray Irradiation at Earth.
• There is a general agreement between each of the accuracies of the three models (Figures 1,4,7 for ACE) (Figures 2,5,8 for MHDs) (Figures 3,6,9) for HDs). Ordinate intercepts for ACE (625 knots2), MHDs (42) and HDs (133) and are within 5% of the other similar figures. Dividing the 90% error into the ordinate-intercept returns a +/- 20% for ACE and HDs, but creates a +/- 40% for MHDs.
• Figures 2_5_8 MHD regression exponents are twice as large as the others! Suggesting process optimization.
• The relatively large errors shown at 90% for Figures 1-9 are discussed in the Error Analysis slides. Figures 1-3, created using the Top 50 Solar Flares, returned the highest Coefficient of Determination, R2=0.42, for each exponential regression in the science fair suggesting further research and data analysis modeling can begin with less cumbersome data sets.
• 2014 (16X-class, 34M-class flares) brought the highest yearly cyclone activities recorded within the 21 year data set spanning nearly two complete 11-yr solar cycles; ACE2015=1069 knots2, MHDs2015=96days, and HDs2015=231days. Suggesting 1) Earth’s removal mechanism is adequate to cushion the impact of large, repeating, X&M-class solar flaring (occurring during solar maximum) and 2) these rare high tropical cyclone activities are bounded by a +90% confidence interval and therefore estimate the upper cyclone activities that Earth could potentially experience (ACEupper=1193 knots2, MHDsupper=113days, and HDsupper=258days).
• Figures 1, 4 and 7 develop a correlation between yearly solar flare energy measured at the Earth and yearly tropical Accumulated Cyclone Energy expended the following year; this exponential relationship suggests that M&X-Class solar flare X-ray Irradiation, i.e. existing above 1E-05 W/m2, represents a new and important parameter in forecasting yearly worldwide tropical cyclone activity.
• The electron population within the Inner Van Allen belt is continually being increased and decreased over time. Since GOES 5-min X-ray data is measured in W/m2, and Power is defined as a Force applied over a Distance/Time, the X-ray’s from the M&X-Class solar flares are doing work to move electrons from the Outer Van Allen Belt across the slot and into the Inner Van Allen Belt. During major X-10+ Class solar flares, the content of the Inner Van Allen Belt may be dumped into the upper atmosphere resulting in an immediate increase in observed cyclone activity during the current year. Lastly, the Inner Van Allen Belt’s electron population leave the belt and leak into the upper atmosphere over the tropics with a decay constant, T, between 200 to 400 days (e-t/T) allowing successive calendar year tropical cyclone activity to be used.
• Figures 1-3 only require simple addition of the M&X-Class X-ray peak events during a calendar year to estimate the future year worldwide tropical cyclone activity and can be used for quick and comparatively accurate calculations.
• Figure 7 provides the most information to geoscientists in that it represents all the GOES 5-min X-ray continuous data available from 1997-current year and therefore provides the clearest energy to energy relationship seen between the two processes; where ACE [knots2] represents an approximation of the worldwide wind energy expended by all tropical systems over one calendar year - and accordingly an estimate of overall damage potential.
• The sunspot cycle provides important information for solar flaring frequency estimation, where a lower number of M&X-Class solar flare events are expected during solar minimum; thereby reducing the energy transfer from these events that is now linked to tropical cyclone activity.
• There were no noted M&X-Class solar flares during calendar year 2018; so Figures 1-6 can be evaluated to estimate 2019 tropical cyclone activity using the ordinate intercepts. Figures 7, 8, and 9 use the 2018 GOES 5-min X-ray sum of 3.273E-03W/m2: Accumulated Cyclone Energy2019 = 628 +/- 124 knots2, with 43 +/- 17 Major Hurricane Days2019, and 134 +/- 27 Hurricane Days2019. (Important Caveat: A major X-10+ Class solar flare and its accompanying CME occurring in 2019 will immediately disturb the Inner Van Allen Belt’s layering, dumping all its stored electrons inward, changing the estimated yearly activity significantly.)
• Lastly, only one reference [Reference 12] was located that could potentially explain how a mature tropical cyclone participates in an electron exchange with the upper atmosphere. With only one citation found, additional investigations are needed to validate the results and conclusions of this science fair.
• See slide “Uses for Society” for applicability of this forecast methodology.
My name is Faris Wald, I am currently a sophomore at Santa Fe High School in Santa Fe, NM. I enjoy playing the clarinet as my main hobby. Playing my clarinet allows me to express myself through the art of music and jazz. Playing the clarinet brings clarity to my academic work and my day. My participation with my school’s advanced band is positive and rewarding for me. As a member of my high school marching band, I participate in various parades, marches, concerts, and symphonies for my school.
I enjoy playing baseball for my school on the Junior Varsity team, where sportsmanship and teamwork come together to support my personal development. Through my involvement in the National Honor Society, I volunteer with a local food shelter during the major holidays. I enjoy down time at school by spending time with the school’s science club as it allows me creative time to code for my classes and perform research on my science fair; this is where I get one-on-one help with my science teacher and upper classmen.
I plan to attend college and graduate school in science or engineering and hope to earn a scholarship to help offset the cost of higher education so my family resources can be shared with my younger brother and sister.
Being a part of a major science fair allows me to interact with professional scientists that help me make more accurate yearly tropical cyclone forecasts; and understand our planet’s behavior a little bit better.
Due to the nature of this project, all research and execution took place using Google and multiple spreadsheets. No laboratory experimentation took place during the course of this science fair. Faris Wald
Mr. Derek Buschman
Santa Fe High School
2100 Yucca Street
Santa Fe, NM 87505
School Phone: 505-467-2400
Personal Cell Phone: 505-467-2914
People who helped me:
1) My mom and dad helped with my excel graphs and data processing using Excel. Google/internet was used to create this science fair in its entirety.
2) I did not understand my results so I sent my graphs to Michael MacCracken, Chief Scientist for Climate Change Programs, Climate Institute, Washington D.C., who sent my results to Professor Kerry Emanuel of MIT and the Harvard Physics Department. Both men sent back important feedback-most importantly, that this was original research and the data was “highly correlated at a significant level.” I also sent my graphs with estimates to Dave Eslinger of NOAA Coastal who manages the website for NOAA hurricane tracks and he said he had never seen this before too-but was impressed with my results. Lastly I sent the graphs to Dr. Luca Bertello, the Head of Solar Atmospheric Science, National Solar Observatory, who indicated he was unaware of any known process to explain the correlations presented in this science fair, and that the interrelationship is just now beginning to be laid down.
3) My Honors Chemistry Teacher at Santa Fe High School, Mr. Derek Buschman, personally spent many hours with me critiquing my submittal package during lunch and after school; Mr. Buschman immeasurably helped me with the statistics and their interpretation.
4) Dr. W. Mark Paris, a Physicist with Los Alamos National Laboratory and Volunteer Santa Fe Public Schools Science Fair Judge associated with "Santa Fe Alliance For Science", shared valuable insight into the terminology: x-ray flux, x-ray fluence, and shared the difference between solar x-ray irradiance and solar x-ray Irradiation.
1. Aschwanden, Markus J., and Samuel L. Freeland. “Automated Solar Flare Statistics In Soft X-Rays Over 37 Years of GOES Observations: The Invariance Of Self-Organized Criticality During Three Solar Cycles.” The Astrophysical Journal, vol. 754, no. 2, 2012, p. 112., doi:10.1088/0004-637x/754/2/112. Figure 6 maps solar cycle to both X and M Class flares
2. Baker, D. N., et al. “An Extreme Distortion of the Van Allen Belt Arising from the ‘Hallowe'en’ Solar Storm in 2003.” Nature, vol. 432, no. 7019, 2004, pp. 878–881., doi:10.1038/nature03116. Figure 1, Images from Energetic Electron Data depicting the shifting of the out Van Allen belt during the storm and filling of the inner Van Allen belt with electrons.
3. Baker, D. N., et al. “Space Weather Effects in the Earth’s Radiation Belts.” Space Science Reviews, vol. 214, no. 1, 2017, doi:10.1007/s11214-017-0452-7.
4. Baker, D.N., et al. “Radiation Belt Responses to the Solar Events of October—November 2003.” Inner Magnetosphere Interactions: New Perspectives From Imaging Geophysical Monograph Series, 2005, pp. 251–259., doi:10.1029/159gm19.
5. Cladis, J. B., and A. J. Dessler. “X Rays from Van Allen Belt Electrons.” Journal of Geophysical Research, vol. 66, no. 2, 1961, p. 343., doi:10.1029/jz066i002p00343. “The primary loss of outer-zone electrons occurs through rapid 'dumping' during geomagnetic storms.”
6. Cladis, J.B. Trapped Radiation Handbook: Ed: J.B. Cladis, et al. NTIS, 1971. Chapter 5, Figure 5-13 "Decay time constants of the Starfish trapped electron belts" and Figure 5-15 "Decay time parameters for trapped electrons on intermediate L Shells following the 1958-1962 High Altitude Nuclear Tests”. Note: Figure 5 shows where the 200 day (L=1.2) to 400 day (L=1.5) time constants are identified.
7. Collins, Douglas J. “Casualty Actuarial Society E-Forum, spring 2018-Volume 2.” Worldwide Tropical Cyclone Activity Measured Using the Actuaries Climate Index Methodology. See Worldwide Accumulated Cyclone Energy per Year Table, Exhibit 1, Sheet 1, years 1961-2017 with data for the table taken from http://tropical.atmos.colostate.edu/Realtime/
8. “Colorado State University.” Real-Time Global Tropical Cyclone Activity, http://tropical.atmos.colostate.edu/Realtime/. Current year tropical cyclone data indicated.
9. “Colorado State University.” Real-Time Global Tropical Cyclone Activity, tropical.atmos.colostate.edu/Realtime/index.php?arch&loc=northatlantic. The 6 ocean basin archives that were summed for tropical cyclone activity statistics are found here from 1996-current.
10. “Data from the NOAA Space Environment Center.” TEC-EPS - NOAA Daily Plots, European Space Agency Link, space-env.esa.int/index.php/NOAA-daily-plots.html. GOES 5-Min X-Ray data may be found for current year. This is GOES-15 data.
11. “The Earths Ionosphere.” Stanford SOLAR Center -- Ask A Solar Physicist FAQs - Answer, Stanford University, 2018, solar-center.stanford.edu/SID/activities/ionosphere.html.
12. “Electric Hurricanes.” NASA, NASA, science.nasa.gov/science-news/science-at-nasa/2006/09jan_electrichurricanes/. "The electric fields above Emily (Category 5, July 2005) were among the strongest ever measured by the aircraft's sensors over any storm, We observed steady fields in excess of 8 kilovolts per meter." "...there must be something else at work." [not related to this article, but NOAA reports that there were 5 M-Class Solar Flares and 6 X-Class Solar Flares all occurring in January 2005 (https://www.spaceweatherlive.com/en/solar-activity/top-50-solar-flares/year/2005)]
13. Filz, R C, et al. Corpuscular Radiation: a Revision of Chapter 17, Handbook of Geophysics and Space Environments. Dec. 1968, www.dtic.mil/dtic/tr/fulltext/u2/686749.pdf.
14. Getlen, Larry. “An Elevator Repairman Once Convinced the US to Nuke the Sky.” New York Post, New York Post, 20 Nov. 2018, nypost.com/2018/11/19/an-elevator-repairman-once-convinced-the-us-to-nuke-the-sky/. “About 3½ hours after Argus 1, [a] satellite passed through the geographical region where the Argus radiation shell was expected to form. Sure enough . . . instruments immediately began registering a sharp rise in electron flux. ‘The “Argus effect” was easily and promptly observed,’ ” Wolverton writes, including a quote from an account of the experiment. ...A second launch two days later failed to reach the needed altitude, but a third, on Sept. 6, was perfection, allowing a satellite to observe “the electron shell forming and spreading around the planet.”
15. Gombosi, T. I., et al. “Anthropogenic Space Weather.” The Scientific Foundation of Space Weather Space Sciences Series of ISSI, 2017, pp. 533–587., doi:10.1007/978-94-024-1588-9_16. Chapter 3, Artificial Radiation Belt, Figure 21, Comparison of Explorer XV from 10 November 1962 with Van Allen Probes data taken with the REPT on 23 March 2015. "James Van Allen could rightfully claim the artificial radiation belts created by the High Altitude Nuclear Tests of 1958-1962...undoubtedly constitute the greatest geophysical experiment ever conducted by man"
16. Horne, Richard B., et al. “Energetic Electron Precipitation from the Outer Radiation Belt during Geomagnetic Storms.” Geophysical Research Letters, vol. 36, no. 19, 2009, doi:10.1029/2009gl040236.
17. Hurricanes, NOAA Coastal, coast.noaa.gov/hurricanes/. World yearly ocean basin tropical cyclone history presented in the Table.
18. Lam, Mai Mai, et al. “Origin of Energetic Electron Precipitation >30 KeV into the Atmosphere.” Journal of Geophysical Research: Space Physics, vol. 115, no. A4, 2010, doi:10.1029/2009ja014619.
19. “Monitoring Energetic Electron Precipitation.” Spatial Frequency 1 | Welcome to the University of Calgary, Science, 2012, www.ucalgary.ca/above/science/precipitation.
20. “The Most Powerful Solar Flares Ever Recorded.” Spaceweather.com Time Machine, spaceweather.com/solarflares/topflares.html. Lists "The most Powerful Solar Flares Ever Recorded"
21. Geophysical Data Center. “Solar and Terrestrial Physics.” Direct Access to GOES and POES Data, U.S. Department of Commerce, 16 Sept. 2009, satdat.ngdc.noaa.gov/sem/goes/data/avg/. Website holds the complete GOES data for all satellites. This data was used for yearly 5-Min X-ray totals for 1997 - current year.
22. O'brien, B. J. “High-Latitude Geophysical Studies with Satellite Injun 3: 3. Precipitation of Electrons into the Atmosphere.” Journal of Geophysical Research, vol. 69, no. 1, 1964, pp. 13–43., doi:10.1029/jz069i001p00013.
23. Pierrard, V., et al. “Space Weather Effects in the Inner Magnetosphere: Plasmasphere and Radiation Belts Dynamics during Geomagnetic Storms.” 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC), 2015, doi:10.1109/ursi-at-rasc.2015.7303154.
24. Plait, Phil. “The 50th Anniversary of Starfish Prime: the Nuke That Shook the World.” D-Brief, Discover Magazine, 9 July 2012, blogs.discovermagazine.com/badastronomy/2012/07/09/the-50th-anniversary-of-starfish-prime-the-nuke-that-shook-the-world/#.W-YEmR9Kick.
25. Rodger, C. J., et al. “The Atmospheric Implications of Radiation Belt Remediation.” Annales Geophysicae, vol. 24, no. 7, 2006, pp. 2025–2041., doi:10.5194/angeo-24-2025-2006. Inner belt electrons have lifetime of approximately 1 year at L of 1.5 and less than 30 days at L<1.2.
26. Rodger, Craig J., et al. “Radiation Belt Electron Precipitation into the Atmosphere: Recovery from a Geomagnetic Storm.” Journal of Geophysical Research: Space Physics, vol. 112, no. A11, 2007, doi:10.1029/2007ja012383.
27. “Solar Coronal Hole History.” Solar Cycles 21, 22 and 23, www.solen.info/solar/coronal_holes.html.
28. “Solar Flares and the Sunspot Cycle.” NASA, NASA, 2013, gloria-project.eu/wp-content/uploads/2013/12/377678main_solar_math.pdf.
29. “Solar Flares (Radio Blackouts).” Earth's Magnetosphere | NOAA / NWS Space Weather Prediction Center, NOAA, www.swpc.noaa.gov/phenomena/solar-flares-radio-blackouts. Article describes the effect to the Ionosphere of M1 class solar flaring (Minor Radio Interference, R1) to X20 class solar flaring (Extreme Radio Interference, R5).
30. “Sunspot Number Graphics.” Daily and Monthly Sunspot Number (Last 13 Years) | SILSO, Sunspot Index and Long-Term Solar Observations, www.sidc.be/silso/ssngraphics.
31. Thompson, Avery. “A Group of Scientists Want to Launch a Satellite to Make an Artificial Aurora.” Popular Mechanics, 29 Oct. 2018. NASA CONNEX Mission will be a 1 MeV Linear Electron Accelerator (10mA Average Current, 1 Joule energy/shot) placed in a low earth orbit that will pulse the ionosphere.
32. “Top 50 Solar Flares of the Year 2003 | Solar Activity.” SpaceWeatherLive.com, www.spaceweatherlive.com/en/solar-activity/top-50-solar-flares/year/2003. Years 1996-2018 can be accessed to create figures shown in this science fair entry.
33. Van Allen, James A. Spatial Distribution and Time Decay of the Intensities of Geomagnetically Trapped Electrons from the High Altitude Nuclear Burst of July 1962. University of Iowa, Dec. 1965, https://apps.dtic.mil/dtic/tr/fulltext/u2/477432.pdf. Figure 18 shows where the 200 day (L=1.2) to 400 day (L=1.5) time constants are clearly identified.
34. Van Allen, James A., et al. “Radiation Observations with Satellite 1958 ε.” Journal of Geophysical Research, vol. 64, no. 3, 1959, pp. 271–286., doi:10.1029/jz064i003p00271.
35. Wald, Faris I. “Private Conversation with W. Mark Paris, Theoretical Physicist and Volunteer Science Fair Judge, Regarding My Axis Titles.” 9 Oct. 2018.
36. Wald, Faris I. The Weather Channel, www.facebook.com/TheWeatherChannel/videos/10156012463715921/. Detailed explanation of my discovery of Dr. Van Allen's Key.
37. Walt, Martin. “Introduction to Geomagnetically Trapped Radiation.” 1994, doi:10.1017/cbo9780511524981.
38. http://www.xuru.org/. Statistical analysis website used for regression analysis and regression error.
39. Youssef, M. “On the Relation between the CMEs and the Solar Flares.” NRIAG Journal of Astronomy and Geophysics, vol. 1, no. 2, 2012, pp. 172–178., doi:10.1016/j.nrjag.2012.12.014. “78% of occurring X-Class Solar Flares are accompanied by a Coronal Mass Ejection.”
40. Zhang, K., et al. “Detailed Characteristics of Radiation Belt Electrons Revealed by CSSWE/REPTile Measurements: Geomagnetic Activity Response and Precipitation Observation.” Journal of Geophysical Research: Space Physics, vol. 122, no. 8, 2017, pp. 8434–8445., doi:10.1002/2017ja024309. Figure 3 shows lower energy electrons penetrating the slot region into the inner belt during high solar activity periods.