# Review of Solar Energetic Particle Prediction Models

Kathryn Whitman, Ricky Egeland, Ian G. Richardson, Clayton Allison, Philip Quinn, Janet Barzilla, Irina Kitiashvili, Viacheslav Sadykov, Hazel M. Bain, Mark Dierckxsens, et al.

► To cite this version:

Kathryn Whitman, Ricky Egeland, Ian G. Richardson, Clayton Allison, Philip Quinn, et al. Review of Solar Energetic Particle Prediction Models. Advances in Space Research, 2023, 72, pp.5161-5242. 10.1016/j.asr.2022.08.006. insu-04473125

HAL Id: insu-04473125

https://insu.hal.science/insu-04473125

Submitted on 23 Feb 2024

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# Review of Solar Energetic Particle Prediction Models

Kathryn Whitman, Ricky Egeland, Ian G. Richardson, Clayton Allison, Philip Quinn, Janet Barzilla, Irina Kitiashvili, Viacheslav Sadykov, Hazel M. Bain, Mark Dierckxsens, et al.

► To cite this version:

Kathryn Whitman, Ricky Egeland, Ian G. Richardson, Clayton Allison, Philip Quinn, et al. Review of Solar Energetic Particle Prediction Models. Advances in Space Research, 2023, 72, pp.5161-5242. 10.1016/j.asr.2022.08.006. insu-04473125

HAL Id: insu-04473125

https://insu.hal.science/insu-04473125v1

Submitted on 23 Feb 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Review

Review of Solar Energetic Particle Prediction Models

Kathryn Whitman<sup>a,b,*</sup>, Ricky Egeland<sup>c</sup>, Ian G. Richardson<sup>d,e</sup>, Clayton Allison<sup>f</sup>, Philip Quinn<sup>f</sup>, Janet Barzilla<sup>f</sup>, Irina Kitiashvili<sup>g</sup>, Viacheslav Sadykov<sup>h</sup>, Hazel M. Bain<sup>i,j</sup>, Mark Dierckxsens<sup>k</sup>, M. Leila Mays<sup>d</sup>, Tilaye Tadesse<sup>f</sup>, Kerry T. Lee<sup>c</sup>, Edward Semones<sup>c</sup>, Janet G. Luhmann<sup>l</sup>, Marlon Núñez<sup>m</sup>, Stephen M. White<sup>n</sup>, Stephen W. Kahler<sup>n,1</sup>, Alan G. Ling<sup>o</sup>, Don F. Smart<sup>p</sup>, Margaret A. Shea<sup>p</sup>, Valeriy Tenishev<sup>l</sup>, Soukaina F. Boubrahimi<sup>r</sup>, Berkay Aydin<sup>h</sup>, Petrus Martens<sup>h</sup>, Rafal Angryk<sup>h</sup>, Michael S. Marsh<sup>s</sup>, Silvia Dalla<sup>t</sup>, Norma Crosby<sup>k</sup>, Nathan A. Schwadron<sup>u</sup>, Kamen Kozarev<sup>v</sup>, Matthew Gorby<sup>w</sup>, Matthew A. Young<sup>u</sup>, Monica Laurenza<sup>x</sup>, Edward W. Cliver<sup>y</sup>, Tommaso Alberti<sup>x</sup>, Mirko Stumpo<sup>z,x</sup>, Simone Benella<sup>x</sup>, Athanasios Papaioannou<sup>aa</sup>, Anastasios Anastasiadis<sup>aa</sup>, Ingmar Sandberg<sup>ab</sup>, Manolis K. Georgoulis<sup>ac</sup>, Anli Ji<sup>h</sup>, Dustin Kempton<sup>h</sup>, Chetraj Pandey<sup>h</sup>, Gang Li<sup>ad</sup>, Junxiang Hu<sup>ad</sup>, Gary P. Zank<sup>ad</sup>, Eleni Lavasa<sup>ae,aa</sup>, Giorgos Giannopoulos<sup>af</sup>, David Falconer<sup>ad,ag</sup>, Yash Kadadi<sup>ah</sup>, Ian Fernandes<sup>ai</sup>, Maher A. Dayeh<sup>aj,al</sup>, Andrés Muñoz-Jaramillo<sup>ak</sup>, Subhamoy Chatterjee<sup>ak</sup>, Kimberly D. Moreland<sup>al,aj</sup>, Igor V. Sokolov<sup>q</sup>, Ilia I. Roussev<sup>l</sup>, Aleksandre Taktakishvili<sup>am</sup>, Frederic Effenberger<sup>an</sup>, Tamas Gombosi<sup>q</sup>, Zhenguang Huang<sup>q</sup>, Lulu Zhao<sup>q</sup>, Nicolas Wijsen<sup>ao</sup>, Angels Aran<sup>ap</sup>, Stefaan Poedts<sup>ao,aq</sup>, Athanasios Kouloumvakos<sup>ar</sup>, Miikka Paassilta<sup>as</sup>, Rami Vainio<sup>as</sup>, Anatoly Belov<sup>at</sup>, Eugenia A. Eroshenko<sup>at,1</sup>, Maria A. Abunina<sup>at</sup>, Artem A. Abunin<sup>at</sup>, Christopher C. Balch<sup>j</sup>, Olga Malandraki<sup>aa</sup>, Michalis Karavolos<sup>aa</sup>, Bernd Heber<sup>au</sup>, Johannes Labrenz<sup>au</sup>, Patrick Kühl<sup>au</sup>, Alexander G. Kosovichev<sup>av,g</sup>, Vincent Oria<sup>av</sup>, Gelu M. Nita<sup>av</sup>, Egor Illarionov<sup>aw,ax</sup>, Patrick M. O’Keefe<sup>av</sup>, Yucheng Jiang<sup>av</sup>, Sheldon H. Fereira<sup>av</sup>, Aatiya Ali<sup>h</sup>, Evangelos Paouris<sup>ay,az</sup>, Sigiava Aminalragia-Giamini<sup>ab,ae</sup>, Piers Jiggens<sup>ba</sup>, Meng Jin<sup>bb</sup>, Christina O. Lee<sup>l</sup>, Erika Palmerio<sup>bc</sup>, Alessandro Bruno<sup>d,am</sup>, Spiridon Kasapis<sup>q</sup>, Xiantong Wang<sup>q</sup>, Yang Chen<sup>q</sup>, Blai Sanahuja<sup>ap</sup>, David Lario<sup>d</sup>, Carla Jacobs<sup>bd</sup>, Du Toit Strauss<sup>be</sup>, Ruhann Steyn<sup>be</sup>, Jabus van den Berg<sup>be,bf</sup>, Bill Swalwell<sup>t</sup>, Charlotte Waterfall<sup>t</sup>, Mohamed Nedal<sup>v</sup>, Rositsa Miteva<sup>v</sup>, Momchil Dechev<sup>v</sup>, Pietro Zucca<sup>bg</sup>, Alec Engell<sup>bh</sup>, Brianna Maze<sup>bh</sup>, Harold Farmer<sup>bh</sup>, Thuha Kerber<sup>bh</sup>, Ben Barnett<sup>bh</sup>, Jeremy Loomis<sup>bh</sup>, Nathan Grey<sup>bh</sup>, Barbara J. Thompson<sup>d</sup>, Jon A. Linker<sup>bc</sup>, Ronald M. Caplan<sup>bc</sup>, Cooper Downs<sup>bc</sup>, Tibor Török<sup>bc</sup>, Roberto Lionello<sup>bc</sup>, Viacheslav Titov<sup>bc</sup>, Ming Zhang<sup>bi</sup>, Pouya Hosseinzadeh<sup>r</sup>

<footnote>* Corresponding author at: KBR, 601 Jefferson Street, Houston, TX 77002, USA.</footnote>

<footnote>E-mail address: kathryn.whitman@nasa.gov (K. Whitman).</footnote>

<footnote n="1">¹ Deceased.</footnote>
Review

Review of Solar Energetic Particle Prediction Models

Kathryn Whitman<sup>a,b,*</sup>, Ricky Egeland<sup>c</sup>, Ian G. Richardson<sup>d,e</sup>, Clayton Allison<sup>f</sup>, Philip Quinn<sup>f</sup>, Janet Barzilla<sup>f</sup>, Irina Kitiashvili<sup>g</sup>, Viacheslav Sadykov<sup>h</sup>, Hazel M. Bain<sup>i,j</sup>, Mark Dierckxsens<sup>k</sup>, M. Leila Mays<sup>d</sup>, Tilaye Tadesse<sup>f</sup>, Kerry T. Lee<sup>c</sup>, Edward Semones<sup>c</sup>, Janet G. Luhmann<sup>l</sup>, Marlon Núñez<sup>m</sup>, Stephen M. White<sup>n</sup>, Stephen W. Kahler<sup>n,1</sup>, Alan G. Ling<sup>o</sup>, Don F. Smart<sup>p</sup>, Margaret A. Shea<sup>p</sup>, Valeriy Tenishev<sup>l</sup>, Soukaina F. Boubrahimi<sup>r</sup>, Berkay Aydin<sup>h</sup>, Petrus Martens<sup>h</sup>, Rafal Angryk<sup>h</sup>, Michael S. Marsh<sup>s</sup>, Silvia Dalla<sup>t</sup>, Norma Crosby<sup>k</sup>, Nathan A. Schwadron<sup>u</sup>, Kamen Kozarev<sup>v</sup>, Matthew Gorby<sup>w</sup>, Matthew A. Young<sup>u</sup>, Monica Laurenza<sup>x</sup>, Edward W. Cliver<sup>y</sup>, Tommaso Alberti<sup>x</sup>, Mirko Stumpo<sup>z,x</sup>, Simone Benella<sup>x</sup>, Athanasios Papaioannou<sup>aa</sup>, Anastasios Anastasiadis<sup>aa</sup>, Ingmar Sandberg<sup>ab</sup>, Manolis K. Georgoulis<sup>ac</sup>, Anli Ji<sup>h</sup>, Dustin Kempton<sup>h</sup>, Chetraj Pandey<sup>h</sup>, Gang Li<sup>ad</sup>, Junxiang Hu<sup>ad</sup>, Gary P. Zank<sup>ad</sup>, Eleni Lavasa<sup>ae,aa</sup>, Giorgos Giannopoulos<sup>af</sup>, David Falconer<sup>ad,ag</sup>, Yash Kadadi<sup>ah</sup>, Ian Fernandes<sup>ai</sup>, Maher A. Dayeh<sup>aj,al</sup>, Andrés Muñoz-Jaramillo<sup>ak</sup>, Subhamoy Chatterjee<sup>ak</sup>, Kimberly D. Moreland<sup>al,aj</sup>, Igor V. Sokolov<sup>q</sup>, Ilia I. Roussev<sup>l</sup>, Aleksandre Taktakishvili<sup>am</sup>, Frederic Effenberger<sup>an</sup>, Tamas Gombosi<sup>q</sup>, Zhenguang Huang<sup>q</sup>, Lulu Zhao<sup>q</sup>, Nicolas Wijsen<sup>ao</sup>, Angels Aran<sup>ap</sup>, Stefaan Poedts<sup>ao,aq</sup>, Athanasios Kouloumvakos<sup>ar</sup>, Miikka Paassilta<sup>as</sup>, Rami Vainio<sup>as</sup>, Anatoly Belov<sup>at</sup>, Eugenia A. Eroshenko<sup>at,1</sup>, Maria A. Abunina<sup>at</sup>, Artem A. Abunin<sup>at</sup>, Christopher C. Balch<sup>j</sup>, Olga Malandraki<sup>aa</sup>, Michalis Karavolos<sup>aa</sup>, Bernd Heber<sup>au</sup>, Johannes Labrenz<sup>au</sup>, Patrick Kühl<sup>au</sup>, Alexander G. Kosovichev<sup>av,g</sup>, Vincent Oria<sup>av</sup>, Gelu M. Nita<sup>av</sup>, Egor Illarionov<sup>aw,ax</sup>, Patrick M. O’Keefe<sup>av</sup>, Yucheng Jiang<sup>av</sup>, Sheldon H. Fereira<sup>av</sup>, Aatiya Ali<sup>h</sup>, Evangelos Paouris<sup>ay,az</sup>, Sigiava Aminalragia-Giamini<sup>ab,ae</sup>, Piers Jiggens<sup>ba</sup>, Meng Jin<sup>bb</sup>, Christina O. Lee<sup>l</sup>, Erika Palmerio<sup>bc</sup>, Alessandro Bruno<sup>d,am</sup>, Spiridon Kasapis<sup>q</sup>, Xiantong Wang<sup>q</sup>, Yang Chen<sup>q</sup>, Blai Sanahuja<sup>ap</sup>, David Lario<sup>d</sup>, Carla Jacobs<sup>bd</sup>, Du Toit Strauss<sup>be</sup>, Ruhann Steyn<sup>be</sup>, Jabus van den Berg<sup>be,bf</sup>, Bill Swalwell<sup>t</sup>, Charlotte Waterfall<sup>t</sup>, Mohamed Nedal<sup>v</sup>, Rositsa Miteva<sup>v</sup>, Momchil Dechev<sup>v</sup>, Pietro Zucca<sup>bg</sup>, Alec Engell<sup>bh</sup>, Brianna Maze<sup>bh</sup>, Harold Farmer<sup>bh</sup>, Thuha Kerber<sup>bh</sup>, Ben Barnett<sup>bh</sup>, Jeremy Loomis<sup>bh</sup>, Nathan Grey<sup>bh</sup>, Barbara J. Thompson<sup>d</sup>, Jon A. Linker<sup>bc</sup>, Ronald M. Caplan<sup>bc</sup>, Cooper Downs<sup>bc</sup>, Tibor Török<sup>bc</sup>, Roberto Lionello<sup>bc</sup>, Viacheslav Titov<sup>bc</sup>, Ming Zhang<sup>bi</sup>, Pouya Hosseinzadeh<sup>r</sup>

<footnote>* Corresponding author at: KBR, 601 Jefferson Street, Houston, TX 77002, USA.</footnote>

<footnote>E-mail address: kathryn.whitman@nasa.gov (K. Whitman).</footnote>

<footnote n="1">¹ Deceased.</footnote>
a University of Houston, 4800 Calhoun Rd, Houston, TX 77204, USA

b KBR, 601 Jefferson Street, Houston, TX 77002, USA

c NASA Johnson Space Center, 2101 E NASA Pkwy, Houston, TX 77058, USA

d NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA

e Department of Astronomy, University of Maryland, 4296 Stadium Dr., College Park, MD 20742, USA

f Leidos, Inc., 555 Forge River Rd, Ste 150A, Webster, TX 77598, USA

g NASA Ames Research Center, Mail Stop 204-14 Moffett Field, CA 94035, USA

h Georgia State University, 25 Park Place NE, Atlanta, GA 30303, USA

i CIRES, University of Colorado Boulder, 216 UCB, Boulder, CO 80309, USA

j NOAA Space Weather Prediction Center, 325 Broadway, Boulder, CO 80305, USA

k Royal Belgian Institute for Space Aeronomy, Ringlaan 3, B-1180 Brussels, Belgium

l Space Sciences Laboratory, University of California at Berkeley, 7 Gauss Way, Berkeley, CA 94720, USA

m University of Malaga, Av. de Cervantes, 2, 29016 Malaga, Spain

n Air Force Research Laboratory, Space Vehicles Directorate, 3550 Aberdeen Avenue, Kirtland AFB, NM 87117, USA

o Atmospheric Environmental Research, 3550 Aberdeen Ave. SE, Albuquerque, NM 87110, USA

p SSSRC, 100 Tennyson Avenue, Nashua, NH 03062, USA

q University of Michigan, 500 S. State Street, Ann Arbor, MI 48109, USA

r Utah State University, 0500 Old Main Hill, Logan, UT 84322-0500, USA

s Met Office, FitzRoy Road, Exeter, DevonEX1 3PB, UK

t University of Central Lancashire, Fylde Rd, Preston, Lancashire PR1 2HE, UK

u University of New Hampshire, 105 Main St, Durham, NH 03824, USA

v Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria

w Cray Inc., 2131 Lindau Ln 1000, Bloomington, MN 55425, USA

x INAF, Institute for Space Astrophysics and Planetology, via del Fosso del Cavaliere 100, 00133 Roma, Italy

y National Solar Observatory, 3665 Discovery Dr 3rd, Boulder, CO 80303, USA

z Università di Roma Tor Vergata, Via Cracovia, 50, 00133 Roma, Italy

aa National Observatory of Athens, Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, Vas. Pavlou & I. Metaxa, GR-15 236 Penteli, Athens, Greece

ab Space Applications & Research Consultancy (SPARC), Aiolou St. 73, 10551 Athens, Greece

ac RCAAM of the Academy of Athens, 4 Soranou Efesiou Street, 115 27 Athens, Greece

ad University of Alabama at Huntsville, 301 Sparkman Drive, Huntsville, AL 35899, USA

ae National and Kapodistrian University of Athens, Athens 157 72, Greece

af Athena Research Center, Επιδραματικό Κωδικό Αρτεμιδού, Marousi 151 25, Greece

ag NASA Marshall Space Flight Center, Martin Rd SW, Huntsville, AL 35812, USA

ah Stanford University, 450 Serra Mall, Stanford, CA 94305, USA

ai Princeton University, P.O. Box 430, Princeton, NJ 08544, USA

aj Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238, USA

ak Southwest Research Institute Boulder, 1050 Walnut St 300, Boulder, CO 80302, USA

al University of Texas at San Antonio, 1 UTSA Circle, San Antonio, TX 78249, USA

am Catholic University of America, 620 Michigan Ave NE, Washington, DC 20064, USA

an University of California at Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095, USA

ao Department of Mathematics/Centre for Mathematical Plasma Astrophysics, KU Leuven, Celestijnenlaan 200 B 3001 Leuven, Leuven, Belgium

ap Departament de Física Quàntica i Astrofísica, Institut de Ciècies del Cosmos (ICCUB), Universitat de Barcelona, UB-IEEC, Martí i Franquès, 1 Barcelona, Spain

aq Institute of Physics, University of Maria Curie-Skłodowska, ul.Radziszewskiego 10, 20-031 Lublin, Poland

ar IRAP, 9 Av.du Colonel Roche, 31400 Toulouse, France

as Department of Physics and Astronomy, FI-20014 University of Turku, Finland

at Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, 108840 Moscow Troitsk, Russia

au IEAP, Christian-Albrechts-Universitaet, Leibnizstraße 11-19, 24118 Kiel, Germany

av New Jersey Institute of Technology, 323 Dr Martin Luther King Jr Blvd, Newark, NJ 07102, USA

aw Department of Mechanics and Mathematics, Moscow State University, Ulitsa Kolmogorova, 1, Moscow 119991, Russia

ax Moscow Center of Fundamental and Applied Mathematics, Moscow 119234, Russia

ay George Mason University, 4400 University Dr, Fairfax, VA 22030, USA

az The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Rd, Laurel, MD 20723, USA

ba European Space Research and Technology Centre (ESTEC), Space Environment and Effects Section Keperlaan 1, 2200AG Noordwijk, the Netherlands

bb Lockheed Martin Solar & Astrophysics Laboratory, 3176 Porter Dr, Palo Alto, CA 94304, USA

bc Predictive Science Inc., 9990 Mesa Rim Rd, Ste 170, San Diego, CA 92121, USA

bd Space Applications Systems, 1932 Zaventem, Belgium

be Centre for Space Research, North-West University, Building G5, Potchefstroom Campus, North-West University, Potchefstroom, South Africa

bf South African National Space Agency, Hospital St, Hermanus 7200, South Africa

bg ASTRON, The Netherlands Institute for Radio Astronomy, Oude Hoogeveensijdjk 4, 7991 PD Dwingeloo, the Netherlands

bh NextGen Federal Systems, 1399 Stewartstown Road, Suite 350, Morgantown, WV 26505, USA

bi Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901, USA

Received 31 March 2022; received in revised form 29 July 2022; accepted 3 August 2022
Available online 13 August 2022
a University of Houston, 4800 Calhoun Rd, Houston, TX 77204, USA

b KBR, 601 Jefferson Street, Houston, TX 77002, USA

c NASA Johnson Space Center, 2101 E NASA Pkwy, Houston, TX 77058, USA

d NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA

e Department of Astronomy, University of Maryland, 4296 Stadium Dr., College Park, MD 20742, USA

f Leidos, Inc., 555 Forge River Rd, Ste 150A, Webster, TX 77598, USA

g NASA Ames Research Center, Mail Stop 204-14 Moffett Field, CA 94035, USA

h Georgia State University, 25 Park Place NE, Atlanta, GA 30303, USA

i CIRES, University of Colorado Boulder, 216 UCB, Boulder, CO 80309, USA

j NOAA Space Weather Prediction Center, 325 Broadway, Boulder, CO 80305, USA

k Royal Belgian Institute for Space Aeronomy, Ringlaan 3, B-1180 Brussels, Belgium

l Space Sciences Laboratory, University of California at Berkeley, 7 Gauss Way, Berkeley, CA 94720, USA

m University of Malaga, Av. de Cervantes, 2, 29016 Malaga, Spain

n Air Force Research Laboratory, Space Vehicles Directorate, 3550 Aberdeen Avenue, Kirtland AFB, NM 87117, USA

o Atmospheric Environmental Research, 3550 Aberdeen Ave. SE, Albuquerque, NM 87110, USA

p SSSRC, 100 Tennyson Avenue, Nashua, NH 03062, USA

q University of Michigan, 500 S. State Street, Ann Arbor, MI 48109, USA

r Utah State University, 0500 Old Main Hill, Logan, UT 84322-0500, USA

s Met Office, FitzRoy Road, Exeter, DevonEX1 3PB, UK

t University of Central Lancashire, Fylde Rd, Preston, Lancashire PR1 2HE, UK

u University of New Hampshire, 105 Main St, Durham, NH 03824, USA

v Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria

w Cray Inc., 2131 Lindau Ln 1000, Bloomington, MN 55425, USA

x INAF, Institute for Space Astrophysics and Planetology, via del Fosso del Cavaliere 100, 00133 Roma, Italy

y National Solar Observatory, 3665 Discovery Dr 3rd, Boulder, CO 80303, USA

z Università di Roma Tor Vergata, Via Cracovia, 50, 00133 Roma, Italy

aa National Observatory of Athens, Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, Vas. Pavlou & I. Metaxa, GR-15 236 Penteli, Athens, Greece

ab Space Applications & Research Consultancy (SPARC), Aiolou St. 73, 10551 Athens, Greece

ac RCAAM of the Academy of Athens, 4 Soranou Efesiou Street, 115 27 Athens, Greece

ad University of Alabama at Huntsville, 301 Sparkman Drive, Huntsville, AL 35899, USA

ae National and Kapodistrian University of Athens, Athens 157 72, Greece

af Athena Research Center, Επιδραματικό Κωδικό Αρτεμιδού, Marousi 151 25, Greece

ag NASA Marshall Space Flight Center, Martin Rd SW, Huntsville, AL 35812, USA

ah Stanford University, 450 Serra Mall, Stanford, CA 94305, USA

ai Princeton University, P.O. Box 430, Princeton, NJ 08544, USA

aj Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238, USA

ak Southwest Research Institute Boulder, 1050 Walnut St 300, Boulder, CO 80302, USA

al University of Texas at San Antonio, 1 UTSA Circle, San Antonio, TX 78249, USA

am Catholic University of America, 620 Michigan Ave NE, Washington, DC 20064, USA

an University of California at Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095, USA

ao Department of Mathematics/Centre for Mathematical Plasma Astrophysics, KU Leuven, Celestijnenlaan 200 B 3001 Leuven, Leuven, Belgium

ap Departament de Física Quàntica i Astrofísica, Institut de Ciècies del Cosmos (ICCUB), Universitat de Barcelona, UB-IEEC, Martí i Franquès, 1 Barcelona, Spain

aq Institute of Physics, University of Maria Curie-Skłodowska, ul.Radziszewskiego 10, 20-031 Lublin, Poland

ar IRAP, 9 Av.du Colonel Roche, 31400 Toulouse, France

as Department of Physics and Astronomy, FI-20014 University of Turku, Finland

at Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, 108840 Moscow Troitsk, Russia

au IEAP, Christian-Albrechts-Universitaet, Leibnizstraße 11-19, 24118 Kiel, Germany

av New Jersey Institute of Technology, 323 Dr Martin Luther King Jr Blvd, Newark, NJ 07102, USA

aw Department of Mechanics and Mathematics, Moscow State University, Ulitsa Kolmogorova, 1, Moscow 119991, Russia

ax Moscow Center of Fundamental and Applied Mathematics, Moscow 119234, Russia

ay George Mason University, 4400 University Dr, Fairfax, VA 22030, USA

az The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Rd, Laurel, MD 20723, USA

ba European Space Research and Technology Centre (ESTEC), Space Environment and Effects Section Keperlaan 1, 2200AG Noordwijk, the Netherlands

bb Lockheed Martin Solar & Astrophysics Laboratory, 3176 Porter Dr, Palo Alto, CA 94304, USA

bc Predictive Science Inc., 9990 Mesa Rim Rd, Ste 170, San Diego, CA 92121, USA

bd Space Applications Systems, 1932 Zaventem, Belgium

be Centre for Space Research, North-West University, Building G5, Potchefstroom Campus, North-West University, Potchefstroom, South Africa

bf South African National Space Agency, Hospital St, Hermanus 7200, South Africa

bg ASTRON, The Netherlands Institute for Radio Astronomy, Oude Hoogeveensijdjk 4, 7991 PD Dwingeloo, the Netherlands

bh NextGen Federal Systems, 1399 Stewartstown Road, Suite 350, Morgantown, WV 26505, USA

bi Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901, USA

Received 31 March 2022; received in revised form 29 July 2022; accepted 3 August 2022

Available online 13 August 2022
Abstract

Solar Energetic Particle (SEP) events are interesting from a scientific perspective as they are the product of a broad set of physical processes from the corona out through the extent of the heliosphere, and provide insight into processes of particle acceleration and transport that are widely applicable in astrophysics. From the operations perspective, SEP events pose a radiation hazard for aviation, electronics in space, and human space exploration, in particular for missions outside of the Earth's protective magnetosphere including to the Moon and Mars. Thus, it is critical to improve the scientific understanding of SEP events and use this understanding to develop and improve SEP forecasting capabilities to support operations. Many SEP models exist or are in development using a wide variety of approaches and with differing goals. These include computationally intensive physics-based models, fast and light empirical models, machine learning-based models, and mixed-model approaches. The aim of this paper is to summarize all of the SEP models currently developed in the scientific community, including a description of model approach, inputs and outputs, free parameters, and any published validations or comparisons with data.

© 2022 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Keywords: Space radiation; Solar energetic particles; Space weather models; Space weather forecasting; SEP models

1. Introduction

Solar Energetic Particle (SEP) events are transient injec-
tions into the heliosphere of protons, electrons, and higher
mass charged particles with a wide range of energies (tens
of keVs to GeVs), spectra, composition, and intensities.
They follow energetic solar eruptions that are generally
associated with flares and Coronal Mass Ejection (CME)
s. They are apparently accelerated by processes associated
with flares, such as wave-particle interactions and recon-
nection, as well as by acceleration at CME-driven shocks
(for reviews, see e.g., Shea and Smart, 1990; Reames,
2004; Reames, 2017; Desai and Giacalone, 2016; Klein
and Dalla, 2017). As has long been recognized since at least
the Apollo era (Hilberg, 1969), SEP events are hazardous
to electronics (e.g., Iucci et al., 2005) and humans in space.
As humans pursue space exploration outside of low Earth
orbit, the understanding, monitoring, and forecasting of
SEP events becomes increasingly important (e.g., Kim
et al., 2011). SEPs are also hazardous to aircraft crews,
in particular on polar routes (Jones et al., 2005), and to
modern technological systems (Eastwood et al., 2017).
Thus, in the last two decades, government agencies around
the world have developed policies related to space weather,
including the need for improved forecasting of SEP events
(Guarnieri et al., 2005; Opgenoorth et al., 2019; National
Science & Technology Council, 2019). Plans for the
National Aeronautics and Space Administration (NASA)
Artemis missions to send astronauts back to the Moon in
the mid-2020s are providing further motivation to improve
SEP forecasting.

Efforts to predict SEP events have a long history (e.g.,
Smart et al., 1979). At present, three dozen SEP models
have been or are being developed in the scientific research
community, as listed in Table 1. These models use a variety
of approaches: Empirical models are based on the identifi-

cation of correlations and other relationships in observa-
tional data that may be related to the underlying physical
processes. They typically give rapid forecasts and are easily
incorporated into forecasting and operations. Such models
might give a binary “all clear” or “not all clear” prediction,
representing the confidence that an event of a given magni-
tude *will not* or *will* occur during a given forecast window,
the probability that an event of a certain intensity will
occur, or deterministic quantities (e.g., onset time, the peak
flux at a certain energy). Physics-based models use our cur-
rent understanding of the processes of particle acceleration
and transport at the Sun and in interplanetary space to
model these processes and predict the properties of the
associated SEP event. Most of these models are computa-
tionally intensive, and the ability to produce a prediction
“in real time” may be limited by the resources available,
so they may not be readily incorporated into a forecasting
workflow. In addition, fundamental parameters required
by the model may be poorly characterized. However, these
complex models hold the promise of modeling the complete
distribution of SEP events with time in 2- or 3-dimensional
space. Machine Learning (ML) approaches are now being
investigated in the hope that they will yield a new class of
SEP models that will produce fast forecasts with improved
accuracy. Lastly, multi-module forecasting systems link
existing models of multiple types to create a chain that
feeds forecasts from one module to the next that can be
updated as real time measurements become available, e.g.
a flare forecast module passes information to a CME fore-
cast module which then passes parameters to produce a
final SEP forecast. All of the models described here focus
on the prediction of SEP protons, as these are the most
abundant particles and the largest contributors to space
radiation. Many of the physics-based models have the
added capability to investigate the behavior of SEP ions
and electrons, which allows them to probe the details of
Abstract

Solar Energetic Particle (SEP) events are interesting from a scientific perspective as they are the product of a broad set of physical
processes from the corona out through the extent of the heliosphere, and provide insight into processes of particle acceleration and trans-
port that are widely applicable in astrophysics. From the operations perspective, SEP events pose a radiation hazard for aviation, elec-
tronics in space, and human space exploration, in particular for missions outside of the Earth’s protective magnetosphere including to the
Moon and Mars. Thus, it is critical to improve the scientific understanding of SEP events and use this understanding to develop and
improve SEP forecasting capabilities to support operations. Many SEP models exist or are in development using a wide variety of
approaches and with differing goals. These include computationally intensive physics-based models, fast and light empirical models,
machine learning-based models, and mixed-model approaches. The aim of this paper is to summarize all of the SEP models currently
developed in the scientific community, including a description of model approach, inputs and outputs, free parameters, and any pub-
lished validations or comparisons with data.

© 2022 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Keywords: Space radiation; Solar energetic particles; Space weather models; Space weather forecasting; SEP models

**1. Introduction**

Solar Energetic Particle (SEP) events are transient injec-
tions into the heliosphere of protons, electrons, and higher
mass charged particles with a wide range of energies (tens
of keVs to GeVs), spectra, composition, and intensities.
They follow energetic solar eruptions that are generally
associated with flares and Coronal Mass Ejection (CME)
s. They are apparently accelerated by processes associated
with flares, such as wave-particle interactions and recon-
nection, as well as by acceleration at CME-driven shocks
(for reviews, see e.g., Shea and Smart, 1990; Reames,
2004; Reames, 2017; Desai and Giacalone, 2016; Klein
and Dalla, 2017). As has long been recognized since at least
the Apollo era (Hilberg, 1969), SEP events are hazardous
to electronics (e.g., Iucci et al., 2005) and humans in space.
As humans pursue space exploration outside of low Earth
orbit, the understanding, monitoring, and forecasting of
SEP events becomes increasingly important (e.g., Kim
et al., 2011). SEPs are also hazardous to aircraft crews,
in particular on polar routes (Jones et al., 2005), and to
modern technological systems (Eastwood et al., 2017).
Thus, in the last two decades, government agencies around
the world have developed policies related to space weather,
including the need for improved forecasting of SEP events
(Guarnieri et al., 2005; Opgenoorth et al., 2019; National
Science & Technology Council, 2019). Plans for the
National Aeronautics and Space Administration (NASA)
Artemis missions to send astronauts back to the Moon in
the mid-2020s are providing further motivation to improve
SEP forecasting.

Efforts to predict SEP events have a long history (e.g.,
Smart et al., 1979). At present, three dozen SEP models
have been or are being developed in the scientific research
community, as listed in Table 1. These models use a variety
of approaches: Empirical models are based on the identifi-

cation of correlations and other relationships in observa-
tional data that may be related to the underlying physical
processes. They typically give rapid forecasts and are easily
incorporated into forecasting and operations. Such models
might give a binary “all clear” or “not all clear” prediction,
representing the confidence that an event of a given magni-
tude *will not* or *will* occur during a given forecast window,
the probability that an event of a certain intensity will
occur, or deterministic quantities (e.g., onset time, the peak
flux at a certain energy). Physics-based models use our cur-
rent understanding of the processes of particle acceleration
and transport at the Sun and in interplanetary space to
model these processes and predict the properties of the
associated SEP event. Most of these models are computa-
tionally intensive, and the ability to produce a prediction
“in real time” may be limited by the resources available,
so they may not be readily incorporated into a forecasting
 workflow. In addition, fundamental parameters required
by the model may be poorly characterized. However, these
complex models hold the promise of modeling the complete
distribution of SEP events with time in 2- or 3-dimensional
space. Machine Learning (ML) approaches are now being
investigated in the hope that they will yield a new class of
SEP models that will produce fast forecasts with improved
accuracy. Lastly, multi-module forecasting systems link
existing models of multiple types to create a chain that
feeds forecasts from one module to the next that can be
updated as real time measurements become available, e.g.
a flare forecast module passes information to a CME fore-
cast module which then passes parameters to produce a
final SEP forecast. All of the models described here focus
on the prediction of SEP protons, as these are the most
abundant particles and the largest contributors to space
radiation. Many of the physics-based models have the
added capability to investigate the behavior of SEP ions
and electrons, which allows them to probe the details of
<table><caption>Table 1

Solar energetic particle models. For any models without an entry in the Access column, we encourage interested readers to contact the model developer. RoR stands for Runs on Request available through CCMC. *Deployment to CCMC in progress, **Will be available on SEP Scoreboard and RoR.</caption><thead><tr><th>Model</th><th>Model Type</th><th>Access to Model</th><th>Reference</th></tr></thead><tbody><tr><td>ADEPT</td><td>Empirical</td><td>-</td><td>Kahler and Ling (2017)</td></tr><tr><td>AFRL PPS</td><td>Empirical</td><td>-</td><td>Smart et al. (1979, 1989, 1992)</td></tr><tr><td>Aminalragia-Giamini model</td><td>ML</td><td>-</td><td>Aminalragia-Giamini et al. (2021)</td></tr><tr><td>AMPS</td><td>Physics-based</td><td>CCMC RoR</td><td>Tenishev et al. (2021)</td></tr><tr><td>Boubrahimi model</td><td>ML</td><td>-</td><td>Boubrahimi et al. (2017)</td></tr><tr><td>COMESEP SEPForecast</td><td>Empirical &amp; Physics-based</td><td>Web</td><td>Dierckxsens et al. (2015), Marsh et al. (2015)</td></tr><tr><td>EPREM</td><td>Physics-based</td><td>-</td><td>Schwadron et al. (2010)</td></tr><tr><td>ESPERTA</td><td>Empirical &amp; ML</td><td>-</td><td>Laurenza et al. (2009, 2018), Stumpo et al. (2021)</td></tr><tr><td>FORSPEF</td><td>Empirical</td><td>Web</td><td>Anastasiadis et al. (2017)</td></tr><tr><td>Georgia State University</td><td>ML</td><td>Web</td><td>Ji et al. (2020,)</td></tr><tr><td>iPATH</td><td>Physics-based</td><td>CCMC RoR**</td><td>Hu et al. (2017)</td></tr><tr><td>Lavasa Model</td><td>ML</td><td>-</td><td>Lavasa et al. (2021)</td></tr><tr><td>MAG4</td><td>Empirical</td><td>Web, CCMC RoR, SEP Scoreboard</td><td>Falconer et al. (2011, 2014)</td></tr><tr><td>MagPy</td><td>Empirical</td><td>**</td><td>Tadesse, T., Fernandes, I., Kadadi, Y., Lee, K. T., and Falconer, D.</td></tr><tr><td>MEMPSEP</td><td>ML</td><td>-</td><td>Moreland et al. 2022, Chatterjee et al. 2022, Dayeh et al. 2022 (all in preparation)</td></tr><tr><td>M-FLAMPA</td><td>Physics-based</td><td>CCMC RoR*</td><td>Sokolov et al. (2004), Borovikov et al. (2015)</td></tr><tr><td>PARADISE</td><td>Physics-based</td><td>Web</td><td>Wijsen (2020, 2022)</td></tr><tr><td>PCA (Papaioannou) model</td><td>Empirical</td><td>-</td><td>Papaioannou et al. (2018)</td></tr><tr><td>PHSVM</td><td>ML</td><td>-</td><td>Pouya Hosseinzadeh, Soukaina Filali Boubrahimi</td></tr><tr><td>PROTONS</td><td>Empirical</td><td>-</td><td>Balch (1999, 2008)</td></tr><tr><td>REleASE</td><td>Empirical</td><td>Web, SEP Scoreboard</td><td>Posner, 2007; Malandraki et al., 2020</td></tr><tr><td>Sadykov et al. (2021) model</td><td>ML</td><td>-</td><td>Sadykov et al. (2021)</td></tr><tr><td>SAWS-ASPECS</td><td>Empirical</td><td>Web, SEP Scoreboard</td><td>Anastasiadis et al. (2017), Georgoulis et al. (2021), Papaioannou et al. (2022)</td></tr><tr><td>SEPCaster</td><td>Physics-based</td><td>-*</td><td>Li et al. (2021)</td></tr><tr><td>SEPMOD</td><td>Physics-based</td><td>CCMC RoR, SEP Scoreboard</td><td>Luhmann et al. (2007)</td></tr><tr><td>SEPSTER</td><td>Empirical</td><td>SEP Scoreboard</td><td>Richardson et al. (2018)</td></tr><tr><td>SEPSTER2D</td><td>Empirical</td><td>SEP Scoreboard</td><td>Bruno and Richardson (2021)</td></tr><tr><td>SMARP Model</td><td>ML</td><td>-</td><td>Kasapis et al. (2022)</td></tr><tr><td>SOLPENCO(2)</td><td>Physics-based</td><td>-</td><td>Aran et al. (2006), Aran et al. (2011), Aran et al. (2017)</td></tr><tr><td>South African model</td><td>Physics-based</td><td>Web</td><td>Strauss and Fichtner (2015)</td></tr><tr><td>SPARX</td><td>Physics-based</td><td>Web</td><td>Marsh et al. (2015)</td></tr><tr><td>SPREAdFAST</td><td>Physics-based</td><td>Web</td><td>Kozarev et al. (2017), Kozarev et al. (2022)</td></tr><tr><td>SPRINTS</td><td>ML</td><td>SEP Scoreboard</td><td>Engell et al. (2017)</td></tr><tr><td>STAT</td><td>Physics-based</td><td>CCMC RoR</td><td>Linker et al. (2019)</td></tr><tr><td>UMASEP</td><td>Empirical &amp; ML</td><td>Web, SEP Scoreboard</td><td>Núñez (2011, 2015), Núñez et al. (2017), Malandraki et al. (2020)</td></tr><tr><td>Zhang model</td><td>Physics-based</td><td>-</td><td>Zhang and Zhao (2017)</td></tr></tbody></table>

particle acceleration and transport. The aim of this paper is to bring together brief summaries of these models in order to provide a comprehensive survey of the current state of SEP event prediction.

In general terms, SEP models have been motivated either by research aimed at understanding the physical processes related to SEPs or by operational forecasting needs. Science-oriented models typically use all historical measurements available to fine-tune their model parameters with the goal of reproducing all aspects of a specific event as accurately as possible. The tuned model parameters then provide insight into the underlying physics.

Models built with a forecasting focus attempt to produce a rapid forecast with high levels of skill and reliability in a statistical sense. The model inputs are restricted to data streams that are available in real time, and typically, forecasts are made using only information that is accessible before or at the start of an SEP event. For this reason, it is critical that operationally supported, high-cadence, reliable and accurate space weather data streams for all phenomena relevant to SEP production are publicly available for operations and the deployment and development of forecasting models. The measurements used by the models discussed in this paper include: solar magnetograms, optical imaging,
<table><caption>Table 1
Solar energetic particle models. For any models without an entry in the Access column, we encourage interested readers to contact the model developer. RoR stands for Runs on Request available through CCMC. *Deployment to CCMC in progress, **Will be available on SEP Scoreboard and RoR.</caption><thead><tr><th>Model</th><th>Model Type</th><th>Access to Model</th><th>Reference</th></tr></thead><tbody><tr><td>ADEPT</td><td>Empirical</td><td>-</td><td>Kahler and Ling (2017)</td></tr><tr><td>AFRL PPS</td><td>Empirical</td><td>-</td><td>Smart et al. (1979, 1989, 1992)</td></tr><tr><td>Aminalragia-Giamini model</td><td>ML</td><td>-</td><td>Aminalragia-Giamini et al. (2021)</td></tr><tr><td>AMPS</td><td>Physics-based</td><td>CCMC RoR</td><td>Tenishev et al. (2021)</td></tr><tr><td>Boubrahimi model</td><td>ML</td><td>-</td><td>Boubrahimi et al. (2017)</td></tr><tr><td>COMESEP SEPForecast</td><td>Empirical &amp; Physics-based</td><td>Web</td><td>Dierckxsens et al. (2015), Marsh et al. (2015)</td></tr><tr><td>EPREM</td><td>Physics-based</td><td>-</td><td>Schwadron et al. (2010)</td></tr><tr><td>ESPERTA</td><td>Empirical &amp; ML</td><td>-</td><td>Laurenza et al. (2009, 2018), Stumpo et al. (2021)</td></tr><tr><td>FORSPEF</td><td>Empirical</td><td>Web</td><td>Anastasiadis et al. (2017)</td></tr><tr><td>Georgia State University</td><td>ML</td><td>Web</td><td>Ji et al. (2020,)</td></tr><tr><td>iPATH</td><td>Physics-based</td><td>CCMC RoR**</td><td>Hu et al. (2017)</td></tr><tr><td>Lavasa Model</td><td>ML</td><td>-</td><td>Lavasa et al. (2021)</td></tr><tr><td>MAG4</td><td>Empirical</td><td>Web, CCMC RoR, SEP Scoreboard</td><td>Falconer et al. (2011, 2014)</td></tr><tr><td>MagPy</td><td>Empirical</td><td>**</td><td>Tadesse, T., Fernandes, I., Kadadi, Y., Lee, K. T., and Falconer, D.</td></tr><tr><td>MEMPSEP</td><td>ML</td><td>-</td><td>Moreland et al. 2022, Chatterjee et al. 2022, Dayeh et al. 2022 (all in preparation)</td></tr><tr><td>M-FLAMPA</td><td>Physics-based</td><td>CCMC RoR*</td><td>Sokolov et al. (2004), Borovikov et al. (2015)</td></tr><tr><td>PARADISE</td><td>Physics-based</td><td>Web</td><td>Wijsen (2020, 2022)</td></tr><tr><td>PCA (Papaioannou) model</td><td>Empirical</td><td>-</td><td>Papaioannou et al. (2018)</td></tr><tr><td>PHSVM</td><td>ML</td><td>-</td><td>Pouya Hosseinzadeh, Soukaina Filali Boubrahimi</td></tr><tr><td>PROTONS</td><td>Empirical</td><td>-</td><td>Balch (1999, 2008)</td></tr><tr><td>REleASE</td><td>Empirical</td><td>Web, SEP Scoreboard</td><td>Posner, 2007; Malandraki et al., 2020</td></tr><tr><td>Sadykov et al. (2021) model</td><td>ML</td><td>-</td><td>Sadykov et al. (2021)</td></tr><tr><td>SAWS-ASPECS</td><td>Empirical</td><td>Web, SEP Scoreboard</td><td>Anastasiadis et al. (2017), Georgoulis et al. (2021), Papaioannou et al. (2022)</td></tr><tr><td>SEPCaster</td><td>Physics-based</td><td>-*</td><td>Li et al. (2021)</td></tr><tr><td>SEPMOD</td><td>Physics-based</td><td>CCMC RoR, SEP Scoreboard</td><td>Luhmann et al. (2007)</td></tr><tr><td>SEPSTER</td><td>Empirical</td><td>SEP Scoreboard</td><td>Richardson et al. (2018)</td></tr><tr><td>SEPSTER2D</td><td>Empirical</td><td>SEP Scoreboard</td><td>Bruno and Richardson (2021)</td></tr><tr><td>SMARP Model</td><td>ML</td><td>-</td><td>Kasapis et al. (2022)</td></tr><tr><td>SOLPENCO(2)</td><td>Physics-based</td><td>-</td><td>Aran et al. (2006), Aran et al. (2011), Aran et al. (2017)</td></tr><tr><td>South African model</td><td>Physics-based</td><td>Web</td><td>Strauss and Fichtner (2015)</td></tr><tr><td>SPARX</td><td>Physics-based</td><td>Web</td><td>Marsh et al. (2015)</td></tr><tr><td>SPREADFAST</td><td>Physics-based</td><td>Web</td><td>Kozarev et al. (2017), Kozarev et al. (2022)</td></tr><tr><td>SPRINTS</td><td>ML</td><td>SEP Scoreboard</td><td>Engell et al. (2017)</td></tr><tr><td>STAT</td><td>Physics-based</td><td>CCMC RoR</td><td>Linker et al. (2019)</td></tr><tr><td>UMASEP</td><td>Empirical &amp; ML</td><td>Web, SEP Scoreboard</td><td>Núñez (2011, 2015), Núñez et al. (2017), Malandraki et al. (2020)</td></tr><tr><td>Zhang model</td><td>Physics-based</td><td>-</td><td>Zhang and Zhao (2017)</td></tr></tbody></table>

particle acceleration and transport. The aim of this paper is to bring together brief summaries of these models in order to provide a comprehensive survey of the current state of SEP event prediction.

In general terms, SEP models have been motivated either by research aimed at understanding the physical processes related to SEPs or by operational forecasting needs. Science-oriented models typically use all historical measurements available to fine-tune their model parameters with the goal of reproducing all aspects of a specific event as accurately as possible. The tuned model parameters then provide insight into the underlying physics.

Models built with a forecasting focus attempt to produce a rapid forecast with high levels of skill and reliability in a statistical sense. The model inputs are restricted to data streams that are available in real time, and typically, forecasts are made using only information that is accessible before or at the start of an SEP event. For this reason, it is critical that operationally supported, high-cadence, reliable and accurate space weather data streams for all phenomena relevant to SEP production are publicly available for operations and the deployment and development of forecasting models. The measurements used by the models discussed in this paper include: solar magnetograms, optical imaging,
extreme ultraviolet (EUV) imaging, Soft X-ray (SXR) measurements, coronagraph imaging of CMEs from single or multiple vantage points, ground and space-based radio observations in the wavelengths that measure Type II, III, and IV radio bursts, in situ energetic proton and electron observations, and in situ measurements of solar wind density, temperature, velocity, and magnetic field. See Vourlidas et al. (2021) for a description of the current state of space weather measurements and anticipated gaps in the future.

Table 1 lists all of the SEP models that the authors are aware of at the time of writing. An overview of different model types will be described in the Overview (Section 2). The models will be described in further detail in Model Descriptions (Section 3). The paper concludes with a comprehensive summary and outlook for future model development (Section 4). Appendix A defines the acronyms used throughout this paper.

## 2. Overview of current SEP prediction models and their approaches

### 2.1. Typical model inputs

SEP events originate with eruptions within the solar corona that are typically associated with filament eruptions, flares, and CMEs. As noted above, particle acceleration appears to occur both via processes associated with flares low in the corona and by diffusive shock acceleration at the shock fronts of CMEs as they propagate outward into the heliosphere; acceleration at CME-driven shocks appears to dominate in the large SEP events that are of most space weather concern (e.g., Desai and Giacalone, 2016). The most prompt and most intense SEP events measured at Earth, and hence the most important to forecast, are usually associated with strong flares and fast CMEs at western longitudes that are well-connected to Earth by the spiral interplanetary magnetic field (Parker, 1965). Magnetic connectivity to the particle source (flare/CME shock) also strongly influences the development and intensity of an SEP event (e.g., Cane et al., 1988; Cane and Lario, 2006; Richardson et al., 2014; Bain et al., 2016). The intensity of an SEP event is also generally correlated with parameters (e.g., intensity, duration) of the associated SXR flare and speed of the CME (e.g. Kahler et al., 1984; Cane et al., 2010, etc). Hence, flare or CME parameters are frequently used as inputs into SEP prediction models. Flare parameters are particularly widely used as solar X-rays are continually monitored and available in near-real time, for example from the Geosynchronous Orbit Earth observing Satellite (GOES) spacecraft, and the onset of a flare is well-defined and may be closely associated with the eruption of a CME and onset of particle acceleration. The flare location may be identified for example in EUV observations. However, SEP events detected at Earth occasionally originate on the far side of the Sun, in particular behind the west

limb [e.g., ~25% of the SEP events discussed by Richardson et al. (2014)] and therefore the flare will not be observed in these cases. While the CMEs from such events may be detected by spacecraft coronagraphs, currently, images from coronagraphs on scientific spacecraft such as Solar and Heliospheric Observatory (SOHO)/ Large Angle and Spectrometric Coronagraph Experiment (LASCO) and Solar TERrestrial Relations Observatory (STEREO)/Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) are not available sufficiently rapidly for real-time forecasting; delays in receiving and analyzing these images to obtain CME parameters may range from hours to even days. Even though models using CME parameters as input may not be suitable for predicting the onsets of prompt SEP events, they are valuable for assessing the use of future near-real time white light coronagraph observations, such as the Compact Coronagraph (CCOR) on the National Oceanic and Atmospheric Administration (NOAA) Space Weather Follow On - Lagrange 1 (SWFO-L1) spacecraft scheduled to launch in 2025, for SEP prediction.

Solar radio observations result from nonthermal electrons and provide another indication of particle acceleration. Bursts at frequencies below a few hundred MHz generally result from plasma emission, which occurs at a frequency related to the plasma density (e.g., Wild et al., 1963; Nelson and Melrose, 1985). In particular, Type II radio emission that slowly drifts downward in frequency with time is believed to indicate particle acceleration at a shock moving away from the Sun towards lower densities (e.g., Nelson and Melrose, 1985). Type III radio bursts with much faster drift rates are signatures of energetic electron beams traveling out from the Sun, having been accelerated at a flare site lower in the corona. Both type II and type III emissions are found to be strongly correlated with the occurrence of SEP events (e.g., Cane et al., 2002; Cliver et al., 2004; Laurenza et al., 2009; Richardson et al., 2014; Papaioannou et al., 2016; Richardson et al., 2018). Solar radio emissions at frequencies above the ionospheric cutoff at about 10 MHz are monitored in real time from the ground by a world-wide network of observatories. However, observations below ~20 MHz are difficult due to the ionospheric cut-off, terrestrial interference, and emission from lightning (e.g., Erickson, 1997). Observations from space-based satellite radio science instruments such as those on WIND, STEREO, Parker Solar Probe (PSP) and Solar Orbiter (SO) can extend to lower frequencies. Unfortunately, data from these scientific spacecraft are not generally available in real time since they were not designed to be operational instruments, and often have very limited telemetry. Because the emission frequency of radio bursts tends to decrease with distance from the Sun, ground-based radio observations provide information on particle acceleration close to the Sun, while spacecraft instruments cover emissions produced in the high corona and solar wind out to the distance of the observing spacecraft.
extreme ultraviolet (EUV) imaging, Soft X-ray (SXR) measurements, coronagraph imaging of CMEs from single or multiple vantage points, ground and space-based radio observations in the wavelengths that measure Type II, III, and IV radio bursts, in situ energetic proton and electron observations, and in situ measurements of solar wind density, temperature, velocity, and magnetic field. See Vourlidas et al. (2021) for a description of the current state of space weather measurements and anticipated gaps in the future.

Table 1 lists all of the SEP models that the authors are aware of at the time of writing. An overview of different model types will be described in the Overview (Section 2). The models will be described in further detail in Model Descriptions (Section 3). The paper concludes with a comprehensive summary and outlook for future model development (Section 4). Appendix A defines the acronyms used throughout this paper.

## 2. Overview of current SEP prediction models and their approaches

### 2.1. Typical model inputs

SEP events originate with eruptions within the solar corona that are typically associated with filament eruptions, flares, and CMEs. As noted above, particle acceleration appears to occur both via processes associated with flares low in the corona and by diffusive shock acceleration at the shock fronts of CMEs as they propagate outward into the heliosphere; acceleration at CME-driven shocks appears to dominate in the large SEP events that are of most space weather concern (e.g., Desai and Giacalone, 2016). The most prompt and most intense SEP events measured at Earth, and hence the most important to forecast, are usually associated with strong flares and fast CMEs at western longitudes that are well-connected to Earth by the spiral interplanetary magnetic field (Parker, 1965). Magnetic connectivity to the particle source (flare/CME shock) also strongly influences the development and intensity of an SEP event (e.g., Cane et al., 1988; Cane and Lario, 2006; Richardson et al., 2014; Bain et al., 2016). The intensity of an SEP event is also generally correlated with parameters (e.g., intensity, duration) of the associated SXR flare and speed of the CME (e.g. Kahler et al., 1984; Cane et al., 2010, etc). Hence, flare or CME parameters are frequently used as inputs into SEP prediction models. Flare parameters are particularly widely used as solar X-rays are continually monitored and available in near-real time, for example from the Geosynchronous Orbit Earth observing Satellite (GOES) spacecraft, and the onset of a flare is well-defined and may be closely associated with the eruption of a CME and onset of particle acceleration. The flare location may be identified for example in EUV observations. However, SEP events detected at Earth occasionally originate on the far side of the Sun, in particular behind the west

limb [e.g., ~25% of the SEP events discussed by Richardson et al. (2014)] and therefore the flare will not be observed in these cases. While the CMEs from such events may be detected by spacecraft coronagraphs, currently, images from coronagraphs on scientific spacecraft such as Solar and Heliospheric Observatory (SOHO)/ Large Angle and Spectrometric Coronagraph Experiment (LASCO) and Solar TERrestrial Relations Observatory (STEREO)/Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) are not available sufficiently rapidly for real-time forecasting; delays in receiving and analyzing these images to obtain CME parameters may range from hours to even days. Even though models using CME parameters as input may not be suitable for predicting the onsets of prompt SEP events, they are valuable for assessing the use of future near-real time white light coronagraph observations, such as the Compact Coronagraph (CCOR) on the National Oceanic and Atmospheric Administration (NOAA) Space Weather Follow On - Lagrange 1 (SWFO-L1) spacecraft scheduled to launch in 2025, for SEP prediction.

Solar radio observations result from nonthermal electrons and provide another indication of particle acceleration. Bursts at frequencies below a few hundred MHz generally result from plasma emission, which occurs at a frequency related to the plasma density (e.g., Wild et al., 1963; Nelson and Melrose, 1985). In particular, Type II radio emission that slowly drifts downward in frequency with time is believed to indicate particle acceleration at a shock moving away from the Sun towards lower densities (e.g., Nelson and Melrose, 1985). Type III radio bursts with much faster drift rates are signatures of energetic electron beams traveling out from the Sun, having been accelerated at a flare site lower in the corona. Both type II and type III emissions are found to be strongly correlated with the occurrence of SEP events (e.g., Cane et al., 2002; Cliver et al., 2004; Laurenza et al., 2009; Richardson et al., 2014; Papaioannou et al., 2016; Richardson et al., 2018). Solar radio emissions at frequencies above the ionospheric cutoff at about 10 MHz are monitored in real time from the ground by a world-wide network of observatories. However, observations below ~20 MHz are difficult due to the ionospheric cut-off, terrestrial interference, and emission from lightning (e.g., Erickson, 1997). Observations from space-based satellite radio science instruments such as those on WIND, STEREO, Parker Solar Probe (PSP) and Solar Orbiter (SO) can extend to lower frequencies. Unfortunately, data from these scientific spacecraft are not generally available in real time since they were not designed to be operational instruments, and often have very limited telemetry. Because the emission frequency of radio bursts tends to decrease with distance from the Sun, ground-based radio observations provide information on particle acceleration close to the Sun, while spacecraft instruments cover emissions produced in the high corona and solar wind out to the distance of the observing spacecraft.
Models may also use near-real time energetic particle observations as an input. For example, near-relativistic/ relativistic SEP electrons may arrive at Earth tens of minutes earlier than, and provide a warning of the impending arrival of, protons with energies of tens of MeV that are of space weather interest (Posner, 2007; Malandraki et al., 2020). The initial rise of the SEP proton intensity may also be used as an early predictor that the intensity may cross a specific threshold of concern (Núñez, 2011).

As will be evident from the model descriptions in Section 3, many SEP forecasting models use one or a combination of these phenomena as inputs into the model. Predicting the largest events of most concern also benefits from what has historically been called the “big flare syndrome”, originally stated by (Kahler, 1982) as “statistically, energetic flare phenomena are more intense in larger flares, regardless of the detailed physics”. In other words (and with less emphasis specifically on flares), the most energetic eruptions are associated with the most intense signatures in a range of related phenomena which may be predictive of a large SEP event even if they have no direct physical connection with the particle acceleration process.

## 2.2. Empirical models

Empirical models are based on approaches that use samples of existing data (e.g., for many historical SEP events) such as those discussed above to discover and characterize (e.g., as mathematical expressions) patterns or relationships between the properties of SEP events and other observable parameters. These models implement relative relationships that are often guided by the known physical processes behind SEP generation (e.g., Posner, 2007; Richardson et al., 2018). Empirical models may produce:

* probabilistic forecasts, e.g., indicating the probability that an SEP event of a certain intensity will occur in a particular time frame (e.g., Falconer et al., 2011; Papaioannou et al., 2018),

* categorical forecasts, such as the NOAA S-scale<fnref n="2" /> with defined thresholds for peak ≥10 MeV proton flux intensity (e.g., Laurenza et al., 2009),

* binary (yes/no) “all clear” forecasts that an event exceeding a specified threshold will or will not occur (e.g., Boubrahimi et al., 2017; Sadykov et al., 2021), or

* deterministic quantities, e.g., time of event onset or peak in a certain energy range, SEP peak intensity/flux, or the event-integrated intensity (fluence) (e.g., Balch, 1999; Bruno and Richardson, 2021).

Because the relationships established from previous data are generally mathematical functions that can be computed quickly, predictions can be made rapidly by applying them

to current observations. Validation statistics and skill scores for many empirical models have been reported in the literature. As is evident from Table 1, a large fraction of current SEP prediction models are based on empirical methods.

## 2.3. Physics-based models

Physics-based SEP models have typically been developed with the primarily scientific motivation to understand the physical processes that produce SEP events, rather than to generate a fast forecast. Some physics-based model developers have begun research to operations efforts to modify their models for real time forecasting purposes, but this work is still in the early stages. In general, these models aim to numerically reproduce the relevant physics related to particle acceleration: the magnetic structure of the low corona, eruption mechanisms for flares and CMEs, particle acceleration associated with flares and at CME-driven shocks, magnetic field connections in the inner heliosphere to the solar event and shock, the properties of the evolving CME shock, and the transport of particles near the Sun and in the heliosphere. Each of these processes may in itself be the subject of intense study, and not fully understood, so combining them into a full model of SEP prediction is extremely challenging, and modelers may choose to simplify certain aspects of the problem or incorporate an empirical component. In addition, fundamental parameters for these processes may be unknown, for example, because they are difficult to observe (in particular when close to the Sun), are difficult to estimate (e.g., from theory), or apparently vary in time and space (e.g., from event to event) in a way that cannot be predicted before an event occurs.

A physics-based SEP modeling method might (1) define the magnetic field connectivity from the corona through the heliosphere to the observer, (2) simulate the source region responsible for particle acceleration, (3) inject test particles or a particle distribution function into the system, and (4) transport the particles from the source to the observer. The magnetic connectivity modeling system may consist of two main parts: An inner coronal module including a semi-empirical near-Sun model, such as Wang-Sheeley-Arge (WSA) (Arge and Pizzo, 2000) or Magneto-hydrodynamic Algorithm outside a Sphere (MAS) (Linker et al., 2019), that approximates the outflow at the base of the solar wind; and a heliospheric module including a sophisticated three-dimensional magneto-hydrodynamic numerical model, like ENLIL (Odstrcil, 2003), Alfvén-wave-turbulence-based solar atmosphere Model (AWSoM) (Sokolov et al., 2021) or European Heliospheric FORecasting Information Asset (EUHFORIA) (Pomoell and Poedts, 2018), that simulates the resulting solar wind flow evolution out to some outer boundary. The inner coronal module may be driven by observations of the solar surface magnetic field accumulated over a solar rotation and composited into a synoptic

<footnote n="2">² https://www.swpc.noaa.gov/noaa-scales-explanation.</footnote>
Models may also use near-real time energetic particle observations as an input. For example, near-relativistic/ relativistic SEP electrons may arrive at Earth tens of minutes earlier than, and provide a warning of the impending arrival of, protons with energies of tens of MeV that are of space weather interest (Posner, 2007; Malandraki et al., 2020). The initial rise of the SEP proton intensity may also be used as an early predictor that the intensity may cross a specific threshold of concern (Núñez, 2011).

As will be evident from the model descriptions in Section 3, many SEP forecasting models use one or a combination of these phenomena as inputs into the model. Predicting the largest events of most concern also benefits from what has historically been called the “big flare syndrome”, originally stated by (Kahler, 1982) as “statistically, energetic flare phenomena are more intense in larger flares, regardless of the detailed physics”. In other words (and with less emphasis specifically on flares), the most energetic eruptions are associated with the most intense signatures in a range of related phenomena which may be predictive of a large SEP event even if they have no direct physical connection with the particle acceleration process.

## 2.2. Empirical models

Empirical models are based on approaches that use samples of existing data (e.g., for many historical SEP events) such as those discussed above to discover and characterize (e.g., as mathematical expressions) patterns or relationships between the properties of SEP events and other observable parameters. These models implement relative relationships that are often guided by the known physical processes behind SEP generation (e.g., Posner, 2007; Richardson et al., 2018). Empirical models may produce:

* probabilistic forecasts, e.g., indicating the probability that an SEP event of a certain intensity will occur in a particular time frame (e.g., Falconer et al., 2011; Papaioannou et al., 2018),

* categorical forecasts, such as the NOAA S-scale<fnref n="2" /> with defined thresholds for peak ≥10 MeV proton flux intensity (e.g., Laurenza et al., 2009),

* binary (yes/no) “all clear” forecasts that an event exceeding a specified threshold will or will not occur (e.g., Boubrahimi et al., 2017; Sadykov et al., 2021), or

* deterministic quantities, e.g., time of event onset or peak in a certain energy range, SEP peak intensity/flux, or the event-integrated intensity (fluence) (e.g., Balch, 1999; Bruno and Richardson, 2021).

Because the relationships established from previous data are generally mathematical functions that can be computed quickly, predictions can be made rapidly by applying them

to current observations. Validation statistics and skill scores for many empirical models have been reported in the literature. As is evident from Table 1, a large fraction of current SEP prediction models are based on empirical methods.

## 2.3. Physics-based models

Physics-based SEP models have typically been developed with the primarily scientific motivation to understand the physical processes that produce SEP events, rather than to generate a fast forecast. Some physics-based model developers have begun research to operations efforts to modify their models for real time forecasting purposes, but this work is still in the early stages. In general, these models aim to numerically reproduce the relevant physics related to particle acceleration: the magnetic structure of the low corona, eruption mechanisms for flares and CMEs, particle acceleration associated with flares and at CME-driven shocks, magnetic field connections in the inner heliosphere to the solar event and shock, the properties of the evolving CME shock, and the transport of particles near the Sun and in the heliosphere. Each of these processes may in itself be the subject of intense study, and not fully understood, so combining them into a full model of SEP prediction is extremely challenging, and models may choose to simplify certain aspects of the problem or incorporate an empirical component. In addition, fundamental parameters for these processes may be unknown, for example, because they are difficult to observe (in particular when close to the Sun), are difficult to estimate (e.g., from theory), or apparently vary in time and space (e.g., from event to event) in a way that cannot be predicted before an event occurs.

A physics-based SEP modeling method might (1) define the magnetic field connectivity from the corona through the heliosphere to the observer, (2) simulate the source region responsible for particle acceleration, (3) inject test particles or a particle distribution function into the system, and (4) transport the particles from the source to the observer. The magnetic connectivity modeling system may consist of two main parts: An inner coronal module including a semi-empirical near-Sun model, such as Wang-Sheeley-Arge (WSA) (Arge and Pizzo, 2000) or Magneto-hydrodynamic Algorithm outside a Sphere (MAS) (Linker et al., 2019), that approximates the outflow at the base of the solar wind; and a heliospheric module including a sophisticated three-dimensional magneto-hydrodynamic numerical model, like ENLIL (Odstrcil, 2003), Alfvén-wave-turbulence-based solar atmosphere Model (AWSoM) (Sokolov et al., 2021) or European Heliospheric FORecasting Information Asset (EUHFORIA) (Pomoell and Poedts, 2018), that simulates the resulting solar wind flow evolution out to some outer boundary. The inner coronal module may be driven by observations of the solar surface magnetic field accumulated over a solar rotation and composited into a synoptic

<footnote n="2">² https://www.swpc.noaa.gov/noaa-scales-explanation.</footnote>
map. CMEs can be included in time-dependent heliospheric models, such as ENLIL + Cone (Odstrcil et al., 2004) or AWSoM + Eruptive Event Generator using Gibson-Low configuration (EEGGL) (Jin et al., 2017), with the parameters of the injected CMEs derived from coronagraph images. Such models may be used to simulate the shock driven by a CME, including how the shock parameters vary along the shock as it moves out through the corona and solar wind, and to infer the connectivity between the shock and the observer.

Understanding particle acceleration at shocks is still an area of active research and, because of the complexity of the problem, SEP prediction models often make certain assumptions. Some physics-based models, like Solar Energetic Particle MODEl (SEPMOD) (Luhmann et al., 2007), assume that the compression regions and shocks that form ahead of CMEs are the only acceleration regions for SEPs. Models such as Multiple Field Line Advection Model for Particle Acceleration (M-FLAMPA) (Sokolov et al., 2004) may require the injection of a suprathermal seed particle population into the shock that is then accelerated according to diffusive shock acceleration theory. However, the seed particle population, especially near the Sun, is poorly characterized (see Tylka and Lee, 2006; Neergaard Parker and Zank, 2012), though observations of suprathmal ion populations observed at 1 AU prior to an SEP event might be used (with suitable scaling) as a proxy for those closer to the Sun. The shock-accelerated particles may then be transported along magnetic field lines, for example by solving the focused-transport equation (Zhang, 2006; Schwadron et al., 2010) or by using a numerical simulation of particle transport that might include parallel and cross-field diffusion, advection with the solar wind, adiabatic cooling, and drifts (e.g., Zhang and Zhao, 2017; Hu et al., 2017). Alternately, a model may assume that particles are detected by an observer only when directly magnetically connected to the shock, as seen in SEPMOD (Luhmann et al., 2007). Physics-based models also face challenges in reproducing SEP intensity profiles both in time and 2- or 3-dimensional space. Some models attempt to reproduce the Energetic Storm Particle (ESP) component of the event that occurs when a CME shock front passes the observer tens of hours after the solar eruption (e.g., SEPMOD), while others may focus on the early stages of the SEP event when particle acceleration occurs close to the Sun and the onset of the SEP event might be modeled by a simple particle injection at the Sun (e.g., Linker et al., 2019).

An issue with all physics-based SEP models is that they have many poorly constrained free parameters such as the choice of particle diffusion coefficients, the seed population spectral shape and normalization, how to “tune” the solar wind model solution to match measurements (e.g., at Earth), and which specific magnetic field line to select to produce a prediction of the particle spectrum at the observer’s location. New observations may help to constrain some of these parameters. For example, an improved

knowledge of the suprathermal seed population in the inner heliosphere and in particular close to the Sun prior to an SEP event would benefit all physics-based models. Measurements close to the sun by PSP (Desai et al., 2020) and at high latitudes by SO should help to characterize the suprathermal ion population and its variability in these regions, at least in a statistical sense, since these observations will not be available in real time to contribute to SEP predictions.

The placement of the inner boundary of the coronal/solar wind model is also a limitation in some physics-based models. Particle acceleration at the beginning of an SEP event is known to happen deep down in the solar corona, below $2 R_⊙$ (Mäkelä et al., 2015) whereas many model inner boundaries are located further from the Sun, e.g., at $10 R_⊙$ for ZEUS or $21.5 R_⊙$ for ENLIL. Hence, it is not feasible for such models to predict the onset phase of an SEP event. Coronal and solar wind models that are computationally tractable lower in the solar corona would benefit all physics-based SEP models.

Because of their complexity, physics-based models may face significant computational challenges in terms of the resources needed to store the large amount of data generated during the simulation and the time needed to complete a model run. Hence, reported simulations are generally aimed at reproducing a limited number of past events, with a focus on understanding the physics involved and the reasons for event-to-event variations. There are rather few cases where physics-based models have been used without “tuning” to make predictions of future events, i.e., without prior information on the properties of the SEP that results. Also, comparisons with measurements reported in the literature have generally been qualitative rather than quantitative.

## 2.4. Machine learning models

ML approaches to SEP prediction use a variety of ML/ Artificial Intelligence (AI) techniques to identify specific combinations of observed parameters, such as those in Section 2.1, that are associated with/precede an SEP event. As such, they are similar to empirical models in that they are based on existing data, but rely on ML/AI to identify relationships between SEP events and other parameters in (ideally) large data sets without any a priori knowledge of the physics involved. The aim is to discover relationships that might not otherwise be evident from a simple analysis of these data. Typically, the data are divided into a “training set”, used to develop the ML/AI model, and a “validation set” which is used to assess, for example, whether the model reliably reproduces the observed properties of SEPs in this set. As for empirical models, the outputs may be probabilistic, categorical, binary or deterministic. Examples of ML models for binary predictions of whether an SEP event will exceed certain energy and particle flux thresholds (e.g., >100 MeV, >1 pfu) utilize the X-ray and proton channels, and proton channel cross-correlations
map. CMEs can be included in time-dependent heliospheric models, such as ENLIL + Cone (Odstrcil et al., 2004) or AWSoM + Eruptive Event Generator using Gibson-Low configuration (EEGGL) (Jin et al., 2017), with the parameters of the injected CMEs derived from coronagraph images. Such models may be used to simulate the shock driven by a CME, including how the shock parameters vary along the shock as it moves out through the corona and solar wind, and to infer the connectivity between the shock and the observer.

Understanding particle acceleration at shocks is still an area of active research and, because of the complexity of the problem, SEP prediction models often make certain assumptions. Some physics-based models, like Solar Energetic Particle MODEl (SEPMOD) (Luhmann et al., 2007), assume that the compression regions and shocks that form ahead of CMEs are the only acceleration regions for SEPs. Models such as Multiple Field Line Advection Model for Particle Acceleration (M-FLAMPA) (Sokolov et al., 2004) may require the injection of a suprathermal seed particle population into the shock that is then accelerated according to diffusive shock acceleration theory. However, the seed particle population, especially near the Sun, is poorly characterized (see Tylka and Lee, 2006; Neergaard Parker and Zank, 2012), though observations of suprathermal ion populations observed at 1 AU prior to an SEP event might be used (with suitable scaling) as a proxy for those closer to the Sun. The shock-accelerated particles may then be transported along magnetic field lines, for example by solving the focused-transport equation (Zhang, 2006; Schwadron et al., 2010) or by using a numerical simulation of particle transport that might include parallel and cross-field diffusion, advection with the solar wind, adiabatic cooling, and drifts (e.g., Zhang and Zhao, 2017; Hu et al., 2017). Alternately, a model may assume that particles are detected by an observer only when directly magnetically connected to the shock, as seen in SEPMOD (Luhmann et al., 2007). Physics-based models also face challenges in reproducing SEP intensity profiles both in time and 2- or 3-dimensional space. Some models attempt to reproduce the Energetic Storm Particle (ESP) component of the event that occurs when a CME shock front passes the observer tens of hours after the solar eruption (e.g., SEPMOD), while others may focus on the early stages of the SEP event when particle acceleration occurs close to the Sun and the onset of the SEP event might be modeled by a simple particle injection at the Sun (e.g., Linker et al., 2019).

An issue with all physics-based SEP models is that they have many poorly constrained free parameters such as the choice of particle diffusion coefficients, the seed population spectral shape and normalization, how to “tune” the solar wind model solution to match measurements (e.g., at Earth), and which specific magnetic field line to select to produce a prediction of the particle spectrum at the observer’s location. New observations may help to constrain some of these parameters. For example, an improved

knowledge of the suprathermal seed population in the inner heliosphere and in particular close to the Sun prior to an SEP event would benefit all physics-based models. Measurements close to the sun by PSP (Desai et al., 2020) and at high latitudes by SO should help to characterize the suprathermal ion population and its variability in these regions, at least in a statistical sense, since these observations will not be available in real time to contribute to SEP predictions.

The placement of the inner boundary of the coronal/solar wind model is also a limitation in some physics-based models. Particle acceleration at the beginning of an SEP event is known to happen deep down in the solar corona, below $2 R_⊙$ (Mäkelä et al., 2015) whereas many model inner boundaries are located further from the Sun, e.g., at $10 R_⊙$ for ZEUS or $21.5 R_⊙$ for ENLIL. Hence, it is not feasible for such models to predict the onset phase of an SEP event. Coronal and solar wind models that are computationally tractable lower in the solar corona would benefit all physics-based SEP models.

Because of their complexity, physics-based models may face significant computational challenges in terms of the resources needed to store the large amount of data generated during the simulation and the time needed to complete a model run. Hence, reported simulations are generally aimed at reproducing a limited number of past events, with a focus on understanding the physics involved and the reasons for event-to-event variations. There are rather few cases where physics-based models have been used without “tuning” to make predictions of future events, i.e., without prior information on the properties of the SEP that results. Also, comparisons with measurements reported in the literature have generally been qualitative rather than quantitative.

## 2.4. Machine learning models

ML approaches to SEP prediction use a variety of ML/ Artificial Intelligence (AI) techniques to identify specific combinations of observed parameters, such as those in Section 2.1, that are associated with/precede an SEP event. As such, they are similar to empirical models in that they are based on existing data, but rely on ML/AI to identify relationships between SEP events and other parameters in (ideally) large data sets without any a priori knowledge of the physics involved. The aim is to discover relationships that might not otherwise be evident from a simple analysis of these data. Typically, the data are divided into a “training set”, used to develop the ML/AI model, and a “validation set” which is used to assess, for example, whether the model reliably reproduces the observed properties of SEPs in this set. As for empirical models, the outputs may be probabilistic, categorical, binary or deterministic. Examples of ML models for binary predictions of whether an SEP event will exceed certain energy and particle flux thresholds (e.g., >100 MeV, >1 pfu) utilize the X-ray and proton channels, and proton channel cross-correlations
from GOES (Boubrahimi et al., 2017), solar radio flux measurements using statistical analysis, neural networks, and genetic algorithms (Kim et al., 2018), and the properties of SXR flares and CMEs employing an ensemble of forecasts (Huang et al., 2012). Many current research efforts are focused on validating ML algorithms to perform reliable SEP nowcasts and forecasts. The cross-comparison of operational forecasts of SEP events also can provide additional validation of ML-driven models. This capability has become available recently through the Community Coordinated Modeling Center (CCMC) SEP Scoreboard<fnref n="3" />, which aims to bring together forecasts from a range of prediction models for current and historical events (although ML models have yet to be onboarded). Studies comparing ML-driven model predictions with the NOAA Space Weather Prediction Center (SWPC) daily operational forecasts and warnings for SEP events may identify weak points in the models and point to potential improvements (e.g., Jeong et al., 2014; Sadykov et al., 2021).

ML/AI-based models face unique challenges related to the preparation of reliable, uniform observational databases for model development and validation, and the efficient validation and verification of new models. Such considerations have motivated the development of publicly-available frameworks and ML-ready data sets (Engell et al., 2017; Martens et al., 2018). Other problems are related to the statistics and physics of SEP events. While ML/AI can harness the predictive power of massive multidimensional data analysis, a major challenge is the rarity of SEP events, leading to a significant imbalance of days with enhanced SEP proton fluxes and ‘quiet’ days. For example, during Solar Cycle (SC) 24, the number of days when the >10 MeV proton flux was above a threshold of 10 pfu (101 days) was about 34 times less than the number of days with a non-enhanced proton flux (3400 days) (Sadykov et al., 2021). This class imbalance ratio eliminates the possibility of using data-hungry ML algorithms directly and requires additional strategies for model training (Ahmadzadeh et al., 2021). Other challenges may include the widespread time delay (from minutes to hours) between the first detection of the SEP event and the onset of the preceding associated solar flare, which may lead to incorrect SEP-flare associations resulting in inaccurate model training or validation, missing information about host active regions in models using active region parameters, and the lack of observations of the sources of SEP events originating on the far side of the Sun.

## 2.5. Multi-module forecasting systems

Some models take an approach that chains multiple forecast modules together, with the prediction from each module feeding into the next. For example, the first module might use magnetograms or EUV imagery of an active

region to generate a prediction of the likelihood that a flare of a certain class will occur in that region. This prediction, together with the flare information, is passed to a module that predicts the likely parameters of the CME that might accompany the flare. The CME information is then input into a final module that predicts parameters of the potential SEP event. When an eruptive event does occur, each module ingests the required flare, CME, or proton flux observations as they become available and updates the prediction that is passed to the downstream module.

Multi-module systems tend to take advantage of mature models that are already developed and can be linked together so that the output from one model can trigger another. They may also combine models of different types, e.g., empirical, machine learning, and physics-based, exploiting the strengths of each type of model and providing a broader-based prediction of an event.

## 2.6. Model validation

In the “Validation” subsection for each model described in Section 3, published validation results are summarized. Some models have performed extensive quantitative validation studies, while others may have simply performed qualitative comparisons with observations for a few test cases. Some models have not yet published any validation. In the Conclusions (Section 4), we will describe our vision for steps that can facilitate more consistent validation across the SEP modeling field.

Throughout the validation sections, there are mentions of many types of metrics and plots typically used for validation. We refer the reader to papers by Liemohn et al. (2021) and Bain et al. (2021) for descriptions and explanations of the commonly used metrics and skill scores and their application and interpretation.

## 3. Model descriptions

This section summarizes the 36 SEP prediction models in Table 1 presented in alphabetical order. For each model, we specify the model developers, an overall description of the model, inputs, outputs, any free parameters, limitations and caveats related to the model, how data or predictions from the model may be accessed, and a summary of any validation efforts. The descriptions and results given here are intentionally brief and contain a limited number of figures or data tables. Interested readers should refer to the cited references for more details.

The terms “forecasting” and “nowcasting” are regularly used throughout the model descriptions. “Forecasting” typically indicates a model prediction that is made prior to any eruptive event on the Sun, e.g. a flare or CME, although it may mean a prediction issued prior to an increase in particle flux. “Nowcasting” is typically applied when predictions have been made directly following a flare, CME, or observed increase in particle flux at 1 AU. “Prediction” is used as a general term that is equivalent to a

<footnote n="3">³ https://ccmc.gsfc.nasa.gov/challenges/sep.php.</footnote>
from GOES (Boubrahimi et al., 2017), solar radio flux measurements using statistical analysis, neural networks, and genetic algorithms (Kim et al., 2018), and the properties of SXR flares and CMEs employing an ensemble of forecasts (Huang et al., 2012). Many current research efforts are focused on validating ML algorithms to perform reliable SEP nowcasts and forecasts. The cross-comparison of operational forecasts of SEP events also can provide additional validation of ML-driven models. This capability has become available recently through the Community Coordinated Modeling Center (CCMC) SEP Scoreboard<fnref n="3" />, which aims to bring together forecasts from a range of prediction models for current and historical events (although ML models have yet to be onboarded). Studies comparing ML-driven model predictions with the NOAA Space Weather Prediction Center (SWPC) daily operational forecasts and warnings for SEP events may identify weak points in the models and point to potential improvements (e.g., Jeong et al., 2014; Sadykov et al., 2021).

ML/AI-based models face unique challenges related to the preparation of reliable, uniform observational databases for model development and validation, and the efficient validation and verification of new models. Such considerations have motivated the development of publicly-available frameworks and ML-ready data sets (Engell et al., 2017; Martens et al., 2018). Other problems are related to the statistics and physics of SEP events. While ML/AI can harness the predictive power of massive multidimensional data analysis, a major challenge is the rarity of SEP events, leading to a significant imbalance of days with enhanced SEP proton fluxes and ‘quiet’ days. For example, during Solar Cycle (SC) 24, the number of days when the >10 MeV proton flux was above a threshold of 10 pfu (101 days) was about 34 times less than the number of days with a non-enhanced proton flux (3400 days) (Sadykov et al., 2021). This class imbalance ratio eliminates the possibility of using data-hungry ML algorithms directly and requires additional strategies for model training (Ahmadzadeh et al., 2021). Other challenges may include the widespread time delay (from minutes to hours) between the first detection of the SEP event and the onset of the preceding associated solar flare, which may lead to incorrect SEP-flare associations resulting in inaccurate model training or validation, missing information about host active regions in models using active region parameters, and the lack of observations of the sources of SEP events originating on the far side of the Sun.

## 2.5. Multi-module forecasting systems

Some models take an approach that chains multiple forecast modules together, with the prediction from each module feeding into the next. For example, the first module might use magnetograms or EUV imagery of an active

region to generate a prediction of the likelihood that a flare of a certain class will occur in that region. This prediction, together with the flare information, is passed to a module that predicts the likely parameters of the CME that might accompany the flare. The CME information is then input into a final module that predicts parameters of the potential SEP event. When an eruptive event does occur, each module ingests the required flare, CME, or proton flux observations as they become available and updates the prediction that is passed to the downstream module.

Multi-module systems tend to take advantage of mature models that are already developed and can be linked together so that the output from one model can trigger another. They may also combine models of different types, e.g., empirical, machine learning, and physics-based, exploiting the strengths of each type of model and providing a broader-based prediction of an event.

## 2.6. Model validation

In the “Validation” subsection for each model described in Section 3, published validation results are summarized. Some models have performed extensive quantitative validation studies, while others may have simply performed qualitative comparisons with observations for a few test cases. Some models have not yet published any validation. In the Conclusions (Section 4), we will describe our vision for steps that can facilitate more consistent validation across the SEP modeling field.

Throughout the validation sections, there are mentions of many types of metrics and plots typically used for validation. We refer the reader to papers by Liemohn et al. (2021) and Bain et al. (2021) for descriptions and explanations of the commonly used metrics and skill scores and their application and interpretation.

## 3. Model descriptions

This section summarizes the 36 SEP prediction models in Table 1 presented in alphabetical order. For each model, we specify the model developers, an overall description of the model, inputs, outputs, any free parameters, limitations and caveats related to the model, how data or predictions from the model may be accessed, and a summary of any validation efforts. The descriptions and results given here are intentionally brief and contain a limited number of figures or data tables. Interested readers should refer to the cited references for more details.

The terms “forecasting” and “nowcasting” are regularly used throughout the model descriptions. “Forecasting” typically indicates a model prediction that is made prior to any eruptive event on the Sun, e.g. a flare or CME, although it may mean a prediction issued prior to an increase in particle flux. “Nowcasting” is typically applied when predictions have been made directly following a flare, CME, or observed increase in particle flux at 1 AU. “Prediction” is used as a general term that is equivalent to a

<footnote n="3">³ https://ccmc.gsfc.nasa.gov/challenges/sep.php.</footnote>
model producing output. “Prediction” may indicate model output for a historical event or in the context of forecasting or nowcasting.

### 3.1. ADEPT - Air Force Dynamic Energetic Particle Tool

**Model developers:** Stephen M. White and Stephen W. Kahler (Air Force Research Laboratory), Alan G. Ling (Atmospheric Environmental Research).

**Model description:** The Air Force Dynamic Energetic Particle Tool (ADEPT) predicts the peak flux from solar particle events by fitting functional forms to the rise phase once energetic protons start arriving at Earth (or any other location). Either Weibull or log-normal functions can be used, as discussed by Kahler and Ling (2017). The current version uses Weibull functions. The fits consistently tend to under-predict the peak during the early rise phase, but an empirical analysis has determined factors as a function of time that can correct for the under-prediction in real time.

**Inputs:** Current inputs are the GOES 5-min measurements of energetic protons: the initial version focuses on >10 MeV protons, and fits for >30, >50 and >100 MeV protons are being implemented. The longitude of the associated solar event is also used, if available, to determine the parameters of the functional form during the rise phase. Fitting starts once the proton flux exceeds a threshold (0.6 pfu for >10 MeV) and is 5σ above the background trend.

**Outputs:** On receipt of a new data point every 5 min, a new functional fit is carried out, providing an estimate of the peak flux and fluence together with an estimate of the uncertainty in the prediction. Once the peak of the event has been reached, the overall timescale for the event is also predicted.

**Free parameters:** The functional forms both have 4 free parameters: 2 shape parameters, a “zero” time (since the functions are distribution functions that are only valid for non-negative arguments), and an amplitude. The shape parameters of the functions need to be fixed in the rise phase in order to achieve successful fits, so for the first 2 h the only free parameter is the amplitude of the event. Thereafter the zero time is also fitted, which allows improved fits for irregular light curves. Once the event has peaked, a shape parameter that reflects the timescale of the event can also be fitted.

**Limitations and caveats:** The intent of ADEPT is to provide a prediction as soon as possible after a solar proton event starts, and to improve that prediction as more data is acquired. This drives the fitting choices described above. Thus, ADEPT provides a prediction of the peak flux of an event that continuously evolves with time during the rise phase.

**Access to model output or forecasts:** This model is under development and is not available to the public.

**Model validation:** A sample of 82 SEP events chosen from the 1986–2017 period was used to determine the empirical correction factor as a function of time. The current metric for validation is the uncertainty in the predicted peak, determined from the spread of the predictions for the event sample. This metric also evolves with time, ranging from a factor of 5 at the 1-h point after event onset, down to a factor of less than 2 at the 6-h point. Validation is being carried out on new-cycle SEP events as they occur.

### 3.2. AFRL PPS - Air Force Research Laboratory Proton Prediction System

**Model developers:** Don F. Smart and Margaret A. Shea (developed at the Air Force Geophysics Laboratory).

**Model description:** The Air Force Research Laboratory (AFRL) Proton Prediction System (PPS) model is a post-eruption model that uses the flare fluence, peak time, peak intensity, and location in order to predict the SEP onset time, peak time, peak intensity, and end time (Smart et al., 1979, 1989, 1992). The predictions are made for 1 AU and for proton energies of >5 MeV, >10 MeV, and >50 MeV. From these quantities, a simplistic time profile prediction can be created. The goal in developing this model was to provide a forecast of the expected solar proton flux within 10 min after the data became available to the operator in the forecast center.

The basis of the PPS model are correlations between SEP events from Interplanetary Monitoring Platform (IMP) satellites and associated flares Smart et al. (1979, 1989, 1992). SEPs are assumed to be accelerated at the flare location 0.25 h after the flare onset. The time between the flare onset and SEP onset is predicted based on the results from Barouch et al. (1971) which found a relation to flare longitude. The time to peak intensity is also based on a relationship with flare longitude which was reported in Van Hollebeke et al. (1975). For protons of $E > 10$ MeV, this relationship is given in Kahler et al. (2007) as:

$$T_{max}(h) = A \times \Theta^2 + 2.7. \qquad (1)$$

where $\Theta$ is the longitudinal angular displacement in radians of the flare site from the Earth’s magnetic footpoint and A is an asymmetric factor dependent upon flare longitude. The end time is based on Roelof. (1969) which discussed the transport of particles in interplanetary space. A few simplifying assumptions are made here.

* The particles travel along the Interplanetary Magnetic Field (IMF) with a velocity which is a function of particle energy.

* Perpendicular diffusion is ignored.

* The minimum distance to travel from the Sun to Earth is along the Parker spiral.

From these assumptions and results, the model uses a 1/e decay function to predict the end time.

PPS calculates the peak intensity of the proton flux, at the optimum connection at W57.3° (Kahler et al., 2007), as

$$J(E > 10\text{MeV}) = 30.67 \times (F_{XW} \times \Delta T)^{1.327} \qquad (2)$$
model producing output. “Prediction” may indicate model output for a historical event or in the context of forecasting or nowcasting.

### 3.1. ADEPT - Air Force Dynamic Energetic Particle Tool

**Model developers:** Stephen M. White and Stephen W. Kahler (Air Force Research Laboratory), Alan G. Ling (Atmospheric Environmental Research).

**Model description:** The Air Force Dynamic Energetic Particle Tool (ADEPT) predicts the peak flux from solar particle events by fitting functional forms to the rise phase once energetic protons start arriving at Earth (or any other location). Either Weibull or log-normal functions can be used, as discussed by Kahler and Ling (2017). The current version uses Weibull functions. The fits consistently tend to under-predict the peak during the early rise phase, but an empirical analysis has determined factors as a function of time that can correct for the under-prediction in real time.

**Inputs:** Current inputs are the GOES 5-min measurements of energetic protons: the initial version focuses on >10 MeV protons, and fits for >30, >50 and >100 MeV protons are being implemented. The longitude of the associated solar event is also used, if available, to determine the parameters of the functional form during the rise phase. Fitting starts once the proton flux exceeds a threshold (0.6 pfu for >10 MeV) and is 5σ above the background trend.

**Outputs:** On receipt of a new data point every 5 min, a new functional fit is carried out, providing an estimate of the peak flux and fluence together with an estimate of the uncertainty in the prediction. Once the peak of the event has been reached, the overall timescale for the event is also predicted.

**Free parameters:** The functional forms both have 4 free parameters: 2 shape parameters, a “zero” time (since the functions are distribution functions that are only valid for non-negative arguments), and an amplitude. The shape parameters of the functions need to be fixed in the rise phase in order to achieve successful fits, so for the first 2 h the only free parameter is the amplitude of the event. Thereafter the zero time is also fitted, which allows improved fits for irregular light curves. Once the event has peaked, a shape parameter that reflects the timescale of the event can also be fitted.

**Limitations and caveats:** The intent of ADEPT is to provide a prediction as soon as possible after a solar proton event starts, and to improve that prediction as more data is acquired. This drives the fitting choices described above. Thus, ADEPT provides a prediction of the peak flux of an event that continuously evolves with time during the rise phase.

**Access to model output or forecasts:** This model is under development and is not available to the public.

**Model validation:** A sample of 82 SEP events chosen from the 1986–2017 period was used to determine the empirical correction factor as a function of time. The current metric for validation is the uncertainty in the predicted peak, determined from the spread of the predictions for the event sample. This metric also evolves with time, ranging from a factor of 5 at the 1-h point after event onset, down to a factor of less than 2 at the 6-h point. Validation is being carried out on new-cycle SEP events as they occur.

### 3.2. AFRL PPS - Air Force Research Laboratory Proton Prediction System

**Model developers:** Don F. Smart and Margaret A. Shea (developed at the Air Force Geophysics Laboratory).

**Model description:** The Air Force Research Laboratory (AFRL) Proton Prediction System (PPS) model is a post-eruption model that uses the flare fluence, peak time, peak intensity, and location in order to predict the SEP onset time, peak time, peak intensity, and end time (Smart et al., 1979, 1989, 1992). The predictions are made for 1 AU and for proton energies of >5 MeV, >10 MeV, and >50 MeV. From these quantities, a simplistic time profile prediction can be created. The goal in developing this model was to provide a forecast of the expected solar proton flux within 10 min after the data became available to the operator in the forecast center.

The basis of the PPS model are correlations between SEP events from Interplanetary Monitoring Platform (IMP) satellites and associated flares Smart et al. (1979, 1989, 1992). SEPs are assumed to be accelerated at the flare location 0.25 h after the flare onset. The time between the flare onset and SEP onset is predicted based on the results from Barouch et al. (1971) which found a relation to flare longitude. The time to peak intensity is also based on a relationship with flare longitude which was reported in Van Hollebeke et al. (1975). For protons of E > 10 MeV, this relationship is given in Kahler et al. (2007) as:

$$T_{max}(h) = A \times \Theta^2 + 2.7. \qquad (1)$$

where Θ is the longitudinal angular displacement in radians of the flare site from the Earth’s magnetic footpoint and A is an asymmetric factor dependent upon flare longitude. The end time is based on Roelof. (1969) which discussed the transport of particles in interplanetary space. A few simplifying assumptions are made here.

* The particles travel along the Interplanetary Magnetic Field (IMF) with a velocity which is a function of particle energy.

* Perpendicular diffusion is ignored.

* The minimum distance to travel from the Sun to Earth is along the Parker spiral.

From these assumptions and results, the model uses a 1/e decay function to predict the end time.

PPS calculates the peak intensity of the proton flux, at the optimum connection at W57.3° (Kahler et al., 2007), as

$$J(E > 10 \text{MeV}) = 30.67 \times (F_{XW} \times \Delta T)^{1.327} \qquad (2)$$
where $F_{XW}$ is the GOES peak 1–8 Å X-ray flare flux in ergs and $\Delta T$ is the X-ray flare rise time from onset to peak in min. The same value can be found using the flare half-power fluence, $F_x$, as

$$J(E > 10\text{MeV}) = 347 \times (F_x)^{0.941}. \quad (3)$$

**Inputs:** The inputs for the PPS model are flare fluence or peak flux, flare location, flare onset time, and flare peak time.

* Radio burst flux from US Air Force Radio Solar Telescope Network (RSTN) for the original PPS76 model

* GOES Soft X-ray flux for the current version (flare fluence, peak flux)

* Optical H-alpha imagery from the Solar Observing Optical Network (SOON) for flare location

* Solar wind speed, if available (default of 404 km/s if not available)

**Outputs:** The PPS model predicts the SEP onset time, peak time, peak intensity, end time, and fluence. From these outputs, a simplistic time profile can also be derived. All output is for >5 MeV, >10 MeV, and >50 MeV integral intensities. The model has non-SEP output as well (i.e., polar riometer absorption at Thule, Greenland, dose rate at polar altitudes), but they will not be discussed here.

**Free parameters:** None.

**Limitations and caveats:** The onset time prediction is defined as the time between the flare peak and when >10 MeV proton flux reaches 10 pfu as observed by GOES. Similarly, the peak time prediction is defined as the time between the flare peak and the SEP peak intensity. The flare peak should be identified as the peak in radio (original version) and X-rays (later versions).

The intensity time profile, if constructed from the timing quantities, tends to be simplistic (i.e., straight lines connecting the onset time, peak time, and end time).

PPS was developed with the capability to update the prediction as additional flare data are received. If a second event occurs while a previous event is in progress, the program has the capability to predict a “summation” event (Margaret Shea, personal communication).

**Access to model output or forecasts:** The PPS model was specifically made for use by the 557th Weather Wing of the US Air Force.

**Model validation:** Kahler et al. (2007) considers 78 GOES X-ray flares between 1997 and 2001. Only flares with known locations and peaks greater than M5 were chosen. A comparison was made between PPS predictions and all SEP events during this time period where GOES >10 MeV proton intensity reaches 10 pfu. Correlation coefficients were calculated between the PPS log peak intensity and GOES log peak intensity ($r = 0.55$), PPS log rise time and GOES log rise time ($r = 0.36$), and PPS log rise time and GOES log rise time ($r$ not given). The study also calculates the Percent Correct as 73%.

<table><caption>Table 2
Ratios and skill scores for four cases of >50 MeV predictions and one case of >10 MeV predictions for the AFRL PPS model.</caption><thead><tr><th>Solar variable</th><th>POD</th><th>FAR</th><th>TSS</th><th>HSS</th></tr></thead><tbody><tr><td>&gt;M5 flares</td><td>0.49</td><td>0.66</td><td>0.40</td><td>0.33</td></tr><tr><td>8800-MHz bursts with &gt;M5 flares</td><td>0.66</td><td>0.82</td><td>0.34</td><td>0.16</td></tr><tr><td>All 8800 MHz bursts &gt;500 sfu</td><td>0.66</td><td>0.83</td><td>0.29</td><td>0.13</td></tr><tr><td>All 8800 MHz bursts &gt;5000 sfu</td><td>0.40</td><td>0.49</td><td>-0.15</td><td>-0.14</td></tr><tr><td>&gt;10 MeV with &gt;M5 flares</td><td>0.40</td><td>0.50</td><td>0.08</td><td>0.09</td></tr></tbody></table>

Kahler et al. (2017) did a similar validation of PPS but for >50 MeV predictions. The study considered SEP events between 1986 and 2016 where GOES >50 MeV intensity reaches 1 pfu. The PPS model is run for four different cases: all flares greater than M5, all >200 sfu 8800-MHz bursts with associated >M5 flares, all >500 sfu 8800-MHz bursts, and all >5000 sfu 8800-MHz bursts. The results are in the table below and also include results for the >10 MeV predictions. The Probability of Detection (POD), Alarm Ratio (FAR), True Skill Score (TSS), and Heidke Skill Score (HSS) are reported (see Table 2).

### 3.3. Aminalragia-Giamini Model

**Model developers:** Sigiava Aminalragia-Giamini (Space Applications and Research Consultancy (SPARC), National and Kapodistrian University of Athens (NKUA)).

**Model description:** The Aminalragia-Giamini model (Aminalragia-Giamini et al., 2021) was designed with a focus on operability that will be as uninterruptible as possible, the use of minimal and consistently available inputs, and the minimization of post-eruptive prediction time. The model uses X-ray GOES measurements for the prediction of SEP occurrence during and immediately after the eruption of a solar flare. During the evolution of the flare a probability $P \in [0, 1]$ that an SEP will occur is provided, and this value is continuously updated by taking into account the real-time X-ray measurement updates of the on-going flare. The probability estimation is finalized after the end of the solar flare eruption. The predictor used is an ensemble of deep feedforward Neural Network (NN) where the final output is the mean of the individual NN predictions. The number of members (N) in the ensemble is set prior to training but the modular implementation used also allows the addition of more NNs; we have used and tested successfully $N = 3$ and $N = 10$. The NNs are trained on 25 years of data, from 1988–2013, which cover the largest part of SC22, the whole SC23, and the rising phase of SC24. This includes several thousands of solar flares (NOAA GOES solar flare catalogue) and more than 200 identified and catalogued SEPs taken and processed from the Solar Energetic Particle Environment Modeling (SEPEM) Reference Event List<fnref n="4" />. The approach employed has a few noteworthy points:

<footnote n="4">⁴ http://sepem.eu/help/event_ref.html.</footnote>
where $F_{XW}$ is the GOES peak 1–8 Å X-ray flare flux in ergs and $\Delta T$ is the X-ray flare rise time from onset to peak in min. The same value can be found using the flare half-power fluence, $F_x$, as

$$J(E > 10\text{MeV}) = 347 \times (F_x)^{0.941}. \quad (3)$$

**Inputs:** The inputs for the PPS model are flare fluence or peak flux, flare location, flare onset time, and flare peak time.

* Radio burst flux from US Air Force Radio Solar Telescope Network (RSTN) for the original PPS76 model

* GOES Soft X-ray flux for the current version (flare fluence, peak flux)

* Optical H-alpha imagery from the Solar Observing Optical Network (SOON) for flare location

* Solar wind speed, if available (default of 404 km/s if not available)

**Outputs:** The PPS model predicts the SEP onset time, peak time, peak intensity, end time, and fluence. From these outputs, a simplistic time profile can also be derived. All output is for >5 MeV, >10 MeV, and >50 MeV integral intensities. The model has non-SEP output as well (i.e., polar riometer absorption at Thule, Greenland, dose rate at polar altitudes), but they will not be discussed here.

**Free parameters:** None.

**Limitations and caveats:** The onset time prediction is defined as the time between the flare peak and when >10 MeV proton flux reaches 10 pfu as observed by GOES. Similarly, the peak time prediction is defined as the time between the flare peak and the SEP peak intensity. The flare peak should be identified as the peak in radio (original version) and X-rays (later versions).

The intensity time profile, if constructed from the timing quantities, tends to be simplistic (i.e., straight lines connecting the onset time, peak time, and end time).

PPS was developed with the capability to update the prediction as additional flare data are received. If a second event occurs while a previous event is in progress, the program has the capability to predict a “summation” event (Margaret Shea, personal communication).

**Access to model output or forecasts:** The PPS model was specifically made for use by the 557th Weather Wing of the US Air Force.

**Model validation:** Kahler et al. (2007) considers 78 GOES X-ray flares between 1997 and 2001. Only flares with known locations and peaks greater than M5 were chosen. A comparison was made between PPS predictions and all SEP events during this time period where GOES >10 MeV proton intensity reaches 10 pfu. Correlation coefficients were calculated between the PPS log peak intensity and GOES log peak intensity ($r = 0.55$), PPS log rise time and GOES log rise time ($r = 0.36$), and PPS log rise time and GOES log rise time ($r$ not given). The study also calculates the Percent Correct as 73%.

<table><caption>Table 2
Ratios and skill scores for four cases of >50 MeV predictions and one case of >10 MeV predictions for the AFRL PPS model.</caption><thead><tr><th>Solar variable</th><th>POD</th><th>FAR</th><th>TSS</th><th>HSS</th></tr></thead><tbody><tr><td>&gt;M5 flares</td><td>0.49</td><td>0.66</td><td>0.40</td><td>0.33</td></tr><tr><td>8800-MHz bursts with &gt;M5 flares</td><td>0.66</td><td>0.82</td><td>0.34</td><td>0.16</td></tr><tr><td>All 8800 MHz bursts &gt;500 sfu</td><td>0.66</td><td>0.83</td><td>0.29</td><td>0.13</td></tr><tr><td>All 8800 MHz bursts &gt;5000 sfu</td><td>0.40</td><td>0.49</td><td>-0.15</td><td>-0.14</td></tr><tr><td>&gt;10 MeV with &gt;M5 flares</td><td>0.40</td><td>0.50</td><td>0.08</td><td>0.09</td></tr></tbody></table>

Kahler et al. (2017) did a similar validation of PPS but for >50 MeV predictions. The study considered SEP events between 1986 and 2016 where GOES >50 MeV intensity reaches 1 pfu. The PPS model is run for four different cases: all flares greater than M5, all >200 sfu 8800-MHz bursts with associated >M5 flares, all >500 sfu 8800-MHz bursts, and all >5000 sfu 8800-MHz bursts. The results are in the table below and also include results for the >10 MeV predictions. The Probability of Detection (POD), Alarm Ratio (FAR), True Skill Score (TSS), and Heidke Skill Score (HSS) are reported (see Table 2).

### 3.3. Aminalragia-Giamini Model

**Model developers:** Sigiava Aminalragia-Giamini (Space Applications and Research Consultancy (SPARC), National and Kapodistrian University of Athens (NKUA)).

**Model description:** The Aminalragia-Giamini model (Aminalragia-Giamini et al., 2021) was designed with a focus on operability that will be as uninterruptible as possible, the use of minimal and consistently available inputs, and the minimization of post-eruptive prediction time. The model uses X-ray GOES measurements for the prediction of SEP occurrence during and immediately after the eruption of a solar flare. During the evolution of the flare a probability $P \in [0, 1]$ that an SEP will occur is provided, and this value is continuously updated by taking into account the real-time X-ray measurement updates of the on-going flare. The probability estimation is finalized after the end of the solar flare eruption. The predictor used is an ensemble of deep feedforward Neural Network (NN) where the final output is the mean of the individual NN predictions. The number of members (N) in the ensemble is set prior to training but the modular implementation used also allows the addition of more NNs; we have used and tested successfully $N = 3$ and $N = 10$. The NNs are trained on 25 years of data, from 1988–2013, which cover the largest part of SC22, the whole SC23, and the rising phase of SC24. This includes several thousands of solar flares (NOAA GOES solar flare catalogue) and more than 200 identified and catalogued SEPs taken and processed from the Solar Energetic Particle Environment Modeling (SEPEM) Reference Event List<fnref n="4" />. The approach employed has a few noteworthy points:

<footnote n="4">⁴ http://sepem.eu/help/event_ref.html.</footnote>
* The use of solely X-ray measurements makes for a robust and future-proof model. GOES X-ray Sensor (XRS) measurements have been continuously available in near-real-time for decades and the GOES missions are not envisioned to be discontinued in the foreseeable future. Additionally, the data from different GOES satellites over the years are curated and harmonized from NOAA providing coherent inputs.

* The use of solely X-ray measurements does not require the detection/characterization of CMEs which can potentially delay the output of an occurrence prediction by several hours.

* Regarding the classic dichotomy, the model performs well for both impulsive events, typically associated with solar flares, as well as gradual events, typically associated with solar flares and CMEs.

* Different ensembles of nets have been trained to consider solar flares of certain magnitudes and above, e.g., ≥C1 and ≥M2, to emphasize the large range of solar flare intensities, which is of prime Space Weather interest.

**Inputs:** X-ray measurements from the XRS instrument on-board GOES satellites. The X-ray time-series of a solar flare are used to calculate 24 features that are fed as input in the NN ensemble. These features are primarily derived from the peak flux and fluence (time-integrated flux) values of the long and short wavelength GOES X-ray channels. Additionally, when available, the heliolongitude of the solar flare associated active region is also used as an input.

**Outputs:** Probability of an SEP occurring during and after a solar flare, regardless of CME occurrence. This can be also collapsed to a categorical yes/no prediction with a thresholding value (typically 0.5).

**Free parameters:** Operationally none. The internal (weights and biases) parameters of the NNs as well as their hyperparameters can be considered as free, however these are set after training and not user-defined.

**Limitations and caveats:** The GOES XRS measurements cannot distinguish different solar flares if they occur concurrently and the measured X-rays are aggregated. This could potentially affect the NN performance, however as of yet we have not found evidence of this.

**Access to model output or forecasts:** The model will be made operational at the start of 2023. After a pilot operational period, its outputs will be available through a dedicated section in the SPARC webpage (www.sparc.gr). The model outputs will be also accessible to users by connecting to the SPARC Application Programming Interface (API) through a publicly available Python module (https://pypi.org/project/sapiadapter).

**Model validation:** The model has been validated using a 25-year dataset of X-ray measurements and SEPs. Multiple random train/test divisions were used for an overall evaluation. The validation was performed using very strict criteria on a leave-one-out process using all the historical flares

<table><caption>Table 3
Aminalragia-Giamini model True Positive rates, False Positive rates, and TSS from the validation of the model on the full 25 years of available historical data.</caption><thead><tr><th></th><th>True Positive Rate (%)</th><th>False Positive Rate (%)</th><th>True Skill Score</th></tr></thead><tbody><tr><td>Flares ≥C1</td><td>86.81</td><td>7.77</td><td>0.790</td></tr><tr><td>Flares ≥M2</td><td>78.36</td><td>19.60</td><td>0.587</td></tr></tbody></table>

and SEPs. Table 3 and Fig. 1 present the validation outcomes.

### 3.4. AMPS - Adaptive Mesh Particle Simulator

**Model developers:** Valeriy Tenishev (University of Michigan).

**Model description:** Adaptive Mesh Particle Simulator (AMPS) is a 3-dimensional physics-based kinetic Monte Carlo particle model for simulating the dynamics of neutral and charged particles. The energy range of ions and electrons simulated with AMPS varies starting from fractions of eV and up to multiple GeVs. In previous applications, the model was successfully applied to study the planetary, magnetospheric, and heliospheric environments (Tenishev et al., 2021).

AMPS is a fully integrated component of the Space Weather Modeling Framework (SWMF). AMPS incorporates two approaches for modeling transport of SEPs in the heliosphere: (1) simulating SEPs transport when they move along a set of evolving magnetic field lines, and (2) simulating SEPs transported in full 3D. The evolving magnetic field lines are derived from the concurrently conducted magnetohydrodynamic (MHD) modeling of solar wind in the inner heliosphere. AMPS also can be used as a stand-alone SEPs transport model. An analytical representation of the magnetic field line (e.g., Parker spiral) is used in the latter case.

AMPS solves the Parker and Focused transport equations in full 3D and along a set of magnetic field lines (e.g., Tenishev et al., 2005). Model particles are injected at the front of a moving shock. Simulated effects include pitch-angle diffusion (Focused transport equation), spatial diffusion in the direction of the magnetic field line (Parker equation), stochastic accelerations, adiabatic cooling and focusing, and particle drift. The latter is included when modeling is conducted in full 3D. The parameters of the Alfvén turbulence, solar wind, and IMF are derived from concurrently performed MHD modeling of plasma in the inner heliosphere.

**Inputs:** AMPS derives solar wind, IMF, and turbulence parameters from MHD modeling of the inner heliosphere via the coupling infrastructure of the SWMF.

**Outputs:** When simulating SEP transport moving along a set of magnetic field lines, AMPS calculates the flux, density, and energy spectrum of SEPs for a set of the
* The use of solely X-ray measurements makes for a robust and future-proof model. GOES X-ray Sensor (XRS) measurements have been continuously available in near-real-time for decades and the GOES missions are not envisioned to be discontinued in the foreseeable future. Additionally, the data from different GOES satellites over the years are curated and harmonized from NOAA providing coherent inputs.

* The use of solely X-ray measurements does not require the detection/characterization of CMEs which can potentially delay the output of an occurrence prediction by several hours.

* Regarding the classic dichotomy, the model performs well for both impulsive events, typically associated with solar flares, as well as gradual events, typically associated with solar flares and CMEs.

* Different ensembles of nets have been trained to consider solar flares of certain magnitudes and above, e.g., ≥C1 and ≥M2, to emphasize the large range of solar flare intensities, which is of prime Space Weather interest.

**Inputs:** X-ray measurements from the XRS instrument on-board GOES satellites. The X-ray time-series of a solar flare are used to calculate 24 features that are fed as input in the NN ensemble. These features are primarily derived from the peak flux and fluence (time-integrated flux) values of the long and short wavelength GOES X-ray channels. Additionally, when available, the heliolongitude of the solar flare associated active region is also used as an input.

**Outputs:** Probability of an SEP occurring during and after a solar flare, regardless of CME occurrence. This can be also collapsed to a categorical yes/no prediction with a thresholding value (typically 0.5).

**Free parameters:** Operationally none. The internal (weights and biases) parameters of the NNs as well as their hyperparameters can be considered as free, however these are set after training and not user-defined.

**Limitations and caveats:** The GOES XRS measurements cannot distinguish different solar flares if they occur concurrently and the measured X-rays are aggregated. This could potentially affect the NN performance, however as of yet we have not found evidence of this.

**Access to model output or forecasts:** The model will be made operational at the start of 2023. After a pilot operational period, its outputs will be available through a dedicated section in the SPARC webpage (www.sparc.gr). The model outputs will be also accessible to users by connecting to the SPARC Application Programming Interface (API) through a publicly available Python module (https://pypi.org/project/sapiadapter).

**Model validation:** The model has been validated using a 25-year dataset of X-ray measurements and SEPs. Multiple random train/test divisions were used for an overall evaluation. The validation was performed using very strict criteria on a leave-one-out process using all the historical flares

<table><caption>Table 3
Aminalragia-Giamini model True Positive rates, False Positive rates, and TSS from the validation of the model on the full 25 years of available historical data.</caption><thead><tr><th></th><th>True Positive Rate (%)</th><th>False Positive Rate (%)</th><th>True Skill Score</th></tr></thead><tbody><tr><td>Flares ≥C1</td><td>86.81</td><td>7.77</td><td>0.790</td></tr><tr><td>Flares ≥M2</td><td>78.36</td><td>19.60</td><td>0.587</td></tr></tbody></table>

and SEPs. Table 3 and Fig. 1 present the validation outcomes.

### 3.4. AMPS - Adaptive Mesh Particle Simulator

**Model developers:** Valeriy Tenishev (University of Michigan).

**Model description:** Adaptive Mesh Particle Simulator (AMPS) is a 3-dimensional physics-based kinetic Monte Carlo particle model for simulating the dynamics of neutral and charged particles. The energy range of ions and electrons simulated with AMPS varies starting from fractions of eV and up to multiple GeVs. In previous applications, the model was successfully applied to study the planetary, magnetospheric, and heliospheric environments (Tenishev et al., 2021).

AMPS is a fully integrated component of the Space Weather Modeling Framework (SWMF). AMPS incorporates two approaches for modeling transport of SEPs in the heliosphere: (1) simulating SEPs transport when they move along a set of evolving magnetic field lines, and (2) simulating SEPs transported in full 3D. The evolving magnetic field lines are derived from the concurrently conducted magnetohydrodynamic (MHD) modeling of solar wind in the inner heliosphere. AMPS also can be used as a stand-alone SEPs transport model. An analytical representation of the magnetic field line (e.g., Parker spiral) is used in the latter case.

AMPS solves the Parker and Focused transport equations in full 3D and along a set of magnetic field lines (e.g., Tenishev et al., 2005). Model particles are injected at the front of a moving shock. Simulated effects include pitch-angle diffusion (Focused transport equation), spatial diffusion in the direction of the magnetic field line (Parker equation), stochastic accelerations, adiabatic cooling and focusing, and particle drift. The latter is included when modeling is conducted in full 3D. The parameters of the Alfvén turbulence, solar wind, and IMF are derived from concurrently performed MHD modeling of plasma in the inner heliosphere.

**Inputs:** AMPS derives solar wind, IMF, and turbulence parameters from MHD modeling of the inner heliosphere via the coupling infrastructure of the SWMF.

**Outputs:** When simulating SEP transport moving along a set of magnetic field lines, AMPS calculates the flux, density, and energy spectrum of SEPs for a set of the
<figure><img src="image_2.png" /><figcaption>Fig. 1. Aminalragia-Giamini model ROC curves derived from the probabilistic outputs of the model showing the relation of true positive rates and false-positive rates for all thresholds values ∈ [0, 1]. Two curves are shown for both the SF≥C1 and SF≥M2 cases. The dashed line denotes the random classifier behavior. (b) Evolution of the TSS score for the same range of applied thresholds. Red circles mark the points for threshold equal to 0.5.</figcaption></figure>

**user-defined heliocentric distances** for each simulated field line. When modeling SEPs transport in 3D, AMPS calculates (1) the integrated density and flux of SEPs at the corners of the grid covering the simulated domain and (2) the energy spectrum of SEPs in a set of user-defined locations.

**Free parameters:** Free parameters include an energy spectrum and a distribution of the source of SEPs. When transporting SEPs along magnetic field lines, AMPS can track the location of the shock that determines where new particles are injected in the model. In the latter case, the solar wind plasma parameters are derived from a concurrently conducted MHD model of the solar wind in the inner heliosphere. In that case, the injection efficiency is an additional free parameter. The choice of the pitch-angle diffusion coefficient is also a free model parameter.

**Limitations and caveats:** AMPS needs to be executed as a component of the SWMF to use evolving magnetic field lines and the solar wind and turbulence parameters.

**Access to model output or forecasts:** AMPS is available in the CCMC at https://ccmc.gsfc.nasa.gov/requests/PP/user Registration.php?model=AMPS. It is also available in source code as a component of the SWMF developed at the University of Michigan.

**Model validation:** Modeling SEP populations is one of the multiple prior applications of AMPS. The core of AMPS is a Monte Carlo solver of kinetic equations. AMPS was extensively validated by comparing with observations when solving the Boltzmann equation in planetary environments and against analytical solutions of plasma wave propagation when solving Vlasov + Maxwell equations. There was no significant validation of the SEP population model when solving Parker or Focused Transport equations conducted so far.

### 3.5. Boubrahimi Model

**Model developers:** Soukaina Filali Boubrahimi, Berkay Aydin, Petrus Martens, Rafal Angryk (developed at Georgia State University).

**Model description:** This model, described in Boubrahimi et al. (2017), predicts the occurrence of SEP events of >100 MeV based on time series correlations among GOES X-ray flux and several proton flux channels using an interpretable decision tree model. A classification decision tree model maps observation attributes as branches to class labels at the leaves. In this model, two class labels are considered: the positive class is composed of X-ray and proton channel time series that led to a >100 MeV SEP event, and the negative class are those data which did not lead to such an event. The SEP event list used for training the model is from Núñez (2011) and consists of 47 impulsive events from the period between 1997 and 2013. Another 47 X-ray events which did not produce any associated SEP event were selected for the negative class, producing a balanced dataset. The observations used to train the model are the GOES XRS, Energetic Particle Sensor (EPS) and High Energy Proton and Alpha Detector (HEPAD) channels – eight in total. As a distinction from previous work (e.g., Núñez, 2011), this model considers not only the correlations between X-ray and energetic proton flux time series, but also correlations across different proton channels. Correlations are expressed using the Vector Autoregression Model (VAR), a stochastic process model used to capture the linear interdependencies among multiple time series. The model considers time windows (called “spans”) before the start of the X-ray event, and each time point within a span is expressed as a linear function of l previous time
<figure><img src="image_2.png" /><figcaption>Fig. 1. Aminalragia-Giamini model ROC curves derived from the probabilistic outputs of the model showing the relation of true positive rates and false-positive rates for all thresholds values ∈ [0, 1]. Two curves are shown for both the SF≥C1 and SF≥M2 cases. The dashed line denotes the random classifier behavior. (b) Evolution of the TSS score for the same range of applied thresholds. Red circles mark the points for threshold equal to 0.5.</figcaption></figure>

**user-defined heliocentric distances** for each simulated field line. When modeling SEPs transport in 3D, AMPS calculates (1) the integrated density and flux of SEPs at the corners of the grid covering the simulated domain and (2) the energy spectrum of SEPs in a set of user-defined locations.

**Free parameters:** Free parameters include an energy spectrum and a distribution of the source of SEPs. When transporting SEPs along magnetic field lines, AMPS can track the location of the shock that determines where new particles are injected in the model. In the latter case, the solar wind plasma parameters are derived from a concurrently conducted MHD model of the solar wind in the inner heliosphere. In that case, the injection efficiency is an additional free parameter. The choice of the pitch-angle diffusion coefficient is also a free model parameter.

**Limitations and caveats:** AMPS needs to be executed as a component of the SWMF to use evolving magnetic field lines and the solar wind and turbulence parameters.

**Access to model output or forecasts:** AMPS is available in the CCMC at https://ccmc.gsfc.nasa.gov/requests/PP/user Registration.php?model=AMPS. It is also available in source code as a component of the SWMF developed at the University of Michigan.

**Model validation:** Modeling SEP populations is one of the multiple prior applications of AMPS. The core of AMPS is a Monte Carlo solver of kinetic equations. AMPS was extensively validated by comparing with observations when solving the Boltzmann equation in planetary environments and against analytical solutions of plasma wave propagation when solving Vlasov + Maxwell equations. There was no significant validation of the SEP population model when solving Parker or Focused Transport equations conducted so far.

### 3.5. Boubrahimi Model

**Model developers:** Soukaina Filali Boubrahimi, Berkay Aydin, Petrus Martens, Rafal Angryk (developed at Georgia State University).

**Model description:** This model, described in Boubrahimi et al. (2017), predicts the occurrence of SEP events of >100 MeV based on time series correlations among GOES X-ray flux and several proton flux channels using an interpretable decision tree model. A classification decision tree model maps observation attributes as branches to class labels at the leaves. In this model, two class labels are considered: the positive class is composed of X-ray and proton channel time series that led to a >100 MeV SEP event, and the negative class are those data which did not lead to such an event. The SEP event list used for training the model is from Núñez (2011) and consists of 47 impulsive events from the period between 1997 and 2013. Another 47 X-ray events which did not produce any associated SEP event were selected for the negative class, producing a balanced dataset. The observations used to train the model are the GOES XRS, Energetic Particle Sensor (EPS) and High Energy Proton and Alpha Detector (HEPAD) channels – eight in total. As a distinction from previous work (e.g., Núñez, 2011), this model considers not only the correlations between X-ray and energetic proton flux time series, but also correlations across different proton channels. Correlations are expressed using the Vector Autoregression Model (VAR), a stochastic process model used to capture the linear interdependencies among multiple time series. The model considers time windows (called “spans”) before the start of the X-ray event, and each time point within a span is expressed as a linear function of *l* previous time
<table><caption>Table 4
GOES X-ray and Proton Instruments and Channels used in Boubrahimi Model.</caption><thead><tr><th>Instrument</th><th>Channel</th><th>Description</th></tr></thead><tbody><tr><td>SX1.</td><td>xs</td><td>Short wavelength channel irradiance (0.5–0.3 nm)</td></tr><tr><td>SX1</td><td>xl</td><td>Long wavelength channel irradiance (0.1–0.8 nm)</td></tr><tr><td>EPS</td><td>p6_flux</td><td>Proton Channel 80.0–165.0 MeV</td></tr><tr><td>EPS</td><td>p7_flux</td><td>Proton Channel 165.0–500.0 MeV</td></tr><tr><td>HEPAD</td><td>p8_flux</td><td>Proton Channel 350.0–420.0 MeV</td></tr><tr><td>HEPAD</td><td>p9_flux</td><td>Proton Channel 420.0–510.0 MeV</td></tr><tr><td>HEPAD</td><td>p10_flux</td><td>Proton Channel 510.0–700.0 MeV</td></tr><tr><td>HEPAD</td><td>p11_flux</td><td>Proton Channel >700.0 MeV</td></tr></tbody></table>

points (called “lags”). The VAR(l) correlation coefficients of the linear function describing the time series are used as the observation attributes for the decision tree. A study was done to determine the optimal span duration (from 3 to 30 h) and number of lags l (from l = 3 to l = 9) using classification accuracy as the metric for success. This work used the Classification And Regression Trees (CART) decision tree algorithm and the Gini impurity and information gain metrics as the splitting criteria for evaluating class separation.

**Inputs:** The model inputs are times series of eight channels from the GOES X-ray and proton instruments, and are summarized in Table 4.

**Outputs:** The model output is a binary flag of the occurrence of a >100 MeV proton event or non-event.

**Free parameters:** This is a machine learning model and it does not contain free parameters in the same sense as a physical model. However, for training the model must set the span window and the number of lag points l in the VAR(l) model for the span time series, as well as choose a metric (e.g. Geni purity or information gain) to use as a splitting criterion. Once the model is trained, no other “free parameters” are provided to the model.

**Limitations and caveats:** The model prediction is a binary flag indicating whether an SEP event will occur in a period immediately following the “span” segment that is analyzed. It is important to emphasize that the model is trained on X-ray and proton channel data that is *prior to an observed X-ray flare*. Therefore, this model does not use the flare event itself as a precursor, but rather the relatively quiet period prior to the flare. The forecast lead time for this model, though unspecified, would be expected to be typical of the time between the onset of a flare and an SEP event.

**Access to model output or forecasts:** This model is under development and is not available publicly.

**Model validation:** The model was trained and evaluated with a 10-fold cross-validation using stratified sampling. The dataset (N = 47 × 2 = 94 samples) is randomly divided into 10 subsamples (or folds), and then 10 tests are done where 9 of the folds are used for training and 1-fold is used for testing. Evaluation metrics for the testing portion are averaged over the 10 tests. The metrics presented are accuracy, recall, precision, the F1 metric (har-

monic mean of recall and precision), and Area Under the Curve (AUC) of the Receiver Operator Characteristic (ROC), which is statistically consistent and more discriminating than accuracy. Models trained using the largest span considered, 30 h, and with intermediate lag, l = 5, performed the best. Of the models with those parameters, the model trained with information gain as the splitting criteria outperformed that trained using the Gini index. For this best model, accuracy = 0.78, recall = 0.73, precision = 0.86, F1 = 0.82, and AUC = 0.77. The accuracy is comparable (3% better) to the University of Malaga Solar Energetic Particles (UMASEP) model (Núñez, 2011) trained using the same data.

### 3.6. COMESEP SEPForecast - Coronal Mass Ejections and Solar Energetic Particles

**Model developers:** Mark Dierckxsens (Royal Belgian Institute for Space Aeronomy (BIRA-IASB)), Michael Marsh (UK Met Office), Silvia Dalla (University of Central Lancashire), Norma Crosby (BIRA-IASB).

**Model description:** Coronal Mass Ejections and Solar Energetic Particles (COMESEP) is an operational alert system that runs without human intervention and contains tools for forecasting geomagnetic storms and SEP radiation storms (https://www.comesep.eu). The system is triggered by solar phenomena - Solar Flare (SF) and CMEs. After the automatic detection in solar data of SF and CMEs, alerts are sent through the system to the relevant modules that need the information. The SEPForecast tool within COMESEP produces SEP predictions. SEPForecast is composed of a statistical model (Dierckxsens et al., 2015), which predicts >10 and >60 MeV SEP probability of occurrence and peak fluxes, and a tool to query a run database produced using the physics-based model SPARX Marsh et al. (2015) to make time profile predictions for >10 and >60 MeV.

An extensive statistical analysis of SEP events observed during SC23 was performed to derive the probability and peak flux relationships implemented in SEPForecast (Dierckxsens et al., 2015). The SEPEM<fnref n="5" /> reference proton

<footnote n="5">⁵ https://www.sepem.eu.</footnote>
<table><caption>Table 4
GOES X-ray and Proton Instruments and Channels used in Boubrahimi Model.</caption><thead><tr><th>Instrument</th><th>Channel</th><th>Description</th></tr></thead><tbody><tr><td>SX1.</td><td>xs</td><td>Short wavelength channel irradiance (0.5–0.3 nm)</td></tr><tr><td>SX1</td><td>xl</td><td>Long wavelength channel irradiance (0.1–0.8 nm)</td></tr><tr><td>EPS</td><td>p6_flux</td><td>Proton Channel 80.0–165.0 MeV</td></tr><tr><td>EPS</td><td>p7_flux</td><td>Proton Channel 165.0–500.0 MeV</td></tr><tr><td>HEPAD</td><td>p8_flux</td><td>Proton Channel 350.0–420.0 MeV</td></tr><tr><td>HEPAD</td><td>p9_flux</td><td>Proton Channel 420.0–510.0 MeV</td></tr><tr><td>HEPAD</td><td>p10_flux</td><td>Proton Channel 510.0–700.0 MeV</td></tr><tr><td>HEPAD</td><td>p11_flux</td><td>Proton Channel >700.0 MeV</td></tr></tbody></table>

points (called “lags”). The VAR(l) correlation coefficients of the linear function describing the time series are used as the observation attributes for the decision tree. A study was done to determine the optimal span duration (from 3 to 30 h) and number of lags l (from l = 3 to l = 9) using classification accuracy as the metric for success. This work used the Classification And Regression Trees (CART) decision tree algorithm and the Gini impurity and information gain metrics as the splitting criteria for evaluating class separation.

**Inputs:** The model inputs are times series of eight channels from the GOES X-ray and proton instruments, and are summarized in Table 4.

**Outputs:** The model output is a binary flag of the occurrence of a >100 MeV proton event or non-event.

**Free parameters:** This is a machine learning model and it does not contain free parameters in the same sense as a physical model. However, for training the model must set the span window and the number of lag points l in the VAR(l) model for the span time series, as well as choose a metric (e.g. Geni purity or information gain) to use as a splitting criterion. Once the model is trained, no other “free parameters” are provided to the model.

**Limitations and caveats:** The model prediction is a binary flag indicating whether an SEP event will occur in a period immediately following the “span” segment that is analyzed. It is important to emphasize that the model is trained on X-ray and proton channel data that is *prior to an observed X-ray flare*. Therefore, this model does not use the flare event itself as a precursor, but rather the relatively quiet period prior to the flare. The forecast lead time for this model, though unspecified, would be expected to be typical of the time between the onset of a flare and an SEP event.

**Access to model output or forecasts:** This model is under development and is not available publicly.

**Model validation:** The model was trained and evaluated with a 10-fold cross-validation using stratified sampling. The dataset (N = 47 × 2 = 94 samples) is randomly divided into 10 subsamples (or folds), and then 10 tests are done where 9 of the folds are used for training and 1-fold is used for testing. Evaluation metrics for the testing portion are averaged over the 10 tests. The metrics presented are accuracy, recall, precision, the F1 metric (har-

monic mean of recall and precision), and Area Under the Curve (AUC) of the Receiver Operator Characteristic (ROC), which is statistically consistent and more discriminating than accuracy. Models trained using the largest span considered, 30 h, and with intermediate lag, l = 5, performed the best. Of the models with those parameters, the model trained with information gain as the splitting criteria outperformed that trained using the Gini index. For this best model, accuracy = 0.78, recall = 0.73, precision = 0.86, F1 = 0.82, and AUC = 0.77. The accuracy is comparable (3% better) to the University of Malaga Solar Energetic Particles (UMASEP) model (Núñez, 2011) trained using the same data.

### 3.6. COMESEP SEPForecast - Coronal Mass Ejections and Solar Energetic Particles

**Model developers:** Mark Dierckxsens (Royal Belgian Institute for Space Aeronomy (BIRA-IASB)), Michael Marsh (UK Met Office), Silvia Dalla (University of Central Lancashire), Norma Crosby (BIRA-IASB).

**Model description:** Coronal Mass Ejections and Solar Energetic Particles (COMESEP) is an operational alert system that runs without human intervention and contains tools for forecasting geomagnetic storms and SEP radiation storms (https://www.comesep.eu). The system is triggered by solar phenomena - Solar Flare (SF) and CMEs. After the automatic detection in solar data of SF and CMEs, alerts are sent through the system to the relevant modules that need the information. The SEPForecast tool within COMESEP produces SEP predictions. SEPForecast is composed of a statistical model (Dierckxsens et al., 2015), which predicts >10 and >60 MeV SEP probability of occurrence and peak fluxes, and a tool to query a run database produced using the physics-based model SPARX Marsh et al. (2015) to make time profile predictions for >10 and >60 MeV.

An extensive statistical analysis of SEP events observed during SC23 was performed to derive the probability and peak flux relationships implemented in SEPForecast (Dierckxsens et al., 2015). The SEPEM<fnref n="5" /> reference proton

<footnote n="5">⁵ https://www.sepem.eu.</footnote>
dataset (Crosby et al., 2015) from European Space Agency (ESA) was used to calculate SEP values. Predictors studied were flare intensity and location for flares ≥M1, CME speed and width, and various combinations of these parameters. A flare list was generated from the NOAA GOES X-ray solar flare catalog. A flare-CME list was compiled from the GOES X-ray solar flare catalog and the Coordinated Data Analysis Workshop (CDAW) SOHO/LASCO CME catalog, linking the two phenomena using temporal and spatial criteria.

COMESEP predictions are derived from combinations of parameters to allow for the potential (un) availability of data after measuring the flare magnitude. In this vein, the probability of SEP occurrence and >10 MeV and >60 MeV peak proton flux values were derived from both the flare only and flare-CME lists. To calculate the integral peak fluxes for >10 MeV and >60 MeV from the SEPEM differential channels, the authors assume a Weibull function to describe the spectral shape of the SEP peak. The flare and CME values are used to directly generate >10 MeV and >60 MeV peak proton fluxes. SEPForecast does not consider the ESP peak due to a passing CME - only the peak prior to the ESP.

All COMESEP forecasts are triggered following an observation of a soft solar X-ray flare with magnitude ≥M1. A first prediction is derived from the statistical model using the flare intensity as derived by the Flaremail tool in combination with the flare location provided by the Solar Dimming and EUV Wave Monitor (DEMON) tool and the CME speed and width provided by Computer Aided CME Tracking catalog (CACTus) for observed CMEs with a width >150°. If the location or CME parameters are available after the flare intensity, the alert is subsequently updated. Via this methodology, the likelihood of SEP occurrence and peak flux are quickly provided from statistical relationships.

The SEP time profile is forecast from a previously generated database of runs by the physics-based SPARX model (see Section 3.31), which is queried to produce profiles at Earth for ten-minute averaged >10 MeV and >60 MeV (Marsh et al., 2015). SPARX assumes a broad acceleration region located at a radius of $2R_{\text{Sun}}$ with a standard width $48° \times 48°$. The injection region can be increased or decreased by combining a set of $6° \times 6°$ tiles. With this approach, SPARX does not need any information about the associated CME and can be triggered solely by flare observations. SPARX is triggered by the automated detection of a flare by the Flaremail tool and the measurement of flare location from Solar DEMON. The injection region is centered around the flare location. The time of particle injection is taken to be the flare peak time. The flare X-ray peak flux value is used to normalize the simulated flux profiles into physical flux units (Marsh et al., 2015). The time to maximum intensity, event start and end times are derived from the predicted profiles by applying the thresholds

of >10 MeV exceeds 10 pfu and >60 MeV exceeds $7.9 \times 10^{-2}$ pfu<fnref n="6" />.

**Inputs:**

1. Flaremail - whenever an M- or X-class flare is detected in the GOES X-ray data, an alert is sent to the COMESEP system.

2. Solar DEMON - Capable of providing information on flares (location, time, and relative intensity) automatically and in real time using Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) data.

3. CACTus - autonomously detects CMEs in image sequences from SOHO/LASCO and STEREO/COR2. For the COMESEP alert system, only the LASCO detections are used. Whenever a CME with angular width larger than 150 degrees is detected, an alert is sent to the COMESEP system.

4. Ground-Level Event (GLE) Alert - this tools monitors the GLE Alert web page provided by NKUA<fnref n="7" /> and sends an alert to the COMESEP alert system when a new GLE Alert is issued.

**Outputs:**

* The probability of occurrence of radiation storms with proton energies $E > 10$ MeV and $E > 60$ MeV

* Peak flux of proton energies $E > 10$ MeV and $E > 60$ MeV

* Time to maximum intensity, event start and end times based on flux thresholds of $E > 10$ MeV exceeds 10 pfu and $> 60$ MeV exceeds $7.9 \times 10^{-2}$ pfu

**Free parameters:** None.

**Limitations and caveats:** Flare magnitude must reach M1 to trigger the SEPForecast tool.

Subsequent updates of the alert will be issued if additional information becomes available after the initial SEPForecast alert has been issued. To predict the probability of occurrence, these combinations of input parameters are used depending on the available information:

* Flare intensity

* Flare intensity + flare location

* Flare intensity + CME and width

* Flare intensity + flare location + CME and width

* GLE Alert: probability is set to 1

To predict the peak intensity, these combinations of input parameters are used:

* Flare intensity

* Flare intensity + CME speed

<footnote n="6">⁶ https://www.comesep.eu/index.php/tools-description.</footnote>

<footnote n="7">⁷ https://swe.ssa.esa.int/anemos-federated.</footnote>
dataset (Crosby et al., 2015) from European Space Agency (ESA) was used to calculate SEP values. Predictors studied were flare intensity and location for flares ≥M1, CME speed and width, and various combinations of these parameters. A flare list was generated from the NOAA GOES X-ray solar flare catalog. A flare-CME list was compiled from the GOES X-ray solar flare catalog and the Coordinated Data Analysis Workshop (CDAW) SOHO/LASCO CME catalog, linking the two phenomena using temporal and spatial criteria.

COMESEP predictions are derived from combinations of parameters to allow for the potential (un) availability of data after measuring the flare magnitude. In this vein, the probability of SEP occurrence and >10 MeV and >60 MeV peak proton flux values were derived from both the flare only and flare-CME lists. To calculate the integral peak fluxes for >10 MeV and >60 MeV from the SEPEM differential channels, the authors assume a Weibull function to describe the spectral shape of the SEP peak. The flare and CME values are used to directly generate >10 MeV and >60 MeV peak proton fluxes. SEPForecast does not consider the ESP peak due to a passing CME - only the peak prior to the ESP.

All COMESEP forecasts are triggered following an observation of a soft solar X-ray flare with magnitude ≥M1. A first prediction is derived from the statistical model using the flare intensity as derived by the Flaremail tool in combination with the flare location provided by the Solar Dimming and EUV Wave Monitor (DEMON) tool and the CME speed and width provided by Computer Aided CME Tracking catalog (CACTus) for observed CMEs with a width >150°. If the location or CME parameters are available after the flare intensity, the alert is subsequently updated. Via this methodology, the likelihood of SEP occurrence and peak flux are quickly provided from statistical relationships.

The SEP time profile is forecast from a previously generated database of runs by the physics-based SPARX model (see Section 3.31), which is queried to produce profiles at Earth for ten-minute averaged >10 MeV and >60 MeV (Marsh et al., 2015). SPARX assumes a broad acceleration region located at a radius of $2R_{Sun}$ with a standard width $48° \times 48°$. The injection region can be increased or decreased by combining a set of $6° \times 6°$ tiles. With this approach, SPARX does not need any information about the associated CME and can be triggered solely by flare observations. SPARX is triggered by the automated detection of a flare by the Flaremail tool and the measurement of flare location from Solar DEMON. The injection region is centered around the flare location. The time of particle injection is taken to be the flare peak time. The flare X-ray peak flux value is used to normalize the simulated flux profiles into physical flux units (Marsh et al., 2015). The time to maximum intensity, event start and end times are derived from the predicted profiles by applying the thresholds

of >10 MeV exceeds 10 pfu and >60 MeV exceeds $7.9 \times 10^{-2}$ pfu<fnref n="6" />.

**Inputs:**

1. Flaremail - whenever an M- or X-class flare is detected in the GOES X-ray data, an alert is sent to the COMESEP system.

2. Solar DEMON - Capable of providing information on flares (location, time, and relative intensity) automatically and in real time using Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) data.

3. CACTus - autonomously detects CMEs in image sequences from SOHO/LASCO and STEREO/COR2. For the COMESEP alert system, only the LASCO detections are used. Whenever a CME with angular width larger than 150 degrees is detected, an alert is sent to the COMESEP system.

4. Ground-Level Event (GLE) Alert - this tools monitors the GLE Alert web page provided by NKUA<fnref n="7" /> and sends an alert to the COMESEP alert system when a new GLE Alert is issued.

**Outputs:**

* The probability of occurrence of radiation storms with proton energies $E > 10$ MeV and $E > 60$ MeV

* Peak flux of proton energies $E > 10$ MeV and $E > 60$ MeV

* Time to maximum intensity, event start and end times based on flux thresholds of $E > 10$ MeV exceeds 10 pfu and $> 60$ MeV exceeds $7.9 \times 10^{-2}$ pfu

**Free parameters:** None.

**Limitations and caveats:** Flare magnitude must reach M1 to trigger the SEPForecast tool.

Subsequent updates of the alert will be issued if additional information becomes available after the initial SEPForecast alert has been issued. To predict the probability of occurrence, these combinations of input parameters are used depending on the available information:

* Flare intensity

* Flare intensity + flare location

* Flare intensity + CME and width

* Flare intensity + flare location + CME and width

* GLE Alert: probability is set to 1

To predict the peak intensity, these combinations of input parameters are used:

* Flare intensity

* Flare intensity + CME speed

<footnote n="6">⁶ https://www.comesep.eu/index.php/tools-description.</footnote>

<footnote n="7">⁷ https://swe.ssa.esa.int/anemos-federated.</footnote>
* GLE Alert (regardless of other info): the expected peak flux is set to the average peak value of GLEs over SC23

When both flare intensity and location are available, the SPARX model is run to provide a prediction of the onset & peak time and duration.

Users should be aware that there are large uncertainties in the SEPForecast predictions, in particular when only flare information is used. Introducing CME information improves predictions, but these measurements are not always available on a useful timescale. Additionally, it should be noted that the CME relationships developed for SEPForecast were calculated using values from the CDAW LASCO CME Catalog, while the model uses CME measurements from the automated CME database CACTus. The parameters in these two catalogs show large differences in derived CME width and speed.

**Access to model output or forecasts:** Forecasts are available through the ESA Space Weather Service Network at https://swe.ssa.esa.int/bira-comesep-federated.

**Model validation:** Model validation for COMESEP has been performed for SC23 events and reported in an internal report that was generated upon delivery of the model as part of the project, however this work has not yet been published. The COMESEP team is working to extend the validation period to the full SC24, as well as perform a validation of the operational performance since Nov 2013 (Mark Dierckxsens, personal communication).

## 3.7. EPREM - Energetic Particle Radiation Environment Module

**Model developers:** Nathan Schwadron, Kamen Kozarev, Matthew Gorby, Philip Quinn, Matthew Young (developed at Boston University and University of New Hampshire (UNH)).

**Model description:** The Energetic Particle Radiation Environment Module (EPREM) is a 3-dimensional, time-dependent, physics-based model of particle transport anywhere in the heliosphere. EPREM is the core particle transport code of such models as Earth-Moon-Mars Radiation Environment Module (EMMREM), Predictions of radiation from REleASE, EMMREM, and Data In-641 corporate CRaTER, COSTEP, and other SEP measurements (PREDICCS), EPREM + ENLIL + Cone, and SPE Threat Assessment Tool (STAT).

EPREM simulates particle transport by solving the Focused Transport Equation (FTE) (Skilling, 1971; Ruffolo, 1995; Kóta et al., 2005) and convection-diffusion equation (Jokipii et al., 1977; Lee and Fisk, 1981). The transport effects included in the FTE and convection-diffusion equation are convection, diffusive streaming, adiabatic cooling, adiabatic focusing, pitch-angle scattering, perpendicular diffusion, particle drift, and stochastic acceleration. The formalization of these equations within EPREM can be found in Schwadron et al. (2010) and Quinn et al. (2016).

EPREM solves the FTE and convection-diffusion equation by using a Lagrangian grid with nodes that spawn on the inner boundary. For most cases, the inner boundary is the surface of the sun unless specified elsewhere by the user. The nodes are then convected out with the solar wind. The inner boundary then rotates. This naturally creates a Parker spiral configuration. The nodes continue with the solar wind until the outer boundary of the domain is reached. The user implicitly sets the outer boundary by choosing a total number of nodes to span the simulation domain. Fig. 2 shows an example of the unperturbed EPREM grid in physical coordinates. EPREM distributes nodes over nested spherical surfaces and the connections between equivalent nodes on neighboring surfaces produce velocity path lines. In the steady-state case, these lines are formal streamlines; in the frozen-in ideal MHD case, these lines also represent magnetic field lines.

Users may specify the resolution of energy and pitch-angle bins via a runtime configuration file. In uncoupled mode (see below), the user may also specify the temporal resolution; simulation runs that use output from an MHD simulation will use the corresponding times. Users may specify the values of parameters in the initial flux spectrum based on observed values of some particle species, $\sigma$, or chosen theoretical values. This spectrum has the analytic form

$$J_s(E, r) = \frac{J_{0s}}{\xi_{\sigma,s}} \left(\frac{r}{r_0}\right)^{-\beta} \left(\frac{E}{E_0}\right)^{-\gamma} \exp\left(-\frac{E}{E_c}\right) \quad (4)$$

where $J_s(E, r)$ [counts cm$^{-2}$ s$^{-1}$ sr$^{-1}$ (MeV/nuc)$^{-1}$] is the flux of simulated species s at radial distance r [au] and energy E [MeV]; $J_{0s}$ is the flux of reference species σ at a reference radial distance, $r_0$, and reference energy, $E_0$; $\xi_{\sigma,s}$ is the solar-wind abundance of σ relative to s; $\beta$ is the power-law dependence on radial distance; $\gamma$ is the power-law dependence on energy; and $E_c$ is a cutoff or roll-over energy. EPREM currently assumes that $\beta$ and $\gamma$ are the same for all simulated species. It also currently uses fixed values of $r_0 = 1.0$ au and $E_0 = 1.0$ MeV. The remaining free parameters, $J_{0s}$, $\xi_{\sigma,s}$, $\beta$, $\gamma$, and $E_c$ determine the initial distribution at all pitch-angles for species s, which EPREM discretizes into energy bins and assigns to all nodes at the first time step. The nodes carry the distribution information – which changes during transport according to the FTE, convection-diffusion equation, and any heliospheric structures – to the outer boundary.

Computing the evolution of the particle distribution(s) requires knowledge of the magnetic field, B, plasma velocity, V, and plasma density, $\rho$, at each node. EPREM currently provides a simple internal (i.e., uncoupled) model that computes values of B, V, and $\rho$ appropriate to a Parker spiral. The user may choose to include an idealized cone-style shock by setting a flag and specifying shock parameters in the runtime configuration file.

EPREM can include more physically realistic MHD quantities (i.e., from a CME) when coupled to either the
* GLE Alert (regardless of other info): the expected peak flux is set to the average peak value of GLEs over SC23

When both flare intensity and location are available, the SPARX model is run to provide a prediction of the onset & peak time and duration.

Users should be aware that there are large uncertainties in the SEPForecast predictions, in particular when only flare information is used. Introducing CME information improves predictions, but these measurements are not always available on a useful timescale. Additionally, it should be noted that the CME relationships developed for SEPForecast were calculated using values from the CDAW LASCO CME Catalog, while the model uses CME measurements from the automated CME database CACTus. The parameters in these two catalogs show large differences in derived CME width and speed.

**Access to model output or forecasts:** Forecasts are available through the ESA Space Weather Service Network at https://swe.ssa.esa.int/bira-comesep-federated.

**Model validation:** Model validation for COMESEP has been performed for SC23 events and reported in an internal report that was generated upon delivery of the model as part of the project, however this work has not yet been published. The COMESEP team is working to extend the validation period to the full SC24, as well as perform a validation of the operational performance since Nov 2013 (Mark Dierckxsens, personal communication).

## 3.7. EPREM - Energetic Particle Radiation Environment Module

**Model developers:** Nathan Schwadron, Kamen Kozarev, Matthew Gorby, Philip Quinn, Matthew Young (developed at Boston University and University of New Hampshire (UNH)).

**Model description:** The Energetic Particle Radiation Environment Module (EPREM) is a 3-dimensional, time-dependent, physics-based model of particle transport anywhere in the heliosphere. EPREM is the core particle transport code of such models as Earth-Moon-Mars Radiation Environment Module (EMMREM), Predictions of radiation from REleASE, EMMREM, and Data In-641 corporating CRA TER, COSTEP, and other SEP measurements (PREDICCS), EPREM + ENLIL + Cone, and SPE Threat Assessment Tool (STAT).

EPREM simulates particle transport by solving the Focused Transport Equation (FTE) (Skilling, 1971; Ruffolo, 1995; Kóta et al., 2005) and convection-diffusion equation (Jokipii et al., 1977; Lee and Fisk, 1981). The transport effects included in the FTE and convection-diffusion equation are convection, diffusive streaming, adiabatic cooling, adiabatic focusing, pitch-angle scattering, perpendicular diffusion, particle drift, and stochastic acceleration. The formalization of these equations within EPREM can be found in Schwadron et al. (2010) and Quinn et al. (2016).

EPREM solves the FTE and convection-diffusion equation by using a Lagrangian grid with nodes that spawn on the inner boundary. For most cases, the inner boundary is the surface of the sun unless specified elsewhere by the user. The nodes are then convected out with the solar wind. The inner boundary then rotates. This naturally creates a Parker spiral configuration. The nodes continue with the solar wind until the outer boundary of the domain is reached. The user implicitly sets the outer boundary by choosing a total number of nodes to span the simulation domain. Fig. 2 shows an example of the unperturbed EPREM grid in physical coordinates. EPREM distributes nodes over nested spherical surfaces and the connections between equivalent nodes on neighboring surfaces produce velocity path lines. In the steady-state case, these lines are formal streamlines; in the frozen-in ideal MHD case, these lines also represent magnetic field lines.

Users may specify the resolution of energy and pitch-angle bins via a runtime configuration file. In uncoupled mode (see below), the user may also specify the temporal resolution; simulation runs that use output from an MHD simulation will use the corresponding times. Users may specify the values of parameters in the initial flux spectrum based on observed values of some particle species, $\sigma$, or chosen theoretical values. This spectrum has the analytic form

$$J_s(E, r) = \frac{J_{0s}}{\xi_{\sigma,s}} \left(\frac{r}{r_0}\right)^{-\beta} \left(\frac{E}{E_0}\right)^{-\gamma} \exp\left(-\frac{E}{E_c}\right) \quad (4)$$

where $J_s(E, r)$ [counts cm$^{-2}$ s$^{-1}$ sr$^{-1}$ (MeV/nuc)$^{-1}$] is the flux of simulated species s at radial distance r [au] and energy E [MeV]; $J_{0s}$ is the flux of reference species $\sigma$ at a reference radial distance, $r_0$, and reference energy, $E_0$; $\xi_{\sigma,s}$ is the solar-wind abundance of $\sigma$ relative to s; $\beta$ is the power-law dependence on radial distance; $\gamma$ is the power-law dependence on energy; and $E_c$ is a cutoff or roll-over energy. EPREM currently assumes that $\beta$ and $\gamma$ are the same for all simulated species. It also currently uses fixed values of $r_0 = 1.0$ au and $E_0 = 1.0$ MeV. The remaining free parameters, $J_{0s}$, $\xi_{\sigma,s}$, $\beta$, $\gamma$, and $E_c$ determine the initial distribution at all pitch-angles for species s, which EPREM discretizes into energy bins and assigns to all nodes at the first time step. The nodes carry the distribution information – which changes during transport according to the FTE, convection-diffusion equation, and any heliospheric structures – to the outer boundary.

Computing the evolution of the particle distribution(s) requires knowledge of the magnetic field, B, plasma velocity, V, and plasma density, $\rho$, at each node. EPREM currently provides a simple internal (i.e., uncoupled) model that computes values of B, V, and $\rho$ appropriate to a Parker spiral. The user may choose to include an idealized cone-style shock by setting a flag and specifying shock parameters in the runtime configuration file.

EPREM can include more physically realistic MHD quantities (i.e., from a CME) when coupled to either the
<figure><img src="image_3.png" /><figcaption>Fig. 2. A representation of the EPREM grid in physical coordinates. Logically connected nodes form velocity path lines throughout the computational domain. This image shows a subset of node lines at the poles and in the ecliptic plane for demonstration purposes; full simulation runs would use enough streams to span the domain. The green line further highlights a subset of nodes along its path.</figcaption></figure>

ENLIL + Cone model or the MAS model. When coupled to either model, EPREM solves the FTE using magnetic field, plasma velocity, and plasma density from the corresponding model. EPREM then pushes the nodes around according to the new plasma parameters. One issue so far is the ENLIL + Cone model uses a spatially limited grid whereas EPREM's grid extended everywhere in the heliosphere. Therefore there are EPREM nodes outside the cone's grid that receive no information. This makes cross-field diffusion and particle drift inaccurate since the EPREM nodes need to communicate with nearby nodes. If there are nodes that exist with no information, then EPREM will give bad results. A non-uniform EPREM grid for use when coupled to the ENLIL + Cone model is currently in development.

**Inputs:** EPREM requires an energy spectrum for a given particle species at a desired location. As described above, the user can provide values of parameters to the initial spectrum (Eq. 4) or use default values. Default values are set to produce a physically reasonable initial spectrum. The user may wish to tailor this spectrum to a particular event by deriving parameter values from observations leading up to the event (for example, by fitting the analytic form to an observed fluence spectrum) or to perform a parameter study by varying input values. If coupled to an MHD model, EPREM treats the model's derived MHD parameters as input at each time step to push the nodes around.

**Outputs:** By default, each stream file contains the following quantities:

* radial (r), polar (θ), and azimuthal (φ) position of all nodes as a function of time

* the solar wind velocity components in spherical coordinates at all nodes as a function of time

* the magnetic field components in spherical coordinates at all nodes as a function of time

* the solar wind density at all nodes as a function of time

* the particle distribution at all nodes as a function of time, species, energy, and pitch-angle

The file also includes time and pitch-angle arrays, the mass and charge of each simulated species, and per-species arrays of speed and energy bins. A runtime configuration option allows the user to request that EPREM pre-compute pitch-angle averaged flux from the pitch-angle resolved distribution and include the flux in the output file instead of the distribution.

Since EPREM treats the particles as an ensemble (kinetic description), the main result is the distribution function, or phase-space density – the number of particles per location and velocity. It has units of $s^3/km^6$. The distribution function is a function of time, location, velocity, and pitch-angle, or $f(t, x, y, z, v_x, v_y, v_z, \mu)$.

**Free parameters:** The free parameters in EPREM include the injected source distribution (i.e., seed population spectrum), the particle mean free path at 1 AU, and the choice of particle transport effects to include in the simulation.

**Limitations and caveats:** Unless coupled to an MHD model, EPREM assumes a nominal Parker spiral with optional idealized shock, as described above. This is an ideal scenario and does not include the typical variations within the IMF. Since EPREM uses a Lagrangian grid, the nodes may not fall directly at Earth's location and therefore relies on interpolating between the nodes to derive the distribution function at Earth.

**Access to model output or forecasts:** There was work to build EPREM at the CCMC, but runs-on-request are not available. Contact UNH for requesting model runs.
<figure><img src="image_3.png" /><figcaption>Fig. 2. A representation of the EPREM grid in physical coordinates. Logically connected nodes form velocity path lines throughout the computational domain. This image shows a subset of node lines at the poles and in the ecliptic plane for demonstration purposes; full simulation runs would use enough streams to span the domain. The green line further highlights a subset of nodes along its path.</figcaption></figure>

ENLIL + Cone model or the MAS model. When coupled to either model, EPREM solves the FTE using magnetic field, plasma velocity, and plasma density from the corresponding model. EPREM then pushes the nodes around according to the new plasma parameters. One issue so far is the ENLIL + Cone model uses a spatially limited grid whereas EPREM's grid extended everywhere in the heliosphere. Therefore there are EPREM nodes outside the cone's grid that receive no information. This makes cross-field diffusion and particle drift inaccurate since the EPREM nodes need to communicate with nearby nodes. If there are nodes that exist with no information, then EPREM will give bad results. A non-uniform EPREM grid for use when coupled to the ENLIL + Cone model is currently in development.

**Inputs:** EPREM requires an energy spectrum for a given particle species at a desired location. As described above, the user can provide values of parameters to the initial spectrum (Eq. 4) or use default values. Default values are set to produce a physically reasonable initial spectrum. The user may wish to tailor this spectrum to a particular event by deriving parameter values from observations leading up to the event (for example, by fitting the analytic form to an observed fluence spectrum) or to perform a parameter study by varying input values. If coupled to an MHD model, EPREM treats the model's derived MHD parameters as input at each time step to push the nodes around.

**Outputs:** By default, each stream file contains the following quantities:

* radial (r), polar (θ), and azimuthal (φ) position of all nodes as a function of time

* the solar wind velocity components in spherical coordinates at all nodes as a function of time

* the magnetic field components in spherical coordinates at all nodes as a function of time

* the solar wind density at all nodes as a function of time

* the particle distribution at all nodes as a function of time, species, energy, and pitch-angle

The file also includes time and pitch-angle arrays, the mass and charge of each simulated species, and per-species arrays of speed and energy bins. A runtime configuration option allows the user to request that EPREM pre-compute pitch-angle averaged flux from the pitch-angle resolved distribution and include the flux in the output file instead of the distribution.

Since EPREM treats the particles as an ensemble (kinetic description), the main result is the distribution function, or phase-space density – the number of particles per location and velocity. It has units of $s^3/km^6$. The distribution function is a function of time, location, velocity, and pitch-angle, or $f(t, x, y, z, v_x, v_y, v_z, \mu)$.

**Free parameters:** The free parameters in EPREM include the injected source distribution (i.e., seed population spectrum), the particle mean free path at 1 AU, and the choice of particle transport effects to include in the simulation.

**Limitations and caveats:** Unless coupled to an MHD model, EPREM assumes a nominal Parker spiral with optional idealized shock, as described above. This is an ideal scenario and does not include the typical variations within the IMF. Since EPREM uses a Lagrangian grid, the nodes may not fall directly at Earth's location and therefore relies on interpolating between the nodes to derive the distribution function at Earth.

**Access to model output or forecasts:** There was work to build EPREM at the CCMC, but runs-on-request are not available. Contact UNH for requesting model runs.
**Model validation:** To date, there has been no rigorous validation performed for EPREM. The majority of studies using EPREM have only made qualitative comparisons (Schwadron et al., 2010; Kozarev et al., 2010; Dayeh et al., 2010; Chen et al., 2015; Quinn et al., 2016; Quinn et al., 2017; Quinn et al., 2018; Quinn et al., 2019; Young et al., 2021).

### 3.8. ESPERTA - Empirical Model for Solar Proton Event Real Time Alert

**Model developers:** Monica Laurenza (National Institute for Astrophysics (INAF)), Edward W. Cliver (National Solar Observatory (NSO)), Alan G. Ling (Atmospheric Environmental Research), Tommaso Alberti (INAF), Mirko Stumpo (Università di Roma Tor Vergata, INAF), Simone Benella (INAF).

**Model description:** The Empirical model for Solar Proton Event Real Time Alert (ESPERTA) forecast tool predicts whether SEP events will exceed S1 or S2 levels (Laurenza et al., 2009; Laurenza et al., 2018) in the NOAA Solar Radiation Storms Scale (https://www.swpc.noaa.gov/noaa-scales-explanation). A main focus of the ESPERTA model is to quickly produce an SEP intensity forecast. For this reason, ESPERTA relies primarily on flare characteristics: location, 1–8 Å SXR fluence, and ~1 MHz radio fluence corresponding to Type III radio bursts. Additionally, the model requires that a flare reaches M2 class or higher to produce a forecast.

The ≥S1 ESPERTA forecast is produced within 10 min following the SXR of a flare (Laurenza et al., 2009). ESPERTA was derived from a database of GOES measurements between 1995–2005, selecting time periods for which >10 MeV proton fluxes exceeded 10 pfu for three consecutive 5-min intervals. Each proton flux increase was associated with its solar flare source, resulting in a list of 93 SEP events. For the ≥S2 ESPERTA model (Laurenza et al., 2018), ≥S2 events were selected from ≥S1 lists spanning 1995–2005 and 2006–2014 from Laurenza et al. (2009) and Alberti et al. (2017), respectively. As was done for the previous version of the model, >10 MeV proton intensity was required to exceed 100 pfu for three consecutive 5-min intervals, resulting in a list of 59 SEP events. SXR fluence values were derived from GOES 1-min 1–8 Å data using an empirical prescription to estimate the fluence at 10 min following the flare peak. The SXR fluence is calculated from the 1/3 power point on the rise of the SXR burst before the peak to the 1/3 power point after. The 1/3 power point is defined as 1/3 of the flare peak X-ray flux. If the X-ray intensity drops by a factor of 3 within 10 min of the peak, the integration stops, otherwise an exponential fit of the flare is used to extrapolate the intensity curve to the 1/3 power point. The fit is based on the intensity values from 6 to 10 min after the peak and it is a reasonable tool to take into account the flare profile. The ~1 MHz radio values were

compiled from the Wind/Radio and Plasma Wave Experiment (WAVES) instrument and integrated from 10 min prior to the flare integration start time to 10 min after the peak (Laurenza et al., 2018; Alberti et al., 2017).

Between 1995 and 2005, there were 704 ≥M2 flares. This increased to 980 ≥M2 flares when the data set was extended up to 2014. To derive ≥S1 and ≥S2 forecasts, ESPERTA developers compared SXR fluence to 1 MHz radio fluence for all flares and identified probability contours in parameter space that contained flares associated with ≥S1 and ≥S2 SEP events. The probability contours were derived using a logistic regression analysis by McCullagh and Nelder (1983) that allows one to compute the probability that an event will occur by using a parametric space with two variables. The probability (P) can be expressed in terms of the X-ray fluence (X) and 1 MHz radio fluence (R) as:

$$P(\log X, \log R) = \frac{e^{\eta}}{1 + e^{\eta}} \qquad (5)$$

where $\eta = \eta(\log X, \log R)$.

First, the flares were grouped within three different longitudinal bands, effectively taking magnetic connectivity into account: 1) E 120° - E 41°, 2) E 40° - W 19°, 3) W 20° - W 120°. Probability contours were found for each longitudinal range individually and a probability threshold for each one was selected by maximizing POD and minimizing FAR. Then, a yes/no ≥S1 and ≥S2 forecast was produced by identifying which side of the probability contour threshold a flare was located. Final probability contours were selected by maximizing POD and minimizing FAR.

The ≥S1 contours were derived using data up to 2005 with the corresponding values:

1. $\eta_1 = -6.07 - 1.75 \log(X) + 1.14 \log(R) + 0.56 \log(X) \log(R)$

2. $\eta_2 = -7.44 - 2.99 \log(X) + 1.21 \log(R) + 0.69 \log(X) \log(R)$

3. $\eta_3 = -5.02 - 1.74 \log(X) + 0.64 \log(R) + 0.40 \log(X) \log(R)$

The associated probability levels were 28%, 28%, and 23% for the three longitudinal ranges, respectively (Alberti et al., 2017).

The ≥S2 contours were derived from the full 1995 to 2014 data set following the same approach. The eastern and central probability thresholds remained the same, however the W 20° - W 120° probability contour was adjusted to 35%. An additional criterion was added such that ≥S2 alerts are only issued for events that cross S1 levels within 30/15/6 h for eastern/central/western events, therefore ESPERTA also monitors >10 MeV proton intensity levels. This modification results in a delay of ≥S2 forecasts compared to ≥S1 forecasts, but with a significant improvement in ≥S2 forecast performance.

**Inputs:**

* Flare location

* Flare SXR fluence (X-ray peak threshold ≥M2)
**Model validation:** To date, there has been no rigorous validation performed for EPREM. The majority of studies using EPREM have only made qualitative comparisons (Schwadron et al., 2010; Kozarev et al., 2010; Dayeh et al., 2010; Chen et al., 2015; Quinn et al., 2016; Quinn et al., 2017; Quinn et al., 2018; Quinn et al., 2019; Young et al., 2021).

### 3.8. ESPERTA - Empirical Model for Solar Proton Event Real Time Alert

**Model developers:** Monica Laurenza (National Institute for Astrophysics (INAF)), Edward W. Cliver (National Solar Observatory (NSO)), Alan G. Ling (Atmospheric Environmental Research), Tommaso Alberti (INAF), Mirko Stumpo (Università di Roma Tor Vergata, INAF), Simone Benella (INAF).

**Model description:** The Empirical model for Solar Proton Event Real Time Alert (ESPERTA) forecast tool predicts whether SEP events will exceed S1 or S2 levels (Laurenza et al., 2009; Laurenza et al., 2018) in the NOAA Solar Radiation Storms Scale (https://www.swpc.noaa.gov/noaa-scales-explanation). A main focus of the ESPERTA model is to quickly produce an SEP intensity forecast. For this reason, ESPERTA relies primarily on flare characteristics: location, 1–8 Å SXR fluence, and ~1 MHz radio fluence corresponding to Type III radio bursts. Additionally, the model requires that a flare reaches M2 class or higher to produce a forecast.

The ≥S1 ESPERTA forecast is produced within 10 min following the SXR of a flare (Laurenza et al., 2009). ESPERTA was derived from a database of GOES measurements between 1995–2005, selecting time periods for which >10 MeV proton fluxes exceeded 10 pfu for three consecutive 5-min intervals. Each proton flux increase was associated with its solar flare source, resulting in a list of 93 SEP events. For the ≥S2 ESPERTA model (Laurenza et al., 2018), ≥S2 events were selected from ≥S1 lists spanning 1995–2005 and 2006–2014 from Laurenza et al. (2009) and Alberti et al. (2017), respectively. As was done for the previous version of the model, >10 MeV proton intensity was required to exceed 100 pfu for three consecutive 5-min intervals, resulting in a list of 59 SEP events. SXR fluence values were derived from GOES 1-min 1–8 Å data using an empirical prescription to estimate the fluence at 10 min following the flare peak. The SXR fluence is calculated from the 1/3 power point on the rise of the SXR burst before the peak to the 1/3 power point after. The 1/3 power point is defined as 1/3 of the flare peak X-ray flux. If the X-ray intensity drops by a factor of 3 within 10 min of the peak, the integration stops, otherwise an exponential fit of the flare is used to extrapolate the intensity curve to the 1/3 power point. The fit is based on the intensity values from 6 to 10 min after the peak and it is a reasonable tool to take into account the flare profile. The ~1 MHz radio values were

compiled from the Wind/Radio and Plasma Wave Experiment (WAVES) instrument and integrated from 10 min prior to the flare integration start time to 10 min after the peak (Laurenza et al., 2018; Alberti et al., 2017).

Between 1995 and 2005, there were 704 ≥M2 flares. This increased to 980 ≥M2 flares when the data set was extended up to 2014. To derive ≥S1 and ≥S2 forecasts, ESPERTA developers compared SXR fluence to 1 MHz radio fluence for all flares and identified probability contours in parameter space that contained flares associated with ≥S1 and ≥S2 SEP events. The probability contours were derived using a logistic regression analysis by McCullagh and Nelder (1983) that allows one to compute the probability that an event will occur by using a parametric space with two variables. The probability (P) can be expressed in terms of the X-ray fluence (X) and 1 MHz radio fluence (R) as:

$$P(\log X, \log R) = \frac{e^{\eta}}{1 + e^{\eta}} \qquad (5)$$

where $\eta = \eta(\log X, \log R)$.

First, the flares were grouped within three different longitudinal bands, effectively taking magnetic connectivity into account: 1) E 120° - E 41°, 2) E 40° - W 19°, 3) W 20° - W 120°. Probability contours were found for each longitudinal range individually and a probability threshold for each one was selected by maximizing POD and minimizing FAR. Then, a yes/no ≥S1 and ≥S2 forecast was produced by identifying which side of the probability contour threshold a flare was located. Final probability contours were selected by maximizing POD and minimizing FAR.

The ≥S1 contours were derived using data up to 2005 with the corresponding values:

$$1. \eta_1 = -6.07 - 1.75 \log(X) + 1.14 \log(R) + 0.56 \log(X) \log(R)$$

$$2. \eta_2 = -7.44 - 2.99 \log(X) + 1.21 \log(R) + 0.69 \log(X) \log(R)$$

$$3. \eta_3 = -5.02 - 1.74 \log(X) + 0.64 \log(R) + 0.40 \log(X) \log(R)$$

The associated probability levels were 28%, 28%, and 23% for the three longitudinal ranges, respectively (Alberti et al., 2017).

The ≥S2 contours were derived from the full 1995 to 2014 data set following the same approach. The eastern and central probability thresholds remained the same, however the W 20° - W 120° probability contour was adjusted to 35%. An additional criterion was added such that ≥S2 alerts are only issued for events that cross S1 levels within 30/15/6 h for eastern/central/western events, therefore ESPERTA also monitors >10 MeV proton intensity levels. This modification results in a delay of ≥S2 forecasts compared to ≥S1 forecasts, but with a significant improvement in ≥S2 forecast performance.

**Inputs:**

* Flare location

* Flare SXR fluence (X-ray peak threshold ≥M2)
* Flare ~1 MHz radio fluence (time-integrated Wind/GOES type III intensity)

* >10 MeV proton flux (for ≥S2 forecast)

**Outputs:** Alert for >10 MeV proton fluxes ≥S1 and ≥S2.

**Free parameters:** None.

**Limitations and caveats:**

* A forecast will only be issued in the case that the model determines a threshold will be crossed. If it is determined that a threshold will not be crossed, then no forecast is produced.

* Model will not trigger for flares below M2

* ≥S2 forecasts are delayed until S1 levels are crossed (Laurenza et al., 2018)

* ≥S2 alerts will not be issued for a flare if the pre-flare background proton flux level already exceeds 100 pfu (Laurenza et al., 2018).

**Access to model output or forecasts:** ESPERTA is not currently available to the public.

**Model validation:** The ≥S1 ESPERTA tool was developed using data between 1995–2005 and initially validated over the same data set (Laurenza et al., 2009). Moreover, it was validated using an independent data set from 2006–2014 (Alberti et al., 2017). Increases in intensity above S1 levels due to the passage of a shock or compression region at Earth were not counted in the development or validation of the model. A total of 36 ≥S1 events with reliable flare source associations were identified in the 2006–2014 time period. These were broken into three categories: 23 SEP events with ≥M2 flares, 9 with <M2 flares, and 4 farside events with no available flare data.

Forecast performance was organized into four categories:

* Hit: correct prediction (19)

* Miss: SEP associated with ≥M2 front-side flares that were not predicted (4)

* MISS: SEP associated with front-side <M2 flares (no prediction possible by definition, 9)

* not counted: SEP associated with backside flares <M2 (data gaps, 4)

The performance resulted in a POD = Hits/(Hits + Misses + MISSES) = 59% (19/(19 + 4+9)), FAR = FAs/(Hits + FAs) = 30% (8/(19 + 8)), HSS = 0.55 (44/80), and Percent Correct (PC) = 87% (240/276) (Alberti et al., 2017). The validation over the whole dataset from 1995 to 2014 led to the results: POD = 63% (69/69 + 20 + 21), and FAR = 38% (42/69 + 42) (Laurenza et al., 2018; Alberti et al., 2019). More recently, Stumpo et al. (2021) reintegrated the ESPERTA model for ≥S1 events in the framework of machine learning. These authors performed a cross validation, leading to a comparable performance. They also demonstrated that a quite high FAR is a natural

consequence of the small size of the SPE sample with respect to the SPE non-associated flares, which is a critical issue of any statistical approach.

In Laurenza et al. (2009), the Advance Warning Time (AWT) was calculated by comparing the time that the ESPERTA forecast was issued with the onset in the SOHO/Electron Proton and Helium Instrument (EPHIN) 31–50 MeV energy channel published by Posner (2007). This choice was made because GOES >10 MeV intensities are not accurate at the onset of SEP events due to electron and proton contamination and post-processing effects (Posner, 2007). Nevertheless, in order to allow a comparison with other forecasting techniques, Alberti et al. (2017) chose to assess the ADWT by calculating the difference between the time that the forecast was issued and the time that the GOES >10 MeV proton intensity reached the S1 threshold (Alberti et al., 2017). For the data between 2006–2014, the median (average) ADWT was ~2 h (~7 h) ranging from 0.4 to 35.9 h. For the full 20-year interval, the median (average) ADWT was 4.8 h (9 h) with a range from 0.4 to 52.8 h for the 66 hit events (Alberti et al., 2017).

The ≥S2 ESPERTA tool was derived from data between 1995–2014 and metrics were calculated based on performance for the same set of events (Laurenza et al., 2018). In this case, increases above the S2 level due to a passing shock are counted in the statistics. Forecasts performance was organized into the four categories described above with the results: 41 Hits, 8 Misses, 6 MISSES, and 4 not counted.

The ≥S2 tool shows improvement over the ≥S1 tool with a POD = 41/(41 + 8+6) = 75% and FAR = 13/(41 + 13) = 24%. The median ADWT for the 41 hits is 1.7 h with a minimum of 0.2 h.

## 3.9. FORSPEF - FForecasting Solar Particle Events and Flares

**Model developers:** Anastasios Anastasiadis (National Observatory of Athens (NOA)), Athanasios Papaioannou (Ingmar Sandberg (SPARC)), Ingmar Sandberg (SPARC), Manolis K. Georgoulis (RCAAN of the Academy of Athens).

**Model description:** FForecasting Solar Particle Events and Flares (FORSPEF) is an operational tool that is composed of three modules that aim to forecast and nowcast 1) the likelihood of upcoming Solar Flare (SF) eruptions, 2) the occurrence of SEPs by making a prediction of the time before onset, and 3) the SEP characteristics of an upcoming event (Papaioannou et al., 2015; Anastasiadis et al., 2017; Papaioannou et al., 2018). In forecasting mode, the model makes predictions when no solar event (flare or CME) has yet taken place. In nowcasting mode, the model will use SF and CME information to predict SEP event characteristics (Anastasiadis et al., 2017).

To develop the flare and CME forecasting module (Anastasiadis et al., 2017), a database of active region (AR) s was compiled from SDO/HMI full-disk magneto-
* Flare ~1 MHz radio fluence (time-integrated Wind/GOES type III intensity)

* >10 MeV proton flux (for ≥S2 forecast)

**Outputs:** Alert for >10 MeV proton fluxes ≥S1 and ≥S2.

**Free parameters:** None.

**Limitations and caveats:**

* A forecast will only be issued in the case that the model determines a threshold will be crossed. If it is determined that a threshold will not be crossed, then no forecast is produced.

* Model will not trigger for flares below M2

* ≥S2 forecasts are delayed until S1 levels are crossed (Laurenza et al., 2018)

* ≥S2 alerts will not be issued for a flare if the pre-flare background proton flux level already exceeds 100 pfu (Laurenza et al., 2018).

**Access to model output or forecasts:** ESPERTA is not currently available to the public.

**Model validation:** The ≥S1 ESPERTA tool was developed using data between 1995–2005 and initially validated over the same data set (Laurenza et al., 2009). Moreover, it was validated using an independent data set from 2006–2014 (Alberti et al., 2017). Increases in intensity above S1 levels due to the passage of a shock or compression region at Earth were not counted in the development or validation of the model. A total of 36 ≥S1 events with reliable flare source associations were identified in the 2006–2014 time period. These were broken into three categories: 23 SEP events with ≥M2 flares, 9 with <M2 flares, and 4 farside events with no available flare data.

Forecast performance was organized into four categories:

* Hit: correct prediction (19)

* Miss: SEP associated with ≥M2 front-side flares that were not predicted (4)

* MISS: SEP associated with front-side <M2 flares (no prediction possible by definition, 9)

* not counted: SEP associated with backside flares <M2 (data gaps, 4)

The performance resulted in a POD = Hits/(Hits + Misses + MISSES) = 59% (19/(19 + 4+9)), FAR = FAs/(Hits + FAs) = 30% (8/(19 + 8)), HSS = 0.55 (44/80), and Percent Correct (PC) = 87% (240/276) (Alberti et al., 2017). The validation over the whole dataset from 1995 to 2014 led to the results: POD = 63% (69/69 + 20 + 21), and FAR = 38% (42/69 + 42) (Laurenza et al., 2018; Alberti et al., 2019). More recently, Stumpo et al. (2021) reintegrated the ESPERTA model for ≥S1 events in the framework of machine learning. These authors performed a cross validation, leading to a comparable performance. They also demonstrated that a quite high FAR is a natural

consequence of the small size of the SPE sample with respect to the SPE non-associated flares, which is a critical issue of any statistical approach.

In Laurenza et al. (2009), the Advance Warning Time (AWT) was calculated by comparing the time that the ESPERTA forecast was issued with the onset in the SOHO/Electron Proton and Helium Instrument (EPHIN) 31–50 MeV energy channel published by Posner (2007). This choice was made because GOES >10 MeV intensities are not accurate at the onset of SEP events due to electron and proton contamination and post-processing effects (Posner, 2007). Nevertheless, in order to allow a comparison with other forecasting techniques, Alberti et al. (2017) chose to assess the ADWT by calculating the difference between the time that the forecast was issued and the time that the GOES >10 MeV proton intensity reached the S1 threshold (Alberti et al., 2017). For the data between 2006–2014, the median (average) ADWT was ~2 h (~7 h) ranging from 0.4 to 35.9 h. For the full 20-year interval, the median (average) ADWT was 4.8 h (9 h) with a range from 0.4 to 52.8 h for the 66 hit events (Alberti et al., 2017).

The ≥S2 ESPERTA tool was derived from data between 1995–2014 and metrics were calculated based on performance for the same set of events (Laurenza et al., 2018). In this case, increases above the S2 level due to a passing shock are counted in the statistics. Forecasts performance was organized into the four categories described above with the results: 41 Hits, 8 Misses, 6 MISSES, and 4 not counted.

The ≥S2 tool shows improvement over the ≥S1 tool with a POD = 41/(41 + 8+6) = 75% and FAR = 13/(41 + 13) = 24%. The median ADWT for the 41 hits is 1.7 h with a minimum of 0.2 h.

## 3.9. FORSPEF - FForecasting Solar Particle Events and Flares

**Model developers:** Anastasios Anastasiadis (National Observatory of Athens (NOA)), Athanasios Papaioannou (Ingmar Sandberg (SPARC)), Ingmar Sandberg (SPARC), Manolis K. Georgoulis (RCAAN of the Academy of Athens).

**Model description:** FForecasting Solar Particle Events and Flares (FORSPEF) is an operational tool that is composed of three modules that aim to forecast and nowcast 1) the likelihood of upcoming Solar Flare (SF) eruptions, 2) the occurrence of SEPs by making a prediction of the time before onset, and 3) the SEP characteristics of an upcoming event (Papaioannou et al., 2015; Anastasiadis et al., 2017; Papaioannou et al., 2018). In forecasting mode, the model makes predictions when no solar event (flare or CME) has yet taken place. In nowcasting mode, the model will use SF and CME information to predict SEP event characteristics (Anastasiadis et al., 2017).

To develop the flare and CME forecasting module (Anastasiadis et al., 2017), a database of active region (AR) s was compiled from SDO/HMI full-disk magneto-